That is not necessary. And the assumption is that errors are correlated across cross-sectional units.
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Sure, thanks Andrew.
I am now using the stacked samples design but I think I need to use reghdfe as I have a lot of fixed effects in one of my specifications. The problem with that though is that it seems to always exclude the constants rather than omit values for the fixed effects. I am attaching an example with both reg and reghdfe. Would you if there is a way to pick the omitted category in reghdfe?
which gives me:Code:sysuse auto, clear rename (mpg price) (depvar1 depvar2) reshape long depvar, i(make) j(which) gen cons=1 regress depvar i.which#(c.weight c.displacement c.cons i.foreign), nocons reghdfe depvar i.which#(c.weight c.displacement c.cons), nocons absorb(i.foreign)
Also the estimates look quite different?Code:. regress depvar i.which#(c.weight c.displacement c.cons i.foreign), nocons note: 2.which#1.foreign omitted because of collinearity Source | SS df MS Number of obs = 148 -------------+---------------------------------- F(8, 140) = 179.68 Model | 3.1419e+09 8 392733056 Prob > F = 0.0000 Residual | 306005883 140 2185756.31 R-squared = 0.9112 -------------+---------------------------------- Adj R-squared = 0.9062 Total | 3.4479e+09 148 23296421.1 Root MSE = 1478.4 -------------------------------------------------------------------------------------- depvar | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------------------+---------------------------------------------------------------- which#c.weight | 1 | -.0067745 .5027539 -0.01 0.989 -1.000746 .9871969 2 | 2.328626 .5027539 4.63 0.000 1.334654 3.322597 | which#c.displacement | 1 | .0019286 4.339999 0.00 1.000 -8.578483 8.58234 2 | 10.25387 4.339999 2.36 0.020 1.673454 18.83428 | which#c.cons | 1 | 41.84795 1013.101 0.04 0.967 -1961.107 2044.803 2 | -148.7127 865.5382 -0.17 0.864 -1859.928 1562.503 | which#foreign | 1#Foreign | -1.600631 479.9575 -0.00 0.997 -950.5024 947.3011 2#Domestic | -3899.63 479.9575 -8.12 0.000 -4848.532 -2950.729 2#Foreign | 0 (omitted) -------------------------------------------------------------------------------------- . reghdfe depvar i.which#(c.weight c.displacement c.cons), nocons absorb(i.foreign) (MWFE estimator converged in 1 iterations) note: 2.which#c.cons omitted because of collinearity HDFE Linear regression Number of obs = 148 Absorbing 1 HDFE group F( 5, 141) = 123.23 Prob > F = 0.0000 R-squared = 0.8138 Adj R-squared = 0.8059 Within R-sq. = 0.8138 Root MSE = 1637.7880 -------------------------------------------------------------------------------------- depvar | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------------------+---------------------------------------------------------------- which#c.weight | 1 | .245959 .5548105 0.44 0.658 -.8508635 1.342781 2 | 2.075892 .5548105 3.74 0.000 .9790696 3.172714 | which#c.displacement | 1 | 4.08701 4.742891 0.86 0.390 -5.289359 13.46338 2 | 6.168784 4.742891 1.30 0.196 -3.207586 15.54515 | which#c.cons | 1 | -207.8225 1353.837 -0.15 0.878 -2884.265 2468.62 2 | 0 (omitted) --------------------------------------------------------------------------------------Comment
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You just have to take care in how you specify the absorb vars in reghdfe (SSC). The intercepts are unnecessary here (specify -nocons- or do not interpret the reported intercept), but you need to interact the absorb vars with their respective group indicators. Don't forget to specify the option -robust- for the standard errors.
