NOTE: INSTALL PACKAGES IN CELL BELOW

# NOTE: INSTALL PACKAGES IN CELL BELOW

!pip install plotnine duckdb jax numpyro pyarrow graphviz --quiet

Data

Data Sources

All data for this project came from two full count decennial census records. The first came from 1860, and the second came from 1920. I picked these years because they are close enough apart to reasonably have adults alive in one census still be alive in the later census, but far enough apart to really grasp longer term life trajectories over one of the fastest changing times in American history. These datasets are full count population level census records, and were accessed through IPUMS USA. The other dataset used was from the Census Linking Project. This is key to the project, as it uses an automated matching procedure to match individuals across time. Without this, we could not measure within-individual change.

Practical problems

This dataset in its raw form is quite big, over 10gb in size while compressed (30+ otherwise), and is >100M rows long. This would most definitely not fit in memory, which caused significant issues. In fact, all figures generated here are using a 1% sample, which is still over a million rows long! Thankfully, the number of linked samples is comparatively less, being somewhere between a million and two million rows long depending on which linking method is used. This is still quite large, but is at least manageable. When loading the data itself, I had to use duckdb. Duckdb is designed for OLAP column-store queries, and doesn’t require it to be in memory. I used this to do almost all of the data processing, and then saved it to a parquet file.

I will attatch the literal .sql file I wrote it in as well as paste it in the cell below. It should be commented significantly. This will not actually run it, though, as I typically either read the .sql file into memory and used con.sql() to run it as a long string, or just directly used the duckdb cli. I’ll include the code to read it in as well, but won’t really be useful to you unless you want me to send you the full database (22+GB). The SQL cell below is just markdown with SQL syntax highlighting.

-- This is just a little table I used to deal with keeping track of the 
-- Indexes of the states in the ICP data across the tables. 
-- Relies on a csv file called icp_conversion.csv that I created from the
-- ICP code conversion chart online.
create or replace table icp_state_conversion(
    idx integer primary key,
    state varchar,
    stateicp integer
);
COPY icp_state_conversion from 'icp_conversion.csv' (AUTO_DETECT TRUE);

-- Copies the data I need off the full dataset
-- Just doing this as I don't use a significant portion of the data
-- that I got from IPUMS.
create or replace view ipums_cleaned as (
    select 
    year, 
    histid, 
    sex,
    age,
    race,
    icp.state as state,
    icp.idx as state_idx,
    ipums_second.stateicp as stateicp,
    -- If not white then 1 else 0 
    case when 
    race != 1 then 1 
    else 0
    end as not_white,
    case when 
    lit = 0 or lit = 1 then 0
    else 1
    end as lit,
    school,
    occ1950,
    occscore,
    -- Signals missing vals
    case when edscor50 = 9999 then 1
    when edscor50 = 999.9 then 1 else 0 end as edscor50_missing,
    -- Replaces missing vals with zero
    case when edscor50_missing == 1 then 0 else edscor50 end as edscor50,

    case when occscore = 0 then 0
    else ln(occscore) end as log_earnings
    from ipums_second left join icp_state_conversion icp 
    on ipums_second.stateicp = icp.stateicp
    where year = 1870 or year = 1910
);


-- Loads in Census Linking Project data as a table

create table if not exists linking_1870_1910 as (
    select 
    * 
    from read_csv_auto("census_linking_proj/1870_1910/crosswalk_1870_1910.csv")
);


create table if not exists state_dist as (
    select 
    * 
    from read_csv_auto("state_distances.csv")
);

-- Creates a view that has the 1870 and 1910 data joined together

CREATE
OR REPLACE VIEW mixed_1870_1910 AS (
    SELECT
        c1870.year AS c1870_year,
        c1870.histid AS c1870_histid,
        -- Mostly redundant, ended up using conservative match
        -- For a lot of the models anyways. 
        case when lk.abe_nysiis_conservative == 1 then 1 else 0 end as conservative_match,
        c1870.stateicp AS c1870_stateicp,
        c1870.state as c1870_state,
        c1870.state_idx as c1870_state_idx,
        c1870.sex AS c1870_sex,
        c1870.age AS c1870_age,
        c1870.race AS c1870_race,
        c1870.not_white AS c1870_not_white,
        c1870.lit AS c1870_lit,
        c1870.school AS c1870_school,
        c1870.occ1950 AS c1870_occ1950,
        c1870.occscore AS c1870_occscore,
        c1870.log_earnings AS c1870_log_earnings,
        c1870.edscor50 AS c1870_edscor50,
        c1870.edscor50_missing as c1870_edscor50_missing,
        c1910.year AS c1910_year,
        c1910.histid AS c1910_histid,
        c1910.stateicp AS c1910_stateicp,
        c1910.state as c1910_state,
        c1910.state_idx as c1910_state_idx,
        c1910.sex AS c1910_sex,
        c1910.age AS c1910_age,
        c1910.race AS c1910_race,
        c1910.not_white AS c1910_not_white,
        c1910.lit AS c1910_lit,
        c1910.school AS c1910_school,
        c1910.occ1950 AS c1910_occ1950,
        c1910.occscore AS c1910_occscore,
        c1910.log_earnings AS c1910_log_earnings,
        c1910.edscor50 AS c1910_edscor50,
        c1910.edscor50_missing as c1910_edscor50_missing,

    -- Joins on census linking project data
    FROM linking_1870_1910 lk 
    LEFT JOIN ipums_cleaned c1870
        ON lk.histid_1870 = c1870.histid 
    LEFT JOIN ipums_cleaned c1910
        ON lk.histid_1910 = c1910.histid
    WHERE
        c1870.year = 1870
        AND c1910.year = 1910
    --     AND c1870.year = 1880
        AND lk.abe_nysiis_conservative = 1
        and c1870.state_idx is not null
        and c1910.state_idx is not null
);


create or replace table comb_1870_1910 as (

with a as (
    select 
    case when c1870_not_white == 1 then 
        case 
            when c1910_not_white == 1 then 1
            else c1870_not_white
        end
        else 
            case 
                when c1910_not_white == 0 then c1870_not_white
                else 1
            end 
        end as not_white,
        case 
            when c1870_state == c1910_state then 0
            else 1
        end as state_changed,
        c1870_state as origin_state,
        c1910_state as destination_state,
        c1870_state_idx as origin_state_idx,
        c1910_state_idx as destination_state_idx,
        c1910_lit - c1870_lit as lit_change,
        c1910_school - c1870_school as school_change,
        c1910_log_earnings - c1870_log_earnings as log_earnings_change,
        c1910_occscore - c1870_occscore as occscore_change,
        c1910_edscor50 - c1870_edscor50 as edscor50_change,
        * EXCLUDE (c1870_not_white, c1910_not_white, c1870_state, c1910_state, c1870_state_idx, c1910_state_idx)

    from mixed_1870_1910 

)

SELECT
    -- Had some encoding issues, so hard coded the dtypes
    not_white::BOOLEAN as not_white,
    state_changed::BOOLEAN as state_changed,
    conservative_match::BOOLEAN as conservative_match,
    origin_state,
    destination_state,
    origin_state_idx::INTEGER - 1 as origin_state_idx,
    destination_state_idx::INTEGER - 1 as destination_state_idx,
    lit_change,
    school_change,
    log_earnings_change,
    occscore_change,
    edscor50_change,
    c1870_lit,
    c1870_school,
    c1870_age,
    c1870_occscore,
    c1870_log_earnings,
    c1870_edscor50,
    c1910_lit,
    c1910_school,
    c1910_age,
    c1910_occscore,
    c1910_log_earnings,
    c1910_edscor50


FROM a

);
create table if not exists comb_1870_1910_state_dist as (
    select 
    c.*,
    s.distance as state_dist
    from comb_1870_1910 c left join state_dist s
    on c.origin_state = s.state1 and c.destination_state = s.state2
);

select * from comb_1870_1910 limit 100;


-- I use this parquet file to load the 'combined' variable in the main analysis

-- Standard Linking 

COPY (select * from comb_1870_1910) to 'comb_1870_1910_std_full.parquet' (FORMAT 'parquet');
COPY (
    select * from comb_1870_1910 USING SAMPLE 10 PERCENT (bernoulli)
) to 'comb_1870_1910_std_full_10pct.parquet' (FORMAT 'parquet');
COPY (
    select * from comb_1870_1910 USING SAMPLE 25 PERCENT (bernoulli)
) to 'comb_1870_1910_std_full_25pct.parquet' (FORMAT 'parquet');

-- Conservative Linking 

COPY (
    select * from comb_1870_1910 where conservative_match == TRUE 
) to 'comb_1870_1910_conservative_full.parquet' (FORMAT 'parquet');
COPY (
    select * from comb_1870_1910 where conservative_match == TRUE USING SAMPLE 10 PERCENT (bernoulli)
) to 'comb_1870_1910_conservative_full_10pct.parquet' (FORMAT 'parquet');
COPY (
    select * from comb_1870_1910 where conservative_match == TRUE USING SAMPLE 25 PERCENT (bernoulli)
) to 'comb_1870_1910_conservative_full_25pct.parquet' (FORMAT 'parquet');

COPY (
    select * from comb_1870_1910_state_dist where conservative_match == TRUE USING SAMPLE 10 PERCENT (bernoulli)
) to 'comb_1870_1910_conservative_full_10pct_state_dist.parquet' (FORMAT 'parquet');
-- Used this to generate the one_pct variable used in the analysis  
--COPY (select * from ipums_cleaned USING SAMPLE 1 PERCENT (bernoulli)) to 'ipums_cleaned_sample.parquet' (FORMAT 'parquet');
# read query.sql and execute it
def run_query_dot_sql():
    con = db.connect("project.db")
    con.begin()
    with open('query.sql', 'r') as file:
        query = file.read()

    con.execute(query).df()

    con.commit()

# If you want to load it just run this function (assuming you have the db)

Variable encodings

When processing some of the datasets, I had to make decisions regarding how I would encoding the different variables for processing. You can see the details of this in the SQL code, but I will summarize them here. The primary variable of interest here is earnings over time, estimated with a 1950 OCCSCORE income estimate. The second of these is the edscor50 variable, representing the chance of having at least one year of college education. Both of these are fundamentally based on occupational categories, and both have a significant number of missing variables.

OCCSCORE

For each individual year, I logged the income variables, swapping log(0) for 0 so it didn’t cause -inf issues. I ended up leaving in the zero values as having no income, but this may not entirely be true and could inflate the numbers somewhat. I have the breakdown attached in the tables below. While there is a very large number of people with zero entries, this seems to be the case for both years. More importantly, when looking at specifically the years of linked data, people who had zero in 1870 were actually less likely to have it for 1910. This is really interesting, but on later inspection, this seems to be a product of age more than anything else, as in the regressions in the cells below controlling for age inverses the effect. I still decided to leave it in, however, as that probably means it simply represents younger people being mostly matched in 1860 (ie, still alive 40yrs later) and would be important. For the actual model itself, I took the difference of the log occscore between the two years. You can see the distribution of the occscores between the years (for the linked group) in the plot below.

print('Overall Breakdown')
one_pct['occscore_0_pct'] = (one_pct['OCCSCORE'] == 0)*100
one_pct['occscore_0'] = (one_pct['OCCSCORE'] == 0)
one_pct[['YEAR', 'not_white', 'OCCSCORE', 'occscore_0']].groupby(['YEAR', 'not_white']).agg(['mean']).reset_index()

print('Mean occscores by if they were 0 in 1870')
combined['c1870_occscore_0'] = (combined['c1870_occscore'] == 0)
combined['c1910_occscore_0'] = (combined['c1910_occscore'] == 0)
combined[['c1870_occscore', 'c1910_occscore', 'c1870_occscore_0', 'c1910_occscore_0']].groupby(['c1870_occscore_0']).agg(['mean'])
Overall Breakdown
Mean occscores by if they were 0 in 1870
YEAR not_white OCCSCORE occscore_0
mean mean
0 1870 0 5.726321 0.691959
1 1870 1 5.055054 0.569423
2 1910 0 8.395745 0.606762
3 1910 1 6.920044 0.474515
c1870_occscore c1910_occscore c1910_occscore_0
mean mean mean
c1870_occscore_0
False 17.372599 15.540056 0.276062
True 0.000000 22.031545 0.078447 
# Hisogram (non linked)
sns.set_theme(style="darkgrid")
sns.displot(
    one_pct, x="OCCSCORE", row="YEAR", col="occscore_0", hue = 'occscore_0',
    binwidth=3,  facet_kws=dict(margin_titles=True),
)
/usr/local/lib/python3.10/dist-packages/seaborn/axisgrid.py:118: UserWarning: The figure layout has changed to tight
  self._figure.tight_layout(*args, **kwargs)

forreg = combined[['c1870_occscore', 'c1910_occscore', 'c1870_occscore_0', 'c1910_occscore_0', 'c1870_age']]
forreg['age_squared'] = forreg['c1870_age']**2
forreg[['c1870_occscore_0', 'c1910_occscore_0']] = forreg[['c1870_occscore_0', 'c1910_occscore_0']].astype(int)
SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  forreg['age_squared'] = forreg['c1870_age']**2
<ipython-input-6-a2528cfad297>:3: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  forreg[['c1870_occscore_0', 'c1910_occscore_0']] = forreg[['c1870_occscore_0', 'c1910_occscore_0']].astype(int)
dmd('#### Unlinked:')

one_pct['age_squared'] = one_pct['AGE']**2
m1 = smf.ols('OCCSCORE ~ 1 + C(YEAR) + AGE + age_squared', data = one_pct ).fit(cov_type = 'HC0')
summary_col(m1, stars = True)


dmd('__Regressions on linked dataset of impact of not having occscore at first on not having occscore at second. Uses logits though.__ \n\n')

# linked:
by_itself = smf.logit('c1910_occscore_0 ~ 1 + c1870_occscore_0',data = forreg).fit()
with_age = smf.logit('c1910_occscore_0 ~ 1 + c1870_occscore_0 + c1870_age + c1870_age:c1870_occscore_0 + c1870_occscore_0:age_squared',data = forreg).fit()
by_itself_linear = smf.ols('c1910_occscore_0 ~ 1 + c1870_occscore_0',data = forreg).fit(cov_type='HC0')
with_age_linear = smf.ols('c1910_occscore_0 ~ 1 + c1870_occscore_0 + c1870_age + c1870_age:c1870_occscore_0 + c1870_occscore_0:age_squared',data = forreg).fit(cov_type='HC0')
summary_col([by_itself, with_age, by_itself_linear, with_age_linear ], stars = True, model_names = ['By Itself', 'With Age', 'By Itself Linear', 'With Age Linear'])

dmd('\n\n #### Plot')
(
    so.Plot(combined, x = 'c1870_occscore', y = 'c1910_occscore', color = 'c1870_occscore_0')
    .add(so.Dot()) 
)

Unlinked:

OCCSCORE
Intercept -4.1027***
(0.0167)
C(YEAR)[T.1910] 1.8771***
(0.0185)
AGE 0.7287***
(0.0014)
age_squared -0.0083***
(0.0000)
R-squared 0.1935
R-squared Adj. 0.1935

Regressions on linked dataset of impact of not having occscore at first on not having occscore at second. Uses logits though.

Optimization terminated successfully.
         Current function value: 0.400085
         Iterations 6
Optimization terminated successfully.
         Current function value: 0.351578
         Iterations 7
By Itself With Age By Itself Linear With Age Linear
Intercept -0.9641*** -4.3816*** 0.2761*** -0.2960***
(0.0030) (0.0127) (0.0006) (0.0015)
R-squared 0.0707 0.2021
R-squared Adj. 0.0707 0.2021
c1870_age 0.1254*** 0.0224***
(0.0004) (0.0001)
c1870_age:c1870_occscore_0 -0.1116*** -0.0265***
(0.0014) (0.0002)
c1870_occscore_0 -1.4996*** 1.4700*** -0.1976*** 0.3580***
(0.0050) (0.0156) (0.0007) (0.0017)
c1870_occscore_0:age_squared 0.0020*** 0.0004***
(0.0000) (0.0000)

#### Plot

### EDSCOR50

This variable is an estimated percent chance of them having at least one year of college education. This is based on the 1950 census, and is using 1950 occupational categories to do the estimation. This will be problematic for a couple reasons. First off, literacy is very very related to percent chance of being linked in the first place. If you look below, you can see both the overall and split by race categories are heavily impacted. Second, literacy is a form of education, which makes this even more complicated. All the variables pretty much have this problem, though. Unfortunate, but the best we can really do in this situation.

# Full dataset Mean edscor50 by race
print('Full dataset mean edscore50 by race')
pd.pivot_table(one_pct[one_pct.YEAR == 1870], values = ['edscor50', 'OCCSCORE', 'lit'], index = 'not_white', aggfunc = 'mean', margins=True, sort=False)


print('Linked mean edscor50 and occscore')

pd.pivot_table(combined, values = ['c1870_occscore', 'c1870_edscor50', 'c1870_lit'], index = 'not_white',  aggfunc = 'mean',   margins = True, sort = False)
Full dataset mean edscore50 by race
Linked mean edscor50 and occscore
edscor50 OCCSCORE lit
not_white
0 2.672299 5.726321 0.664598
1 1.632862 5.055054 0.195398
All 2.540660 5.641309 0.605176
c1870_occscore c1870_edscor50 c1870_lit
not_white
False 7.016287 3.034022 0.582167
True 5.742842 1.912048 0.238922
All 6.917581 2.947057 0.555562

Stateicp

This is pretty much the most important variable here, because it’s what the model will be using for geographic variation. While I often mention ‘state’ in this paper, that is not quite accurate. There are non-state territories in the ICP coding system, and I included those as well. Included, there is a icp_conversion.csv file that has to mapping between the encodings of the state names and ICP codes I used. The ones used in the model later are different entirely, and is from an index I just created in SQL, as it had to be in order and not skip any for pymc to let it work.

I also generated the ‘state_changed’ variable, which is just a boolean of whether or not they moved states between the two census years. This is important, as it allows us to see if there is any difference in the trajectories of those who moved states and those who stayed in the same state, a primary question posed by this paper.

State Distance

I used a dataset I found on github to generate a big list of distances from state to state, then joined that csv into a special dataframe. I did this with the 10% model only since by the time I did all of this I had already discovered the extra time largely wasn’t worth it.

Race

For this variable I decided to encode it in a quite simple “not_white” scheme, as I found that that would greatly simplify things as all non black or white races were very rare in the dataset. If I was to collapse them into one category, including the dominant race as it’s own category seems to make the most sense to me. This variable is used quite a lot within the analysis, as it is very important to this time period and one of the most clear cut variables likely to have distinct regional differences.

The yearly difference causes some issues with linked too. I ended up doing a system where if the race values disagreed (on non-white status), then it would use the earlier value. Not certain this is the best way to handle it, but it seems to make more sense than the other way around.

# Descriptive Stats on Race
race_id_to_str = dict(zip(
    [1,2,3,4,5,6,7,8,9],
    ['White', 'Black/African American', 'American Indian or Alaskan Native', \
     'Chinese', 'Japanese', 'Other Asian or Pacific Islander', \
        'Other Race, nec', 'Two major races', 'Three or more major races']
))
one_pct['race_detailed'] = one_pct.RACE.replace(race_id_to_str)
one_pct['n'] = 1
one_pct.groupby('race_detailed').agg({'n': 'sum'}) \
    .reset_index() \
    .sort_values('n', ascending = False) \
    .assign(pct = lambda x: 100* x.n / x.n.sum())
race_detailed n pct
5 White 1150980 88.324401
1 Black/African American 147321 11.305183
0 American Indian or Alaskan Native 2787 0.213870
2 Chinese 1278 0.098072
3 Japanese 756 0.058014
4 Other Asian or Pacific Islander 6 0.000460

Age

Age is a very tricky one for this analysis. For one, it is essential to the whole exercise. Effectively, the entire goal is to observe someone over the course of their lifetime. Of course, then, the linked datasets will be drastically different before and after in terms of the age distribution. You can see this below in the histograms and the table. I can’t really put age into the model directly outside of testing purposes for this reason, as it would be very endogenous.

dmd('#### __All (including non linked)__')
(
    so.Plot(one_pct, x = 'AGE')
        .add(so.Bars(), so.Hist(bins = 20, stat = 'density'))
        .facet('YEAR')
    #.facet('YEAR')
)
dmd('#### __ONLY linked__')
(
    so.Plot(combined)
    .pair(x = ['c1870_age', 'c1910_age'])
    .add(so.Bars(), so.Hist(bins = 20, stat = 'density'))
    #.facet('YEAR')
)

dmd('#### __Average Age by Year__')

dmd('__All__')
one_pct.groupby('YEAR').agg({'AGE': ['mean', 'std']}).reset_index()
dmd('__Linked__')
combined.agg({'c1870_age': ['mean', 'std'], 'c1910_age': ['mean', 'std']}).transpose()

All (including non linked)

ONLY linked

Average Age by Year

All

YEAR AGE
mean std
0 1870 23.482835 18.216810
1 1910 26.630187 19.074487

Linked

mean std
c1870_age 15.168708 11.339750
c1910_age 54.917268 11.486817

Statistical Statement / Model

Background

This model is fundamentally a much expanded and bayesian flavor of a project I did for another class. In this project, I analyzed only Virginia data and compared that with specifically within Williamsburg. While this was informative, I was restricted by both inadequite tooling and a limited geographic location. Within state variation is interesting, but it is also important to understand how this varies across the country. The goal of this project is to get a bigger look into the regional composition of this effect, and be able to model entire distributions at once.

Dependent Variables

All models have one of two dependent variables:

  1. Change in Log Earnigns: \[\Theta_{inc} = ln(OCCSCORE_{1910}) - ln(OCCSCORE_{1870})\]

  2. Change in percent chance of having at least one year of college education:

\[\Theta_{edu} = EDSCOR50_{1910} - EDSCOR50_{1870}\]

The change in log earnings should approximate (very roughly, breaks down with large changes) percent chance in income. Education variable is already a percent estimate so I just left it be the raw change.

Hyperpriors

I chose pretty similar priors across all the groups. For the sigmas, I always used HalfCauchy with either beta = 2 or beta = 3. For the betas I used either uniform or normal.

Simple Race Models

For the simple models only dealing with race as a coefficient in the regression equation, I (roughly) targeted the priors to the means of a similar overall linear model for the whole country, but kept the standard deviations and the distribution of the mu’s quite large. They shouldn’t be that informative, but I think it helped speed up training a bit. The exact priors I used are below. For log earnings:

Technical Information

Various Datasets

There are two main variations of the primary dataset. The first is just the Census linking project’s standard nysiis match, and the second is their more conservative matching standard. Some of these I sampled into smaller datasets to test things and save time, but the full dataset is the one used for the final analysis. The models themselves are somewhat all over the place, but that is because the log wage standard full datasets flat out failed after 8+ hours of running on an A100 somehow, and errored out most of the way through. The education ones didn’t crash, strangely.

Codename Description Models used in
conservative_full Full dataset, conservative match ln_wages
conservative_10pct 10% sample, conservative match ln_wages_age, ln_wages_state_change, both state distance models
conservative_25pct 25% sample, conservative match ln_wages
std_full Full dataset, standard match edu_race, ln_wages_state_change
std_10pct 10% sample, standard match N/A
std_25pct 25% sample, standard match ln_wages_conservative_25pct

Each file is named comb_1870_1910_{codename}.parquet, with comb standing for combined.

Centered vs Non-Centered

All of the models were run in a non-centered way for performance reasons. I tried one without it, but it was not worth the time. The model is complicated enough a non-centered approach definitely makes sense.

Very bad bug

After running a large number of my models and being almost done, I just now spotted a bug where any model with a beta 3 has it using the beta 1 offset. Now, all that does is generate a mu 0 sigma 1 random sample, but they would be correlated together when sampling. This effected multiple of my models, unfortunately. I have fixed it now, but I am not going to rerun all of them.

Practical Problems

This project in general ran into some very serious technical problems. The most important of these was just getting the model to runa at all. It straight up does not run whatsoever on my own machine, even when I only run it on a random sample of the full dataset. I tried quite a few things, mainly switching the backend to JAX (Numpyro), which allows it to be JIT compiled. This made it technically start running, but basically had zero progress. From there, I ended up putting it on Google cloud and just eating the cost. Most of the model were run on a VM with a Nvidia A100 GPU, except one which I had running on a V100. Each one took around 7 hours, and I had to redo them a few times. I had original plans to run the model on the raw dataset as well, not just the linked one, but I don’t think that would be practical given how absolutely massive it is. There may be something with my model causing this, but I wasn’t able to identify it. I’ll discuss this further in the model section.

Model Specification

ln_wages

This is the simplest of all the models shown. It has the following specification:

Hyperpriors: \[ \begin{aligned} \mu_{\beta_0} &\sim N(1.9,1.5)\\ \sigma_{\beta_0} &\sim HalfCauchy(2)\\ \mu_{\beta_1} &\sim N(-1, 1.5)\\ \sigma_{\beta_1} &\sim HalfCauchy(2)\\ \sigma &\sim HalfCauchy(2)\\ \end{aligned} \]

Group Priors:

\[ \begin{aligned} \beta_{0i} &\sim N(\mu_{\beta_0}, \sigma_{\beta_0})\\ \beta_{1i} &\sim N(\mu_{\beta_1}, \sigma_{\beta_1}) \\ \end{aligned} \]

Deterministic:

\[ \begin{aligned} \mu_{i} = \beta_{0i} + \beta_{1i} not\_white_{i} \\ \end{aligned} \]

For the hyperpriors on this model, I roughly put the mean on a mean generated by a simple linear regression for the whole country, and made the SD large compared to the real SD, but still in a general range. This was just to help the model converge faster. All sigmas are just HalfCauchy with beta = 2. So slightly informative priors but not really that much. The group priors are just the hierarchal splitting by state, using the ICP code (The index used is not actually the ICP code, I have a csv converting it). This model itself is a very simple regression with race as the only variable, and is the simplest model here. This model was run on the conservative_full dataset, and used conservative linking. The standard model unfortunately failed to run in it’s full form, although a 25% model did manage to run.

The code used to run the model is below:

# ln_wages_conservative_full 
# Used conservative linking

def ln_wages_conservative(data, y_hat_str):
    shape_val = data['origin_state_idx'].nunique()
    with pm.Model() as model:
        # Priors
        mu_beta_0 = pm.Normal('mu_beta_0', mu = 1.9, sigma = 1.5)
        sigma_beta_0 = pm.HalfCauchy('sigma_beta_0', beta = 2)
        mu_beta_1 = pm.Normal('mu_beta_1', mu = -1, sigma = 1.5)
        sigma_beta_1 = pm.HalfCauchy('sigma_beta_1', beta = 2)
        sigma = pm.HalfCauchy('sigma', beta = 2)

        # Hierarchical Priors
        beta_0_offset = pm.Normal('beta_0_offset', mu=0, sigma=1, shape = shape_val)
        beta_0 = pm.Deterministic('beta_0', mu_beta_0 + beta_0_offset * sigma_beta_0)

        beta_1_offset = pm.Normal('beta_1_offset', mu=0, sigma=1, shape = shape_val)
        beta_1 = pm.Deterministic('beta_1', mu_beta_1 + beta_1_offset * sigma_beta_1)

        # Deterministic

        mu_all = beta_0[data.origin_state_idx] + beta_1[data.origin_state_idx] * data.not_white  

        # Likelihood

        y_like = pm.Normal('y_like', mu=mu_all, sigma=sigma, observed=data[y_hat_str])

    return model

# IF YOU WANT TO ACTUALLY RUN THIS, UNCOMMENT OUT ONE OF THESE DATASETS!!!!!
# 10pct
dataset = comb_1870_1910_conservative_full_10pct
# 25pct
# dataset = comb_1870_1910_conservative_full_25pct
# full
# dataset = comb_1870_1910_conservative_full
model = ln_wages_conservative(dataset, 'log_earnings_change')
with model:
    ### YOU MUST CHOOSE ONE _IF_ YOU WANT TO RUN THIS. Nothing else in this document assumes you will run this.
# JAX
    #ln_wages_conservative_trace = pm_jax.sample_numpyro_nuts(4000, return_inferencedata=True, progressbar=True, chain_method = 'vectorized')
# Normal NUTS (Might run slower)
    #ln_wages_conservative_trace = pm.sample(draws = 4000, return_inferencedata=True, progressbar=True)
    pass
pm.model_to_graphviz(model)

#At the end of the last slide there should be a graphviz diagram showing up. If there is not, run this cell!

pm.model_to_graphviz(model).view()

edu_race

\[ \begin{aligned} \mu_{\beta_0} &\sim N(6.5,1.5)\\ \sigma_{\beta_0} &\sim HalfCauchy(2)\\ \mu_{\beta_1} &\sim N(-2.5, 1.5)\\ \sigma_{\beta_1} &\sim HalfCauchy(2)\\ \sigma &\sim HalfCauchy(2)\\ \end{aligned} \]

Group Priors:

\[ \begin{aligned} \beta_{0i} &\sim N(\mu_{\beta_0}, \sigma_{\beta_0})\\ \beta_{1i} &\sim N(\mu_{\beta_1}, \sigma_{\beta_1}) \\ \end{aligned} \]

Deterministic:

\[ \begin{aligned} \mu_{i} = \beta_{0i} + \beta_{1i} not\_white_{i} \\ \end{aligned} \]

This is a very very similar model to the last one, but targeting education instead. The main difference is I set up different, but similarly calculated values for the priors to help with convergence. They were different because the outcome variable this time was education.

