Panel data, county-level data, but state level intercept

[Yancheng Li]

Dear all,

I'm working on a thesis about the impact of economic growth on local obesity rates. I have US nation wide county-level data (non-metropolitan counties only) and a time period from 2012 through 2017. I'm using the fixed-effects model. There are over 9,000 observations and 1,809 panels (counties). My unit observations are counties.
The results, however, were insignificant. So I did some modification. I include state dummy variables. So as a result, I have county-level data, but state level intercepts.
My question is that, how would I test for heteroscedasticity and autocorrelation? I don't think the xttest3 and xtserial will still work in this case.

Thank you!

[Yancheng Li]

. global id FIPS

. global t Year

. global ylist Obese

. global xlist Ln_PC_GDP PI Unem Age AfricanA NativeA AsianA HispanicA Ln_Pop Pov FSI dumt* dumtst*

. sort $id $t

. xtset $id $t
       panel variable:  FIPS (strongly balanced)
        time variable:  Year, 2012 to 2017
                delta:  1 unit

. reg $ylist $xlist
note: dumtst2 omitted because of collinearity
note: dumtst10 omitted because of collinearity

      Source |       SS           df       MS      Number of obs   =     9,928
-------------+----------------------------------   F(61, 9866)     =    428.69
       Model |  130822.294        61  2144.62777   Prob > F        =    0.0000
    Residual |  49356.6266     9,866  5.00269882   R-squared       =    0.7261
-------------+----------------------------------   Adj R-squared   =    0.7244
       Total |  180178.921     9,927  18.1503899   Root MSE        =    2.2367