Res.:Code:gen which1= 1.which gen which2= 2.which reghdfe depvar i.which#(c.weight c.disp), absorb(i.foreign#which1 i.foreign#which2) vce(robust)
Code:. reghdfe depvar i.which#(c.weight c.disp), absorb(i.foreign#which1 i.foreign#which2) vce(robust) (MWFE estimator converged in 2 iterations) HDFE Linear regression Number of obs = 148 Absorbing 2 HDFE groups F( 4, 140) = 48.76 Prob > F = 0.0000 R-squared = 0.8494 Adj R-squared = 0.8419 Within R-sq. = 0.5170 Root MSE = 1478.4304 -------------------------------------------------------------------------------------- | Robust depvar | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------------------+---------------------------------------------------------------- which#c.weight | 1 | -.0067745 .0008357 -8.11 0.000 -.0084267 -.0051222 2 | 2.328626 .6200661 3.76 0.000 1.102721 3.55453 | which#c.displacement | 1 | .0019286 .0073599 0.26 0.794 -.0126223 .0164796 2 | 10.25387 5.3106 1.93 0.056 -.2454767 20.75321 | _cons | -1423.811 699.1867 -2.04 0.044 -2806.14 -41.48112 -------------------------------------------------------------------------------------- Absorbed degrees of freedom: ----------------------------------------------------------+ Absorbed FE | Categories - Redundant = Num. Coefs | ------------------+---------------------------------------| foreign#which1 | 4 0 4 | foreign#which2 | 4 4 0 | ----------------------------------------------------------+ .Last edited by Andrew Musau; 01 Sep 2021, 11:56.Comment
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Hi Andrew, yes sorry I forgot about the interactions of the absorbed variables in the example. The thing is I like having the constants as in my regressions the main slope is the "female" coefficient so then the constant gives me the value for "male" alone. And that was fine as long as I could use reg, except this one specifications seems to have too many controls for reg..Comment
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The constant is meaningless in a fixed effects model. It is collinear with the fixed effects and therefore its coefficient is not identified. So you should not look to interpret it. reghdfe partials it out. Below, in regress, you see that its coefficient depends on the base category of the firm indicators.
Res.:Code:webuse grunfeld regress invest mvalue kstock i.company regress invest mvalue kstock ib2.company
Code:. webuse grunfeld . regress invest mvalue kstock i.company Source | SS df MS Number of obs = 200 -------------+---------------------------------- F(11, 188) = 288.50 Model | 8836465.8 11 803315.073 Prob > F = 0.0000 Residual | 523478.114 188 2784.45805 R-squared = 0.9441 -------------+---------------------------------- Adj R-squared = 0.9408 Total | 9359943.92 199 47034.8941 Root MSE = 52.768 ------------------------------------------------------------------------------ invest | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mvalue | .1101238 .0118567 9.29 0.000 .0867345 .1335131 kstock | .3100653 .0173545 17.87 0.000 .2758308 .3442999 | company | 2 | 172.2025 31.16126 5.53 0.000 110.7319 233.6732 3 | -165.2751 31.77556 -5.20 0.000 -227.9576 -102.5927 4 | 42.4874 43.90987 0.97 0.334 -44.13197 129.1068 5 | -44.32013 50.49225 -0.88 0.381 -143.9243 55.28406 6 | 47.13539 46.81068 1.01 0.315 -45.20629 139.4771 7 | 3.743212 50.56493 0.07 0.941 -96.00433 103.4908 8 | 12.75103 44.05263 0.29 0.773 -74.14994 99.652 9 | -16.92558 48.45326 -0.35 0.727 -112.5075 78.65636 10 | 63.72884 50.33023 1.27 0.207 -35.55572 163.0134 | _cons | -70.29669 49.70796 -1.41 0.159 -168.3537 27.76035 ------------------------------------------------------------------------------ . regress invest mvalue kstock ib2.company Source | SS df MS Number of obs = 200 -------------+---------------------------------- F(11, 188) = 288.50 Model | 8836465.8 11 803315.073 Prob > F = 0.0000 Residual | 523478.114 188 2784.45805 R-squared = 0.9441 -------------+---------------------------------- Adj R-squared = 0.9408 Total | 9359943.92 199 47034.8941 Root MSE = 52.768 ------------------------------------------------------------------------------ invest | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mvalue | .1101238 .0118567 9.29 0.000 .0867345 .1335131 kstock | .3100653 .0173545 17.87 0.000 .2758308 .3442999 | company | 1 | -172.2025 31.16126 -5.53 0.000 -233.6732 -110.7319 3 | -337.4777 16.80518 -20.08 0.000 -370.6286 -304.3267 4 | -129.7151 21.97637 -5.90 0.000 -173.0671 -86.36315 5 | -216.5226 27.69626 -7.82 0.000 -271.158 -161.8873 6 | -125.0671 24.12802 -5.18 0.000 -172.6636 -77.47068 7 | -168.4593 27.40332 -6.15 0.000 -222.5168 -114.4018 8 | -159.4515 22.0766 -7.22 0.000 -203.0012 -115.9018 9 | -189.1281 25.62201 -7.38 0.000 -239.6717 -138.5845 10 | -108.4737 26.95322 -4.02 0.000 -161.6433 -55.30405 | _cons | 101.9058 24.93832 4.09 0.000 52.71093 151.1007 ------------------------------------------------------------------------------ .Comment
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Predict the DV after suest, get corrrelation of yfit and y, square it, call it pseudoR2?Comment
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Thanks George!