The code used to run the model is below. I ran this only on the standard (non-conservative) dataset. No education models were run on the conservative dataset.


# edu_race_std_full
def edu_race_std(data):
    shape_val = data['origin_state_idx'].nunique()
    with pm.Model() as model:
        # Priors
        mu_beta_0 = pm.Normal('mu_beta_0', mu = 6.5, sigma = 1.5)
        sigma_beta_0 = pm.HalfCauchy('sigma_beta_0', beta = 2)
        mu_beta_1 = pm.Normal('mu_beta_1', mu = -2.5, sigma = 1.5)
        sigma_beta_1 = pm.HalfCauchy('sigma_beta_1', beta = 2)
        sigma = pm.HalfCauchy('sigma', beta = 2)

        # Hierarchical Priors
        beta_0_offset = pm.Normal('beta_0_offset', mu=0, sigma=1, shape = shape_val)
        beta_0 = pm.Deterministic('beta_0', mu_beta_0 + beta_0_offset * sigma_beta_0)

        beta_1_offset = pm.Normal('beta_1_offset', mu=0, sigma=1, shape = shape_val)
        beta_1 = pm.Deterministic('beta_1', mu_beta_1 + beta_1_offset * sigma_beta_1)

        # Deterministic

        mu_all = beta_0[data.origin_state_idx] + beta_1[data.origin_state_idx] * data.not_white  

        # Likelihood

        y_like = pm.Normal('y_like', mu=mu_all, sigma=sigma, observed=data.edscor50_change)

    return model

# IF YOU WANT TO ACTUALLY RUN THIS, UNCOMMENT OUT ONE OF THESE DATASETS!!!!!
# 10pct
dataset = comb_1870_1910_std_full_10pct
# 25pct
#dataset = comb_1870_1910_std_full_25pct
# full
#dataset = comb_1870_1910_std_full
model = edu_race_std(dataset)
with model:
    ### YOU MUST CHOOSE ONE _IF_ YOU WANT TO RUN THIS. Nothing else in this document assumes you will run this.
# JAX
    #edu_race_std_trace = pm_jax.sample_numpyro_nuts(4000, return_inferencedata=True, progressbar=True, chain_method = 'vectorized')
# Normal NUTS (Might run slower)
    #edu_race_std_trace = pm.sample(draws = 4000, return_inferencedata=True, progressbar=True)
    pass
pm.model_to_graphviz(model)


#At the end of the last slide there should be a graphviz diagram showing up. If there is not, run this cell!

pm.model_to_graphviz(model).view()
'.gv.pdf'

Log Earnings State Change / Distance with race

\[ \begin{aligned} \mu_{\beta_0} &\sim Uniform(-10, 10)\\ \sigma_{\beta_0} &\sim HalfCauchy(2)\\ \mu_{\beta_1} &\sim N(-10, 10)\\ \sigma_{\beta_1} &\sim HalfCauchy(2)\\ \mu_{\beta_2} &\sim N(-10, 10)\\ \sigma_{\beta_2} &\sim HalfCauchy(2)\\ \mu_{\beta_3} &\sim N(-10, 10)\\ \sigma_{\beta_3} &\sim HalfCauchy(2)\\ \sigma &\sim HalfCauchy(2)\\ \end{aligned} \]

Group Priors:

\[ \begin{aligned} \beta_{0i} &\sim N(\mu_{\beta_0}, \sigma_{\beta_0})\\ \beta_{1i} &\sim N(\mu_{\beta_1}, \sigma_{\beta_1}) \\ \beta_{2i} &\sim N(\mu_{\beta_2}, \sigma_{\beta_2}) \\ \beta_{3i} &\sim N(\mu_{\beta_3}, \sigma_{\beta_3}) \\ \end{aligned} \]

Deterministic:

  1. List item
  2. List item

\[ \begin{aligned} \mu_{i} = \beta_{0i} + \beta_{1i} not\_white_{i} + \beta_{2i} state\_changed_i + \beta_{3i} state\_changed_i \times not\_white_i \\ \end{aligned} \]

This is also a ‘state distance w/ race’ model, you only need to swap out the state_changed with state_distance. That is what I did. I will include the code for both below.

This is the most interesting and important of the models I created. It is more difficult to estimate, with the regression requiring more parameters distributions to be estimated, but it very important to the primary question of interest. The census tracts where you live in both years. For the geographic area in the model, I defaulted to where you have ended up. In this model, I added a term to the regression in two areas that indicate you now live in a different state. I also interacted these terms with race and measured the log earnings change. The effect here is to see if people who changed states end up in better life outcomes, and to see if that is different depending on your race or what location you were from originally.

The code used to run the model is below. I ran this only on the standard (non-conservative) dataset. Additionally there was a weird bug where I used the same offset variable for two variables. It’s just a random N(0,1) offset so I’m not sure if it will matter but I added an additional 10% model just in case.


# ln_wages_state_change_std_full (codename I gave trace file)
# full nysiis
def ln_wages_state_change(data, y_hat_str):
    shape_val = data['origin_state_idx'].nunique()
    with pm.Model() as model:
        # Priors
        mu_beta_0 = pm.Uniform('mu_beta_0', lower=-10, upper=10)
        sigma_beta_0 = pm.HalfCauchy('sigma_beta_0', beta = 2)
        mu_beta_1 = pm.Uniform('mu_beta_1', lower=-10, upper=10)
        sigma_beta_1 = pm.HalfCauchy('sigma_beta_1', beta = 2)
        mu_beta_2 = pm.Uniform('mu_beta_2', lower=-10, upper=10)
        sigma_beta_2 = pm.HalfCauchy('sigma_beta_2', beta = 2)
        mu_beta_3 = pm.Uniform('mu_beta_3', lower=-10, upper=10)
        sigma_beta_3 = pm.HalfCauchy('sigma_beta_3', beta = 2)
        sigma = pm.HalfCauchy('sigma', beta = 2)

        # Hierarchical Priors
        beta_0_offset = pm.Normal('beta_0_offset', mu=0, sigma=1, shape = shape_val)
        beta_0 = pm.Deterministic('beta_0', mu_beta_0 + beta_0_offset * sigma_beta_0)

        beta_1_offset = pm.Normal('beta_1_offset', mu=0, sigma=1, shape = shape_val)
        beta_1 = pm.Deterministic('beta_1', mu_beta_1 + beta_1_offset * sigma_beta_1)
        beta_2_offset = pm.Normal('beta_2_offset', mu=0, sigma=1, shape = shape_val)
        beta_2 = pm.Deterministic('beta_2', mu_beta_2 + beta_2_offset * sigma_beta_2)
        beta_3_offset = pm.Normal('beta_3_offset', mu=0, sigma=1, shape = shape_val)
        beta_3 = pm.Deterministic('beta_3', mu_beta_3 + beta_3_offset * sigma_beta_3)
        # THERE WAS ORIGINALLY A TYPO HERE! I fixed it for the 10% model. 
        

        # Deterministic

        mu_all = beta_0[data.origin_state_idx] + beta_1[data.origin_state_idx] * data.not_white \
                + beta_2[data.origin_state_idx] * data.state_changed + beta_3[data.origin_state_idx]*data.state_changed * data.not_white
        # Likelihood

        y_like = pm.Normal('y_like', mu=mu_all, sigma=sigma, observed=data[y_hat_str])

    return model

# IF YOU WANT TO ACTUALLY RUN THIS, UNCOMMENT OUT ONE OF THESE DATASETS!!!!!
# 10pct
dataset = comb_1870_1910_std_full_10pct
# 25pct
#dataset = comb_1870_1910_std_full_25pct
# full
#dataset = comb_1870_1910_std_full
model = ln_wages_state_change(dataset, 'log_earnings_change')
with model:
    ### YOU MUST CHOOSE ONE _IF_ YOU WANT TO RUN THIS. Nothing else in this document assumes you will run this.
# JAX
    #ln_wages_state_change_trace = pm_jax.sample_numpyro_nuts(4000, return_inferencedata=True, progressbar=True, chain_method = 'vectorized')
# Normal NUTS (Might run slower)
    #ln_wages_state_change_trace = pm.sample(draws = 4000, return_inferencedata=True, progressbar=True)
    pass
pm.model_to_graphviz(model)

#At the end of the last slide there should be a graphviz diagram showing up. If there is not, run this cell!

pm.model_to_graphviz(model).view()
def state_dist_race_model(data, y_hat_str):
    shape_val = data['origin_state_idx'].nunique()
    with pm.Model() as model:
        # Priors
        mu_beta_0 = pm.Uniform('mu_beta_0', lower=-10, upper=10)
        sigma_beta_0 = pm.HalfCauchy('sigma_beta_0', beta = 2)
        mu_beta_1 = pm.Uniform('mu_beta_1', lower=-10, upper=10)
        sigma_beta_1 = pm.HalfCauchy('sigma_beta_1', beta = 2)
        mu_beta_2 = pm.Uniform('mu_beta_2', lower=-10, upper=10)
        sigma_beta_2 = pm.HalfCauchy('sigma_beta_2', beta = 2)
        mu_beta_3 = pm.Uniform('mu_beta_3', lower=-10, upper=10)
        sigma_beta_3 = pm.HalfCauchy('sigma_beta_3', beta = 2)
        sigma = pm.HalfCauchy('sigma', beta = 2)

        # Hierarchical Priors
        beta_0_offset = pm.Normal('beta_0_offset', mu=0, sigma=1, shape = shape_val)
        beta_0 = pm.Deterministic('beta_0', mu_beta_0 + beta_0_offset * sigma_beta_0)

        beta_1_offset = pm.Normal('beta_1_offset', mu=0, sigma=1, shape = shape_val)
        beta_1 = pm.Deterministic('beta_1', mu_beta_1 + beta_1_offset * sigma_beta_1)
        beta_2_offset = pm.Normal('beta_2_offset', mu=0, sigma=1, shape = shape_val)
        beta_2 = pm.Deterministic('beta_2', mu_beta_2 + beta_2_offset * sigma_beta_2)
        beta_3_offset = pm.Normal('beta_3_offset', mu=0, sigma=1, shape = shape_val)
        beta_3 = pm.Deterministic('beta_3', mu_beta_3 + beta_3_offset * sigma_beta_3)


        # Deterministic

        mu_all = beta_0[data.origin_state_idx] + beta_1[data.origin_state_idx] * data.state_dist + \
               beta_2[data.origin_state_idx]*data.not_white +  beta_3[data.origin_state_idx] * data.state_dist * data.not_white
        # Likelihood

        y_like = pm.Normal('y_like', mu=mu_all, sigma=sigma, observed=data[y_hat_str])

    return model
#Only works with this dataset
dataset = state_dist_dataset_special

model = state_dist_race_model(dataset, 'log_earnings_change')
with model:
    ### YOU MUST CHOOSE ONE _IF_ YOU WANT TO RUN THIS. Nothing else in this document assumes you will run this.
# JAX
    #ln_wages_state_change_trace = pm_jax.sample_numpyro_nuts(4000, return_inferencedata=True, progressbar=True, chain_method = 'vectorized')
# Normal NUTS (Might run slower)
    #ln_wages_state_change_trace = pm.sample(draws = 4000, return_inferencedata=True, progressbar=True)
    pass
pm.model_to_graphviz(model)

Log Earnings State Distance (w/o race)

\[ \begin{aligned} \mu_{\beta_0} &\sim Uniform(-10, 10)\\ \sigma_{\beta_0} &\sim HalfCauchy(2)\\ \mu_{\beta_1} &\sim N(-10, 10)\\ \sigma_{\beta_1} &\sim HalfCauchy(2)\\ \sigma &\sim HalfCauchy(2)\\ \end{aligned} \]

Group Priors:

\[ \begin{aligned} \beta_{0i} &\sim N(\mu_{\beta_0}, \sigma_{\beta_0})\\ \beta_{1i} &\sim N(\mu_{\beta_1}, \sigma_{\beta_1}) \\ \end{aligned} \]

Deterministic:

\[ \begin{aligned} \mu_{i} = \beta_{0i} + \beta_{1i} state\_dist_{i} \end{aligned} \]

This is a very simple modification of the base state_dist w/ race model for comparisons sake. model below.

def state_dist_basic_model(data, y_hat_str):
    shape_val = data['origin_state_idx'].nunique()
    with pm.Model() as model:
        # Priors
        mu_beta_0 = pm.Uniform('mu_beta_0', lower=-10, upper=10)
        sigma_beta_0 = pm.HalfCauchy('sigma_beta_0', beta = 2)
        mu_beta_1 = pm.Uniform('mu_beta_1', lower=-10, upper=10)
        sigma_beta_1 = pm.HalfCauchy('sigma_beta_1', beta = 2)
        sigma = pm.HalfCauchy('sigma', beta = 2)

        # Hierarchical Priors
        beta_0_offset = pm.Normal('beta_0_offset', mu=0, sigma=1, shape = shape_val)
        beta_0 = pm.Deterministic('beta_0', mu_beta_0 + beta_0_offset * sigma_beta_0)

        beta_1_offset = pm.Normal('beta_1_offset', mu=0, sigma=1, shape = shape_val)
        beta_1 = pm.Deterministic('beta_1', mu_beta_1 + beta_1_offset * sigma_beta_1)

        # Deterministic

        mu_all = beta_0[data.origin_state_idx] + beta_1[data.origin_state_idx] * data.state_dist 
        # Likelihood

        y_like = pm.Normal('y_like', mu=mu_all, sigma=sigma, observed=data[y_hat_str])

    return model
#Only works with this dataset
dataset = state_dist_dataset_special

model = state_dist_basic_model(dataset, 'log_earnings_change')
with model:
    ### YOU MUST CHOOSE ONE _IF_ YOU WANT TO RUN THIS. Nothing else in this document assumes you will run this.
# JAX
    #ln_wages_state_change_trace = pm_jax.sample_numpyro_nuts(4000, return_inferencedata=True, progressbar=True, chain_method = 'vectorized')
# Normal NUTS (Might run slower)
    #ln_wages_state_change_trace = pm.sample(draws = 4000, return_inferencedata=True, progressbar=True)
    pass
pm.model_to_graphviz(model)

Age and Race Model

\[ \begin{aligned} \mu_{\beta_0} &\sim Uniform(-10, 10)\\ \sigma_{\beta_0} &\sim HalfCauchy(2)\\ \mu_{\beta_1} &\sim N(-10, 10)\\ \sigma_{\beta_1} &\sim HalfCauchy(2)\\ \mu_{\beta_2} &\sim N(-50, 50)\\ \sigma_{\beta_2} &\sim HalfCauchy(3)\\ \mu_{\beta_3} &\sim N(-50, 50)\\ \sigma_{\beta_3} &\sim HalfCauchy(3)\\ \sigma &\sim HalfCauchy(2)\\ \end{aligned} \]

Group Priors:

\[ \begin{aligned} \beta_{0i} &\sim N(\mu_{\beta_0}, \sigma_{\beta_0})\\ \beta_{1i} &\sim N(\mu_{\beta_1}, \sigma_{\beta_1}) \\ \beta_{2i} &\sim N(\mu_{\beta_2}, \sigma_{\beta_2}) \\ \beta_{3i} &\sim N(\mu_{\beta_3}, \sigma_{\beta_3}) \\ \end{aligned} \]

Deterministic:

\[ \begin{aligned} \mu_{i} = \beta_{0i} + \beta_{1i} not\_white_{i} + \beta_{2i} age_i + \beta_{3i} age_i \times not\_white_i \\ \end{aligned} \]

This model was mostly made out of curiosity after I saw the histograms around ace in earlier data exploration. Essentially, the time cutoff and linking means almost all the people who are linked are by necessity older. I wanted to see if outright controlling for age made any large differences. Now, this may introduce addtional endogeneity issues, but I think it is still interesting to see.

The code used to run the model is below. I ran this only on the conservative dataset. Additionally there was a weird bug where I used the same offset variable for two variables. It’s just a random N(0,1) offset so I’m not sure if it will matter but I added an additional 10% model just in case.


# ln_wage_age_conservative_10pct 
def ln_wage_age(data, y_hat_str):
    shape_val = data['origin_state_idx'].nunique()
    with pm.Model() as model:
        # Priors
        mu_beta_0 = pm.Uniform('mu_beta_0', lower=-10, upper=10)
        sigma_beta_0 = pm.HalfCauchy('sigma_beta_0', beta = 2)
        mu_beta_1 = pm.Uniform('mu_beta_1', lower=-10, upper=10)
        sigma_beta_1 = pm.HalfCauchy('sigma_beta_1', beta = 2)
        mu_beta_2 = pm.Uniform('mu_beta_2', lower=-50, upper=50)
        sigma_beta_2 = pm.HalfCauchy('sigma_beta_2', beta = 3)
        mu_beta_3 = pm.Uniform('mu_beta_3', lower=-50, upper=50)
        sigma_beta_3 = pm.HalfCauchy('sigma_beta_3', beta = 3)
        sigma = pm.HalfCauchy('sigma', beta = 2)

        # Hierarchical Priors
        beta_0_offset = pm.Normal('beta_0_offset', mu=0, sigma=1, shape = shape_val)
        beta_0 = pm.Deterministic('beta_0', mu_beta_0 + beta_0_offset * sigma_beta_0)

        beta_1_offset = pm.Normal('beta_1_offset', mu=0, sigma=1, shape = shape_val)
        beta_1 = pm.Deterministic('beta_1', mu_beta_1 + beta_1_offset * sigma_beta_1)
        beta_2_offset = pm.Normal('beta_2_offset', mu=0, sigma=1, shape = shape_val)
        beta_2 = pm.Deterministic('beta_2', mu_beta_2 + beta_2_offset * sigma_beta_2)
        beta_3_offset = pm.Normal('beta_3_offset', mu=0, sigma=1, shape = shape_val) # NOTE!!!! This WAS a typo. I fixed it with a 10% model.  
       # beta_3 = pm.Deterministic('beta_3', mu_beta_3 + beta_1_offset * sigma_beta_3)
        beta_3 = pm.Deterministic('beta_3', mu_beta_3 + beta_3_offset * sigma_beta_3)


        # Deterministic

        mu_all = beta_0[data.origin_state_idx] + beta_1[data.origin_state_idx] * data.not_white \
                + beta_2[data.origin_state_idx] * data.c1870_age + beta_3[data.origin_state_idx]*data.c1870_age * data.not_white
        # Likelihood

        y_like = pm.Normal('y_like', mu=mu_all, sigma=sigma, observed=data[y_hat_str])

    return model

# IF YOU WANT TO ACTUALLY RUN THIS, UNCOMMENT OUT ONE OF THESE DATASETS!!!!!
# 10pct
dataset = comb_1870_1910_std_full_10pct
# 25pct
#dataset = comb_1870_1910_std_full_25pct
# full
#dataset = comb_1870_1910_std_full
model = ln_wage_age(dataset, 'log_earnings_change')
with model:
    ### YOU MUST CHOOSE ONE _IF_ YOU WANT TO RUN THIS. Nothing else in this document assumes you will run this.
# JAX
    #ln_wages_state_change_trace = pm_jax.sample_numpyro_nuts(4000, return_inferencedata=True, progressbar=True, chain_method = 'vectorized')
# Normal NUTS (Might run slower)
    #ln_wages_state_change_trace = pm.sample(draws = 4000, return_inferencedata=True, progressbar=True)
    pass
pm.model_to_graphviz(model)


<contextlib.ExitStack at 0x7fea59315690>
#At the end of the last slide there should be a graphviz diagram showing up. If there is not, run this cell!

pm.model_to_graphviz(model).view()
'.gv.pdf'

make sure you run this cell!



def print_model_diag(chain, name = 'This Model', commentary = [None]*8, var_names = ['beta_0', 'beta_1'], var_not = [ '~beta_0_offset', '~beta_1_offset']):
    dmd(F'## __{name}__')   
    #dmd('#### __Rhat__ and other summary stats')
    #display(pm.su##).reset_index()
    dmd('#### __Trace Plots__')
    dmd('#### __Detailed Trace Plots__')
    az.plot_trace(chain, var_names = var_not);
    plt.savefig(f'Figures/{name}.pdf')
    for beta in var_names:
        dmd(F'#### __{beta}__')
        az.plot_trace(chain, var_names = [beta], compact=False)
        plt.savefig(f'Figures/{name}{beta}.pdf')
    dmd(f'__printed under Figures/ starting with {name}.pdf__')
    plt.close()
plt.ioff()
<contextlib.ExitStack at 0x7ff0c661bfd0>

Results

Convergence

Education Models

This is a good place to start with analyzing the convergence, as there is currently only one education model out there. In terms of simple convergence, the model seems to have done quite well. There is not a single r_hat value above 1.01 at the very least, which is a very good sign. One interesting thing is that the ESS is honestly… weirdly good? Every model in this paper had 4000 draws from it, and almost all of the ESS values are far above the actual number sampled. Either way, there does not seem to be significant signs of autocorrelation.

dmd('## __Education and Race Model Diagnostics__')
with pd.option_context('display.max_rows', None, 'display.max_columns', None):  
    az.summary(edu_race_std_full_trace, var_names=['~beta_0_offset', '~beta_1_offset'])