------------------------------------------------------------------------------
       Obese |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   Ln_PC_GDP |  -.1662111    .061285    -2.71   0.007    -.2863421     -.04608
          PI |    .330414   .0078796    41.93   0.000     .3149684    .3458595
        Unem |   .0419582   .0137615     3.05   0.002     .0149829    .0689336
         Age |   -.147153   .0081741   -18.00   0.000    -.1631759   -.1311301
    AfricanA |   .0974043   .0028607    34.05   0.000     .0917968    .1030118
     NativeA |   .0792675   .0044013    18.01   0.000       .07064    .0878949
      AsianA |  -.3008478   .0389516    -7.72   0.000    -.3772008   -.2244948
   HispanicA |   .0044405   .0028539     1.56   0.120    -.0011538    .0100347
      Ln_Pop |   .0282906   .0365977     0.77   0.440    -.0434485    .1000297
         Pov |   .0124562   .0061536     2.02   0.043     .0003938    .0245186
         FSI |   .0122276   .0067539     1.81   0.070    -.0010113    .0254666
       dumt2 |   .1129401   .0766705     1.47   0.141    -.0373498      .26323
       dumt3 |   .5356621   .0798241     6.71   0.000     .3791906    .6921336
       dumt4 |   1.120177   .0824697    13.58   0.000     .9585197    1.281835
       dumt5 |   1.428756   .0884824    16.15   0.000     1.255313      1.6022
       dumt6 |   2.084956   .1041754    20.01   0.000     1.880751    2.289161
     dumtst1 |  -2.301074   1.212767    -1.90   0.058    -4.678345     .076197
     dumtst2 |          0  (omitted)
     dumtst3 |  -4.682929   1.249387    -3.75   0.000    -7.131982   -2.233876
     dumtst4 |  -2.663434   1.203714    -2.21   0.027    -5.022959   -.3039082
     dumtst5 |  -6.043856   1.187723    -5.09   0.000    -8.372036   -3.715676
     dumtst6 |   -10.3035   1.210718    -8.51   0.000    -12.67675   -7.930241
     dumtst7 |  -8.346763    1.48672    -5.61   0.000    -11.26104   -5.432489
     dumtst8 |  -2.567838   1.213167    -2.12   0.034    -4.945893   -.1897823
     dumtst9 |  -5.157617   1.200839    -4.30   0.000    -7.511508   -2.803727
    dumtst10 |          0  (omitted)
    dumtst11 |  -4.128245   1.207748    -3.42   0.001    -6.495679   -1.760811
    dumtst12 |  -3.598398   1.203918    -2.99   0.003    -5.958325   -1.238472
    dumtst13 |  -2.194015   1.209193    -1.81   0.070    -4.564281     .176251
    dumtst14 |  -1.706496    1.19357    -1.43   0.153    -4.046137    .6331458
    dumtst15 |  -.5360579   1.196557    -0.45   0.654    -2.881553    1.809437
    dumtst16 |  -1.968943   1.209388    -1.63   0.104    -4.339591     .401705
    dumtst17 |  -2.396011   1.220001    -1.96   0.050    -4.787462     -.00456
    dumtst18 |  -2.573323    1.22882    -2.09   0.036    -4.982061   -.1645854
    dumtst19 |  -3.247927   1.253463    -2.59   0.010    -5.704971   -.7908824
    dumtst20 |  -8.679261   1.304115    -6.66   0.000    -11.23559   -6.122928
    dumtst21 |  -.4645406   1.203306    -0.39   0.699    -2.823267    1.894186
    dumtst22 |  -2.608897   1.193061    -2.19   0.029     -4.94754   -.2702544
    dumtst23 |  -3.512423   1.213943    -2.89   0.004    -5.891999   -1.132846
    dumtst24 |  -2.515525   1.202097    -2.09   0.036     -4.87188   -.1591703
    dumtst25 |   -6.67561   1.206563    -5.53   0.000    -9.040719   -4.310501
    dumtst26 |  -2.441683   1.204631    -2.03   0.043    -4.803006   -.0803602
    dumtst27 |   -4.44801   1.206213    -3.69   0.000    -6.812435   -2.083586
    dumtst28 |  -3.819311   1.232831    -3.10   0.002    -6.235913    -1.40271
    dumtst29 |  -7.183298   1.209644    -5.94   0.000    -9.554449   -4.812148
    dumtst30 |  -4.458591   1.208229    -3.69   0.000    -6.826968   -2.090214
    dumtst31 |   -4.67003   1.201636    -3.89   0.000    -7.025482   -2.314578
    dumtst32 |  -2.487525   1.210331    -2.06   0.040    -4.860022   -.1150277
    dumtst33 |  -2.122199   1.210159    -1.75   0.080    -4.494358    .2499591
    dumtst34 |  -3.141755   1.202074    -2.61   0.009    -5.498065   -.7854448
    dumtst35 |  -2.428995   1.205262    -2.02   0.044    -4.791554   -.0664363
    dumtst36 |  -1.694886   1.213153    -1.40   0.162    -4.072915    .6831429
    dumtst37 |  -2.113261   1.221135    -1.73   0.084    -4.506935    .2804144
    dumtst38 |  -2.224742   1.202957    -1.85   0.064    -4.582785    .1333002
    dumtst39 |  -3.422371   1.205625    -2.84   0.005    -5.785643     -1.0591
    dumtst40 |  -4.321752    1.20425    -3.59   0.000    -6.682329   -1.961176
    dumtst41 |  -6.784274   1.221157    -5.56   0.000    -9.177991   -4.390557
    dumtst42 |  -5.224776   1.229687    -4.25   0.000    -7.635215   -2.814338
    dumtst43 |  -3.912981   1.209416    -3.24   0.001    -6.283683   -1.542279
    dumtst44 |  -1.611378   1.178494    -1.37   0.172    -3.921467    .6987103
    dumtst45 |  -1.238978   1.213714    -1.02   0.307    -3.618105    1.140148
    dumtst46 |  -1.476022   1.203195    -1.23   0.220    -3.834531    .8824867
    dumtst47 |  -6.825201   1.217414    -5.61   0.000     -9.21158   -4.438821
       _cons |   26.94015   1.469827    18.33   0.000     24.05899    29.82131
------------------------------------------------------------------------------

.

The "dumt"s are time dummies.

[Joro Kolev]

Is there a question here, or are you just reporting on this great success?

[Yancheng Li]

Dear Kolev.

May I ask, in this case, how would I test for heteroscedasticity and autocorrelation? I don't think the xttest3 and xtserial will still work in this case.

Thank you!

[Yancheng Li]

For example, I think if I just apply xttest3, Stata will test for county-level heteroscedasticity...but I want to test for state-level heteroscedasticity

[Joro Kolev]

Hi Yancheng, I cannot see how adding a couple of dummy variables can invalidate the heteroskedasticity and autocorrelation tests you are carrying out. Also nowadays with these huge panels nobody is doing heteroskedasticity and autocorrelation tests anymore, you can make your inference robust to those two by , robust cluster(county)

However you did not explain your data well at all.

1. What is the unit of observation? Is it the county, or is it the individual?

2. What do you call "1,809 panels", are these counties?

3. Are the counties nested within the states?

I think something wrong is going on there, because if counties are your panels, you should not be able to include state dummies on the top of the county dummies--they would be perfectly collinear with the county dummies.

[Joro Kolev]

Heteroskedasticity is not a level phenomenon. It is a relationship between the variance of the error term and the regressors. So you do not have a problem here for sure.

Correlation is different, indeed the test for correlation in the error would change depending on how you define the set where you are looking for correlation.

Again both of these problems can be dealt with by , robust cluster(some_level).

