Treatment of model misspecification

[Tim Meier]

Dear all,

I compute xtreg, re with robust standard errors:

quietly xtreg c.BNP c.TO  c.VRI  c.ALR  c.TO#c.VRI  c.TO#c.ALR  HH c.LMN c.POL c.ZRI c.SDT,fe vce(robust)

To calculate any misspecification, I do the following test:

predict yhat, xb
gen yhat2 = yhat^2
gen yhat3 = yhat^3
gen yhat4 = yhat^4

quietly xtreg c.BNP c.TO  c.VRI  c.ALR  c.TO#c.VRI  c.TO#c.ALR  HH c.LMN c.POL c.ZRI c.SDT yhat2 yhat3 yhat4,fe vce(robust)
test yhat2=yhat3=yhat4=0

The p-value is significant, accordingly there is a misspecification. Now to my topic, which is why I am posting here:

I have checked that my independent variable is no mathematical functions of dependent variables, I have included my independent variable as a squared term, I have log-transformed any non-linear variables, I have changed the number of yhat, I have changed the independent variable once and changed the independent variable and the two moderators on another occasion. None of this helped to fix the misspecification. Only the selection of a new dependent variable removed the misspecification. However, this cannot be a solution, since I want to examine the dependent variable on the one hand and have derived it theoretically on the other hand. It can't be the data set itself, because I found out from several samples of this data set that my model has no misspecification within the samples.

So my question is, what else can I do to fix misspecification in a model without having to change my dependent variable?

Thanks a lot for your help and support!

[Carlo Lazzaro]

Tim:
could you please share the -xtreg,fe- outcome table? Thanks.

[Tim Meier]

My dependent variable is a ratio. However, I have already calculated the misspecification test with reg and fracreg. The misspecification remains.

[Carlo Lazzaro]

Tim:
are you sure that you have a panel-wise effect (the negative correlation of u with the vector of predictors is very low, the within Rsq is low too and sigma_e>sigma_u)?

[Tim Meier]

The regression results as well as the results from the misspecification test actually remain identical whether I use xtreg,fe or reg (pooled ols).

[Tim Meier]

Could the problem be that the auxiliary regression is heteroskedastic, which biases the RESET test?

So far, only a reduction of the data and an alternative dependent variable have helped to remove the misspecification of the model. Unfortunately, neither of these is a useful option for solving the problem.

[Carlo Lazzaro]

Tim:
have you tried -linktest- after pooled OLS (with -vce(cluster panelid)- standard errors?

[Tim Meier]

I tried -linktest- after pooled OLS (with -vce(cluster panelid)- standard errors. The result still shows a misspecification. -ovtest- gives the same result.

Can it really be that the misspecification is only because of the dependent variable? Could I ignore the test results in this specific case, because I want to examine exactly this dependent variable?

[Carlo Lazzaro]

Tim:
what if you remove -c.TO##c.ALR-?

[Tim Meier]

Unfortunately, this does not change the test result.

quietly xtreg c.BNP c.TO c.VRI c.ALR HH c.LMN c.POL c.ZRI c.SDT,fe vce(robust)
predict yhat, xb
gen yhat2 = yhat^2
gen yhat3 = yhat^3
gen yhat4 = yhat^4
quietly xtreg c.BNP c.TO c.VRI c.ALR HH c.LMN c.POL c.ZRI c.SDT yhat2 yhat3 yhat4,fe vce(robust)
test yhat2=yhat3=yhat4=0

[Carlo Lazzaro]

Tim:
logging the regressand?

[Tim Meier]

I had actually already tried that, without success.

[Tim Meier]

Is it an option to multiply the dependent variable by 100 to "break" the fractional structure of the variable? Because in this case, the RESET test will not be significant and I will no longer have a misspecification.

[Carlo Lazzaro]

Tim:
I think it works as long as you are able to interpret the coefficients in the right way.

[Tim Meier]

Is it necessary to multiply all fractional variables in the model by 100 for a correct interpretation of the coefficients in this case. So far, I have only multiplied the dependent variable by one hundred, but the independent variable and the two moderators are also fractional variables.