Education and Race Model Diagnostics

mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail r_hat
mu_beta_0 6.977 0.164 6.663 7.275 0.006 0.004 826.0 1601.0 1.01
mu_beta_1 -2.417 0.161 -2.720 -2.113 0.003 0.002 3059.0 5219.0 1.00
sigma_beta_0 1.044 0.126 0.815 1.280 0.002 0.002 2586.0 5218.0 1.00
sigma_beta_1 0.820 0.137 0.583 1.086 0.002 0.001 4875.0 8231.0 1.00
sigma 17.810 0.008 17.795 17.825 0.000 0.000 16237.0 9136.0 1.00
beta_0[Connecticut (0)] 7.923 0.087 7.762 8.091 0.001 0.000 17127.0 10682.0 1.00
beta_0[Maine (1)] 7.268 0.076 7.130 7.413 0.001 0.000 17074.0 10147.0 1.00
beta_0[Massachusetts (2)] 8.000 0.057 7.895 8.110 0.000 0.000 16877.0 12566.0 1.00
beta_0[New Hampshire (3)] 7.649 0.109 7.455 7.860 0.001 0.001 20828.0 10663.0 1.00
beta_0[Rhode Island (4)] 8.047 0.137 7.793 8.308 0.001 0.001 21946.0 10592.0 1.00
beta_0[Vermont (5)] 7.533 0.109 7.325 7.737 0.001 0.001 21385.0 10507.0 1.00
beta_0[Delaware (6)] 7.660 0.175 7.328 7.982 0.001 0.001 26002.0 11441.0 1.00
beta_0[New Jersey (7)] 7.795 0.069 7.665 7.925 0.001 0.000 16804.0 11005.0 1.00
beta_0[New York (8)] 6.986 0.037 6.917 7.055 0.000 0.000 17082.0 12040.0 1.00
beta_0[Pennsylvania (9)] 7.115 0.038 7.046 7.187 0.000 0.000 16607.0 10797.0 1.00
beta_0[Illinois (10)] 6.588 0.041 6.513 6.668 0.000 0.000 16415.0 12304.0 1.00
beta_0[Indiana (11)] 6.524 0.049 6.431 6.616 0.000 0.000 16846.0 11674.0 1.00
beta_0[Michigan (12)] 6.859 0.057 6.749 6.966 0.000 0.000 16678.0 11126.0 1.00
beta_0[Ohio (13)] 7.010 0.041 6.935 7.088 0.000 0.000 15693.0 11823.0 1.00
beta_0[Wisconsin (14)] 7.427 0.062 7.308 7.540 0.000 0.000 17427.0 10601.0 1.00
beta_0[Iowa (15)] 7.036 0.059 6.923 7.147 0.000 0.000 16696.0 10008.0 1.00
beta_0[Kansas (16)] 6.326 0.109 6.116 6.525 0.001 0.001 21021.0 12188.0 1.00
beta_0[Minnesota (17)] 7.453 0.098 7.274 7.640 0.001 0.000 19593.0 10874.0 1.00
beta_0[Missouri (18)] 6.457 0.055 6.355 6.558 0.000 0.000 17276.0 11929.0 1.00
beta_0[Nebraska (19)] 6.173 0.182 5.832 6.510 0.001 0.001 31228.0 11113.0 1.00
beta_0[North Dakota (20)] 6.069 0.909 4.414 7.823 0.007 0.005 16266.0 11043.0 1.00
beta_0[South Dakota (21)] 6.115 0.510 5.184 7.106 0.003 0.002 25330.0 11534.0 1.00
beta_0[Virginia (22)] 7.058 0.086 6.895 7.220 0.001 0.000 22409.0 13452.0 1.00
beta_0[Alabama (23)] 6.819 0.108 6.614 7.019 0.001 0.000 27238.0 13390.0 1.00
beta_0[Arkansas (24)] 6.466 0.127 6.228 6.699 0.001 0.001 22583.0 13913.0 1.00
beta_0[Florida (25)] 6.949 0.227 6.523 7.379 0.002 0.001 22595.0 13202.0 1.00
beta_0[Georgia (26)] 6.847 0.093 6.669 7.017 0.001 0.000 25360.0 13991.0 1.00
beta_0[Louisiana (27)] 7.306 0.135 7.053 7.567 0.001 0.001 27406.0 13272.0 1.00
beta_0[Mississippi (28)] 7.357 0.133 7.103 7.602 0.001 0.001 26544.0 12835.0 1.00
beta_0[North Carolina (29)] 5.888 0.088 5.723 6.054 0.001 0.000 22224.0 14507.0 1.00
beta_0[South Carolina (30)] 7.391 0.148 7.107 7.662 0.001 0.001 27253.0 12309.0 1.00
beta_0[Texas (31)] 7.308 0.098 7.122 7.494 0.001 0.000 22550.0 13345.0 1.00
beta_0[Kentucky (32)] 6.288 0.067 6.166 6.415 0.000 0.000 18275.0 13259.0 1.00
beta_0[Maryland (33)] 7.832 0.083 7.678 7.989 0.001 0.000 20509.0 13864.0 1.00
beta_0[Tennessee (34)] 6.475 0.081 6.326 6.630 0.001 0.000 20256.0 14123.0 1.00
beta_0[West Virginia (35)] 7.032 0.107 6.835 7.239 0.001 0.000 23426.0 13454.0 1.00
beta_0[Colorado (36)] 4.911 0.318 4.324 5.509 0.002 0.001 30643.0 11624.0 1.00
beta_0[Nevada (37)] 4.584 0.410 3.825 5.361 0.003 0.002 23198.0 11226.0 1.00
beta_0[New Mexico (38)] 4.040 0.267 3.539 4.532 0.002 0.001 22213.0 11971.0 1.00
beta_0[Utah (39)] 7.516 0.205 7.137 7.903 0.001 0.001 36155.0 11097.0 1.00
beta_0[California (40)] 7.721 0.095 7.549 7.903 0.001 0.000 18779.0 11979.0 1.00
beta_0[Oregon (41)] 7.544 0.198 7.171 7.920 0.001 0.001 33884.0 11616.0 1.00
beta_0[Washington (42)] 7.578 0.382 6.847 8.287 0.002 0.002 29585.0 11421.0 1.00
beta_0[District of Columbia (43)] 10.195 0.223 9.774 10.612 0.002 0.001 18021.0 13953.0 1.00
beta_1[Connecticut (0)] -2.087 0.546 -3.122 -1.055 0.003 0.002 26341.0 12075.0 1.00
beta_1[Maine (1)] -2.522 0.670 -3.760 -1.238 0.004 0.003 23527.0 10640.0 1.00
beta_1[Massachusetts (2)] -2.183 0.478 -3.115 -1.307 0.003 0.002 25902.0 11506.0 1.00
beta_1[New Hampshire (3)] -2.541 0.774 -4.017 -1.108 0.005 0.004 22133.0 11383.0 1.00
beta_1[Rhode Island (4)] -2.382 0.640 -3.655 -1.244 0.004 0.003 26792.0 11960.0 1.00
beta_1[Vermont (5)] -2.494 0.743 -3.893 -1.087 0.005 0.004 20007.0 10937.0 1.00
beta_1[Delaware (6)] -2.648 0.425 -3.433 -1.826 0.003 0.002 26816.0 12403.0 1.00
beta_1[New Jersey (7)] -2.308 0.367 -3.006 -1.626 0.002 0.001 31555.0 11944.0 1.00
beta_1[New York (8)] -1.849 0.314 -2.457 -1.274 0.002 0.001 35199.0 11585.0 1.00
beta_1[Pennsylvania (9)] -1.583 0.289 -2.140 -1.053 0.002 0.001 32387.0 11359.0 1.00
beta_1[Illinois (10)] -2.330 0.339 -2.955 -1.688 0.002 0.001 27438.0 12346.0 1.00
beta_1[Indiana (11)] -2.384 0.370 -3.076 -1.692 0.002 0.001 31599.0 12075.0 1.00
beta_1[Michigan (12)] -1.309 0.440 -2.153 -0.493 0.003 0.002 23688.0 10933.0 1.00
beta_1[Ohio (13)] -1.635 0.273 -2.137 -1.118 0.001 0.001 34102.0 12877.0 1.00
beta_1[Wisconsin (14)] -2.247 0.605 -3.354 -1.071 0.004 0.003 25715.0 10965.0 1.00
beta_1[Iowa (15)] -2.509 0.544 -3.520 -1.468 0.003 0.002 26392.0 11500.0 1.00
beta_1[Kansas (16)] -1.845 0.472 -2.731 -0.958 0.003 0.002 27484.0 10820.0 1.00
beta_1[Minnesota (17)] -2.327 0.669 -3.608 -1.090 0.004 0.003 23994.0 11423.0 1.00
beta_1[Missouri (18)] -2.029 0.215 -2.431 -1.631 0.001 0.001 33061.0 12906.0 1.00
beta_1[Nebraska (19)] -2.122 0.766 -3.535 -0.661 0.005 0.004 23503.0 10954.0 1.00
beta_1[North Dakota (20)] -2.433 0.843 -4.058 -0.866 0.006 0.004 22407.0 11048.0 1.00
beta_1[South Dakota (21)] -2.345 0.824 -3.863 -0.794 0.006 0.004 20601.0 11295.0 1.00
beta_1[Virginia (22)] -2.298 0.143 -2.571 -2.034 0.001 0.001 31661.0 12741.0 1.00
beta_1[Alabama (23)] -2.240 0.156 -2.529 -1.946 0.001 0.001 30327.0 12442.0 1.00
beta_1[Arkansas (24)] -2.309 0.240 -2.771 -1.874 0.001 0.001 29616.0 12395.0 1.00
beta_1[Florida (25)] -1.982 0.325 -2.596 -1.375 0.002 0.002 23139.0 13210.0 1.00
beta_1[Georgia (26)] -2.604 0.141 -2.869 -2.340 0.001 0.001 27727.0 12809.0 1.00
beta_1[Louisiana (27)] -2.742 0.195 -3.101 -2.375 0.001 0.001 26744.0 11968.0 1.00
beta_1[Mississippi (28)] -2.586 0.178 -2.930 -2.258 0.001 0.001 28977.0 11881.0 1.00
beta_1[North Carolina (29)] -1.633 0.147 -1.904 -1.348 0.001 0.001 23579.0 11812.0 1.00
beta_1[South Carolina (30)] -2.702 0.192 -3.067 -2.346 0.001 0.001 27076.0 13137.0 1.00
beta_1[Texas (31)] -2.624 0.175 -2.960 -2.303 0.001 0.001 30120.0 11993.0 1.00
beta_1[Kentucky (32)] -1.602 0.165 -1.908 -1.290 0.001 0.001 25410.0 13211.0 1.00
beta_1[Maryland (33)] -2.973 0.192 -3.337 -2.608 0.001 0.001 27530.0 13033.0 1.00
beta_1[Tennessee (34)] -1.589 0.157 -1.891 -1.296 0.001 0.001 26787.0 13706.0 1.00
beta_1[West Virginia (35)] -2.798 0.336 -3.445 -2.181 0.002 0.001 32224.0 12824.0 1.00
beta_1[Colorado (36)] -2.884 0.777 -4.384 -1.461 0.006 0.004 18896.0 11868.0 1.00
beta_1[Nevada (37)] -2.420 0.709 -3.754 -1.089 0.005 0.004 21453.0 11926.0 1.00
beta_1[New Mexico (38)] -2.604 0.748 -4.043 -1.234 0.005 0.004 22969.0 11064.0 1.00
beta_1[Utah (39)] -2.604 0.803 -4.113 -1.091 0.006 0.004 20082.0 10843.0 1.00
beta_1[California (40)] -4.833 0.450 -5.669 -3.972 0.003 0.002 16498.0 12311.0 1.00
beta_1[Oregon (41)] -3.282 0.706 -4.655 -2.006 0.005 0.004 20583.0 11031.0 1.00
beta_1[Washington (42)] -2.707 0.755 -4.179 -1.334 0.005 0.004 21973.0 12017.0 1.00
beta_1[District of Columbia (43)] -4.214 0.446 -5.039 -3.375 0.003 0.002 17735.0 11600.0 1.00

Visual Inspection

This was going to show the plots below, but it crashed my jupyter setup when trying to open them… I changed it to go to Figures/ as a pdf. This crashing also somehow corrupted my entire .ipynb and I lost a good bit of work. Thankfully, I have been comitting it on git so I was able to restore most of the damage. If this whole project is a bit finnekey, I’m really sorry. Nothing is going my way…

print_model_diag(edu_race_std_full_trace, 'Edu Race (std full)')

Edu Race (std full)

Trace Plots

Detailed Trace Plots

beta_0

beta_1

__printed under Figures/ starting with Edu Race (std full).pdf

Upon visual inspection, the primary (nation-level) overall betas look mostly good. The histograms of mu_beta_0 does look a little messed up between chains, but the rest look mostly good. The chains themselves look fine, nothing clearly wrong with them. The wobbling in between the various chains is pretty concerning, though.

Interestingly, the variation inside of individual states almost seems better, with the chains honestly being quite consistent. I don’t see any issue with individual chain plots, and the histograms mostly look good. There is definitely some wobble between chains though, and this appears to be worst with states that seem like they would be newer during the time period. Overall I think this chain is actually very well converged, and can’t see any significant issues.

Simple Wage and race models

[ Context: I had a whole section written out here that got destroyed by a corrupted ipynb. Apologies. ]

This is a total of three models:

  1. ln_wages_conservative_full: Just the full model of diff in log wages by location and race. Using the conservative linking standard
  2. ln_wages_std_25pct: This is the same thing as before, with one key difference. the full model for the non-conservative standard linking style failed running several times. Each time took over 5 hours. I eventually just ran it with a random sample of 25% of the sample and it ran fine.
  3. ln_wages_conservative_25pct: I just ran this to make sure the 25% sampling thing wouldn’t mess up the results too much. To compare apples with apples.

Overall this is a pretty similar story to the previous case. The r_hat is better actually, with nothing about 1.0 whatsoever. The ESS is way more than we ever need to worry about, etc. On a diagnostic side there is nothing really to worry about.

Visual:

The visual inspection

ln_wages_std_25pct:

Anyways, I don’t see any super glaring issues once again. sigma_beta_0 seems quite off center though. That might be a mapping thing, but the chain looks somewhat off too, like it is missing exploring one of the tails. mu_beta_0 has also looked better. Once again, the individual plots themselves actually look quite a bit better than the overall means. I’m not really sure why exactly that is. Beta 1 is an exception though, where the distributions just look very… not normal. Almost like L1 norm? with some lookin gfar more like lognormal than normal (much more spikey on avg though, thats only a few).

ln_wages_conservative_full:

These look mostly fine on the individual main ones. sigma_beta_0/1 look a bit skewed, especially in like a ‘which part of the distribution is explored’ way. the mu’s look mostly fine though.

when we go into the individual states, it’s actually really excellent. None of the weird spikeyness of std_25 and the chains all look quite stationary.

the conservative 25% one looks nearly identical to the full one, maybe with a bit more noise here and there. I honestly can barely tell though. This makes me think the noisyness is not as much because of the sample being smaller and may just be the links being worse. Conservative linking might be the way to go.


dmd('## __ln_wages_conservative_full__')
with pd.option_context('display.max_rows', None, 'display.max_columns', None):  
    az.summary(ln_wages_conservative_full, var_names=['~beta_0_offset', '~beta_1_offset'])
               

dmd('## __ln_wages_conservative_25pct__')
with pd.option_context('display.max_rows', None, 'display.max_columns', None):  
    az.summary(ln_wages_conservative_25pct, var_names=['~beta_0_offset', '~beta_1_offset'])
dmd('## __ln_wages_std_25pct__')
with pd.option_context('display.max_rows', None, 'display.max_columns', None):  
    az.summary(ln_wages_std_25pct, var_names=['~beta_0_offset', '~beta_1_offset'])

print_model_diag(ln_wages_conservative_full, 'ln_wages_conservative_full')
print_model_diag(ln_wages_conservative_25pct, 'ln_wages_conservative_25pct')
print_model_diag(ln_wages_std_25pct, 'ln_wages_std_25pct')

ln_wages_conservative_full

mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail r_hat
mu_beta_0 1.487 0.036 1.419 1.556 0.001 0.001 613.0 1265.0 1.0
mu_beta_1 -0.149 0.031 -0.207 -0.090 0.001 0.001 1691.0 3305.0 1.0
sigma_beta_0 0.235 0.030 0.183 0.294 0.001 0.001 1322.0 3239.0 1.0
sigma_beta_1 0.168 0.030 0.116 0.225 0.000 0.000 3732.0 6592.0 1.0
sigma 2.042 0.001 2.040 2.045 0.000 0.000 17082.0 9732.0 1.0
beta_0[Connecticut (0)] 1.349 0.013 1.323 1.372 0.000 0.000 16756.0 10915.0 1.0
beta_0[Maine (1)] 1.430 0.011 1.410 1.450 0.000 0.000 16202.0 11238.0 1.0
beta_0[Massachusetts (2)] 1.179 0.009 1.161 1.195 0.000 0.000 16335.0 13596.0 1.0
beta_0[New Hampshire (3)] 1.360 0.016 1.330 1.389 0.000 0.000 19172.0 10153.0 1.0
beta_0[Rhode Island (4)] 1.351 0.020 1.313 1.387 0.000 0.000 24796.0 11520.0 1.0
beta_0[Vermont (5)] 1.410 0.015 1.382 1.439 0.000 0.000 20395.0 10093.0 1.0
beta_0[Delaware (6)] 1.547 0.025 1.501 1.593 0.000 0.000 28609.0 12457.0 1.0
beta_0[New Jersey (7)] 1.580 0.011 1.560 1.600 0.000 0.000 16076.0 10684.0 1.0
beta_0[New York (8)] 1.331 0.006 1.320 1.342 0.000 0.000 16471.0 11687.0 1.0
beta_0[Pennsylvania (9)] 1.580 0.006 1.568 1.591 0.000 0.000 16724.0 12655.0 1.0
beta_0[Illinois (10)] 1.314 0.006 1.302 1.326 0.000 0.000 16014.0 12048.0 1.0
beta_0[Indiana (11)] 1.466 0.007 1.452 1.479 0.000 0.000 16227.0 11248.0 1.0
beta_0[Michigan (12)] 1.395 0.008 1.379 1.411 0.000 0.000 16299.0 11548.0 1.0
beta_0[Ohio (13)] 1.437 0.006 1.425 1.448 0.000 0.000 15668.0 11365.0 1.0
beta_0[Wisconsin (14)] 1.609 0.009 1.591 1.626 0.000 0.000 16287.0 12216.0 1.0
beta_0[Iowa (15)] 1.453 0.009 1.437 1.469 0.000 0.000 15602.0 10736.0 1.0
beta_0[Kansas (16)] 1.394 0.016 1.365 1.426 0.000 0.000 21238.0 11192.0 1.0
beta_0[Minnesota (17)] 1.701 0.014 1.673 1.727 0.000 0.000 16770.0 11818.0 1.0
beta_0[Missouri (18)] 1.441 0.008 1.425 1.456 0.000 0.000 16239.0 11532.0 1.0
beta_0[Nebraska (19)] 1.368 0.027 1.317 1.419 0.000 0.000 33896.0 10820.0 1.0
beta_0[North Dakota (20)] 0.945 0.204 0.557 1.326 0.003 0.002 5504.0 9119.0 1.0
beta_0[South Dakota (21)] 1.162 0.082 1.013 1.318 0.001 0.000 21361.0 11814.0 1.0
beta_0[Virginia (22)] 1.527 0.013 1.502 1.551 0.000 0.000 20779.0 13215.0 1.0
beta_0[Alabama (23)] 1.521 0.016 1.488 1.551 0.000 0.000 24435.0 12408.0 1.0
beta_0[Arkansas (24)] 1.601 0.019 1.565 1.637 0.000 0.000 22640.0 12824.0 1.0
beta_0[Florida (25)] 1.625 0.032 1.564 1.684 0.000 0.000 21562.0 13290.0 1.0
beta_0[Georgia (26)] 1.368 0.014 1.342 1.394 0.000 0.000 23708.0 14404.0 1.0
beta_0[Louisiana (27)] 1.761 0.019 1.725 1.797 0.000 0.000 21353.0 14510.0 1.0
beta_0[Mississippi (28)] 1.532 0.020 1.496 1.572 0.000 0.000 22609.0 13770.0 1.0
beta_0[North Carolina (29)] 1.439 0.013 1.414 1.464 0.000 0.000 21474.0 14775.0 1.0
beta_0[South Carolina (30)] 1.620 0.022 1.579 1.662 0.000 0.000 21688.0 13356.0 1.0
beta_0[Texas (31)] 1.681 0.015 1.653 1.708 0.000 0.000 21093.0 13472.0 1.0
beta_0[Kentucky (32)] 1.474 0.010 1.455 1.492 0.000 0.000 17288.0 12292.0 1.0
beta_0[Maryland (33)] 1.653 0.012 1.629 1.675 0.000 0.000 17949.0 11426.0 1.0
beta_0[Tennessee (34)] 1.502 0.013 1.478 1.526 0.000 0.000 19444.0 12275.0 1.0
beta_0[West Virginia (35)] 1.887 0.016 1.856 1.917 0.000 0.000 16008.0 12557.0 1.0
beta_0[Colorado (36)] 1.101 0.048 1.007 1.187 0.000 0.000 31788.0 10688.0 1.0
beta_0[Nevada (37)] 0.831 0.066 0.710 0.959 0.000 0.000 20756.0 9788.0 1.0
beta_0[New Mexico (38)] 1.648 0.041 1.573 1.725 0.000 0.000 32723.0 12280.0 1.0
beta_0[Utah (39)] 1.920 0.028 1.867 1.974 0.000 0.000 22061.0 11220.0 1.0
beta_0[California (40)] 1.632 0.014 1.605 1.657 0.000 0.000 17047.0 11343.0 1.0
beta_0[Oregon (41)] 1.771 0.027 1.721 1.821 0.000 0.000 28421.0 10957.0 1.0
beta_0[Washington (42)] 1.742 0.055 1.639 1.844 0.000 0.000 28660.0 10858.0 1.0
beta_0[District of Columbia (43)] 1.830 0.031 1.771 1.888 0.000 0.000 23573.0 13206.0 1.0
beta_1[Connecticut (0)] -0.020 0.102 -0.207 0.173 0.001 0.001 17201.0 11548.0 1.0
beta_1[Maine (1)] -0.104 0.127 -0.340 0.137 0.001 0.001 17257.0 11693.0 1.0
beta_1[Massachusetts (2)] 0.017 0.086 -0.148 0.173 0.001 0.001 18714.0 12433.0 1.0
beta_1[New Hampshire (3)] -0.080 0.152 -0.365 0.205 0.001 0.001 15387.0 11071.0 1.0
beta_1[Rhode Island (4)] 0.001 0.115 -0.216 0.215 0.001 0.001 16634.0 12168.0 1.0
beta_1[Vermont (5)] -0.059 0.143 -0.341 0.199 0.001 0.001 14952.0 12604.0 1.0
beta_1[Delaware (6)] -0.091 0.071 -0.222 0.044 0.001 0.000 18339.0 12799.0 1.0
beta_1[New Jersey (7)] -0.285 0.069 -0.412 -0.155 0.000 0.000 22096.0 12638.0 1.0
beta_1[New York (8)] -0.043 0.058 -0.153 0.065 0.000 0.000 23398.0 11915.0 1.0
beta_1[Pennsylvania (9)] -0.150 0.052 -0.251 -0.055 0.000 0.000 28031.0 11921.0 1.0
beta_1[Illinois (10)] -0.169 0.064 -0.289 -0.051 0.000 0.000 24262.0 12400.0 1.0
beta_1[Indiana (11)] -0.264 0.069 -0.396 -0.137 0.000 0.000 22064.0 11551.0 1.0
beta_1[Michigan (12)] 0.086 0.078 -0.059 0.232 0.001 0.000 19690.0 11556.0 1.0
beta_1[Ohio (13)] -0.101 0.048 -0.190 -0.012 0.000 0.000 25255.0 12145.0 1.0
beta_1[Wisconsin (14)] -0.158 0.109 -0.357 0.049 0.001 0.001 18587.0 11746.0 1.0
beta_1[Iowa (15)] -0.283 0.100 -0.476 -0.103 0.001 0.001 16768.0 12083.0 1.0
beta_1[Kansas (16)] -0.067 0.081 -0.221 0.083 0.001 0.001 19745.0 12387.0 1.0
beta_1[Minnesota (17)] -0.142 0.122 -0.367 0.089 0.001 0.001 17940.0 11251.0 1.0
beta_1[Missouri (18)] -0.072 0.040 -0.150 0.001 0.000 0.000 30017.0 12053.0 1.0
beta_1[Nebraska (19)] -0.061 0.150 -0.337 0.229 0.001 0.001 15228.0 11142.0 1.0
beta_1[North Dakota (20)] -0.152 0.169 -0.457 0.185 0.001 0.001 15224.0 12563.0 1.0
beta_1[South Dakota (21)] -0.181 0.161 -0.481 0.130 0.001 0.001 15403.0 12288.0 1.0
beta_1[Virginia (22)] -0.071 0.025 -0.117 -0.025 0.000 0.000 28354.0 12432.0 1.0
beta_1[Alabama (23)] -0.052 0.026 -0.100 -0.003 0.000 0.000 26766.0 12889.0 1.0
beta_1[Arkansas (24)] -0.099 0.041 -0.177 -0.024 0.000 0.000 24454.0 13206.0 1.0
beta_1[Florida (25)] -0.107 0.052 -0.204 -0.011 0.000 0.000 19113.0 12730.0 1.0
beta_1[Georgia (26)] -0.047 0.023 -0.090 -0.003 0.000 0.000 28447.0 12176.0 1.0
beta_1[Louisiana (27)] -0.242 0.031 -0.299 -0.183 0.000 0.000 26969.0 12872.0 1.0
beta_1[Mississippi (28)] -0.104 0.029 -0.158 -0.050 0.000 0.000 25625.0 13191.0 1.0
beta_1[North Carolina (29)] -0.101 0.024 -0.144 -0.056 0.000 0.000 28226.0 12485.0 1.0
beta_1[South Carolina (30)] -0.185 0.031 -0.242 -0.127 0.000 0.000 24090.0 12541.0 1.0
beta_1[Texas (31)] -0.136 0.029 -0.190 -0.081 0.000 0.000 29673.0 12919.0 1.0
beta_1[Kentucky (32)] -0.064 0.030 -0.120 -0.009 0.000 0.000 30538.0 11795.0 1.0
beta_1[Maryland (33)] -0.171 0.034 -0.235 -0.107 0.000 0.000 28487.0 13131.0 1.0
beta_1[Tennessee (34)] 0.003 0.028 -0.049 0.056 0.000 0.000 26372.0 13167.0 1.0
beta_1[West Virginia (35)] -0.319 0.063 -0.437 -0.198 0.000 0.000 23442.0 11943.0 1.0
beta_1[Colorado (36)] -0.188 0.152 -0.486 0.089 0.001 0.001 15613.0 11964.0 1.0
beta_1[Nevada (37)] -0.330 0.152 -0.618 -0.043 0.001 0.001 13129.0 11766.0 1.0
beta_1[New Mexico (38)] -0.239 0.149 -0.519 0.041 0.001 0.001 15521.0 11857.0 1.0
beta_1[Utah (39)] -0.245 0.164 -0.558 0.059 0.001 0.001 13898.0 11270.0 1.0
beta_1[California (40)] -0.672 0.087 -0.836 -0.509 0.001 0.001 14030.0 11604.0 1.0
beta_1[Oregon (41)] -0.433 0.145 -0.704 -0.162 0.001 0.001 10310.0 10365.0 1.0
beta_1[Washington (42)] -0.059 0.139 -0.315 0.205 0.001 0.001 13794.0 11341.0 1.0
beta_1[District of Columbia (43)] -0.286 0.073 -0.422 -0.148 0.001 0.000 21300.0 11739.0 1.0

ln_wages_conservative_25pct

mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail r_hat
mu_beta_0 1.428 0.045 1.344 1.513 0.002 0.001 656.0 1289.0 1.0
mu_beta_1 -0.114 0.038 -0.189 -0.046 0.001 0.001 2231.0 4044.0 1.0
sigma_beta_0 0.294 0.039 0.225 0.368 0.001 0.001 1951.0 3720.0 1.0
sigma_beta_1 0.190 0.038 0.120 0.262 0.001 0.000 3791.0 7208.0 1.0
sigma 2.038 0.002 2.035 2.041 0.000 0.000 15838.0 8746.0 1.0
beta_0[Connecticut (0)] 1.363 0.020 1.326 1.400 0.000 0.000 19570.0 11577.0 1.0
beta_0[Maine (1)] 1.482 0.017 1.449 1.514 0.000 0.000 17499.0 10344.0 1.0
beta_0[Massachusetts (2)] 1.211 0.013 1.187 1.235 0.000 0.000 16578.0 14336.0 1.0
beta_0[New Hampshire (3)] 1.393 0.025 1.346 1.439 0.000 0.000 27682.0 10577.0 1.0
beta_0[Rhode Island (4)] 1.292 0.030 1.235 1.349 0.000 0.000 30260.0 10844.0 1.0
beta_0[Vermont (5)] 1.457 0.024 1.413 1.505 0.000 0.000 25826.0 11150.0 1.0
beta_0[Delaware (6)] 1.513 0.039 1.440 1.586 0.000 0.000 27112.0 12471.0 1.0
beta_0[New Jersey (7)] 1.566 0.016 1.537 1.596 0.000 0.000 16665.0 11671.0 1.0
beta_0[New York (8)] 1.354 0.008 1.338 1.370 0.000 0.000 16842.0 13079.0 1.0
beta_0[Pennsylvania (9)] 1.578 0.009 1.562 1.594 0.000 0.000 16795.0 12592.0 1.0
beta_0[Illinois (10)] 1.325 0.009 1.307 1.343 0.000 0.000 15282.0 13267.0 1.0
beta_0[Indiana (11)] 1.492 0.011 1.471 1.512 0.000 0.000 15566.0 11131.0 1.0
beta_0[Michigan (12)] 1.405 0.013 1.381 1.431 0.000 0.000 16187.0 10966.0 1.0
beta_0[Ohio (13)] 1.446 0.009 1.428 1.462 0.000 0.000 16847.0 12117.0 1.0
beta_0[Wisconsin (14)] 1.606 0.014 1.579 1.633 0.000 0.000 15893.0 10809.0 1.0
beta_0[Iowa (15)] 1.462 0.013 1.438 1.487 0.000 0.000 16043.0 9908.0 1.0
beta_0[Kansas (16)] 1.315 0.026 1.268 1.363 0.000 0.000 24470.0 11853.0 1.0
beta_0[Minnesota (17)] 1.604 0.023 1.562 1.647 0.000 0.000 21425.0 10513.0 1.0
beta_0[Missouri (18)] 1.439 0.012 1.416 1.462 0.000 0.000 17171.0 11873.0 1.0
beta_0[Nebraska (19)] 1.186 0.042 1.111 1.267 0.000 0.000 32443.0 11938.0 1.0
beta_0[North Dakota (20)] 0.818 0.263 0.317 1.313 0.003 0.002 6786.0 9679.0 1.0
beta_0[South Dakota (21)] 0.943 0.124 0.714 1.178 0.001 0.001 19614.0 11425.0 1.0
beta_0[Virginia (22)] 1.525 0.020 1.489 1.563 0.000 0.000 22126.0 13741.0 1.0
beta_0[Alabama (23)] 1.549 0.025 1.503 1.596 0.000 0.000 25072.0 13983.0 1.0
beta_0[Arkansas (24)] 1.607 0.029 1.554 1.661 0.000 0.000 23402.0 12701.0 1.0
beta_0[Florida (25)] 1.544 0.051 1.449 1.642 0.000 0.000 18666.0 12122.0 1.0
beta_0[Georgia (26)] 1.361 0.022 1.321 1.402 0.000 0.000 24318.0 13419.0 1.0
beta_0[Louisiana (27)] 1.706 0.031 1.651 1.767 0.000 0.000 21635.0 14581.0 1.0
beta_0[Mississippi (28)] 1.525 0.030 1.470 1.583 0.000 0.000 22015.0 13910.0 1.0
beta_0[North Carolina (29)] 1.497 0.020 1.459 1.534 0.000 0.000 21701.0 14432.0 1.0
beta_0[South Carolina (30)] 1.612 0.034 1.547 1.676 0.000 0.000 20123.0 12812.0 1.0
beta_0[Texas (31)] 1.670 0.022 1.626 1.710 0.000 0.000 18618.0 13281.0 1.0
beta_0[Kentucky (32)] 1.466 0.015 1.437 1.494 0.000 0.000 18637.0 12085.0 1.0
beta_0[Maryland (33)] 1.602 0.019 1.566 1.637 0.000 0.000 18880.0 13012.0 1.0
beta_0[Tennessee (34)] 1.546 0.019 1.512 1.582 0.000 0.000 21070.0 13587.0 1.0
beta_0[West Virginia (35)] 1.867 0.025 1.821 1.914 0.000 0.000 17806.0 12980.0 1.0
beta_0[Colorado (36)] 0.712 0.073 0.569 0.845 0.000 0.000 24790.0 11826.0 1.0
beta_0[Nevada (37)] 0.306 0.099 0.122 0.495 0.001 0.001 13942.0 10924.0 1.0
beta_0[New Mexico (38)] 1.598 0.062 1.478 1.711 0.000 0.000 28673.0 12095.0 1.0
beta_0[Utah (39)] 1.785 0.047 1.697 1.871 0.000 0.000 31401.0 11290.0 1.0
beta_0[California (40)] 1.456 0.022 1.415 1.499 0.000 0.000 21428.0 11650.0 1.0
beta_0[Oregon (41)] 1.640 0.045 1.555 1.726 0.000 0.000 32631.0 11064.0 1.0
beta_0[Washington (42)] 1.417 0.085 1.262 1.581 0.001 0.000 23482.0 12411.0 1.0
beta_0[District of Columbia (43)] 1.587 0.051 1.497 1.687 0.000 0.000 22756.0 12145.0 1.0
beta_1[Connecticut (0)] -0.153 0.129 -0.394 0.092 0.001 0.001 19982.0 12249.0 1.0
beta_1[Maine (1)] -0.204 0.158 -0.496 0.093 0.001 0.001 15965.0 11945.0 1.0
beta_1[Massachusetts (2)] 0.031 0.111 -0.175 0.240 0.001 0.001 19450.0 11752.0 1.0
beta_1[New Hampshire (3)] -0.085 0.184 -0.452 0.246 0.001 0.001 15483.0 11460.0 1.0
beta_1[Rhode Island (4)] -0.007 0.147 -0.277 0.274 0.001 0.001 17997.0 11776.0 1.0
beta_1[Vermont (5)] -0.257 0.179 -0.613 0.056 0.002 0.001 13619.0 11851.0 1.0
beta_1[Delaware (6)] -0.057 0.095 -0.236 0.120 0.001 0.001 19839.0 12851.0 1.0
beta_1[New Jersey (7)] -0.139 0.084 -0.297 0.021 0.001 0.000 22526.0 12432.0 1.0
beta_1[New York (8)] -0.158 0.071 -0.292 -0.026 0.000 0.000 25703.0 12815.0 1.0
beta_1[Pennsylvania (9)] 0.000 0.064 -0.117 0.124 0.000 0.001 21914.0 12456.0 1.0
beta_1[Illinois (10)] -0.191 0.079 -0.342 -0.044 0.001 0.000 24380.0 13213.0 1.0
beta_1[Indiana (11)] -0.288 0.088 -0.456 -0.126 0.001 0.000 22136.0 11747.0 1.0
beta_1[Michigan (12)] 0.058 0.103 -0.139 0.248 0.001 0.001 17674.0 12138.0 1.0
beta_1[Ohio (13)] -0.060 0.062 -0.173 0.060 0.000 0.000 24863.0 11419.0 1.0
beta_1[Wisconsin (14)] -0.171 0.142 -0.446 0.088 0.001 0.001 16723.0 12423.0 1.0
beta_1[Iowa (15)] -0.319 0.123 -0.546 -0.084 0.001 0.001 16503.0 11875.0 1.0
beta_1[Kansas (16)] 0.030 0.112 -0.179 0.241 0.001 0.001 16825.0 11247.0 1.0
beta_1[Minnesota (17)] -0.093 0.155 -0.386 0.202 0.001 0.001 14860.0 11208.0 1.0
beta_1[Missouri (18)] -0.002 0.049 -0.095 0.091 0.000 0.000 29870.0 11834.0 1.0
beta_1[Nebraska (19)] 0.007 0.183 -0.325 0.363 0.002 0.001 12779.0 11503.0 1.0
beta_1[North Dakota (20)] -0.125 0.196 -0.505 0.238 0.002 0.001 16253.0 11317.0 1.0
beta_1[South Dakota (21)] -0.125 0.188 -0.479 0.234 0.001 0.001 16742.0 12324.0 1.0
beta_1[Virginia (22)] 0.021 0.033 -0.042 0.082 0.000 0.000 26803.0 12784.0 1.0
beta_1[Alabama (23)] 0.028 0.036 -0.039 0.096 0.000 0.000 26561.0 13140.0 1.0
beta_1[Arkansas (24)] -0.100 0.056 -0.202 0.008 0.000 0.000 23715.0 13269.0 1.0
beta_1[Florida (25)] 0.011 0.074 -0.129 0.149 0.001 0.001 16572.0 12323.0 1.0
beta_1[Georgia (26)] 0.025 0.032 -0.035 0.087 0.000 0.000 26045.0 12991.0 1.0
beta_1[Louisiana (27)] -0.087 0.044 -0.168 -0.003 0.000 0.000 23439.0 12786.0 1.0
beta_1[Mississippi (28)] -0.032 0.041 -0.108 0.045 0.000 0.000 21934.0 12681.0 1.0
beta_1[North Carolina (29)] -0.054 0.033 -0.118 0.007 0.000 0.000 30114.0 12809.0 1.0
beta_1[South Carolina (30)] -0.080 0.045 -0.162 0.005 0.000 0.000 20697.0 12439.0 1.0
beta_1[Texas (31)] -0.031 0.040 -0.108 0.044 0.000 0.000 28669.0 12458.0 1.0
beta_1[Kentucky (32)] -0.015 0.037 -0.084 0.056 0.000 0.000 28839.0 11959.0 1.0
beta_1[Maryland (33)] -0.081 0.043 -0.163 0.000 0.000 0.000 28441.0 12761.0 1.0
beta_1[Tennessee (34)] 0.018 0.037 -0.051 0.088 0.000 0.000 29045.0 12844.0 1.0
beta_1[West Virginia (35)] -0.153 0.079 -0.299 -0.005 0.001 0.000 24163.0 12178.0 1.0
beta_1[Colorado (36)] -0.113 0.179 -0.434 0.242 0.001 0.001 17005.0 11884.0 1.0
beta_1[Nevada (37)] -0.161 0.167 -0.476 0.159 0.001 0.001 17163.0 12121.0 1.0
beta_1[New Mexico (38)] -0.359 0.192 -0.711 0.001 0.002 0.001 11099.0 11797.0 1.0
beta_1[Utah (39)] -0.162 0.193 -0.524 0.206 0.002 0.001 16480.0 11332.0 1.0
beta_1[California (40)] -0.719 0.114 -0.926 -0.498 0.001 0.001 11366.0 10639.0 1.0
beta_1[Oregon (41)] -0.405 0.176 -0.742 -0.085 0.002 0.001 10141.0 11944.0 1.0
beta_1[Washington (42)] -0.030 0.175 -0.368 0.291 0.001 0.001 17764.0 12170.0 1.0
beta_1[District of Columbia (43)] -0.183 0.097 -0.370 -0.008 0.001 0.001 16633.0 12951.0 1.0