Example given if you think that errors are correlated at county level but uncorrelated for different counties, you do

regression command, robust cluster(county)

If you think that errors are correlated across counties and within states, but uncorrelated across states, you do

regression command, robust cluster(state)

For example, I think if I just apply xttest3, Stata will test for county-level heteroscedasticity...but I want to test for state-level heteroscedasticity

[Yancheng Li]

Hi Joro,

I modified the first post and made some clarifications, and yes, counties are nested within the states.

Counties are my panels. But I didn't include county dummies. I tried including county dummies, and the results are not so satisfying.
I think maybe the assumption that the intercept for each county are different is too strong. So, by inserting state dummies, I can have state-level intercept rather than county level intercepts.

[Yancheng Li]

Heteroskedasticity is not a level phenomenon. It is a relationship between the variance of the error term and the regressors. So you do not have a problem here for sure.

Correlation is different, indeed the test for correlation in the error would change depending on how you define the set where you are looking for correlation.

Again both of these problems can be dealt with by , robust cluster(some_level).

Example given if you think that errors are correlated at county level but uncorrelated for different counties, you do

regression command, robust cluster(county)

If you think that errors are correlated across counties and within states, but uncorrelated across states, you do

regression command, robust cluster(state)

Hi Joro,

Ok. Thank you so much for your clarification. I think I get some clues now. I think I can understand your approach, but do you mind to explain how I can 'test' if there exist autocorrelation at county level or at state level?

Thank you!

[Jeff Wooldridge]

Yancheng: Joro is recommending that you don't even test for autocorrelation or heteroskedasticity, and I concur. You can compute fully robust standard errors and you have plenty of counties so that clustering will produce good results. But you should at least use a robust Hausman test to provide support for not using fixed effects at the county level, as many researchers would (and should) be skeptical. You should set the id variable at the county level, not the state level. I won't use your globals but show you genererically.

xtset countyid year
xtreg y x1 ... xK i.FIPS i.year, re vce(cluster countyid)
xtoverid

The xtreg command allows state intercepts and assumes the county effects are uncorrelated with the explanatory variables. The xtoverid command (user written and needs to be installed) compares fixed effects at the county level with random effects, and you hope to not reject. If you do reject, it is saying you should really control for county-
level fixed effects. If you don't "like" the results, well, that's just the way it goes. You can try using different variables.

JW

[Carlo Lazzaro]

Yancheng:
just an aside to previous helpful comments.
Being a bit old-fashioned, the glorious community-contributed command -xtoverid- does not support -fvvarlist- notation; hence, you have to prefix your -xtreg- code with -xi:-.
Elaborating a bit on Jeff's code:

xtset countyid year
xi: xtreg y x1 ... xK i.FIPS i.year, re vce(cluster countyid)
xtoverid

[Jeff Wooldridge]

Thanks Carlo. I always forget that about the older, user-written commands.

[Carlo Lazzaro]

Jeff:
at least there's something that you're allowed to forget in econometrics!

[Yancheng Li]

Yancheng: Joro is recommending that you don't even test for autocorrelation or heteroskedasticity, and I concur. You can compute fully robust standard errors and you have plenty of counties so that clustering will produce good results. But you should at least use a robust Hausman test to provide support for not using fixed effects at the county level, as many researchers would (and should) be skeptical. You should set the id variable at the county level, not the state level. I won't use your globals but show you genererically.

xtset countyid year
xtreg y x1 ... xK i.FIPS i.year, re vce(cluster countyid)
xtoverid

The xtreg command allows state intercepts and assumes the county effects are uncorrelated with the explanatory variables. The xtoverid command (user written and needs to be installed) compares fixed effects at the county level with random effects, and you hope to not reject. If you do reject, it is saying you should really control for county-
level fixed effects. If you don't "like" the results, well, that's just the way it goes. You can try using different variables.

JW

Dr. Wooldridge,

Thank you very much for the clarification! I will definitely try the method you suggested!
There is just one thing I want to make sure; that is, the "FIPS" I use is a county-level id...I'm very sorry I didn't clarify that.So, when writing this line of code:

xtreg y x1 ... xK i.FIPS i.year, re vce(cluster countyid)

I think what you suggest is to insert "i.stateid", is that correct? Or did I misunderstand anything?...
Thank you again for your time!


Best regards,
Yancheng

[Yancheng Li]

Yancheng:
just an aside to previous helpful comments.
Being a bit old-fashioned, the glorious community-contributed command -xtoverid- does not support -fvvarlist- notation; hence, you have to prefix your -xtreg- code with -xi:-.
Elaborating a bit on Jeff's code:

xtset countyid year
xi: xtreg y x1 ... xK i.FIPS i.year, re vce(cluster countyid)
xtoverid

Dr. Lazzaro,

Thank you for the complement!

Best regards,
Yancheng