And thanks Andrew for the clarification, that makes sense. Although I guess I am still a bit confused by the fact that even in the simplest model without fixed effects reghdfe still seems to exclude a constant while reg doesn't. So excluding the foreign fixed effects in my example in #17, I now get
And again, I am happy with why I should not consider the constant in my models, but I am afraid I might be missing something of how reghdfe works.Code:. regress depvar i.which#(c.weight c.displacement c.cons), nocons Source | SS df MS Number of obs = 148 -------------+---------------------------------- F(6, 142) = 157.55 Model | 2.9976e+09 6 499595356 Prob > F = 0.0000 Residual | 450298194 142 3171114.04 R-squared = 0.8694 -------------+---------------------------------- Adj R-squared = 0.8639 Total | 3.4479e+09 148 23296421.1 Root MSE = 1780.8 -------------------------------------------------------------------------------------- depvar | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------------------+---------------------------------------------------------------- which#c.weight | 1 | -.0065671 .6009143 -0.01 0.991 -1.194461 1.181327 2 | 1.823366 .6009143 3.03 0.003 .6354719 3.01126 | which#c.displacement | 1 | .0052808 5.085375 0.00 0.999 -10.04755 10.05811 2 | 2.087054 5.085375 0.41 0.682 -7.965772 12.13988 | which#c.cons | 1 | 40.08452 1040.877 0.04 0.969 -2017.533 2097.702 2 | 247.907 1040.877 0.24 0.812 -1809.711 2305.525 -------------------------------------------------------------------------------------- . reghdfe depvar i.which#(c.weight c.displacement c.cons), nocons noabsorb (MWFE estimator converged in 1 iterations) note: 2.which#c.cons omitted because of collinearity HDFE Linear regression Number of obs = 148 Absorbing 1 HDFE group F( 5, 142) = 99.74 Prob > F = 0.0000 R-squared = 0.7784 Adj R-squared = 0.7706 Within R-sq. = 0.7784 Root MSE = 1780.7622 -------------------------------------------------------------------------------------- depvar | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------------------+---------------------------------------------------------------- which#c.weight | 1 | -.0065671 .6009143 -0.01 0.991 -1.194461 1.181327 2 | 1.823366 .6009143 3.03 0.003 .6354719 3.01126 | which#c.displacement | 1 | .0052808 5.085375 0.00 0.999 -10.04755 10.05811 2 | 2.087054 5.085375 0.41 0.682 -7.965772 12.13988 | which#c.cons | 1 | -207.8225 1472.023 -0.14 0.888 -3117.733 2702.088 2 | 0 (omitted) --------------------------------------------------------------------------------------
I should add I am working with version 5.7.3 (nov2019) of reghdfe.Last edited by Maria Ventura; 02 Sep 2021, 01:39.Comment
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As reghdfe was written mainly for efficient estimation of linear regression with multiple levels of fixed effects, the author did not anticipate that it would be used for standard linear regression. Therefore, it has no true -nocons- option. Its -nocons- option is more like -hidecons-.Comment
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I see, I did not know that, it all makes sense now. Thanks!Comment
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Hey Andrew Musau, sorry to get back on this but I figured a few more things while working on it.
First, it seems that the constant in reghdfe is such that the sum of fixed effects is zero (apparently it is the same in xtreg),which would mean that it can actually be interpreted?
Secondly, I was wondering if you had references for the equivalence of the stacked samples estimation of a few posts ago and SUR models. I have seen this https://journals.sagepub.com/doi/pdf...867X0400400407 but it seems to require a few other steps (I am actually not sure of why the author is a using a whole different command rather than doing what you suggested above?).
Thanks!Last edited by Maria Ventura; 15 Sep 2021, 07:39.Comment
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Have a look at the following FAQ by Bill Gould. The intercept in a fixed effects model just reflects the kind of constraint you place on the model. There is no way to separately identify the intercept and the fixed effects, and therefore as I said, it is meaningless.
https://www.stata.com/support/faqs/s...effects-model/
For references on stacked regressions, have a look at the references within the Stata manual entry of suest as the procedure is exactly what suest does.Comment
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The reference to back #26 is found on page 15 of the suest manual
The stacking method can be applied not only to the testing of cross-model hypotheses for logit models but also to any estimation command that supports the vce(cluster clustvar) option. The stacking approach clearly generalizes to stacking more than two logit or other models, testing more general linear hypotheses, and testing nonlinear cross-model hypotheses (see [R] testnl). In all of these cases, suest would yield identical statistical results but at smaller costs in terms of data management, computer storage, and computer time.Comment
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Thanks Andrew, that's incredibly useful!Comment
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