ln_wages_std_25pct

mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail r_hat
mu_beta_0 1.496 0.035 1.429 1.563 0.001 0.001 870.0 1561.0 1.0
mu_beta_1 -0.133 0.025 -0.179 -0.088 0.000 0.000 6736.0 8402.0 1.0
sigma_beta_0 0.216 0.028 0.167 0.271 0.001 0.000 1975.0 4442.0 1.0
sigma_beta_1 0.079 0.035 0.008 0.143 0.001 0.000 2498.0 2520.0 1.0
sigma 2.040 0.002 2.035 2.045 0.000 0.000 16123.0 9418.0 1.0
beta_0[Connecticut (0)] 1.396 0.025 1.349 1.443 0.000 0.000 32078.0 11557.0 1.0
beta_0[Maine (1)] 1.443 0.022 1.403 1.483 0.000 0.000 27777.0 10809.0 1.0
beta_0[Massachusetts (2)] 1.157 0.018 1.124 1.190 0.000 0.000 16364.0 11889.0 1.0
beta_0[New Hampshire (3)] 1.352 0.031 1.294 1.410 0.000 0.000 29744.0 11186.0 1.0
beta_0[Rhode Island (4)] 1.343 0.040 1.270 1.421 0.000 0.000 30407.0 10806.0 1.0
beta_0[Vermont (5)] 1.406 0.030 1.349 1.461 0.000 0.000 29936.0 11584.0 1.0
beta_0[Delaware (6)] 1.494 0.048 1.406 1.585 0.000 0.000 23346.0 11711.0 1.0
beta_0[New Jersey (7)] 1.574 0.021 1.534 1.613 0.000 0.000 26876.0 11854.0 1.0
beta_0[New York (8)] 1.339 0.012 1.317 1.362 0.000 0.000 17595.0 11969.0 1.0
beta_0[Pennsylvania (9)] 1.587 0.012 1.565 1.609 0.000 0.000 16696.0 12551.0 1.0
beta_0[Illinois (10)] 1.309 0.012 1.285 1.332 0.000 0.000 16990.0 12663.0 1.0
beta_0[Indiana (11)] 1.462 0.015 1.434 1.489 0.000 0.000 20010.0 11502.0 1.0
beta_0[Michigan (12)] 1.393 0.016 1.361 1.424 0.000 0.000 22116.0 11901.0 1.0
beta_0[Ohio (13)] 1.445 0.012 1.422 1.469 0.000 0.000 18073.0 10651.0 1.0
beta_0[Wisconsin (14)] 1.598 0.018 1.563 1.632 0.000 0.000 23362.0 11156.0 1.0
beta_0[Iowa (15)] 1.464 0.017 1.434 1.496 0.000 0.000 24373.0 11136.0 1.0
beta_0[Kansas (16)] 1.413 0.032 1.353 1.473 0.000 0.000 32286.0 11153.0 1.0
beta_0[Minnesota (17)] 1.646 0.028 1.593 1.699 0.000 0.000 33168.0 11784.0 1.0
beta_0[Missouri (18)] 1.426 0.016 1.395 1.457 0.000 0.000 21354.0 11973.0 1.0
beta_0[Nebraska (19)] 1.400 0.052 1.299 1.496 0.000 0.000 26114.0 12012.0 1.0
beta_0[North Dakota (20)] 1.358 0.207 0.977 1.746 0.002 0.001 10064.0 10734.0 1.0
beta_0[South Dakota (21)] 1.275 0.139 1.018 1.541 0.001 0.001 14077.0 11208.0 1.0
beta_0[Virginia (22)] 1.517 0.025 1.469 1.564 0.000 0.000 19546.0 12720.0 1.0
beta_0[Alabama (23)] 1.552 0.030 1.493 1.607 0.000 0.000 21877.0 13381.0 1.0
beta_0[Arkansas (24)] 1.595 0.036 1.526 1.659 0.000 0.000 25076.0 12186.0 1.0
beta_0[Florida (25)] 1.619 0.057 1.513 1.726 0.000 0.000 19094.0 12653.0 1.0
beta_0[Georgia (26)] 1.392 0.026 1.344 1.443 0.000 0.000 24179.0 14248.0 1.0
beta_0[Louisiana (27)] 1.739 0.037 1.670 1.807 0.000 0.000 12261.0 12563.0 1.0
beta_0[Mississippi (28)] 1.526 0.037 1.459 1.596 0.000 0.000 21430.0 13910.0 1.0
beta_0[North Carolina (29)] 1.429 0.025 1.383 1.477 0.000 0.000 21628.0 12921.0 1.0
beta_0[South Carolina (30)] 1.594 0.039 1.522 1.667 0.000 0.000 17469.0 11487.0 1.0
beta_0[Texas (31)] 1.702 0.028 1.650 1.754 0.000 0.000 21534.0 13200.0 1.0
beta_0[Kentucky (32)] 1.526 0.020 1.486 1.561 0.000 0.000 23410.0 11894.0 1.0
beta_0[Maryland (33)] 1.648 0.024 1.605 1.693 0.000 0.000 22544.0 12559.0 1.0
beta_0[Tennessee (34)] 1.556 0.024 1.512 1.601 0.000 0.000 25713.0 13672.0 1.0
beta_0[West Virginia (35)] 1.889 0.032 1.828 1.949 0.000 0.000 22799.0 12396.0 1.0
beta_0[Colorado (36)] 1.089 0.089 0.926 1.261 0.001 0.000 19052.0 10547.0 1.0
beta_0[Nevada (37)] 0.839 0.118 0.623 1.066 0.001 0.001 9689.0 11167.0 1.0
beta_0[New Mexico (38)] 1.587 0.080 1.437 1.740 0.001 0.000 22516.0 11999.0 1.0
beta_0[Utah (39)] 1.902 0.055 1.802 2.008 0.000 0.000 27082.0 11280.0 1.0
beta_0[California (40)] 1.633 0.028 1.580 1.687 0.000 0.000 33210.0 11603.0 1.0
beta_0[Oregon (41)] 1.753 0.052 1.656 1.853 0.000 0.000 27483.0 11890.0 1.0
beta_0[Washington (42)] 1.630 0.100 1.448 1.821 0.001 0.001 18185.0 11578.0 1.0
beta_0[District of Columbia (43)] 1.923 0.058 1.816 2.032 0.000 0.000 23072.0 10933.0 1.0
beta_1[Connecticut (0)] -0.099 0.085 -0.248 0.082 0.001 0.001 17651.0 10901.0 1.0
beta_1[Maine (1)] -0.122 0.088 -0.298 0.050 0.001 0.001 18266.0 11736.0 1.0
beta_1[Massachusetts (2)] -0.139 0.080 -0.297 0.010 0.001 0.001 17277.0 11182.0 1.0
beta_1[New Hampshire (3)] -0.116 0.089 -0.284 0.066 0.001 0.001 19101.0 10541.0 1.0
beta_1[Rhode Island (4)] -0.123 0.085 -0.287 0.045 0.001 0.001 19075.0 11141.0 1.0
beta_1[Vermont (5)] -0.139 0.090 -0.319 0.031 0.001 0.001 14761.0 10583.0 1.0
beta_1[Delaware (6)] -0.100 0.074 -0.237 0.052 0.001 0.000 19086.0 12309.0 1.0
beta_1[New Jersey (7)] -0.211 0.090 -0.390 -0.068 0.001 0.001 5772.0 11216.0 1.0
beta_1[New York (8)] -0.115 0.067 -0.244 0.016 0.000 0.000 20824.0 12605.0 1.0
beta_1[Pennsylvania (9)] -0.118 0.065 -0.248 0.003 0.000 0.000 22397.0 12658.0 1.0
beta_1[Illinois (10)] -0.164 0.074 -0.316 -0.036 0.001 0.000 12344.0 12637.0 1.0
beta_1[Indiana (11)] -0.196 0.082 -0.359 -0.061 0.001 0.001 7174.0 11553.0 1.0
beta_1[Michigan (12)] -0.065 0.083 -0.209 0.101 0.001 0.001 10829.0 11804.0 1.0
beta_1[Ohio (13)] -0.093 0.063 -0.208 0.034 0.000 0.000 17464.0 12676.0 1.0
beta_1[Wisconsin (14)] -0.117 0.083 -0.279 0.046 0.001 0.001 18581.0 11671.0 1.0
beta_1[Iowa (15)] -0.163 0.089 -0.344 -0.006 0.001 0.001 12713.0 11168.0 1.0
beta_1[Kansas (16)] -0.136 0.077 -0.293 0.007 0.001 0.000 17045.0 12092.0 1.0
beta_1[Minnesota (17)] -0.142 0.085 -0.313 0.019 0.001 0.001 15945.0 11189.0 1.0
beta_1[Missouri (18)] -0.100 0.057 -0.209 0.009 0.000 0.000 21814.0 12094.0 1.0
beta_1[Nebraska (19)] -0.128 0.089 -0.307 0.040 0.001 0.001 18976.0 11933.0 1.0
beta_1[North Dakota (20)] -0.129 0.090 -0.315 0.039 0.001 0.001 17618.0 11651.0 1.0
beta_1[South Dakota (21)] -0.138 0.089 -0.312 0.033 0.001 0.001 17453.0 11486.0 1.0
beta_1[Virginia (22)] -0.063 0.045 -0.143 0.020 0.000 0.000 9462.0 12333.0 1.0
beta_1[Alabama (23)] -0.092 0.043 -0.167 -0.007 0.000 0.000 15308.0 12598.0 1.0
beta_1[Arkansas (24)] -0.072 0.060 -0.182 0.043 0.001 0.000 11955.0 12708.0 1.0
beta_1[Florida (25)] -0.145 0.066 -0.277 -0.023 0.001 0.000 15315.0 12352.0 1.0
beta_1[Georgia (26)] -0.106 0.039 -0.181 -0.035 0.000 0.000 21461.0 14234.0 1.0
beta_1[Louisiana (27)] -0.198 0.057 -0.301 -0.096 0.001 0.000 6522.0 9057.0 1.0
beta_1[Mississippi (28)] -0.117 0.046 -0.201 -0.025 0.000 0.000 18874.0 14168.0 1.0
beta_1[North Carolina (29)] -0.088 0.041 -0.164 -0.011 0.000 0.000 14370.0 13993.0 1.0
beta_1[South Carolina (30)] -0.143 0.048 -0.234 -0.053 0.000 0.000 14814.0 12780.0 1.0
beta_1[Texas (31)] -0.153 0.047 -0.245 -0.070 0.000 0.000 15158.0 13429.0 1.0
beta_1[Kentucky (32)] -0.063 0.050 -0.149 0.036 0.001 0.000 8623.0 12559.0 1.0
beta_1[Maryland (33)] -0.190 0.058 -0.303 -0.093 0.001 0.000 7771.0 11444.0 1.0
beta_1[Tennessee (34)] -0.095 0.045 -0.179 -0.011 0.000 0.000 17317.0 13248.0 1.0
beta_1[West Virginia (35)] -0.172 0.076 -0.322 -0.038 0.001 0.001 11858.0 12292.0 1.0
beta_1[Colorado (36)] -0.127 0.089 -0.300 0.048 0.001 0.001 15259.0 10245.0 1.0
beta_1[Nevada (37)] -0.162 0.094 -0.348 0.008 0.001 0.001 11397.0 10635.0 1.0
beta_1[New Mexico (38)] -0.131 0.087 -0.302 0.035 0.001 0.001 15284.0 11438.0 1.0
beta_1[Utah (39)] -0.142 0.090 -0.323 0.024 0.001 0.001 15196.0 10572.0 1.0
beta_1[California (40)] -0.230 0.105 -0.433 -0.067 0.002 0.001 4647.0 11035.0 1.0
beta_1[Oregon (41)] -0.177 0.096 -0.370 -0.011 0.001 0.001 9527.0 11382.0 1.0
beta_1[Washington (42)] -0.128 0.086 -0.301 0.034 0.001 0.001 16073.0 11303.0 1.0
beta_1[District of Columbia (43)] -0.193 0.085 -0.358 -0.045 0.001 0.001 7558.0 11364.0 1.0

ln_wages_conservative_full

Trace Plots

Detailed Trace Plots

beta_0

beta_1

__printed under Figures/ starting with ln_wages_conservative_full.pdf

ln_wages_conservative_25pct

Trace Plots

Detailed Trace Plots

beta_0

beta_1

__printed under Figures/ starting with ln_wages_conservative_25pct.pdf

ln_wages_std_25pct

Trace Plots

Detailed Trace Plots

beta_0

beta_1

__printed under Figures/ starting with ln_wages_std_25pct.pdf

## the age model.

there is only one age model that actually made it / didn’t fail over and over again. This one seemed particuarly hard to estimate, which makes sense. It is estimating a linear relationship between age and other variables as well as, well, everything else. The only one left is the 10% conservative one, but it’s worth a look.

On just a convergence level, the diagnostic stats don’t appear to have much of an issue at all. The ESS is quite low, so I don’t think autocorrelation will be a major problem. The r_hat never gets above 1.01 either, which is excellent.

Visually, it is quite weird. Well, only somewhat, and that someone is sigma_beta_1. The sigma is only like, near zero? and I only see one tail of it. I’ll leave discussion of why until later but it is an…interesting result. it looks mostly converged on there though.

dmd('## __ln_wages_age_conservative_10pct__')
with pd.option_context('display.max_rows', None, 'display.max_columns', None):  
    az.summary(ln_wages_age_conservative_10pct, var_names=['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset']) 
print_model_diag(ln_wages_age_conservative_10pct, 'ln_wages_age_conservative_10pct', var_names = ['beta_0', 'beta_1', 'beta_2', 'beta_3'], var_not = ['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset'])

