Dynamic Panel regression with large T and small N

[vaibhav lalwani]

Hello

I am trying to run a model with GDP growth at t+1 as the dependent variable and values of some leading indicators (aggregate corporate earnings and the OECD composite leading indicator) at as the independent variables. These independent variables are measured at time t. The idea is to test if corporate earnings provide unique information about future economic growth.

The panel consists of 8 countries with 20 - 25 years of data for each.

Till now i was using fixed effects however i was told to add a lag of gdp growth (gdp growth at time t) as another control variable. I ran arima (1,0,0) for Gdp growth variable for the eight countries and three turned out to be significant, thus suggesting that a lag of dependent variable could be required on the RHS.

As i understand, fixed effects estimator becomes inconsistent and biased with lag of dependent variable and so i need to use dynamic panel estimation.

However, as far as i know, dynamic models like Arellano bond (xtabond,xtdpdsys) don't seem to suitable for a small N large T panel like this and the corrected least squares dummy variables require assumption of strict exogeneity, which i feel is a bit too strong in my case.

Is there any other way to correct the bias in FE estimators in this kind of a panel structure.

[Joao Santos Silva]

With T>=20 I would say that it is OK to use the fixed effects estimator.

Best wishes,

Joao

[vaibhav lalwani]

Thanks a lot. Your comment is helpful.

[Andrew Musau]

Joao Santos Silva, isn't fixed effects problematic with \( N=8\)? The large sample justification of FE relies on \( N \rightarrow \infty \) and not \( T\). With small \( N\), I would recommend that you search for literature on Zellner's seemingly unrelated regressions (SURE), which in Stata can be implemented using sureg and xtgls, among others. The lagged dependent variable is usually not problematic with large \( T\) .

[Joao Santos Silva]

Dear Andrew Musau,

I may be wrong here, but I believe that the FE estimator is valid with either N or T (or both) going to infinity.

Best wishes,

Joao

[Andrew Musau]

Joao Santos Silva, I agree that the results will be valid, but there may be an issue with inference with small \(N\). This is summarized by Wooldridge (2012, p.490)

When T is large, and especially when N is not very large (for example, N = 20 and T = 30), we must exercise caution in using the fixed effects estimator. Although exact distributional results hold for any N and T under the classical fixed effects assumptions, inference can be very sensitive to violations of the assumptions when N is small and T is large. In particular, if we are using unit root processes—see Chapter 11—the spurious regression problem can arise. First differencing has the advantage of turning an integrated time series process into a weakly dependent process. Therefore, if we apply first differencing, we can appeal to the central limit theorem even in cases where T is larger than N. Normality in the idiosyncratic errors is not needed, and heteroskedasticity and serial correlation can be dealt with as we touched on in Chapter 13. Inference with the fixed effects estimator is potentially more sensitive to nonnormality, heteroskedasticity, and serial correlation in the idiosyncratic errors.

Reference
Wooldridge, Jeffrey M., 2012. Introductory Econometrics : a Modern Approach. 5th Edition. Mason, Ohio :South-Western Cengage Learning.

[Joao Santos Silva]

Dear Andrew Musau,

Thank you for getting back to me on this. Indeed, if we are doing large-T-small-N asymptotics we need to worry about stationarity, cointegration, and all these issues that can be ignored with large-N-small-T. Also, we probably want to compute standard errors differently (DK rather than clustered). However, the initial post states that the dependent variable is GDP growth, which should be stationary as it is already in first differences. So, using FE should be OK in this context.

Best wishes,

Joao

[Andrew Musau]

Thank you, this is very useful.

[Jean ANGUI]

Hello,
it is possible to make an estimate by Dynamic Panel with the command "xtabond", according to Romilio Labra and Celia Torrecillas (2018, p.14), when the period is long. You can execute the "xtabond" command, and also the "xtdpdsys" command. I consulted work on growth in Africa whose authors have especially used the second command "xtdpdsys" for long panels (i.e the period is long). However, the command "xtabond2 is better for short panels.
The trouble you may have is with the validity of overidentification restrictions, by the Sargan test. If the Sargan test indicates that the overidentification restrictions are invalid, you will get some shaking by manipulating the different lags, hoping to validate the Sargan test; Because I have this problem, and I do not know how to fix it.
Perhaps someone among us knows more about overidentification restrictions.
Here is the link (and attachment) for the article by Romilio Labra and Celia Torrecillas (2018), for you: https://revistas.unal.edu.co/index.p...cle/view/61885

Regards

Jean(John)

[Jean ANGUI]

More on GMM estimation of dynamic panel models in Stata:
XTDPDGMM: new Stata command for efficient GMM estimation of linear (dynamic) panel models with nonlinear moment conditions (By Sebastian Kripfganz)