Panel Data: Should I use xtreg, re robust OR xtregar, re?

[Charlotte Ormerod]

Hi All,

I have a question about the use of random effect models and using the correct estimators.

Data characteristics:
- Panel data
- Unbalanced
- T > N
- Dependent variable is yield
- Independent variable is liquidity

Aim of analysis:
- To perform a regression analysis that is efficient and consistent under robustness tests

Method:
1. Perform OLS / FE and RE models
regress yield liquidity
xtreg yield liquidity, fe
xtreg yield liquidity, re

2. Perform the Breusch-Pagan LM test for individual effects
xtreg yield liquidity, re
xttest0
RESULT: Individual effects present

3. Perform the Hausman test
xtreg yield liquidty, re
store estimates random
xtreg yield liquidity, fe
strore estimates fixed
hausman random fixed
RESULT: RE is better than FE

4. Determine what standard errors are most appropriate i.e., check for heteroskedasticity and autocorrelation
regress yield liquidity
hettest
RESULT: No heteroskedasticity
xtserial yield liquidity
RESULT: Autocorrelation present

Questions:
1. Should I proceed with either (1) xtregar yield liquidity, re OR (2) xtreg yield liquidity, re robust
2. Please explain the logic of the decision

Thank you,

Charlotte

[Andrew Musau]

3. Perform the Hausman test
xtreg yield liquidty, re
store estimates random
xtreg yield liquidity, fe
strore estimates fixed
hausman random fixed
RESULT: RE is better than FE

The order should be reversed in hausman. Fixed effects is the consistent estimator whereas random effects is efficient in the case that it is consistent. So it is OK to use fixed effects without any justification, but you must justify using random effects.

2. Please explain the logic of the decision

Wooldridge has some discussion in the chapter on advanced panel data models in his textbook Introductory Econometrics: A Modern Approach on some issues with FE in \(T>N\) panels:

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.

So a suggestion here is to use the first-differences estimator and compare with the FE estimator. xtregar assumes that the disturbance term is first-order autoregressive and is not the magic pill that addresses all problems that arise with long panels.

[Charlotte Ormerod]

Thank you for your response.

To clarify the first part do you mean that if the results of the Hausman test is not significant you can in fact use either the FE or RE model and simply need to justify the choice?

If so, please could you give an example of when an FE model would be more appropriate than an RE model even if the results of the Hausman test are not significant?

[Andrew Musau]

To clarify the first part do you mean that if the results of the Hausman test is not significant you can in fact use either the FE or RE model

Random effects relies on the assumption that the unobserved individual characteristics are uncorrelated with the RHS variables. This is a very strong assumption. But yes, even if the random effects assumption holds, you can use fixed effects. Bill Gould has a nice discussion on this at https://www.stata.com/support/faqs/s...effects-model/. Look at the \(2\times 2\) table that he draws relating the estimator to the model.

If so, please could you give an example of when an FE model would be more appropriate than an RE model even if the results of the Hausman test are not significant?

There was no mention of "more than" in my statement. I just said that if you need to use RE, you must justify your choice. But you need not justify using FE.