ln_wages_age_conservative_10pct

mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail r_hat
mu_beta_0 3.520 0.022 3.478 3.561 0.001 0.001 721.0 1685.0 1.00
sigma_beta_0 0.125 0.016 0.095 0.157 0.000 0.000 1990.0 3445.0 1.00
mu_beta_1 -0.494 0.026 -0.543 -0.447 0.000 0.000 11171.0 11256.0 1.00
sigma_beta_1 0.017 0.016 0.000 0.046 0.000 0.000 3542.0 4038.0 1.00
mu_beta_2 -0.136 0.001 -0.138 -0.134 0.000 0.000 902.0 2098.0 1.00
sigma_beta_2 0.007 0.001 0.005 0.008 0.000 0.000 2165.0 4995.0 1.00
mu_beta_3 0.026 0.002 0.023 0.029 0.000 0.000 4709.0 9347.0 1.00
sigma_beta_3 0.005 0.002 0.001 0.008 0.000 0.000 1607.0 2729.0 1.00
sigma 1.355 0.003 1.350 1.359 0.000 0.000 41398.0 10401.0 1.00
beta_0[Connecticut (0)] 3.608 0.042 3.526 3.682 0.001 0.000 4067.0 6455.0 1.00
beta_0[Maine (1)] 3.652 0.037 3.585 3.723 0.000 0.000 5875.0 9004.0 1.00
beta_0[Massachusetts (2)] 3.686 0.030 3.628 3.742 0.000 0.000 21734.0 13207.0 1.00
beta_0[New Hampshire (3)] 3.611 0.049 3.521 3.703 0.001 0.001 2259.0 5387.0 1.00
beta_0[Rhode Island (4)] 3.506 0.059 3.396 3.615 0.001 0.001 4080.0 6555.0 1.00
beta_0[Vermont (5)] 3.564 0.047 3.476 3.653 0.001 0.001 2598.0 5522.0 1.00
beta_0[Delaware (6)] 3.556 0.064 3.436 3.675 0.002 0.001 1219.0 2643.0 1.00
beta_0[New Jersey (7)] 3.670 0.035 3.607 3.737 0.000 0.000 9047.0 11161.0 1.00
beta_0[New York (8)] 3.664 0.021 3.624 3.704 0.000 0.000 16631.0 11569.0 1.00
beta_0[Pennsylvania (9)] 3.684 0.021 3.646 3.724 0.000 0.000 13972.0 12215.0 1.00
beta_0[Illinois (10)] 3.476 0.022 3.434 3.516 0.000 0.000 23821.0 13020.0 1.00
beta_0[Indiana (11)] 3.594 0.024 3.548 3.640 0.000 0.000 16689.0 12269.0 1.00
beta_0[Michigan (12)] 3.568 0.029 3.515 3.623 0.000 0.000 10419.0 11429.0 1.00
beta_0[Ohio (13)] 3.581 0.021 3.541 3.622 0.000 0.000 11910.0 12597.0 1.00
beta_0[Wisconsin (14)] 3.632 0.030 3.577 3.689 0.000 0.000 6655.0 9347.0 1.00
beta_0[Iowa (15)] 3.500 0.028 3.447 3.552 0.000 0.000 14074.0 13443.0 1.00
beta_0[Kansas (16)] 3.477 0.048 3.384 3.563 0.001 0.001 2909.0 5168.0 1.00
beta_0[Minnesota (17)] 3.571 0.043 3.487 3.648 0.001 0.000 5049.0 8106.0 1.00
beta_0[Missouri (18)] 3.552 0.027 3.502 3.603 0.000 0.000 6950.0 10302.0 1.00
beta_0[Nebraska (19)] 3.427 0.067 3.299 3.549 0.001 0.001 4599.0 7496.0 1.00
beta_0[North Dakota (20)] 3.551 0.132 3.311 3.803 0.009 0.006 239.0 409.0 1.01
beta_0[South Dakota (21)] 3.542 0.110 3.328 3.743 0.003 0.002 1405.0 2190.0 1.00
beta_0[Virginia (22)] 3.429 0.037 3.361 3.500 0.000 0.000 10171.0 11417.0 1.00
beta_0[Alabama (23)] 3.400 0.043 3.317 3.478 0.001 0.000 6878.0 9995.0 1.00
beta_0[Arkansas (24)] 3.422 0.052 3.320 3.516 0.001 0.001 3790.0 7064.0 1.00
beta_0[Florida (25)] 3.490 0.069 3.354 3.616 0.001 0.001 2189.0 4172.0 1.00
beta_0[Georgia (26)] 3.284 0.039 3.215 3.360 0.000 0.000 7887.0 11286.0 1.00
beta_0[Louisiana (27)] 3.500 0.046 3.414 3.589 0.001 0.001 3648.0 6718.0 1.00
beta_0[Mississippi (28)] 3.385 0.047 3.297 3.473 0.001 0.001 2861.0 4418.0 1.00
beta_0[North Carolina (29)] 3.293 0.038 3.220 3.364 0.000 0.000 14647.0 12115.0 1.00
beta_0[South Carolina (30)] 3.480 0.050 3.385 3.574 0.001 0.001 3991.0 7901.0 1.00
beta_0[Texas (31)] 3.441 0.040 3.366 3.516 0.000 0.000 9588.0 11631.0 1.00
beta_0[Kentucky (32)] 3.309 0.032 3.248 3.367 0.000 0.000 10443.0 10882.0 1.00
beta_0[Maryland (33)] 3.643 0.036 3.576 3.710 0.000 0.000 7564.0 11150.0 1.00
beta_0[Tennessee (34)] 3.409 0.037 3.340 3.479 0.000 0.000 7713.0 10190.0 1.00
beta_0[West Virginia (35)] 3.401 0.044 3.319 3.484 0.001 0.000 6681.0 8967.0 1.00
beta_0[Colorado (36)] 3.444 0.091 3.268 3.611 0.003 0.002 1123.0 2554.0 1.00
beta_0[Nevada (37)] 3.427 0.108 3.226 3.633 0.005 0.003 561.0 418.0 1.00
beta_0[New Mexico (38)] 3.495 0.086 3.335 3.658 0.002 0.002 1334.0 2440.0 1.00
beta_0[Utah (39)] 3.454 0.069 3.325 3.583 0.001 0.001 3525.0 6320.0 1.00
beta_0[California (40)] 3.724 0.043 3.644 3.804 0.001 0.000 7119.0 10568.0 1.00
beta_0[Oregon (41)] 3.541 0.067 3.419 3.669 0.002 0.001 1810.0 3850.0 1.00
beta_0[Washington (42)] 3.536 0.097 3.350 3.720 0.007 0.005 186.0 391.0 1.02
beta_0[District of Columbia (43)] 3.641 0.073 3.508 3.780 0.002 0.001 1569.0 3173.0 1.00
beta_1[Connecticut (0)] -0.502 0.035 -0.567 -0.439 0.001 0.001 1866.0 4720.0 1.00
beta_1[Maine (1)] -0.495 0.033 -0.559 -0.435 0.000 0.000 5235.0 7104.0 1.00
beta_1[Massachusetts (2)] -0.497 0.033 -0.556 -0.435 0.001 0.000 3295.0 6251.0 1.00
beta_1[New Hampshire (3)] -0.496 0.034 -0.560 -0.434 0.001 0.001 2010.0 4602.0 1.00
beta_1[Rhode Island (4)] -0.489 0.034 -0.550 -0.424 0.000 0.000 5623.0 7285.0 1.00
beta_1[Vermont (5)] -0.492 0.035 -0.555 -0.428 0.001 0.000 4347.0 6989.0 1.00
beta_1[Delaware (6)] -0.511 0.036 -0.581 -0.449 0.000 0.000 7243.0 8858.0 1.00
beta_1[New Jersey (7)] -0.502 0.033 -0.562 -0.441 0.000 0.000 5798.0 8313.0 1.00
beta_1[New York (8)] -0.507 0.033 -0.569 -0.448 0.000 0.000 4970.0 7843.0 1.00
beta_1[Pennsylvania (9)] -0.502 0.032 -0.563 -0.446 0.000 0.000 8694.0 9585.0 1.00
beta_1[Illinois (10)] -0.478 0.035 -0.539 -0.411 0.000 0.000 7189.0 9833.0 1.00
beta_1[Indiana (11)] -0.487 0.032 -0.547 -0.427 0.000 0.000 7423.0 9038.0 1.00
beta_1[Michigan (12)] -0.499 0.033 -0.558 -0.435 0.001 0.000 3665.0 6283.0 1.00
beta_1[Ohio (13)] -0.493 0.031 -0.549 -0.437 0.000 0.000 9223.0 10416.0 1.00
beta_1[Wisconsin (14)] -0.497 0.034 -0.558 -0.434 0.001 0.001 2007.0 4182.0 1.00
beta_1[Iowa (15)] -0.495 0.034 -0.555 -0.427 0.001 0.001 1741.0 4016.0 1.00
beta_1[Kansas (16)] -0.487 0.033 -0.548 -0.425 0.000 0.000 5991.0 8854.0 1.00
beta_1[Minnesota (17)] -0.489 0.035 -0.554 -0.427 0.001 0.000 3399.0 6310.0 1.00
beta_1[Missouri (18)] -0.477 0.033 -0.539 -0.417 0.000 0.000 7775.0 9235.0 1.00
beta_1[Nebraska (19)] -0.491 0.034 -0.553 -0.426 0.000 0.000 5155.0 8100.0 1.00
beta_1[North Dakota (20)] -0.494 0.035 -0.560 -0.432 0.000 0.000 6765.0 8696.0 1.00
beta_1[South Dakota (21)] -0.496 0.035 -0.561 -0.432 0.000 0.000 4943.0 7914.0 1.00
beta_1[Virginia (22)] -0.495 0.027 -0.545 -0.442 0.000 0.000 11944.0 10900.0 1.00
beta_1[Alabama (23)] -0.491 0.028 -0.543 -0.439 0.000 0.000 11993.0 10729.0 1.00
beta_1[Arkansas (24)] -0.473 0.035 -0.536 -0.406 0.000 0.000 7160.0 8966.0 1.00
beta_1[Florida (25)] -0.497 0.031 -0.556 -0.440 0.000 0.000 9776.0 9481.0 1.00
beta_1[Georgia (26)] -0.480 0.029 -0.534 -0.426 0.000 0.000 11945.0 12627.0 1.00
beta_1[Louisiana (27)] -0.496 0.028 -0.551 -0.446 0.000 0.000 12293.0 10742.0 1.00
beta_1[Mississippi (28)] -0.496 0.028 -0.548 -0.444 0.000 0.000 10572.0 10958.0 1.00
beta_1[North Carolina (29)] -0.500 0.028 -0.552 -0.448 0.000 0.000 11728.0 11534.0 1.00
beta_1[South Carolina (30)] -0.514 0.033 -0.576 -0.453 0.000 0.000 7445.0 10681.0 1.00
beta_1[Texas (31)] -0.493 0.028 -0.543 -0.438 0.000 0.000 13953.0 11706.0 1.00
beta_1[Kentucky (32)] -0.484 0.030 -0.541 -0.429 0.000 0.000 8586.0 8214.0 1.00
beta_1[Maryland (33)] -0.494 0.029 -0.548 -0.439 0.000 0.000 8009.0 9282.0 1.00
beta_1[Tennessee (34)] -0.495 0.028 -0.548 -0.443 0.000 0.000 11588.0 10704.0 1.00
beta_1[West Virginia (35)] -0.495 0.031 -0.551 -0.433 0.001 0.000 3938.0 6717.0 1.00
beta_1[Colorado (36)] -0.488 0.035 -0.553 -0.422 0.001 0.001 1820.0 4781.0 1.00
beta_1[Nevada (37)] -0.490 0.035 -0.554 -0.427 0.001 0.000 3642.0 6760.0 1.00
beta_1[New Mexico (38)] -0.501 0.036 -0.567 -0.433 0.001 0.001 1485.0 4170.0 1.00
beta_1[Utah (39)] -0.494 0.035 -0.557 -0.430 0.001 0.000 2553.0 4719.0 1.00
beta_1[California (40)] -0.501 0.033 -0.564 -0.442 0.000 0.000 4569.0 7969.0 1.00
beta_1[Oregon (41)] -0.494 0.034 -0.557 -0.430 0.000 0.000 4996.0 7809.0 1.00
beta_1[Washington (42)] -0.497 0.035 -0.564 -0.435 0.001 0.000 2643.0 5481.0 1.00
beta_1[District of Columbia (43)] -0.510 0.036 -0.578 -0.445 0.000 0.000 6148.0 8110.0 1.00
beta_2[Connecticut (0)] -0.139 0.002 -0.142 -0.135 0.000 0.000 3780.0 5870.0 1.00
beta_2[Maine (1)] -0.135 0.002 -0.139 -0.132 0.000 0.000 5775.0 8901.0 1.00
beta_2[Massachusetts (2)] -0.146 0.001 -0.149 -0.144 0.000 0.000 23345.0 12906.0 1.00
beta_2[New Hampshire (3)] -0.137 0.002 -0.141 -0.132 0.000 0.000 2367.0 4644.0 1.00
beta_2[Rhode Island (4)] -0.146 0.003 -0.151 -0.140 0.000 0.000 3452.0 5749.0 1.00
beta_2[Vermont (5)] -0.135 0.002 -0.139 -0.130 0.000 0.000 2080.0 4546.0 1.00
beta_2[Delaware (6)] -0.139 0.003 -0.146 -0.133 0.000 0.000 1398.0 3215.0 1.00
beta_2[New Jersey (7)] -0.135 0.002 -0.138 -0.131 0.000 0.000 9699.0 10780.0 1.00
beta_2[New York (8)] -0.142 0.001 -0.144 -0.140 0.000 0.000 16362.0 12592.0 1.00
beta_2[Pennsylvania (9)] -0.137 0.001 -0.139 -0.135 0.000 0.000 13014.0 12389.0 1.00
beta_2[Illinois (10)] -0.141 0.001 -0.143 -0.139 0.000 0.000 22981.0 12864.0 1.00
beta_2[Indiana (11)] -0.141 0.001 -0.143 -0.138 0.000 0.000 16094.0 12337.0 1.00
beta_2[Michigan (12)] -0.140 0.002 -0.143 -0.137 0.000 0.000 10042.0 11465.0 1.00
beta_2[Ohio (13)] -0.137 0.001 -0.139 -0.135 0.000 0.000 12295.0 12691.0 1.00
beta_2[Wisconsin (14)] -0.141 0.002 -0.144 -0.137 0.000 0.000 6176.0 8620.0 1.00
beta_2[Iowa (15)] -0.141 0.002 -0.144 -0.138 0.000 0.000 13514.0 12854.0 1.00
beta_2[Kansas (16)] -0.139 0.002 -0.144 -0.134 0.000 0.000 2673.0 4708.0 1.00
beta_2[Minnesota (17)] -0.135 0.002 -0.140 -0.131 0.000 0.000 4153.0 6638.0 1.00
beta_2[Missouri (18)] -0.139 0.001 -0.141 -0.136 0.000 0.000 6172.0 9158.0 1.00
beta_2[Nebraska (19)] -0.140 0.004 -0.147 -0.133 0.000 0.000 3415.0 5730.0 1.00
beta_2[North Dakota (20)] -0.132 0.006 -0.143 -0.120 0.000 0.000 804.0 1315.0 1.00
beta_2[South Dakota (21)] -0.135 0.006 -0.146 -0.125 0.000 0.000 1525.0 3403.0 1.00
beta_2[Virginia (22)] -0.129 0.002 -0.133 -0.125 0.000 0.000 8906.0 10920.0 1.00
beta_2[Alabama (23)] -0.129 0.003 -0.135 -0.124 0.000 0.000 6031.0 7919.0 1.00
beta_2[Arkansas (24)] -0.128 0.003 -0.134 -0.123 0.000 0.000 3986.0 6975.0 1.00
beta_2[Florida (25)] -0.134 0.004 -0.142 -0.127 0.000 0.000 2060.0 4438.0 1.00
beta_2[Georgia (26)] -0.133 0.002 -0.138 -0.129 0.000 0.000 5338.0 7773.0 1.00
beta_2[Louisiana (27)] -0.137 0.003 -0.143 -0.132 0.000 0.000 2839.0 5061.0 1.00
beta_2[Mississippi (28)] -0.129 0.003 -0.134 -0.124 0.000 0.000 2598.0 5397.0 1.00
beta_2[North Carolina (29)] -0.125 0.002 -0.129 -0.121 0.000 0.000 13932.0 12879.0 1.00
beta_2[South Carolina (30)] -0.128 0.003 -0.134 -0.122 0.000 0.000 2974.0 5776.0 1.00
beta_2[Texas (31)] -0.126 0.002 -0.131 -0.122 0.000 0.000 9509.0 11834.0 1.00
beta_2[Kentucky (32)] -0.129 0.002 -0.132 -0.125 0.000 0.000 10483.0 11154.0 1.00
beta_2[Maryland (33)] -0.137 0.002 -0.141 -0.134 0.000 0.000 6403.0 9877.0 1.00
beta_2[Tennessee (34)] -0.131 0.002 -0.135 -0.127 0.000 0.000 7118.0 9884.0 1.00
beta_2[West Virginia (35)] -0.125 0.003 -0.130 -0.120 0.000 0.000 6690.0 9680.0 1.00
beta_2[Colorado (36)] -0.137 0.004 -0.145 -0.128 0.000 0.000 1367.0 2915.0 1.00
beta_2[Nevada (37)] -0.145 0.005 -0.155 -0.135 0.000 0.000 1562.0 3634.0 1.00
beta_2[New Mexico (38)] -0.130 0.005 -0.140 -0.121 0.000 0.000 771.0 1917.0 1.01
beta_2[Utah (39)] -0.128 0.004 -0.136 -0.120 0.000 0.000 3362.0 6535.0 1.00
beta_2[California (40)] -0.141 0.002 -0.145 -0.137 0.000 0.000 5987.0 9841.0 1.00
beta_2[Oregon (41)] -0.140 0.004 -0.148 -0.134 0.000 0.000 1152.0 2039.0 1.00
beta_2[Washington (42)] -0.138 0.005 -0.148 -0.128 0.000 0.000 796.0 1581.0 1.00
beta_2[District of Columbia (43)] -0.142 0.004 -0.149 -0.134 0.000 0.000 1544.0 2997.0 1.00
beta_3[Connecticut (0)] 0.023 0.005 0.013 0.033 0.000 0.000 510.0 1387.0 1.00
beta_3[Maine (1)] 0.025 0.005 0.016 0.034 0.000 0.000 2037.0 4398.0 1.00
beta_3[Massachusetts (2)] 0.025 0.005 0.016 0.034 0.000 0.000 1220.0 3511.0 1.00
beta_3[New Hampshire (3)] 0.025 0.005 0.014 0.035 0.000 0.000 606.0 1602.0 1.00
beta_3[Rhode Island (4)] 0.028 0.005 0.019 0.038 0.000 0.000 2577.0 5223.0 1.00
beta_3[Vermont (5)] 0.027 0.005 0.017 0.037 0.000 0.000 1758.0 4002.0 1.00
beta_3[Delaware (6)] 0.021 0.005 0.011 0.029 0.000 0.000 2377.0 4906.0 1.00
beta_3[New Jersey (7)] 0.024 0.004 0.016 0.032 0.000 0.000 1783.0 4866.0 1.00
beta_3[New York (8)] 0.022 0.005 0.013 0.030 0.000 0.000 1143.0 3225.0 1.01
beta_3[Pennsylvania (9)] 0.024 0.004 0.016 0.031 0.000 0.000 4392.0 8259.0 1.00
beta_3[Illinois (10)] 0.031 0.004 0.024 0.039 0.000 0.000 2951.0 7348.0 1.00
beta_3[Indiana (11)] 0.028 0.004 0.021 0.036 0.000 0.000 3898.0 6557.0 1.00
beta_3[Michigan (12)] 0.024 0.005 0.015 0.034 0.000 0.000 1041.0 2213.0 1.01
beta_3[Ohio (13)] 0.026 0.004 0.019 0.033 0.000 0.000 4650.0 7962.0 1.00
beta_3[Wisconsin (14)] 0.025 0.005 0.016 0.035 0.000 0.000 645.0 1762.0 1.01
beta_3[Iowa (15)] 0.026 0.005 0.016 0.035 0.000 0.000 598.0 1730.0 1.01
beta_3[Kansas (16)] 0.028 0.005 0.020 0.037 0.000 0.000 2366.0 4944.0 1.00
beta_3[Minnesota (17)] 0.027 0.005 0.018 0.038 0.000 0.000 1282.0 2607.0 1.00
beta_3[Missouri (18)] 0.031 0.004 0.025 0.038 0.000 0.000 3309.0 7839.0 1.00
beta_3[Nebraska (19)] 0.027 0.005 0.017 0.037 0.000 0.000 2661.0 4827.0 1.00
beta_3[North Dakota (20)] 0.026 0.005 0.015 0.036 0.000 0.000 3362.0 5949.0 1.00
beta_3[South Dakota (21)] 0.026 0.005 0.014 0.036 0.000 0.000 2096.0 3960.0 1.00
beta_3[Virginia (22)] 0.026 0.003 0.021 0.031 0.000 0.000 13135.0 13025.0 1.00
beta_3[Alabama (23)] 0.027 0.003 0.022 0.032 0.000 0.000 9448.0 11485.0 1.00
beta_3[Arkansas (24)] 0.032 0.004 0.025 0.040 0.000 0.000 1968.0 3893.0 1.00
beta_3[Florida (25)] 0.026 0.004 0.018 0.033 0.000 0.000 4806.0 8676.0 1.00
beta_3[Georgia (26)] 0.030 0.003 0.025 0.035 0.000 0.000 4374.0 7580.0 1.00
beta_3[Louisiana (27)] 0.026 0.003 0.020 0.031 0.000 0.000 9084.0 10888.0 1.00
beta_3[Mississippi (28)] 0.026 0.003 0.021 0.031 0.000 0.000 9008.0 11814.0 1.00
beta_3[North Carolina (29)] 0.024 0.003 0.019 0.029 0.000 0.000 7182.0 12997.0 1.00
beta_3[South Carolina (30)] 0.021 0.004 0.014 0.027 0.000 0.000 3289.0 4986.0 1.00
beta_3[Texas (31)] 0.026 0.003 0.021 0.032 0.000 0.000 11317.0 11540.0 1.00
beta_3[Kentucky (32)] 0.028 0.003 0.023 0.034 0.000 0.000 5216.0 9392.0 1.00
beta_3[Maryland (33)] 0.026 0.003 0.020 0.032 0.000 0.000 5951.0 9361.0 1.00
beta_3[Tennessee (34)] 0.025 0.003 0.020 0.030 0.000 0.000 7326.0 10985.0 1.00
beta_3[West Virginia (35)] 0.025 0.004 0.018 0.033 0.000 0.000 1380.0 3751.0 1.00
beta_3[Colorado (36)] 0.028 0.005 0.018 0.039 0.000 0.000 638.0 1845.0 1.01
beta_3[Nevada (37)] 0.027 0.005 0.018 0.038 0.000 0.000 1634.0 3707.0 1.00
beta_3[New Mexico (38)] 0.024 0.006 0.013 0.034 0.000 0.000 480.0 846.0 1.00
beta_3[Utah (39)] 0.026 0.005 0.016 0.036 0.000 0.000 889.0 2051.0 1.01
beta_3[California (40)] 0.024 0.004 0.015 0.032 0.000 0.000 1796.0 4844.0 1.00
beta_3[Oregon (41)] 0.026 0.005 0.015 0.036 0.000 0.000 2070.0 3859.0 1.00
beta_3[Washington (42)] 0.025 0.005 0.015 0.035 0.000 0.000 1033.0 2651.0 1.00
beta_3[District of Columbia (43)] 0.021 0.006 0.010 0.030 0.000 0.000 2014.0 5033.0 1.00

ln_wages_age_conservative_10pct

Trace Plots

Detailed Trace Plots

beta_0

beta_1

/usr/local/lib/python3.10/dist-packages/arviz/plots/backends/matplotlib/traceplot.py:224: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`). Consider using `matplotlib.pyplot.close()`.

beta_2

beta_3

printed under Figures/ starting with ln_wages_age_conservative_10pct.pdf

State change [Binary]

The convergence of the state change model(s) once again seem very good from a diagnostic side. r_hat’s are essentially zero, large ESS’s, etc. Once again, the 10% model seems to perform about the same convergence wise as the larger model. I might have wasted a lot of time, ahah.

Visuaually speaking, the standard model looks pretty good. there is definitely some wobble in mu_beta0, and some chains looks better than others. mu_beta_2 also doesn’t look great. Overall not bad, though. The biggest thing is that once again we see the HalfCauchy dominating one of the variables, this time sigma_beta_3. The individual state models all look nearly perfect. Well, mostly, they look a bit skewed at times.

the conservative 10% is considerably worse off, with sigma_beta_1 and sigma_beta_3 both having the halfcauchy shape. Otherwise they look pretty good overall, though. beta_1’s of individual counties look relatively spikey though, although might just be low variance.

dmd('## __ln_wages_state_change_std_full__')
with pd.option_context('display.max_rows', None, 'display.max_columns', None):  
    az.summary(ln_wages_state_change_std_full, var_names=['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset']) 
               
print_model_diag(ln_wages_state_change_std_full, 'ln_wages_state_change_std_full', var_names = ['beta_0', 'beta_1', 'beta_2', 'beta_3'], var_not = ['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset'])

dmd('## __ln_wages_state_change_conservative_10pct__')
with pd.option_context('display.max_rows', None, 'display.max_columns', None):  
    az.summary(ln_wages_state_change_conservative_10pct, var_names=['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset']) 
               
print_model_diag(ln_wages_state_change_conservative_10pct, 'ln_wages_state_change_conservative_10pct', var_names = ['beta_0', 'beta_1', 'beta_2', 'beta_3'], var_not = ['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset'])

ln_wages_state_change_std_full

mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail r_hat
mu_beta_0 1.533 0.037 1.468 1.604 0.001 0.001 717.0 1849.0 1.0
sigma_beta_0 0.236 0.028 0.187 0.289 0.001 0.000 1762.0 3629.0 1.0
mu_beta_1 -0.071 0.026 -0.118 -0.021 0.000 0.000 3601.0 6028.0 1.0
sigma_beta_1 0.127 0.026 0.080 0.175 0.000 0.000 4365.0 7480.0 1.0
mu_beta_2 -0.124 0.065 -0.250 -0.007 0.002 0.002 804.0 1911.0 1.0
sigma_beta_2 0.433 0.052 0.344 0.533 0.001 0.001 2653.0 5254.0 1.0
mu_beta_3 -0.164 0.016 -0.195 -0.135 0.000 0.000 37417.0 12074.0 1.0
sigma_beta_3 0.005 0.005 0.000 0.015 0.000 0.000 20778.0 9048.0 1.0
sigma 2.039 0.001 2.037 2.041 0.000 0.000 16550.0 9004.0 1.0
beta_0[Connecticut (0)] 1.284 0.015 1.257 1.313 0.000 0.000 16007.0 11542.0 1.0
beta_0[Maine (1)] 1.246 0.013 1.221 1.270 0.000 0.000 16216.0 12569.0 1.0
beta_0[Massachusetts (2)] 1.193 0.010 1.175 1.213 0.000 0.000 16538.0 14055.0 1.0
beta_0[New Hampshire (3)] 1.162 0.020 1.125 1.199 0.000 0.000 16143.0 11832.0 1.0
beta_0[Rhode Island (4)] 1.368 0.024 1.323 1.413 0.000 0.000 27833.0 12891.0 1.0
beta_0[Vermont (5)] 1.191 0.020 1.154 1.229 0.000 0.000 16278.0 10806.0 1.0
beta_0[Delaware (6)] 1.399 0.030 1.343 1.455 0.000 0.000 35210.0 12534.0 1.0
beta_0[New Jersey (7)] 1.588 0.012 1.565 1.611 0.000 0.000 16221.0 11836.0 1.0
beta_0[New York (8)] 1.388 0.007 1.375 1.401 0.000 0.000 16369.0 13283.0 1.0
beta_0[Pennsylvania (9)] 1.606 0.007 1.593 1.619 0.000 0.000 16048.0 12977.0 1.0
beta_0[Illinois (10)] 1.279 0.008 1.263 1.295 0.000 0.000 15781.0 13104.0 1.0
beta_0[Indiana (11)] 1.433 0.009 1.416 1.450 0.000 0.000 15948.0 12483.0 1.0
beta_0[Michigan (12)] 1.383 0.010 1.364 1.401 0.000 0.000 16083.0 11757.0 1.0
beta_0[Ohio (13)] 1.425 0.007 1.411 1.439 0.000 0.000 16584.0 11440.0 1.0
beta_0[Wisconsin (14)] 1.620 0.012 1.596 1.643 0.000 0.000 15579.0 10044.0 1.0
beta_0[Iowa (15)] 1.381 0.012 1.359 1.405 0.000 0.000 15783.0 11336.0 1.0
beta_0[Kansas (16)] 1.428 0.023 1.385 1.471 0.000 0.000 29638.0 11729.0 1.0
beta_0[Minnesota (17)] 1.763 0.019 1.727 1.799 0.000 0.000 19129.0 11864.0 1.0
beta_0[Missouri (18)] 1.502 0.010 1.483 1.521 0.000 0.000 16118.0 12085.0 1.0
beta_0[Nebraska (19)] 1.434 0.038 1.362 1.504 0.000 0.000 33876.0 11342.0 1.0
beta_0[North Dakota (20)] 1.277 0.221 0.854 1.683 0.002 0.002 9387.0 10603.0 1.0
beta_0[South Dakota (21)] 1.391 0.121 1.170 1.624 0.001 0.001 16774.0 12343.0 1.0
beta_0[Virginia (22)] 1.436 0.015 1.410 1.465 0.000 0.000 20099.0 13848.0 1.0
beta_0[Alabama (23)] 1.543 0.019 1.507 1.580 0.000 0.000 24314.0 13821.0 1.0
beta_0[Arkansas (24)] 1.706 0.023 1.662 1.748 0.000 0.000 25343.0 13131.0 1.0
beta_0[Florida (25)] 1.689 0.034 1.627 1.755 0.000 0.000 26426.0 14075.0 1.0
beta_0[Georgia (26)] 1.330 0.016 1.301 1.362 0.000 0.000 19454.0 13780.0 1.0
beta_0[Louisiana (27)] 1.838 0.021 1.798 1.875 0.000 0.000 21818.0 13454.0 1.0
beta_0[Mississippi (28)] 1.518 0.024 1.475 1.565 0.000 0.000 28342.0 13789.0 1.0
beta_0[North Carolina (29)] 1.383 0.014 1.356 1.409 0.000 0.000 19027.0 14516.0 1.0
beta_0[South Carolina (30)] 1.561 0.023 1.517 1.603 0.000 0.000 27310.0 14047.0 1.0
beta_0[Texas (31)] 1.775 0.015 1.748 1.804 0.000 0.000 17717.0 14770.0 1.0
beta_0[Kentucky (32)] 1.445 0.012 1.421 1.466 0.000 0.000 16444.0 11588.0 1.0
beta_0[Maryland (33)] 1.615 0.014 1.589 1.641 0.000 0.000 17077.0 11688.0 1.0
beta_0[Tennessee (34)] 1.477 0.015 1.449 1.506 0.000 0.000 18981.0 12574.0 1.0
beta_0[West Virginia (35)] 1.909 0.019 1.872 1.945 0.000 0.000 18638.0 12600.0 1.0
beta_0[Colorado (36)] 1.416 0.063 1.298 1.536 0.000 0.000 26049.0 12331.0 1.0
beta_0[Nevada (37)] 1.686 0.124 1.457 1.922 0.001 0.001 18745.0 12087.0 1.0
beta_0[New Mexico (38)] 1.766 0.044 1.682 1.849 0.000 0.000 32490.0 13048.0 1.0
beta_0[Utah (39)] 2.018 0.031 1.960 2.078 0.000 0.000 18527.0 13031.0 1.0
beta_0[California (40)] 1.890 0.016 1.858 1.919 0.000 0.000 16353.0 13777.0 1.0
beta_0[Oregon (41)] 1.831 0.031 1.773 1.891 0.000 0.000 25921.0 13162.0 1.0
beta_0[Washington (42)] 1.947 0.065 1.828 2.069 0.000 0.000 28215.0 13196.0 1.0
beta_0[District of Columbia (43)] 1.895 0.036 1.827 1.963 0.000 0.000 27754.0 12889.0 1.0
beta_1[Connecticut (0)] 0.009 0.091 -0.162 0.180 0.001 0.001 26135.0 10780.0 1.0
beta_1[Maine (1)] -0.067 0.106 -0.267 0.133 0.001 0.001 26793.0 11821.0 1.0
beta_1[Massachusetts (2)] 0.063 0.078 -0.086 0.207 0.001 0.000 21033.0 12278.0 1.0
beta_1[New Hampshire (3)] -0.030 0.122 -0.255 0.209 0.001 0.001 25872.0 11109.0 1.0
beta_1[Rhode Island (4)] 0.028 0.098 -0.152 0.220 0.001 0.001 21202.0 12350.0 1.0
beta_1[Vermont (5)] -0.026 0.116 -0.249 0.195 0.001 0.001 24814.0 11444.0 1.0
beta_1[Delaware (6)] -0.045 0.065 -0.167 0.080 0.000 0.000 30773.0 11933.0 1.0
beta_1[New Jersey (7)] -0.208 0.065 -0.328 -0.084 0.000 0.000 24200.0 11427.0 1.0
beta_1[New York (8)] 0.019 0.055 -0.087 0.123 0.000 0.000 33142.0 11723.0 1.0
beta_1[Pennsylvania (9)] -0.082 0.050 -0.177 0.010 0.000 0.000 33540.0 11369.0 1.0
beta_1[Illinois (10)] -0.079 0.060 -0.196 0.030 0.000 0.000 34702.0 11988.0 1.0
beta_1[Indiana (11)] -0.181 0.065 -0.305 -0.060 0.000 0.000 27828.0 11885.0 1.0
beta_1[Michigan (12)] 0.115 0.074 -0.021 0.257 0.001 0.000 18939.0 10637.0 1.0
beta_1[Ohio (13)] -0.041 0.046 -0.126 0.047 0.000 0.000 31526.0 11281.0 1.0
beta_1[Wisconsin (14)] -0.077 0.095 -0.262 0.096 0.001 0.001 30318.0 11266.0 1.0
beta_1[Iowa (15)] -0.169 0.089 -0.344 -0.004 0.001 0.000 24422.0 11300.0 1.0
beta_1[Kansas (16)] 0.019 0.076 -0.118 0.168 0.000 0.001 25491.0 11961.0 1.0
beta_1[Minnesota (17)] -0.068 0.101 -0.255 0.123 0.001 0.001 26920.0 12026.0 1.0
beta_1[Missouri (18)] 0.007 0.039 -0.063 0.083 0.000 0.000 30302.0 10947.0 1.0
beta_1[Nebraska (19)] -0.007 0.122 -0.235 0.229 0.001 0.001 22459.0 11545.0 1.0
beta_1[North Dakota (20)] -0.066 0.131 -0.325 0.177 0.001 0.001 23152.0 10435.0 1.0
beta_1[South Dakota (21)] -0.092 0.129 -0.330 0.154 0.001 0.001 26563.0 11130.0 1.0
beta_1[Virginia (22)] -0.040 0.025 -0.087 0.007 0.000 0.000 33453.0 12098.0 1.0
beta_1[Alabama (23)] -0.005 0.026 -0.054 0.044 0.000 0.000 30097.0 11957.0 1.0
beta_1[Arkansas (24)] -0.026 0.040 -0.102 0.047 0.000 0.000 33213.0 11059.0 1.0
beta_1[Florida (25)] -0.038 0.051 -0.131 0.060 0.000 0.000 31038.0 12403.0 1.0
beta_1[Georgia (26)] -0.001 0.023 -0.045 0.043 0.000 0.000 28284.0 12701.0 1.0
beta_1[Louisiana (27)] -0.179 0.030 -0.235 -0.122 0.000 0.000 27512.0 12974.0 1.0
beta_1[Mississippi (28)] -0.046 0.029 -0.100 0.007 0.000 0.000 32644.0 12714.0 1.0
beta_1[North Carolina (29)] -0.084 0.024 -0.129 -0.038 0.000 0.000 31355.0 12866.0 1.0
beta_1[South Carolina (30)] -0.145 0.030 -0.203 -0.091 0.000 0.000 31566.0 13797.0 1.0
beta_1[Texas (31)] -0.023 0.029 -0.078 0.030 0.000 0.000 34514.0 11772.0 1.0
beta_1[Kentucky (32)] -0.009 0.029 -0.066 0.044 0.000 0.000 36078.0 12216.0 1.0
beta_1[Maryland (33)] -0.122 0.034 -0.186 -0.056 0.000 0.000 34178.0 12614.0 1.0
beta_1[Tennessee (34)] 0.060 0.028 0.006 0.112 0.000 0.000 26708.0 14536.0 1.0
beta_1[West Virginia (35)] -0.168 0.061 -0.282 -0.054 0.000 0.000 27754.0 12790.0 1.0
beta_1[Colorado (36)] -0.061 0.123 -0.292 0.170 0.001 0.001 27187.0 12772.0 1.0
beta_1[Nevada (37)] -0.159 0.119 -0.390 0.059 0.001 0.001 18217.0 11757.0 1.0
beta_1[New Mexico (38)] -0.131 0.120 -0.360 0.094 0.001 0.001 21168.0 11075.0 1.0
beta_1[Utah (39)] -0.108 0.128 -0.344 0.136 0.001 0.001 23910.0 12243.0 1.0
beta_1[California (40)] -0.406 0.084 -0.562 -0.247 0.001 0.001 12662.0 11188.0 1.0
beta_1[Oregon (41)] -0.253 0.122 -0.477 -0.019 0.001 0.001 13458.0 10872.0 1.0
beta_1[Washington (42)] -0.009 0.113 -0.222 0.208 0.001 0.001 21562.0 11494.0 1.0
beta_1[District of Columbia (43)] -0.164 0.068 -0.296 -0.040 0.000 0.000 28844.0 12003.0 1.0
beta_2[Connecticut (0)] 0.232 0.028 0.180 0.285 0.000 0.000 15859.0 11904.0 1.0
beta_2[Maine (1)] 0.617 0.024 0.572 0.661 0.000 0.000 16553.0 13037.0 1.0
beta_2[Massachusetts (2)] -0.060 0.021 -0.099 -0.021 0.000 0.000 16140.0 10025.0 1.0
beta_2[New Hampshire (3)] 0.528 0.032 0.468 0.589 0.000 0.000 15970.0 12162.0 1.0
beta_2[Rhode Island (4)] -0.053 0.043 -0.133 0.027 0.000 0.000 26849.0 12996.0 1.0
beta_2[Vermont (5)] 0.539 0.031 0.478 0.596 0.000 0.000 16449.0 12748.0 1.0
beta_2[Delaware (6)] 0.440 0.049 0.349 0.534 0.000 0.000 23973.0 13013.0 1.0
beta_2[New Jersey (7)] -0.031 0.024 -0.076 0.013 0.000 0.000 16295.0 12159.0 1.0
beta_2[New York (8)] -0.195 0.013 -0.219 -0.171 0.000 0.000 16699.0 12698.0 1.0
beta_2[Pennsylvania (9)] -0.107 0.014 -0.133 -0.082 0.000 0.000 15965.0 13135.0 1.0
beta_2[Illinois (10)] 0.077 0.013 0.053 0.100 0.000 0.000 15645.0 12977.0 1.0
beta_2[Indiana (11)] 0.103 0.015 0.075 0.132 0.000 0.000 15807.0 13809.0 1.0
beta_2[Michigan (12)] 0.043 0.018 0.010 0.078 0.000 0.000 15718.0 11388.0 1.0
beta_2[Ohio (13)] 0.038 0.013 0.012 0.062 0.000 0.000 16667.0 12111.0 1.0
beta_2[Wisconsin (14)] -0.024 0.019 -0.060 0.010 0.000 0.000 16049.0 10827.0 1.0
beta_2[Iowa (15)] 0.135 0.017 0.103 0.166 0.000 0.000 15632.0 12387.0 1.0
beta_2[Kansas (16)] -0.064 0.031 -0.122 -0.005 0.000 0.000 28340.0 12974.0 1.0
beta_2[Minnesota (17)] -0.145 0.029 -0.198 -0.091 0.000 0.000 19445.0 11908.0 1.0
beta_2[Missouri (18)] -0.161 0.016 -0.192 -0.131 0.000 0.000 16074.0 12091.0 1.0
beta_2[Nebraska (19)] -0.125 0.053 -0.223 -0.026 0.000 0.000 29876.0 12829.0 1.0
beta_2[North Dakota (20)] -0.880 0.302 -1.446 -0.311 0.003 0.002 13295.0 12452.0 1.0
beta_2[South Dakota (21)] -0.401 0.155 -0.697 -0.111 0.001 0.001 17165.0 12632.0 1.0
beta_2[Virginia (22)] 0.323 0.025 0.277 0.369 0.000 0.000 15899.0 13514.0 1.0
beta_2[Alabama (23)] -0.056 0.027 -0.108 -0.005 0.000 0.000 17493.0 13151.0 1.0
beta_2[Arkansas (24)] -0.281 0.035 -0.347 -0.216 0.000 0.000 21006.0 11424.0 1.0
beta_2[Florida (25)] -0.324 0.062 -0.445 -0.213 0.000 0.000 31281.0 12615.0 1.0
beta_2[Georgia (26)] 0.130 0.026 0.080 0.177 0.000 0.000 16998.0 12456.0 1.0
beta_2[Louisiana (27)] -0.350 0.036 -0.417 -0.281 0.000 0.000 19272.0 12406.0 1.0
beta_2[Mississippi (28)] 0.033 0.031 -0.027 0.090 0.000 0.000 20076.0 13811.0 1.0
beta_2[North Carolina (29)] 0.318 0.029 0.265 0.371 0.000 0.000 16101.0 12903.0 1.0
beta_2[South Carolina (30)] 0.248 0.037 0.178 0.315 0.000 0.000 19352.0 13318.0 1.0
beta_2[Texas (31)] -0.624 0.033 -0.684 -0.561 0.000 0.000 15912.0 12737.0 1.0
beta_2[Kentucky (32)] 0.097 0.020 0.059 0.135 0.000 0.000 15651.0 11913.0 1.0
beta_2[Maryland (33)] 0.141 0.026 0.094 0.191 0.000 0.000 16331.0 11681.0 1.0
beta_2[Tennessee (34)] 0.074 0.024 0.028 0.117 0.000 0.000 16300.0 11812.0 1.0
beta_2[West Virginia (35)] -0.074 0.034 -0.137 -0.009 0.000 0.000 19720.0 10803.0 1.0
beta_2[Colorado (36)] -0.712 0.095 -0.888 -0.531 0.001 0.000 21769.0 12816.0 1.0
beta_2[Nevada (37)] -1.132 0.142 -1.399 -0.872 0.001 0.001 17929.0 12742.0 1.0
beta_2[New Mexico (38)] -0.847 0.116 -1.064 -0.628 0.001 0.000 30208.0 12742.0 1.0
beta_2[Utah (39)] -0.659 0.080 -0.809 -0.511 0.000 0.000 34636.0 11203.0 1.0
beta_2[California (40)] -1.174 0.034 -1.235 -1.109 0.000 0.000 15958.0 14294.0 1.0
beta_2[Oregon (41)] -0.202 0.057 -0.307 -0.094 0.000 0.000 32860.0 12344.0 1.0
beta_2[Washington (42)] -0.635 0.111 -0.838 -0.422 0.001 0.000 27665.0 12800.0 1.0
beta_2[District of Columbia (43)] -0.199 0.060 -0.316 -0.089 0.000 0.000 33954.0 12112.0 1.0
beta_3[Connecticut (0)] -0.161 0.017 -0.193 -0.129 0.000 0.000 30773.0 11064.0 1.0
beta_3[Maine (1)] -0.164 0.017 -0.196 -0.132 0.000 0.000 29991.0 12412.0 1.0
beta_3[Massachusetts (2)] -0.159 0.017 -0.190 -0.126 0.000 0.000 29922.0 11649.0 1.0
beta_3[New Hampshire (3)] -0.162 0.017 -0.195 -0.130 0.000 0.000 30323.0 11644.0 1.0
beta_3[Rhode Island (4)] -0.160 0.017 -0.193 -0.129 0.000 0.000 30693.0 12033.0 1.0
beta_3[Vermont (5)] -0.162 0.017 -0.194 -0.130 0.000 0.000 28981.0 12311.0 1.0
beta_3[Delaware (6)] -0.163 0.016 -0.194 -0.132 0.000 0.000 32548.0 11909.0 1.0
beta_3[New Jersey (7)] -0.170 0.018 -0.202 -0.136 0.000 0.000 33600.0 12953.0 1.0
beta_3[New York (8)] -0.160 0.016 -0.192 -0.129 0.000 0.000 33898.0 11958.0 1.0
beta_3[Pennsylvania (9)] -0.165 0.016 -0.196 -0.134 0.000 0.000 32935.0 12169.0 1.0
beta_3[Illinois (10)] -0.165 0.016 -0.195 -0.134 0.000 0.000 35003.0 11749.0 1.0
beta_3[Indiana (11)] -0.169 0.017 -0.201 -0.136 0.000 0.000 32594.0 12887.0 1.0
beta_3[Michigan (12)] -0.157 0.018 -0.190 -0.123 0.000 0.000 30168.0 12195.0 1.0
beta_3[Ohio (13)] -0.163 0.016 -0.193 -0.132 0.000 0.000 33476.0 11674.0 1.0
beta_3[Wisconsin (14)] -0.164 0.017 -0.197 -0.133 0.000 0.000 31801.0 12729.0 1.0
beta_3[Iowa (15)] -0.168 0.017 -0.200 -0.136 0.000 0.000 33383.0 12361.0 1.0
beta_3[Kansas (16)] -0.160 0.017 -0.191 -0.129 0.000 0.000 32137.0 12576.0 1.0
beta_3[Minnesota (17)] -0.164 0.017 -0.198 -0.133 0.000 0.000 32787.0 11795.0 1.0
beta_3[Missouri (18)] -0.161 0.016 -0.191 -0.130 0.000 0.000 32667.0 12357.0 1.0
beta_3[Nebraska (19)] -0.162 0.017 -0.193 -0.128 0.000 0.000 28171.0 11811.0 1.0
beta_3[North Dakota (20)] -0.164 0.018 -0.197 -0.131 0.000 0.000 31603.0 12331.0 1.0
beta_3[South Dakota (21)] -0.165 0.018 -0.197 -0.131 0.000 0.000 29376.0 13364.0 1.0
beta_3[Virginia (22)] -0.163 0.016 -0.194 -0.133 0.000 0.000 33838.0 11580.0 1.0
beta_3[Alabama (23)] -0.161 0.016 -0.191 -0.130 0.000 0.000 33336.0 11855.0 1.0
beta_3[Arkansas (24)] -0.162 0.016 -0.192 -0.131 0.000 0.000 33581.0 12332.0 1.0
beta_3[Florida (25)] -0.163 0.016 -0.193 -0.131 0.000 0.000 33205.0 12249.0 1.0
beta_3[Georgia (26)] -0.161 0.016 -0.191 -0.130 0.000 0.000 33469.0 12399.0 1.0
beta_3[Louisiana (27)] -0.169 0.017 -0.201 -0.137 0.000 0.000 33995.0 13063.0 1.0
beta_3[Mississippi (28)] -0.163 0.016 -0.193 -0.132 0.000 0.000 34467.0 12343.0 1.0
beta_3[North Carolina (29)] -0.165 0.016 -0.194 -0.133 0.000 0.000 34516.0 12147.0 1.0
beta_3[South Carolina (30)] -0.167 0.017 -0.199 -0.136 0.000 0.000 35038.0 12269.0 1.0
beta_3[Texas (31)] -0.162 0.016 -0.193 -0.132 0.000 0.000 33540.0 12017.0 1.0
beta_3[Kentucky (32)] -0.162 0.016 -0.192 -0.131 0.000 0.000 32916.0 11977.0 1.0
beta_3[Maryland (33)] -0.166 0.016 -0.198 -0.136 0.000 0.000 35332.0 12403.0 1.0
beta_3[Tennessee (34)] -0.159 0.017 -0.190 -0.127 0.000 0.000 32238.0 12304.0 1.0
beta_3[West Virginia (35)] -0.168 0.017 -0.201 -0.138 0.000 0.000 33560.0 12804.0 1.0
beta_3[Colorado (36)] -0.164 0.017 -0.197 -0.131 0.000 0.000 28972.0 12477.0 1.0
beta_3[Nevada (37)] -0.168 0.018 -0.201 -0.134 0.000 0.000 30326.0 13288.0 1.0
beta_3[New Mexico (38)] -0.167 0.018 -0.199 -0.133 0.000 0.000 31148.0 12541.0 1.0
beta_3[Utah (39)] -0.166 0.018 -0.198 -0.132 0.000 0.000 30814.0 12635.0 1.0
beta_3[California (40)] -0.178 0.022 -0.220 -0.138 0.000 0.000 33130.0 13429.0 1.0
beta_3[Oregon (41)] -0.172 0.019 -0.209 -0.136 0.000 0.000 30840.0 13499.0 1.0
beta_3[Washington (42)] -0.162 0.017 -0.194 -0.129 0.000 0.000 30174.0 11708.0 1.0
beta_3[District of Columbia (43)] -0.168 0.017 -0.201 -0.137 0.000 0.000 33294.0 13115.0 1.0

ln_wages_state_change_std_full

Trace Plots

Detailed Trace Plots

beta_0

beta_1

beta_2

beta_3

printed under Figures/ starting with ln_wages_state_change_std_full.pdf

ln_wages_state_change_conservative_10pct

mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail r_hat
mu_beta_0 1.523 0.037 1.454 1.591 0.001 0.001 1187.0 2600.0 1.0
sigma_beta_0 0.226 0.029 0.172 0.280 0.001 0.000 2566.0 5097.0 1.0
mu_beta_1 -0.083 0.030 -0.142 -0.028 0.000 0.000 12376.0 11820.0 1.0
sigma_beta_1 0.039 0.029 0.000 0.091 0.000 0.000 5579.0 6490.0 1.0
mu_beta_2 -0.047 0.058 -0.155 0.061 0.002 0.001 1256.0 2937.0 1.0
sigma_beta_2 0.352 0.049 0.267 0.448 0.001 0.001 2908.0 6072.0 1.0
mu_beta_3 -0.163 0.052 -0.262 -0.066 0.000 0.000 11172.0 9436.0 1.0
sigma_beta_3 0.065 0.049 0.000 0.151 0.001 0.000 5556.0 6815.0 1.0
sigma 2.042 0.004 2.035 2.049 0.000 0.000 28259.0 10870.0 1.0
beta_0[Connecticut (0)] 1.352 0.045 1.268 1.438 0.000 0.000 25848.0 13733.0 1.0
beta_0[Maine (1)] 1.214 0.040 1.141 1.290 0.000 0.000 27213.0 13586.0 1.0
beta_0[Massachusetts (2)] 1.261 0.032 1.204 1.322 0.000 0.000 24199.0 14199.0 1.0
beta_0[New Hampshire (3)] 1.210 0.061 1.101 1.327 0.000 0.000 21630.0 14104.0 1.0
beta_0[Rhode Island (4)] 1.301 0.072 1.164 1.437 0.001 0.000 18676.0 13223.0 1.0
beta_0[Vermont (5)] 1.141 0.060 1.032 1.257 0.000 0.000 22234.0 12478.0 1.0
beta_0[Delaware (6)] 1.468 0.085 1.314 1.630 0.001 0.000 16709.0 12908.0 1.0
beta_0[New Jersey (7)] 1.567 0.038 1.497 1.641 0.000 0.000 23721.0 13982.0 1.0
beta_0[New York (8)] 1.404 0.022 1.364 1.447 0.000 0.000 26407.0 13451.0 1.0
beta_0[Pennsylvania (9)] 1.579 0.022 1.537 1.618 0.000 0.000 25204.0 14342.0 1.0
beta_0[Illinois (10)] 1.377 0.027 1.327 1.426 0.000 0.000 27336.0 13282.0 1.0
beta_0[Indiana (11)] 1.438 0.028 1.387 1.492 0.000 0.000 25586.0 14212.0 1.0
beta_0[Michigan (12)] 1.382 0.031 1.323 1.440 0.000 0.000 26185.0 14106.0 1.0
beta_0[Ohio (13)] 1.423 0.023 1.380 1.467 0.000 0.000 23354.0 12485.0 1.0
beta_0[Wisconsin (14)] 1.631 0.039 1.560 1.705 0.000 0.000 23158.0 13202.0 1.0
beta_0[Iowa (15)] 1.373 0.039 1.302 1.448 0.000 0.000 23462.0 13450.0 1.0
beta_0[Kansas (16)] 1.525 0.070 1.398 1.657 0.001 0.000 14204.0 13566.0 1.0
beta_0[Minnesota (17)] 1.686 0.057 1.577 1.792 0.000 0.000 17401.0 13654.0 1.0
beta_0[Missouri (18)] 1.495 0.031 1.434 1.552 0.000 0.000 25500.0 13386.0 1.0
beta_0[Nebraska (19)] 1.421 0.102 1.230 1.609 0.001 0.001 13169.0 12519.0 1.0
beta_0[North Dakota (20)] 1.463 0.226 1.039 1.882 0.002 0.001 15079.0 11957.0 1.0
beta_0[South Dakota (21)] 1.443 0.192 1.092 1.815 0.002 0.001 11674.0 11514.0 1.0
beta_0[Virginia (22)] 1.405 0.044 1.322 1.485 0.000 0.000 22162.0 13457.0 1.0
beta_0[Alabama (23)] 1.556 0.052 1.457 1.654 0.000 0.000 17752.0 13560.0 1.0
beta_0[Arkansas (24)] 1.700 0.065 1.576 1.822 0.000 0.000 17916.0 13219.0 1.0
beta_0[Florida (25)] 1.744 0.085 1.586 1.905 0.001 0.000 18766.0 12202.0 1.0
beta_0[Georgia (26)] 1.320 0.044 1.239 1.405 0.000 0.000 19338.0 14183.0 1.0
beta_0[Louisiana (27)] 1.810 0.056 1.705 1.915 0.000 0.000 19877.0 13192.0 1.0
beta_0[Mississippi (28)] 1.568 0.060 1.453 1.679 0.000 0.000 16643.0 13226.0 1.0
beta_0[North Carolina (29)] 1.377 0.041 1.303 1.458 0.000 0.000 25078.0 13378.0 1.0
beta_0[South Carolina (30)] 1.508 0.058 1.402 1.619 0.000 0.000 17536.0 12887.0 1.0
beta_0[Texas (31)] 1.806 0.044 1.725 1.888 0.000 0.000 27639.0 14176.0 1.0
beta_0[Kentucky (32)] 1.477 0.036 1.408 1.545 0.000 0.000 25395.0 13655.0 1.0
beta_0[Maryland (33)] 1.564 0.042 1.484 1.641 0.000 0.000 22687.0 13658.0 1.0
beta_0[Tennessee (34)] 1.453 0.044 1.371 1.538 0.000 0.000 19124.0 13773.0 1.0
beta_0[West Virginia (35)] 1.902 0.057 1.793 2.007 0.000 0.000 20465.0 13773.0 1.0
beta_0[Colorado (36)] 1.308 0.149 1.029 1.588 0.001 0.001 13418.0 12118.0 1.0
beta_0[Nevada (37)] 1.355 0.195 0.995 1.728 0.002 0.001 10289.0 10690.0 1.0
beta_0[New Mexico (38)] 1.779 0.116 1.553 1.988 0.001 0.001 21169.0 12771.0 1.0
beta_0[Utah (39)] 1.968 0.092 1.794 2.139 0.001 0.000 19891.0 12055.0 1.0
beta_0[California (40)] 1.872 0.049 1.780 1.963 0.000 0.000 28281.0 13430.0 1.0
beta_0[Oregon (41)] 1.781 0.091 1.609 1.949 0.001 0.000 18546.0 12892.0 1.0
beta_0[Washington (42)] 1.759 0.148 1.485 2.037 0.001 0.001 14841.0 12218.0 1.0
beta_0[District of Columbia (43)] 1.811 0.097 1.632 1.997 0.001 0.001 15411.0 11916.0 1.0
beta_1[Connecticut (0)] -0.084 0.056 -0.191 0.024 0.000 0.000 15552.0 12720.0 1.0
beta_1[Maine (1)] -0.079 0.058 -0.194 0.030 0.000 0.000 15661.0 11158.0 1.0
beta_1[Massachusetts (2)] -0.077 0.056 -0.182 0.035 0.000 0.000 14003.0 12481.0 1.0
beta_1[New Hampshire (3)] -0.081 0.056 -0.183 0.034 0.000 0.000 15398.0 11909.0 1.0
beta_1[Rhode Island (4)] -0.077 0.057 -0.178 0.040 0.000 0.000 15190.0 12130.0 1.0
beta_1[Vermont (5)] -0.091 0.058 -0.202 0.022 0.000 0.000 15144.0 11660.0 1.0
beta_1[Delaware (6)] -0.080 0.056 -0.197 0.020 0.000 0.000 16603.0 12226.0 1.0
beta_1[New Jersey (7)] -0.089 0.055 -0.200 0.014 0.000 0.000 16050.0 12650.0 1.0
beta_1[New York (8)] -0.082 0.053 -0.184 0.022 0.000 0.000 17275.0 12972.0 1.0
beta_1[Pennsylvania (9)] -0.106 0.059 -0.222 -0.002 0.001 0.000 12773.0 12263.0 1.0
beta_1[Illinois (10)] -0.088 0.055 -0.196 0.017 0.000 0.000 15978.0 12992.0 1.0
beta_1[Indiana (11)] -0.093 0.057 -0.204 0.011 0.000 0.000 16261.0 12936.0 1.0
beta_1[Michigan (12)] -0.075 0.056 -0.179 0.038 0.000 0.000 15755.0 12940.0 1.0
beta_1[Ohio (13)] -0.073 0.054 -0.174 0.031 0.000 0.000 15340.0 12856.0 1.0
beta_1[Wisconsin (14)] -0.086 0.056 -0.196 0.021 0.000 0.000 16572.0 12320.0 1.0
beta_1[Iowa (15)] -0.085 0.057 -0.198 0.023 0.000 0.000 15186.0 11573.0 1.0
beta_1[Kansas (16)] -0.070 0.059 -0.175 0.043 0.000 0.000 14673.0 11603.0 1.0
beta_1[Minnesota (17)] -0.082 0.057 -0.184 0.030 0.000 0.000 16562.0 12786.0 1.0
beta_1[Missouri (18)] -0.078 0.051 -0.175 0.018 0.000 0.000 16111.0 13611.0 1.0
beta_1[Nebraska (19)] -0.084 0.057 -0.192 0.029 0.000 0.000 14693.0 11853.0 1.0
beta_1[North Dakota (20)] -0.083 0.058 -0.190 0.033 0.000 0.000 15269.0 12198.0 1.0
beta_1[South Dakota (21)] -0.083 0.058 -0.193 0.027 0.000 0.000 15551.0 12581.0 1.0
beta_1[Virginia (22)] -0.071 0.047 -0.154 0.024 0.000 0.000 15371.0 13577.0 1.0
beta_1[Alabama (23)] -0.105 0.048 -0.203 -0.020 0.000 0.000 11940.0 13402.0 1.0
beta_1[Arkansas (24)] -0.076 0.051 -0.174 0.023 0.000 0.000 17316.0 13209.0 1.0
beta_1[Florida (25)] -0.072 0.054 -0.173 0.034 0.000 0.000 14252.0 12898.0 1.0
beta_1[Georgia (26)] -0.072 0.045 -0.155 0.016 0.000 0.000 15032.0 13000.0 1.0
beta_1[Louisiana (27)] -0.106 0.052 -0.208 -0.017 0.000 0.000 12246.0 12458.0 1.0
beta_1[Mississippi (28)] -0.087 0.047 -0.179 0.001 0.000 0.000 16738.0 13349.0 1.0
beta_1[North Carolina (29)] -0.096 0.045 -0.183 -0.013 0.000 0.000 14931.0 13622.0 1.0
beta_1[South Carolina (30)] -0.084 0.046 -0.175 0.005 0.000 0.000 16622.0 13810.0 1.0
beta_1[Texas (31)] -0.086 0.046 -0.175 0.002 0.000 0.000 17651.0 12495.0 1.0
beta_1[Kentucky (32)] -0.071 0.049 -0.160 0.026 0.000 0.000 14952.0 13626.0 1.0
beta_1[Maryland (33)] -0.091 0.049 -0.181 0.006 0.000 0.000 17246.0 13141.0 1.0
beta_1[Tennessee (34)] -0.066 0.050 -0.153 0.038 0.000 0.000 13820.0 13569.0 1.0
beta_1[West Virginia (35)] -0.088 0.055 -0.193 0.019 0.000 0.000 16836.0 12533.0 1.0
beta_1[Colorado (36)] -0.083 0.057 -0.192 0.026 0.000 0.000 14733.0 12032.0 1.0
beta_1[Nevada (37)] -0.081 0.057 -0.192 0.030 0.000 0.000 16327.0 13081.0 1.0
beta_1[New Mexico (38)] -0.084 0.058 -0.194 0.028 0.000 0.000 14289.0 12102.0 1.0
beta_1[Utah (39)] -0.084 0.057 -0.197 0.021 0.000 0.000 15294.0 12346.0 1.0
beta_1[California (40)] -0.095 0.057 -0.203 0.017 0.000 0.000 14456.0 11809.0 1.0
beta_1[Oregon (41)] -0.084 0.057 -0.196 0.025 0.000 0.000 17507.0 12706.0 1.0
beta_1[Washington (42)] -0.082 0.057 -0.193 0.024 0.000 0.000 15481.0 12466.0 1.0
beta_1[District of Columbia (43)] -0.073 0.057 -0.171 0.045 0.000 0.000 15941.0 12496.0 1.0
beta_2[Connecticut (0)] 0.274 0.089 0.104 0.439 0.001 0.000 23135.0 12496.0 1.0
beta_2[Maine (1)] 0.509 0.073 0.368 0.642 0.000 0.000 25022.0 13533.0 1.0
beta_2[Massachusetts (2)] -0.112 0.063 -0.232 0.004 0.000 0.000 27273.0 11826.0 1.0
beta_2[New Hampshire (3)] 0.449 0.099 0.264 0.634 0.001 0.000 20968.0 13884.0 1.0
beta_2[Rhode Island (4)] 0.085 0.125 -0.146 0.326 0.001 0.001 17682.0 13445.0 1.0
beta_2[Vermont (5)] 0.516 0.094 0.345 0.693 0.001 0.000 21204.0 13538.0 1.0
beta_2[Delaware (6)] 0.446 0.146 0.180 0.728 0.001 0.001 17621.0 12656.0 1.0
beta_2[New Jersey (7)] -0.032 0.074 -0.172 0.110 0.000 0.001 22533.0 12900.0 1.0
beta_2[New York (8)] -0.163 0.041 -0.240 -0.087 0.000 0.000 29783.0 13433.0 1.0
beta_2[Pennsylvania (9)] -0.022 0.043 -0.101 0.063 0.000 0.000 29313.0 12918.0 1.0
beta_2[Illinois (10)] -0.072 0.039 -0.144 0.002 0.000 0.000 29103.0 12174.0 1.0
beta_2[Indiana (11)] 0.087 0.048 -0.005 0.175 0.000 0.000 27324.0 13001.0 1.0
beta_2[Michigan (12)] -0.016 0.056 -0.120 0.091 0.000 0.000 28231.0 13082.0 1.0
beta_2[Ohio (13)] 0.079 0.041 0.001 0.156 0.000 0.000 25280.0 13383.0 1.0
beta_2[Wisconsin (14)] -0.083 0.058 -0.191 0.026 0.000 0.000 24354.0 13575.0 1.0
beta_2[Iowa (15)] 0.175 0.054 0.074 0.274 0.000 0.000 23565.0 13583.0 1.0
beta_2[Kansas (16)] -0.048 0.097 -0.225 0.137 0.001 0.001 14805.0 13254.0 1.0
beta_2[Minnesota (17)] -0.154 0.088 -0.320 0.011 0.001 0.000 18467.0 12580.0 1.0
beta_2[Missouri (18)] -0.114 0.051 -0.207 -0.016 0.000 0.000 23604.0 12876.0 1.0
beta_2[Nebraska (19)] -0.106 0.145 -0.367 0.178 0.001 0.001 13302.0 12352.0 1.0
beta_2[North Dakota (20)] -0.185 0.346 -0.839 0.465 0.003 0.002 14202.0 11849.0 1.0
beta_2[South Dakota (21)] -0.228 0.254 -0.698 0.256 0.002 0.002 12211.0 12267.0 1.0
beta_2[Virginia (22)] 0.321 0.080 0.174 0.473 0.001 0.000 20982.0 13348.0 1.0
beta_2[Alabama (23)] 0.064 0.086 -0.096 0.225 0.001 0.001 19371.0 14024.0 1.0
beta_2[Arkansas (24)] -0.217 0.107 -0.426 -0.021 0.001 0.001 17615.0 13439.0 1.0
beta_2[Florida (25)] -0.186 0.173 -0.515 0.132 0.001 0.001 17125.0 12753.0 1.0
beta_2[Georgia (26)] 0.091 0.083 -0.065 0.251 0.001 0.000 17614.0 12715.0 1.0
beta_2[Louisiana (27)] -0.236 0.110 -0.441 -0.026 0.001 0.001 20015.0 12529.0 1.0
beta_2[Mississippi (28)] -0.095 0.096 -0.276 0.085 0.001 0.001 16098.0 12709.0 1.0
beta_2[North Carolina (29)] 0.233 0.090 0.066 0.409 0.001 0.000 21937.0 13703.0 1.0
beta_2[South Carolina (30)] 0.361 0.116 0.138 0.576 0.001 0.001 16365.0 13216.0 1.0
beta_2[Texas (31)] -0.452 0.106 -0.658 -0.262 0.001 0.000 22803.0 12966.0 1.0
beta_2[Kentucky (32)] 0.145 0.065 0.022 0.268 0.000 0.000 23668.0 13033.0 1.0
beta_2[Maryland (33)] 0.202 0.080 0.049 0.350 0.001 0.000 23830.0 13433.0 1.0
beta_2[Tennessee (34)] 0.067 0.074 -0.076 0.204 0.001 0.000 19175.0 13938.0 1.0
beta_2[West Virginia (35)] -0.062 0.098 -0.252 0.115 0.001 0.001 19829.0 13017.0 1.0
beta_2[Colorado (36)] -0.364 0.218 -0.772 0.047 0.002 0.001 12865.0 12526.0 1.0
beta_2[Nevada (37)] -0.671 0.249 -1.127 -0.197 0.002 0.002 10011.0 11950.0 1.0
beta_2[New Mexico (38)] -0.665 0.272 -1.188 -0.176 0.003 0.002 11483.0 11294.0 1.0
beta_2[Utah (39)] -0.381 0.205 -0.779 -0.005 0.002 0.001 16927.0 12454.0 1.0
beta_2[California (40)] -1.068 0.107 -1.267 -0.863 0.001 0.001 21139.0 13320.0 1.0
beta_2[Oregon (41)] -0.117 0.164 -0.424 0.188 0.001 0.001 17530.0 12325.0 1.0
beta_2[Washington (42)] -0.271 0.256 -0.759 0.202 0.002 0.002 13348.0 12112.0 1.0
beta_2[District of Columbia (43)] 0.035 0.164 -0.268 0.348 0.001 0.001 16306.0 12198.0 1.0
beta_3[Connecticut (0)] -0.158 0.094 -0.350 0.014 0.001 0.001 16708.0 12028.0 1.0
beta_3[Maine (1)] -0.163 0.097 -0.351 0.023 0.001 0.001 16468.0 12933.0 1.0
beta_3[Massachusetts (2)] -0.169 0.093 -0.352 0.007 0.001 0.001 15865.0 11966.0 1.0
beta_3[New Hampshire (3)] -0.163 0.095 -0.351 0.014 0.001 0.001 15308.0 12239.0 1.0
beta_3[Rhode Island (4)] -0.155 0.096 -0.336 0.034 0.001 0.001 14939.0 11586.0 1.0
beta_3[Vermont (5)] -0.180 0.101 -0.374 0.005 0.001 0.001 12943.0 10342.0 1.0
beta_3[Delaware (6)] -0.146 0.094 -0.319 0.034 0.001 0.001 15778.0 12984.0 1.0
beta_3[New Jersey (7)] -0.160 0.092 -0.335 0.017 0.001 0.001 16123.0 11680.0 1.0
beta_3[New York (8)] -0.151 0.091 -0.323 0.030 0.001 0.001 16330.0 12611.0 1.0
beta_3[Pennsylvania (9)] -0.197 0.099 -0.393 -0.023 0.001 0.001 11601.0 12216.0 1.0
beta_3[Illinois (10)] -0.172 0.089 -0.349 -0.008 0.001 0.001 15666.0 12815.0 1.0
beta_3[Indiana (11)] -0.180 0.096 -0.368 -0.006 0.001 0.001 14278.0 12180.0 1.0
beta_3[Michigan (12)] -0.169 0.093 -0.345 0.009 0.001 0.001 16194.0 11980.0 1.0
beta_3[Ohio (13)] -0.167 0.088 -0.343 -0.001 0.001 0.001 16848.0 12478.0 1.0
beta_3[Wisconsin (14)] -0.170 0.096 -0.360 0.007 0.001 0.001 14360.0 12272.0 1.0
beta_3[Iowa (15)] -0.166 0.093 -0.348 0.010 0.001 0.001 15996.0 12558.0 1.0
beta_3[Kansas (16)] -0.126 0.102 -0.301 0.080 0.001 0.001 12856.0 10938.0 1.0
beta_3[Minnesota (17)] -0.155 0.095 -0.340 0.031 0.001 0.001 15453.0 12359.0 1.0
beta_3[Missouri (18)] -0.162 0.082 -0.316 -0.002 0.001 0.000 16786.0 12102.0 1.0
beta_3[Nebraska (19)] -0.164 0.094 -0.353 0.011 0.001 0.001 16440.0 12501.0 1.0
beta_3[North Dakota (20)] -0.162 0.097 -0.340 0.035 0.001 0.001 15394.0 12045.0 1.0
beta_3[South Dakota (21)] -0.163 0.098 -0.350 0.026 0.001 0.001 15421.0 12256.0 1.0
beta_3[Virginia (22)] -0.177 0.077 -0.328 -0.033 0.001 0.000 14735.0 13769.0 1.0
beta_3[Alabama (23)] -0.167 0.076 -0.312 -0.022 0.001 0.000 16072.0 13526.0 1.0
beta_3[Arkansas (24)] -0.181 0.089 -0.362 -0.021 0.001 0.001 14331.0 12561.0 1.0
beta_3[Florida (25)] -0.187 0.097 -0.376 -0.007 0.001 0.001 13189.0 11725.0 1.0
beta_3[Georgia (26)] -0.120 0.085 -0.270 0.051 0.001 0.001 11937.0 13340.0 1.0
beta_3[Louisiana (27)] -0.174 0.084 -0.348 -0.020 0.001 0.001 14295.0 12972.0 1.0
beta_3[Mississippi (28)] -0.155 0.078 -0.308 -0.006 0.001 0.000 15226.0 13529.0 1.0
beta_3[North Carolina (29)] -0.139 0.081 -0.287 0.021 0.001 0.000 14409.0 13205.0 1.0
beta_3[South Carolina (30)] -0.158 0.082 -0.315 0.002 0.001 0.001 14385.0 12868.0 1.0
beta_3[Texas (31)] -0.195 0.090 -0.381 -0.039 0.001 0.001 12187.0 11976.0 1.0
beta_3[Kentucky (32)] -0.147 0.078 -0.294 0.005 0.001 0.000 15723.0 13354.0 1.0
beta_3[Maryland (33)] -0.166 0.083 -0.332 -0.011 0.001 0.000 16739.0 12602.0 1.0
beta_3[Tennessee (34)] -0.129 0.082 -0.284 0.024 0.001 0.001 13250.0 13097.0 1.0
beta_3[West Virginia (35)] -0.173 0.089 -0.347 -0.003 0.001 0.001 16566.0 11910.0 1.0
beta_3[Colorado (36)] -0.161 0.096 -0.336 0.030 0.001 0.001 15195.0 12377.0 1.0
beta_3[Nevada (37)] -0.158 0.095 -0.336 0.030 0.001 0.001 14907.0 12075.0 1.0
beta_3[New Mexico (38)] -0.160 0.095 -0.340 0.029 0.001 0.001 15019.0 11853.0 1.0
beta_3[Utah (39)] -0.165 0.097 -0.349 0.026 0.001 0.001 16139.0 12483.0 1.0
beta_3[California (40)] -0.159 0.092 -0.336 0.017 0.001 0.001 16302.0 12967.0 1.0
beta_3[Oregon (41)] -0.171 0.097 -0.367 0.003 0.001 0.001 15890.0 12430.0 1.0
beta_3[Washington (42)] -0.162 0.097 -0.350 0.021 0.001 0.001 16207.0 11629.0 1.0
beta_3[District of Columbia (43)] -0.158 0.090 -0.326 0.019 0.001 0.001 14855.0 12071.0 1.0

ln_wages_state_change_conservative_10pct

Trace Plots

Detailed Trace Plots

beta_0

beta_1

beta_2

beta_3

printed under Figures/ starting with ln_wages_state_change_conservative_10pct.pdf

dmd('## __ln_wages_state_change_std_full__')
with pd.option_context('display.max_rows', None, 'display.max_columns', None):  
    az.summary(ln_wages_state_change_std_full, var_names=['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset']) 
               
print_model_diag(ln_wages_state_change_std_full, 'ln_wages_state_change_std_full', var_names = ['beta_0', 'beta_1', 'beta_2', 'beta_3'], var_not = ['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset'])


dmd('## __ln_wages_state_change_std_full__')
with pd.option_context('display.max_rows', None, 'display.max_columns', None):  
    az.summary(ln_wages_state_change_std_full, var_names=['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset']) 
               
print_model_diag(ln_wages_state_change_std_full, 'ln_wages_state_change_std_full', var_names = ['beta_0', 'beta_1', 'beta_2', 'beta_3'], var_not = ['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset'])

State Distance Change [ single level ]

First chain (w/o race)

This deals with models who have the raw distance measure instead of the binary ‘did they switch states or not’ measure. It should be noted that people’s whos state did not change got a distance of zero. In terms of simple ‘did it converge’, the answer seems to be yes for any of the stats. r_hat stayed pegged at one, ESS never dropped below a thousand or so. Visually, however, mu_beta_0 is quiiiite wobbly, and the chains look noticably worse than I am used to seeing them. Not terrible, just worse. The chains themselves look fine though for individual states.

Second chain (w/o race)

Frankly this chain seems… messed up. ESS and r_hat tells a pretty good story, but looking at it is just kinda wild. mu_beta_2 clearly just stayed a uniform distribution. I don’t really have any idea why, but basically this chain is useless ahah

dmd('## __ln_wage_state_dist_conservative_10pct__')
with pd.option_context('display.max_rows', None, 'display.max_columns', None):  
    az.summary(ln_wage_state_dist_conservative_10pct, var_names=['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset']) 
               
print_model_diag(ln_wage_state_dist_conservative_10pct, 'ln_wage_state_dist_conservative_10pct')


dmd('## __ln_wage_state_dist_race_conservative_10pct__')
with pd.option_context('display.max_rows', None, 'display.max_columns', None):  
    az.summary(ln_wage_state_dist_race_conservative_10pct, var_names=['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset']) 
               
print_model_diag(ln_wage_state_dist_race_conservative_10pct, 'ln_wage_state_dist_race_conservative_10pct', var_names = ['beta_0', 'beta_1', 'beta_2', 'beta_3'], var_not = ['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset'])

ln_wage_state_dist_conservative_10pct

/usr/local/lib/python3.10/dist-packages/arviz/utils.py:134: UserWarning: Items starting with ~: ['beta_2_offset', 'beta_3_offset'] have not been found and will be ignored
  warnings.warn(
mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail r_hat
mu_beta_0 1.513 0.032 1.450 1.571 0.001 0.001 1251.0 2056.0 1.0
sigma_beta_0 0.186 0.025 0.143 0.235 0.001 0.000 2205.0 3961.0 1.0
mu_beta_1 -0.008 0.003 -0.014 -0.002 0.000 0.000 1526.0 3470.0 1.0
sigma_beta_1 0.018 0.003 0.013 0.023 0.000 0.000 2529.0 4371.0 1.0
sigma 2.044 0.004 2.036 2.051 0.000 0.000 19197.0 7875.0 1.0
beta_0[Connecticut (0)] 1.344 0.041 1.266 1.418 0.000 0.000 18205.0 9474.0 1.0
beta_0[Maine (1)] 1.364 0.037 1.295 1.432 0.000 0.000 17977.0 9752.0 1.0
beta_0[Massachusetts (2)] 1.205 0.029 1.149 1.258 0.000 0.000 16837.0 9736.0 1.0
beta_0[New Hampshire (3)] 1.351 0.052 1.253 1.446 0.000 0.000 16263.0 9395.0 1.0
beta_0[Rhode Island (4)] 1.467 0.061 1.352 1.580 0.001 0.000 14811.0 8847.0 1.0
beta_0[Vermont (5)] 1.316 0.051 1.218 1.410 0.000 0.000 18045.0 10375.0 1.0
beta_0[Delaware (6)] 1.483 0.072 1.351 1.619 0.001 0.000 14585.0 9531.0 1.0
beta_0[New Jersey (7)] 1.545 0.034 1.482 1.611 0.000 0.000 18732.0 10571.0 1.0
beta_0[New York (8)] 1.345 0.020 1.307 1.381 0.000 0.000 16383.0 10447.0 1.0
beta_0[Pennsylvania (9)] 1.597 0.020 1.561 1.635 0.000 0.000 17473.0 10712.0 1.0
beta_0[Illinois (10)] 1.291 0.023 1.247 1.334 0.000 0.000 17634.0 11287.0 1.0
beta_0[Indiana (11)] 1.454 0.025 1.408 1.503 0.000 0.000 18382.0 10153.0 1.0
beta_0[Michigan (12)] 1.359 0.029 1.305 1.415 0.000 0.000 19176.0 10646.0 1.0
beta_0[Ohio (13)] 1.387 0.022 1.345 1.427 0.000 0.000 18043.0 10600.0 1.0
beta_0[Wisconsin (14)] 1.579 0.034 1.516 1.641 0.000 0.000 15259.0 8937.0 1.0
beta_0[Iowa (15)] 1.474 0.033 1.412 1.536 0.000 0.000 16093.0 10064.0 1.0
beta_0[Kansas (16)] 1.474 0.060 1.362 1.589 0.001 0.000 11603.0 9376.0 1.0
beta_0[Minnesota (17)] 1.722 0.052 1.626 1.822 0.000 0.000 13018.0 10051.0 1.0
beta_0[Missouri (18)] 1.457 0.029 1.401 1.509 0.000 0.000 18130.0 10203.0 1.0
beta_0[Nebraska (19)] 1.322 0.093 1.141 1.488 0.001 0.001 10672.0 9078.0 1.0
beta_0[North Dakota (20)] 1.436 0.189 1.072 1.774 0.002 0.001 9579.0 8346.0 1.0
beta_0[South Dakota (21)] 1.390 0.164 1.070 1.688 0.002 0.001 10994.0 8943.0 1.0
beta_0[Virginia (22)] 1.507 0.037 1.439 1.578 0.000 0.000 17685.0 9635.0 1.0
beta_0[Alabama (23)] 1.458 0.045 1.371 1.539 0.000 0.000 14975.0 9274.0 1.0
beta_0[Arkansas (24)] 1.609 0.058 1.496 1.714 0.000 0.000 14625.0 10075.0 1.0
beta_0[Florida (25)] 1.567 0.079 1.420 1.715 0.001 0.000 13384.0 9337.0 1.0
beta_0[Georgia (26)] 1.335 0.038 1.263 1.406 0.000 0.000 16579.0 9637.0 1.0
beta_0[Louisiana (27)] 1.717 0.051 1.625 1.814 0.000 0.000 15683.0 9652.0 1.0
beta_0[Mississippi (28)] 1.475 0.051 1.377 1.567 0.000 0.000 13738.0 9336.0 1.0
beta_0[North Carolina (29)] 1.393 0.037 1.325 1.465 0.000 0.000 17415.0 8968.0 1.0
beta_0[South Carolina (30)] 1.487 0.050 1.390 1.579 0.000 0.000 15001.0 9024.0 1.0
beta_0[Texas (31)] 1.747 0.041 1.671 1.827 0.000 0.000 17894.0 9847.0 1.0
beta_0[Kentucky (32)] 1.456 0.033 1.394 1.516 0.000 0.000 18452.0 9678.0 1.0
beta_0[Maryland (33)] 1.702 0.037 1.633 1.772 0.000 0.000 18710.0 9905.0 1.0
beta_0[Tennessee (34)] 1.514 0.039 1.443 1.590 0.000 0.000 13848.0 10123.0 1.0
beta_0[West Virginia (35)] 1.825 0.053 1.720 1.919 0.000 0.000 15658.0 9946.0 1.0
beta_0[Colorado (36)] 1.467 0.131 1.220 1.717 0.001 0.001 10259.0 9367.0 1.0
beta_0[Nevada (37)] 1.329 0.154 1.049 1.621 0.002 0.001 7966.0 8940.0 1.0
beta_0[New Mexico (38)] 1.732 0.113 1.519 1.942 0.001 0.001 12992.0 8459.0 1.0
beta_0[Utah (39)] 1.911 0.086 1.749 2.066 0.001 0.001 12878.0 8739.0 1.0
beta_0[California (40)] 1.734 0.048 1.645 1.824 0.000 0.000 16805.0 9274.0 1.0
beta_0[Oregon (41)] 1.806 0.079 1.655 1.952 0.001 0.001 12070.0 8991.0 1.0
beta_0[Washington (42)] 1.666 0.130 1.416 1.904 0.001 0.001 13169.0 9296.0 1.0
beta_0[District of Columbia (43)] 1.729 0.086 1.571 1.890 0.001 0.001 12044.0 9415.0 1.0
beta_1[Connecticut (0)] -0.003 0.005 -0.011 0.007 0.000 0.000 16522.0 8524.0 1.0
beta_1[Maine (1)] 0.011 0.003 0.006 0.016 0.000 0.000 16090.0 10177.0 1.0
beta_1[Massachusetts (2)] -0.003 0.003 -0.008 0.003 0.000 0.000 18352.0 9228.0 1.0
beta_1[New Hampshire (3)] 0.002 0.005 -0.008 0.012 0.000 0.000 16316.0 8832.0 1.0
beta_1[Rhode Island (4)] -0.018 0.007 -0.031 -0.006 0.000 0.000 15601.0 9847.0 1.0
beta_1[Vermont (5)] 0.010 0.004 0.002 0.018 0.000 0.000 16623.0 10048.0 1.0
beta_1[Delaware (6)] -0.002 0.011 -0.022 0.018 0.000 0.000 12888.0 8671.0 1.0
beta_1[New Jersey (7)] -0.007 0.004 -0.015 0.002 0.000 0.000 17272.0 9109.0 1.0
beta_1[New York (8)] -0.007 0.002 -0.011 -0.004 0.000 0.000 19085.0 9860.0 1.0
beta_1[Pennsylvania (9)] -0.002 0.002 -0.006 0.003 0.000 0.000 19075.0 10228.0 1.0
beta_1[Illinois (10)] 0.008 0.002 0.004 0.013 0.000 0.000 17938.0 9751.0 1.0
beta_1[Indiana (11)] 0.011 0.003 0.005 0.017 0.000 0.000 18719.0 9552.0 1.0
beta_1[Michigan (12)] 0.003 0.003 -0.003 0.008 0.000 0.000 17984.0 9700.0 1.0
beta_1[Ohio (13)] 0.008 0.002 0.004 0.013 0.000 0.000 16749.0 10479.0 1.0
beta_1[Wisconsin (14)] 0.002 0.003 -0.004 0.008 0.000 0.000 16187.0 10290.0 1.0
beta_1[Iowa (15)] 0.005 0.003 -0.001 0.011 0.000 0.000 15488.0 10033.0 1.0
beta_1[Kansas (16)] -0.003 0.006 -0.013 0.008 0.000 0.000 12605.0 9677.0 1.0
beta_1[Minnesota (17)] -0.006 0.005 -0.015 0.002 0.000 0.000 13317.0 9378.0 1.0
beta_1[Missouri (18)] -0.009 0.003 -0.015 -0.003 0.000 0.000 16996.0 9668.0 1.0
beta_1[Nebraska (19)] 0.003 0.008 -0.013 0.019 0.000 0.000 10322.0 9366.0 1.0
beta_1[North Dakota (20)] -0.017 0.017 -0.050 0.015 0.000 0.000 10923.0 8316.0 1.0
beta_1[South Dakota (21)] -0.021 0.015 -0.049 0.007 0.000 0.000 10002.0 8700.0 1.0
beta_1[Virginia (22)] 0.008 0.005 -0.002 0.019 0.000 0.000 16287.0 9130.0 1.0
beta_1[Alabama (23)] 0.006 0.007 -0.007 0.019 0.000 0.000 14164.0 9407.0 1.0
beta_1[Arkansas (24)] -0.017 0.008 -0.032 -0.002 0.000 0.000 13723.0 9728.0 1.0
beta_1[Florida (25)] -0.008 0.012 -0.029 0.015 0.000 0.000 13738.0 9160.0 1.0
beta_1[Georgia (26)] 0.004 0.006 -0.008 0.016 0.000 0.000 15269.0 8913.0 1.0
beta_1[Louisiana (27)] -0.033 0.009 -0.051 -0.016 0.000 0.000 14094.0 9469.0 1.0
beta_1[Mississippi (28)] -0.003 0.008 -0.019 0.013 0.000 0.000 12263.0 9443.0 1.0
beta_1[North Carolina (29)] 0.008 0.006 -0.004 0.019 0.000 0.000 15315.0 8614.0 1.0
beta_1[South Carolina (30)] 0.002 0.009 -0.015 0.019 0.000 0.000 13417.0 9214.0 1.0
beta_1[Texas (31)] -0.040 0.006 -0.052 -0.028 0.000 0.000 15827.0 10652.0 1.0
beta_1[Kentucky (32)] 0.008 0.005 -0.001 0.017 0.000 0.000 16590.0 9419.0 1.0
beta_1[Maryland (33)] -0.003 0.005 -0.012 0.007 0.000 0.000 16282.0 8643.0 1.0
beta_1[Tennessee (34)] -0.001 0.005 -0.011 0.008 0.000 0.000 14449.0 8951.0 1.0
beta_1[West Virginia (35)] 0.005 0.007 -0.008 0.018 0.000 0.000 15634.0 9149.0 1.0
beta_1[Colorado (36)] -0.025 0.011 -0.046 -0.003 0.000 0.000 10360.0 8841.0 1.0
beta_1[Nevada (37)] -0.044 0.013 -0.068 -0.020 0.000 0.000 8471.0 8088.0 1.0
beta_1[New Mexico (38)] -0.025 0.016 -0.054 0.006 0.000 0.000 10093.0 8371.0 1.0
beta_1[Utah (39)] -0.036 0.011 -0.057 -0.016 0.000 0.000 12263.0 9137.0 1.0
beta_1[California (40)] -0.038 0.003 -0.044 -0.033 0.000 0.000 13951.0 11092.0 1.0
beta_1[Oregon (41)] -0.038 0.009 -0.054 -0.021 0.000 0.000 12751.0 8716.0 1.0
beta_1[Washington (42)] -0.018 0.011 -0.039 0.004 0.000 0.000 12699.0 8971.0 1.0
beta_1[District of Columbia (43)] -0.009 0.009 -0.027 0.009 0.000 0.000 13740.0 9297.0 1.0

ln_wage_state_dist_conservative_10pct

Trace Plots

Detailed Trace Plots

beta_0

beta_1

printed under Figures/ starting with ln_wage_state_dist_conservative_10pct.pdf

ln_wage_state_dist_race_conservative_10pct

mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail r_hat
mu_beta_0 1.516 0.031 1.458 1.574 0.001 0.000 1974.0 4005.0 1.0
sigma_beta_0 0.187 0.026 0.142 0.237 0.000 0.000 3126.0 5730.0 1.0
mu_beta_1 -0.006 0.003 -0.012 -0.000 0.000 0.000 2373.0 4676.0 1.0
sigma_beta_1 0.018 0.003 0.013 0.023 0.000 0.000 3793.0 6308.0 1.0
mu_beta_2 0.019 5.780 -8.834 10.000 0.035 0.072 26084.0 6085.0 1.0
sigma_beta_2 24.905 1195.925 0.000 20.968 10.961 7.751 25534.0 6396.0 1.0
mu_beta_3 -0.018 0.004 -0.025 -0.011 0.000 0.000 14608.0 10308.0 1.0
sigma_beta_3 0.009 0.006 0.000 0.019 0.000 0.000 3335.0 5017.0 1.0
sigma 2.043 0.004 2.036 2.051 0.000 0.000 11654.0 7152.0 1.0
beta_0[Connecticut (0)] 1.344 0.041 1.265 1.418 0.000 0.000 23421.0 8979.0 1.0
beta_0[Maine (1)] 1.364 0.037 1.296 1.434 0.000 0.000 22033.0 9627.0 1.0
beta_0[Massachusetts (2)] 1.205 0.029 1.150 1.260 0.000 0.000 14253.0 10011.0 1.0
beta_0[New Hampshire (3)] 1.352 0.052 1.256 1.449 0.000 0.000 24573.0 9068.0 1.0
beta_0[Rhode Island (4)] 1.468 0.062 1.349 1.583 0.000 0.000 27403.0 9327.0 1.0
beta_0[Vermont (5)] 1.317 0.051 1.218 1.410 0.000 0.000 24029.0 9026.0 1.0
beta_0[Delaware (6)] 1.487 0.072 1.354 1.622 0.000 0.000 28707.0 9177.0 1.0
beta_0[New Jersey (7)] 1.545 0.035 1.481 1.613 0.000 0.000 23927.0 8650.0 1.0
beta_0[New York (8)] 1.345 0.020 1.309 1.384 0.000 0.000 14120.0 10616.0 1.0
beta_0[Pennsylvania (9)] 1.597 0.020 1.559 1.634 0.000 0.000 15246.0 10289.0 1.0
beta_0[Illinois (10)] 1.292 0.024 1.248 1.338 0.000 0.000 15890.0 9456.0 1.0
beta_0[Indiana (11)] 1.455 0.025 1.405 1.499 0.000 0.000 17497.0 9732.0 1.0
beta_0[Michigan (12)] 1.360 0.030 1.302 1.414 0.000 0.000 19505.0 10029.0 1.0
beta_0[Ohio (13)] 1.387 0.022 1.346 1.428 0.000 0.000 15304.0 10443.0 1.0
beta_0[Wisconsin (14)] 1.579 0.034 1.516 1.642 0.000 0.000 22848.0 9621.0 1.0
beta_0[Iowa (15)] 1.474 0.032 1.413 1.533 0.000 0.000 22683.0 9921.0 1.0
beta_0[Kansas (16)] 1.475 0.062 1.365 1.597 0.000 0.000 21336.0 10125.0 1.0
beta_0[Minnesota (17)] 1.722 0.051 1.630 1.822 0.000 0.000 19349.0 9470.0 1.0
beta_0[Missouri (18)] 1.458 0.029 1.404 1.511 0.000 0.000 21719.0 9647.0 1.0
beta_0[Nebraska (19)] 1.321 0.091 1.153 1.496 0.001 0.000 19984.0 9038.0 1.0
beta_0[North Dakota (20)] 1.437 0.190 1.078 1.785 0.001 0.001 18213.0 8188.0 1.0
beta_0[South Dakota (21)] 1.394 0.162 1.082 1.692 0.001 0.001 18534.0 9017.0 1.0
beta_0[Virginia (22)] 1.515 0.037 1.447 1.587 0.000 0.000 21683.0 9245.0 1.0
beta_0[Alabama (23)] 1.467 0.045 1.382 1.551 0.000 0.000 21543.0 10333.0 1.0
beta_0[Arkansas (24)] 1.618 0.057 1.512 1.724 0.000 0.000 22898.0 9414.0 1.0
beta_0[Florida (25)] 1.581 0.081 1.426 1.730 0.001 0.000 25036.0 9305.0 1.0
beta_0[Georgia (26)] 1.342 0.039 1.270 1.415 0.000 0.000 21104.0 9995.0 1.0
beta_0[Louisiana (27)] 1.727 0.051 1.632 1.826 0.000 0.000 20888.0 9339.0 1.0
beta_0[Mississippi (28)] 1.491 0.051 1.398 1.587 0.000 0.000 23126.0 9759.0 1.0
beta_0[North Carolina (29)] 1.402 0.037 1.331 1.471 0.000 0.000 21959.0 9273.0 1.0
beta_0[South Carolina (30)] 1.507 0.050 1.414 1.603 0.000 0.000 24253.0 8181.0 1.0
beta_0[Texas (31)] 1.756 0.041 1.678 1.833 0.000 0.000 17909.0 9803.0 1.0
beta_0[Kentucky (32)] 1.459 0.032 1.400 1.521 0.000 0.000 21933.0 9951.0 1.0
beta_0[Maryland (33)] 1.705 0.037 1.636 1.777 0.000 0.000 15878.0 9580.0 1.0
beta_0[Tennessee (34)] 1.519 0.040 1.442 1.592 0.000 0.000 22058.0 9699.0 1.0
beta_0[West Virginia (35)] 1.828 0.053 1.727 1.926 0.000 0.000 18336.0 10077.0 1.0
beta_0[Colorado (36)] 1.466 0.133 1.221 1.722 0.001 0.001 19870.0 9788.0 1.0
beta_0[Nevada (37)] 1.330 0.154 1.029 1.609 0.001 0.001 16553.0 8985.0 1.0
beta_0[New Mexico (38)] 1.733 0.114 1.517 1.945 0.001 0.001 22612.0 8490.0 1.0
beta_0[Utah (39)] 1.912 0.084 1.749 2.065 0.001 0.000 19173.0 9028.0 1.0
beta_0[California (40)] 1.734 0.048 1.647 1.829 0.000 0.000 21836.0 8491.0 1.0
beta_0[Oregon (41)] 1.804 0.079 1.655 1.948 0.001 0.000 22083.0 8878.0 1.0
beta_0[Washington (42)] 1.669 0.130 1.431 1.920 0.001 0.001 22493.0 8858.0 1.0
beta_0[District of Columbia (43)] 1.732 0.088 1.560 1.890 0.001 0.000 24438.0 8546.0 1.0
beta_1[Connecticut (0)] -0.002 0.005 -0.011 0.007 0.000 0.000 28520.0 9669.0 1.0
beta_1[Maine (1)] 0.011 0.003 0.005 0.016 0.000 0.000 17610.0 10282.0 1.0
beta_1[Massachusetts (2)] -0.002 0.003 -0.008 0.003 0.000 0.000 21918.0 8820.0 1.0
beta_1[New Hampshire (3)] 0.002 0.005 -0.007 0.012 0.000 0.000 28532.0 9094.0 1.0
beta_1[Rhode Island (4)] -0.017 0.007 -0.029 -0.004 0.000 0.000 23733.0 9494.0 1.0
beta_1[Vermont (5)] 0.010 0.004 0.002 0.019 0.000 0.000 23366.0 9667.0 1.0
beta_1[Delaware (6)] -0.002 0.011 -0.022 0.018 0.000 0.000 27688.0 8511.0 1.0
beta_1[New Jersey (7)] -0.006 0.004 -0.015 0.002 0.000 0.000 27046.0 9354.0 1.0
beta_1[New York (8)] -0.007 0.002 -0.011 -0.003 0.000 0.000 16652.0 10673.0 1.0
beta_1[Pennsylvania (9)] -0.002 0.002 -0.006 0.003 0.000 0.000 18401.0 10293.0 1.0
beta_1[Illinois (10)] 0.008 0.002 0.004 0.013 0.000 0.000 18639.0 9927.0 1.0
beta_1[Indiana (11)] 0.011 0.003 0.005 0.017 0.000 0.000 18210.0 10315.0 1.0
beta_1[Michigan (12)] 0.003 0.003 -0.003 0.008 0.000 0.000 19462.0 9382.0 1.0
beta_1[Ohio (13)] 0.009 0.002 0.004 0.013 0.000 0.000 17514.0 9675.0 1.0
beta_1[Wisconsin (14)] 0.002 0.003 -0.004 0.008 0.000 0.000 22865.0 9720.0 1.0
beta_1[Iowa (15)] 0.005 0.003 -0.001 0.011 0.000 0.000 20717.0 10122.0 1.0
beta_1[Kansas (16)] -0.003 0.006 -0.014 0.008 0.000 0.000 20579.0 9451.0 1.0
beta_1[Minnesota (17)] -0.006 0.005 -0.014 0.003 0.000 0.000 22066.0 9496.0 1.0
beta_1[Missouri (18)] -0.009 0.003 -0.015 -0.003 0.000 0.000 22406.0 9192.0 1.0
beta_1[Nebraska (19)] 0.004 0.008 -0.011 0.020 0.000 0.000 21360.0 9662.0 1.0
beta_1[North Dakota (20)] -0.016 0.017 -0.048 0.016 0.000 0.000 22891.0 8759.0 1.0
beta_1[South Dakota (21)] -0.019 0.015 -0.048 0.008 0.000 0.000 18328.0 8949.0 1.0
beta_1[Virginia (22)] 0.013 0.006 0.003 0.024 0.000 0.000 20560.0 9050.0 1.0
beta_1[Alabama (23)] 0.008 0.007 -0.004 0.022 0.000 0.000 22130.0 9874.0 1.0
beta_1[Arkansas (24)] -0.014 0.008 -0.029 0.000 0.000 0.000 22665.0 9693.0 1.0
beta_1[Florida (25)] -0.005 0.012 -0.028 0.017 0.000 0.000 22543.0 9621.0 1.0
beta_1[Georgia (26)] 0.008 0.007 -0.005 0.020 0.000 0.000 23492.0 8744.0 1.0
beta_1[Louisiana (27)] -0.029 0.009 -0.047 -0.012 0.000 0.000 18993.0 9118.0 1.0
beta_1[Mississippi (28)] 0.001 0.008 -0.014 0.017 0.000 0.000 21760.0 10113.0 1.0
beta_1[North Carolina (29)] 0.014 0.007 0.002 0.027 0.000 0.000 24039.0 9698.0 1.0
beta_1[South Carolina (30)] 0.009 0.010 -0.009 0.027 0.000 0.000 21462.0 9143.0 1.0
beta_1[Texas (31)] -0.034 0.007 -0.048 -0.022 0.000 0.000 18367.0 10418.0 1.0
beta_1[Kentucky (32)] 0.009 0.005 0.000 0.018 0.000 0.000 24046.0 9370.0 1.0
beta_1[Maryland (33)] -0.002 0.005 -0.012 0.008 0.000 0.000 26146.0 8839.0 1.0
beta_1[Tennessee (34)] 0.001 0.005 -0.008 0.011 0.000 0.000 22359.0 9264.0 1.0
beta_1[West Virginia (35)] 0.006 0.007 -0.007 0.019 0.000 0.000 25035.0 9132.0 1.0
beta_1[Colorado (36)] -0.023 0.011 -0.044 -0.002 0.000 0.000 19997.0 9669.0 1.0
beta_1[Nevada (37)] -0.042 0.012 -0.065 -0.019 0.000 0.000 13777.0 9808.0 1.0
beta_1[New Mexico (38)] -0.024 0.016 -0.055 0.005 0.000 0.000 19544.0 9260.0 1.0
beta_1[Utah (39)] -0.035 0.011 -0.056 -0.015 0.000 0.000 17172.0 7918.0 1.0
beta_1[California (40)] -0.038 0.003 -0.044 -0.032 0.000 0.000 14530.0 11074.0 1.0
beta_1[Oregon (41)] -0.034 0.009 -0.051 -0.018 0.000 0.000 17209.0 9510.0 1.0
beta_1[Washington (42)] -0.016 0.011 -0.037 0.006 0.000 0.000 22868.0 9129.0 1.0
beta_1[District of Columbia (43)] -0.007 0.010 -0.025 0.011 0.000 0.000 23290.0 9332.0 1.0
beta_2[Connecticut (0)] 11.488 871.812 -17.319 20.101 7.862 5.625 13855.0 8783.0 1.0
beta_2[Maine (1)] 5.556 455.385 -19.312 16.812 4.155 2.938 14113.0 8151.0 1.0
beta_2[Massachusetts (2)] 20.501 2041.979 -18.285 16.441 18.585 13.172 12982.0 7851.0 1.0
beta_2[New Hampshire (3)] -0.749 186.102 -20.091 16.360 1.748 1.236 14497.0 8638.0 1.0
beta_2[Rhode Island (4)] 15.657 2056.359 -18.166 18.367 18.727 13.265 15122.0 8361.0 1.0
beta_2[Vermont (5)] 20.441 2408.054 -17.454 19.295 21.933 15.534 13844.0 8383.0 1.0
beta_2[Delaware (6)] 11.880 1212.375 -18.469 17.358 11.060 7.821 12768.0 7753.0 1.0
beta_2[New Jersey (7)] 16.446 1918.897 -18.712 17.618 17.480 12.379 13587.0 7746.0 1.0
beta_2[New York (8)] 8.810 1387.280 -19.405 18.686 12.646 8.949 13549.0 8223.0 1.0
beta_2[Pennsylvania (9)] -3.525 671.976 -18.005 18.070 6.135 4.338 13825.0 7846.0 1.0
beta_2[Illinois (10)] 6.501 911.324 -19.038 17.216 8.290 5.879 12277.0 8154.0 1.0
beta_2[Indiana (11)] -5.954 593.247 -18.103 18.359 5.411 3.827 14137.0 8762.0 1.0
beta_2[Michigan (12)] 1.988 195.213 -18.612 17.147 1.781 1.264 15112.0 8640.0 1.0
beta_2[Ohio (13)] -8.332 515.229 -16.597 19.751 4.681 3.324 13950.0 8395.0 1.0
beta_2[Wisconsin (14)] 6.304 673.609 -16.660 18.908 6.133 4.345 13991.0 8498.0 1.0
beta_2[Iowa (15)] -16.159 2470.630 -17.061 20.522 22.514 15.938 13510.0 7798.0 1.0
beta_2[Kansas (16)] 9.597 1483.017 -17.808 19.197 13.470 9.567 14036.0 8040.0 1.0
beta_2[Minnesota (17)] 7.648 874.014 -19.768 18.912 8.008 5.663 13317.0 7794.0 1.0
beta_2[Missouri (18)] -15.746 1446.690 -17.845 18.696 13.199 9.333 12608.0 8200.0 1.0
beta_2[Nebraska (19)] 10.734 1433.694 -19.047 17.834 13.055 9.249 13561.0 7677.0 1.0
beta_2[North Dakota (20)] 9.570 1009.554 -17.724 19.369 9.202 6.512 13099.0 8328.0 1.0
beta_2[South Dakota (21)] -9.626 1271.283 -18.562 17.492 11.571 8.201 13440.0 7946.0 1.0
beta_2[Virginia (22)] 15.620 2104.465 -19.086 19.222 19.159 13.576 14060.0 8047.0 1.0
beta_2[Alabama (23)] -14.514 1222.454 -18.932 18.333 11.207 7.925 13012.0 8006.0 1.0
beta_2[Arkansas (24)] 8.368 1004.325 -18.918 18.182 9.147 6.479 12748.0 8032.0 1.0
beta_2[Florida (25)] -19.186 1798.689 -19.029 18.214 16.373 11.603 14593.0 8436.0 1.0
beta_2[Georgia (26)] -11.865 1120.131 -18.410 19.075 10.195 7.226 13721.0 8075.0 1.0
beta_2[Louisiana (27)] 10.366 1357.833 -18.332 17.453 12.381 8.759 12557.0 8145.0 1.0
beta_2[Mississippi (28)] -9.823 1050.914 -18.794 17.918 9.564 6.779 14583.0 8187.0 1.0
beta_2[North Carolina (29)] -3.311 407.136 -17.974 19.434 3.718 2.629 13480.0 8250.0 1.0
beta_2[South Carolina (30)] -15.716 1727.731 -17.905 18.081 15.733 11.145 13607.0 8286.0 1.0
beta_2[Texas (31)] -17.709 2340.236 -18.984 16.781 21.332 15.096 13108.0 8590.0 1.0
beta_2[Kentucky (32)] 0.815 471.337 -19.355 17.479 4.328 3.061 13808.0 8303.0 1.0
beta_2[Maryland (33)] -12.892 1436.931 -20.453 18.818 13.091 9.269 13753.0 7384.0 1.0
beta_2[Tennessee (34)] -4.228 879.671 -18.400 19.383 7.996 5.675 13219.0 8396.0 1.0
beta_2[West Virginia (35)] 11.561 826.678 -18.427 17.766 7.516 5.333 13748.0 8270.0 1.0
beta_2[Colorado (36)] 7.673 602.916 -18.858 18.493 5.570 3.939 13668.0 8596.0 1.0
beta_2[Nevada (37)] -12.597 1347.918 -17.973 19.235 12.294 8.695 13601.0 7951.0 1.0
beta_2[New Mexico (38)] -12.521 1817.841 -18.557 18.116 16.558 11.727 13815.0 7601.0 1.0
beta_2[Utah (39)] 29.760 2844.742 -17.575 19.314 25.913 18.351 14153.0 8118.0 1.0
beta_2[California (40)] 15.821 1859.810 -18.309 19.732 16.943 11.997 13569.0 8078.0 1.0
beta_2[Oregon (41)] 9.126 1176.918 -19.147 17.213 10.754 7.604 13725.0 7987.0 1.0
beta_2[Washington (42)] 7.264 707.601 -20.145 17.080 6.541 4.626 12902.0 7515.0 1.0
beta_2[District of Columbia (43)] 25.290 2822.744 -18.847 18.322 25.712 18.209 13190.0 8015.0 1.0
beta_3[Connecticut (0)] -0.018 0.011 -0.038 0.005 0.000 0.000 21547.0 10023.0 1.0
beta_3[Maine (1)] -0.017 0.012 -0.039 0.006 0.000 0.000 21945.0 8191.0 1.0
beta_3[Massachusetts (2)] -0.014 0.009 -0.031 0.005 0.000 0.000 12845.0 9995.0 1.0
beta_3[New Hampshire (3)] -0.018 0.012 -0.040 0.005 0.000 0.000 21823.0 9033.0 1.0
beta_3[Rhode Island (4)] -0.022 0.011 -0.045 -0.001 0.000 0.000 17478.0 9047.0 1.0
beta_3[Vermont (5)] -0.018 0.011 -0.040 0.005 0.000 0.000 21070.0 9093.0 1.0
beta_3[Delaware (6)] -0.017 0.011 -0.039 0.006 0.000 0.000 21937.0 8887.0 1.0
beta_3[New Jersey (7)] -0.018 0.011 -0.041 0.002 0.000 0.000 22898.0 9691.0 1.0
beta_3[New York (8)] -0.017 0.009 -0.034 0.001 0.000 0.000 19826.0 9396.0 1.0
beta_3[Pennsylvania (9)] -0.017 0.009 -0.035 0.002 0.000 0.000 19641.0 9700.0 1.0
beta_3[Illinois (10)] -0.017 0.010 -0.036 0.002 0.000 0.000 21304.0 9346.0 1.0
beta_3[Indiana (11)] -0.020 0.010 -0.041 -0.001 0.000 0.000 21021.0 9543.0 1.0
beta_3[Michigan (12)] -0.011 0.012 -0.030 0.016 0.000 0.000 10406.0 8784.0 1.0
beta_3[Ohio (13)] -0.030 0.013 -0.055 -0.011 0.000 0.000 5743.0 9912.0 1.0
beta_3[Wisconsin (14)] -0.023 0.012 -0.050 -0.003 0.000 0.000 12368.0 7887.0 1.0
beta_3[Iowa (15)] -0.016 0.011 -0.037 0.005 0.000 0.000 20269.0 9475.0 1.0
beta_3[Kansas (16)] -0.013 0.011 -0.031 0.010 0.000 0.000 14106.0 8900.0 1.0
beta_3[Minnesota (17)] -0.020 0.011 -0.042 0.001 0.000 0.000 21444.0 9090.0 1.0
beta_3[Missouri (18)] -0.015 0.009 -0.031 0.003 0.000 0.000 17022.0 9826.0 1.0
beta_3[Nebraska (19)] -0.019 0.011 -0.041 0.004 0.000 0.000 20261.0 8513.0 1.0
beta_3[North Dakota (20)] -0.018 0.012 -0.041 0.005 0.000 0.000 23699.0 8620.0 1.0
beta_3[South Dakota (21)] -0.019 0.011 -0.043 0.001 0.000 0.000 22341.0 8881.0 1.0
beta_3[Virginia (22)] -0.021 0.007 -0.036 -0.008 0.000 0.000 15872.0 11048.0 1.0
beta_3[Alabama (23)] -0.014 0.009 -0.029 0.004 0.000 0.000 14011.0 10108.0 1.0
beta_3[Arkansas (24)] -0.021 0.010 -0.041 -0.004 0.000 0.000 15914.0 10163.0 1.0
beta_3[Florida (25)] -0.020 0.011 -0.042 -0.001 0.000 0.000 19016.0 9023.0 1.0
beta_3[Georgia (26)] -0.014 0.008 -0.028 0.002 0.000 0.000 13707.0 11035.0 1.0
beta_3[Louisiana (27)] -0.017 0.009 -0.033 0.001 0.000 0.000 18145.0 10097.0 1.0
beta_3[Mississippi (28)] -0.020 0.009 -0.037 -0.004 0.000 0.000 16677.0 10425.0 1.0
beta_3[North Carolina (29)] -0.021 0.008 -0.036 -0.007 0.000 0.000 14927.0 10614.0 1.0
beta_3[South Carolina (30)] -0.024 0.010 -0.044 -0.008 0.000 0.000 10088.0 10145.0 1.0
beta_3[Texas (31)] -0.023 0.008 -0.039 -0.009 0.000 0.000 11279.0 9987.0 1.0
beta_3[Kentucky (32)] -0.018 0.008 -0.035 -0.002 0.000 0.000 22342.0 9596.0 1.0
beta_3[Maryland (33)] -0.018 0.010 -0.036 0.002 0.000 0.000 21244.0 9198.0 1.0
beta_3[Tennessee (34)] -0.015 0.008 -0.030 0.000 0.000 0.000 16241.0 10014.0 1.0
beta_3[West Virginia (35)] -0.021 0.011 -0.043 -0.002 0.000 0.000 17045.0 9165.0 1.0
beta_3[Colorado (36)] -0.020 0.011 -0.044 -0.001 0.000 0.000 17760.0 9386.0 1.0
beta_3[Nevada (37)] -0.014 0.012 -0.035 0.010 0.000 0.000 17245.0 9259.0 1.0
beta_3[New Mexico (38)] -0.018 0.011 -0.041 0.004 0.000 0.000 21065.0 9213.0 1.0
beta_3[Utah (39)] -0.018 0.011 -0.041 0.004 0.000 0.000 20456.0 9184.0 1.0
beta_3[California (40)] -0.012 0.009 -0.027 0.005 0.000 0.000 9954.0 10067.0 1.0
beta_3[Oregon (41)] -0.021 0.010 -0.041 -0.002 0.000 0.000 17566.0 8195.0 1.0
beta_3[Washington (42)] -0.014 0.011 -0.034 0.009 0.000 0.000 15001.0 8649.0 1.0
beta_3[District of Columbia (43)] -0.015 0.010 -0.034 0.006 0.000 0.000 17090.0 9096.0 1.0

ln_wage_state_dist_race_conservative_10pct

Trace Plots

Detailed Trace Plots

beta_0

beta_1

beta_2

beta_3

printed under Figures/ starting with ln_wage_state_dist_race_conservative_10pct.pdf

southern = ['Alabama', 'Arkansas','Delaware','Florida','Georgia','Kentucky','Louisiana','Maryland','Mississippi','North Carolina','Oklahoma','South Carolina','Tennessee','Texas','Virginia','West Virginia']
state_idx_to_state
idx state stateicp
0 1 Connecticut 1
1 2 Maine 2
2 3 Massachusetts 3
3 4 New Hampshire 4
4 5 Rhode Island 5
5 6 Vermont 6
6 7 Delaware 11
7 8 New Jersey 12
8 9 New York 13
9 10 Pennsylvania 14
10 11 Illinois 21
11 12 Indiana 22
12 13 Michigan 23
13 14 Ohio 24
14 15 Wisconsin 25
15 16 Iowa 31
16 17 Kansas 32
17 18 Minnesota 33
18 19 Missouri 34
19 20 Nebraska 35
20 21 North Dakota 36
21 22 South Dakota 37
22 23 Virginia 40
23 24 Alabama 41
24 25 Arkansas 42
25 26 Florida 43
26 27 Georgia 44
27 28 Louisiana 45
28 29 Mississippi 46
29 30 North Carolina 47
30 31 South Carolina 48
31 32 Texas 49
32 33 Kentucky 51
33 34 Maryland 52
34 35 Tennessee 54
35 36 West Virginia 56
36 37 Colorado 62
37 38 Nevada 65
38 39 New Mexico 66
39 40 Utah 67
40 41 California 71
41 42 Oregon 72
42 43 Washington 73
43 44 District of Columbia 98

Findings

education / race model

In terms of overall aggregates, the lesson of this model is that without race at all, people’s overall education went up by an average of a 6% chance of having at least one year of college over the time period. That might not sound like a lot, but honestly thats huge! This makes sense given the time period it occurs at and moderity generally.

In terms of race specifically, it seems that on average being nonwhite decreases the degree to which you increase your education, on the aggregate level. Unfortunately, this is mu_beta_1 is also interesting, as it is on average negative, but if you look at the trace plots (downloaded earlier), you see little state by state effect or variation at all. So this means

If you look at beta_1 sepcifically, they seem to be largely offset a similar amount as the main distribution of mu_beta_11. There are some notable outliers, for instance. The worst were california, DC, oregeon, maryland, and colorado. This is an interesting result, as this is specifically to do with race as well. If you look at beta_0 this calms down a bit, however, as their base rates are also very high. So the difference in education is larger in absolute terms, but they a rising tide lifts all boats. Apologies, if I was in R I would make tons of fancy graphs about this right now, but I honestly have no idea how to work indexes within the plot summary object so I am using the gui filter tool built into google colab to find most of these interesting insights.

Wages / Race models

The primary insight I got from here is just the fact that the overall impact in log wages is enough to be 1.4 overall! in log form! thats gigantic. Enough that you can’t convert that into a percent and have it be remotely close. The aggregate impact on it for nonwhites is -.149 on average, which while bad, honestly is not that terrible compared to the gigantic increase. I think this should be seen positively. This overall aggregate positive change is very consistent as well, with only south dakota and nevada having a mean of under 1 logged wage difference. In terms of beta_1, the race variable, it is mostly consistent between states, but with a few very noticable exceptions, namely california, and less so oregon and nevada (but still close), with almost -.675 logged less than before. And because these are log values, you can’t really make the rising tides lift all boats argument as before. Californias beta 0 isn’t that especially large either! I think this likely has something to do with the settling of california during that time period, I’m not especially familiar with the history there. There are also states where this reverses entirely, but only marginally. Michigan has a log increase of .086, almost as half as the average decrease, for nonwhites above whites. There are a couple others but most hover around ‘its the same’ (ie, not a decrease happening). There doesn’t seem to be a super noticable trend either.

State change models (Binary / Race)

This model is pretty simple overall, but I think the effects are relatively profund. The basic idea is that beta_0 is just the effects of not white, then you have beta 2, which is just the effects of states changing, then you have the nonwhite state change specifically. It seems here that something really interesing happens, where your racial difference in average income loss between white and black people decreases quite a bit when controlled for state moving. But the realy key part here is much more interesting, where a straight state move is negative for all parties involves on average, and even more negative on top of that for nonwhites. I am honestly relatively shocked by this result, as it is not at all what I would have expected. The effect of changing states is not significant for whites, though, which is interesting. But the difference between the two is absolutely significant. It is also lower for all states involved, and the ones with the worst white:nonwhite difference are western ones. I think this is likely noise though.

[NOTE: when using conservative linking, this appears to go away quite a bit. Wish I had more time to look into this / spent less time fixing technical issues.]

Log earnings with state distance

The very basic state distance model is extremely simple, and is just a baseline. The results are mostly a wash, however, as the effect of state distance overall is very very small and just barely significant by itself. I think this might be problematic though, since well, the units are extremely small. I really should have used bigger units, ahah. It does seem that income change over time decreases with general distance increasing though, or at least the model leans in that direction.

With respect to trying to control for waste, I am afraid that is a fool’s errand. The chain just went full uniform prior distribution on me, and the sigma is insane. This is a true converged posterior distribution it seems, just a somewhat insane one that I can’t draw any conclusions from.

pm.summary(ln_wage_state_dist_race_conservative_10pct, var_names = ['~beta_0_offset', '~beta_1_offset', '~beta_2_offset', '~beta_3_offset'])
mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail r_hat
mu_beta_0 1.516 0.031 1.458 1.574 0.001 0.000 1974.0 4005.0 1.0
sigma_beta_0 0.187 0.026 0.142 0.237 0.000 0.000 3126.0 5730.0 1.0
mu_beta_1 -0.006 0.003 -0.012 -0.000 0.000 0.000 2373.0 4676.0 1.0
sigma_beta_1 0.018 0.003 0.013 0.023 0.000 0.000 3793.0 6308.0 1.0
mu_beta_2 0.019 5.780 -8.834 10.000 0.035 0.072 26084.0 6085.0 1.0
... ... ... ... ... ... ... ... ... ...
beta_3[Utah (39)] -0.018 0.011 -0.041 0.004 0.000 0.000 20456.0 9184.0 1.0
beta_3[California (40)] -0.012 0.009 -0.027 0.005 0.000 0.000 9954.0 10067.0 1.0
beta_3[Oregon (41)] -0.021 0.010 -0.041 -0.002 0.000 0.000 17566.0 8195.0 1.0
beta_3[Washington (42)] -0.014 0.011 -0.034 0.009 0.000 0.000 15001.0 8649.0 1.0
beta_3[District of Columbia (43)] -0.015 0.010 -0.034 0.006 0.000 0.000 17090.0 9096.0 1.0

185 rows × 9 columns

Conclusion

Overall my findings show that in direct person by person census records, nonwhites americans faced significant hurdles nearly every step of the way. This data in particular showed that education and income growth, while they still happened, was significantly hampered.

In terms of my more general question, that is more complicated. I wanted to measure the geographic changes over time and between places, and I think this could do that, but I frankly would neeed to dedciate a much longer period of time doing a mix of analyzing this existing data to a much greater degree, or changing my approach a lot.

I did get some significant information though. The binary ‘yes/no’ has moved state model has appeared to bring some interesting conclusions, especially around the seemingly very geographically consistent differences in how it seems to be worse on average for nonwhites, but about the same for whites. This actually goes against my own intutions significantly, especially around the great migration and other such historical events being such a key point in american history.

Another interesting observation was that the states that seemed to consistently have the largest racial gap were the far western states. I think a deep historical dive into when those states were established and their race relations would make this analysis significantly more interesting overall. In conclusion, I think this project was a very good learning experience for me, even if it wasn’t quite as I hoped. I don’t want to be super down on it though, I do feel like I got some very valuable information, but I think more time spent digging deep into the results of this would help a lot.

Improvements for next time / etc

While overall I am relatively happy with how this project turned out, I think I could have improved in a lot of areas. The biggest one was I should have spent a lot less time on technical issues and a lot more on a very focused model. I ended up making a lot of models, and spend a ton of time attempting to wrangle them into actually working correctly / running. The dataset was big but at the end of the day it didn’t truly matter all that much, as I ran the models with 1/10th the data and they ended up turning out roughly the same. I think a much more focused in depth look at one very specific question would be more beneficial in the future. I eventually settled on a pretty specific thing, but I think your feedback from my presentation was very correct in that regard.

Additionally, while the hierarchal model was interesting, I think I could have actually made it more hierarchal. I know this might go against the technical debt point I just made in the last paragraph, but I truly don’t think having one level of hierarchy and then what is essentially a linear regression is really the best it could be. Another thing, while im on the topic, is that basically my speed in analysis generally is much, much slower on anything python related than in R. This is very much a nitpick, but if I was bouncing files back and fourth between R and python whenever I needed to data vis or wrangle anything I would have gotten way more done, ahah. Mostly just because I’m used to it, partly genuinely. Jupyter crashed on me a insane number of times in times I would have really preferred it not to crash as well. I probably spent 80% of my time debugging python and pymc performance issues and trying to get the models to train, 30% everything else. The biggest thing is that I just can’t make visualizations in a few seconds on demand in the same way, and can barely interact with the arviz xdata thing well enough aside from using the built in colab gui.

Bibliography

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