4 Violations of Assumptions

4.1 Assumption 2 in Panel Data

  • Panel data is characterized by time dependency for each panel unit.

  • As discussed in Week 6, this is a violation of the regression Assumption 2 (X and Y are i.i.d).

4.1.1 Serial Correlation

  • Time dependency is often described as autocorrelation or serial correlation.

  • The main approach to deal with serial correlation is by adjusting standard errors to take into account autocorrelation.

  • If there is substantial autocorrelation (serial correlation) in the error term, even heteroskedasticity-robust standard errors will be inconsistent.

  • In panel data as in any other time series data, autocorrelation can be a very serious concern.

  • We can test for serial correlation after our fixed effects estimation using the Breusch-Godfrey test.

  • The null hypothesis in this test is that the autocorrelation of the error term is 0.

4.1.2 Cross-sectional dependence

  • Cross-sectional dependence in panels may arise when e.g. countries respond to common shocks or if spatial diffusion processes are present (think Arab Spring, or shocks from the financial crisis).

  • If cross-sectional dependence is present, this results, at least, in the inefficiency of the estimators and invalid inference when using standard estimation techniques.

  • This is another instance of the violation of regression Assumption 2.

  • If we assume that our earlier two-way fixed effects model specification is consistent, then we can test for residual cross-sectional dependence after the introduction of two-way fixed effects to account for common shocks.

4.2 Panel-corrected Standard Errors

  • Panel-corrected standard errors (Beck and Katz 1995)

    • panel heteroskedasticity: each country may have its own error variance

    • contemporaneous correlation of the errors: the error for one country may be correlated with the errors for other countries in the same year

    • serially correlated errors: the errors for a given country are correlated with previous errors for that country

4.3 General Approach to Correlation Between Panels

  • Driscoll and Kraay (1998) propose an estimator producing heteroskedasticity- and autocorrelation- consistent standard errors that are robust to general forms of spatial and temporal dependence. Often known as the SCC estimator.

  • Panel Corrected Standard Errors (PCSE), while popular in political science, may not work well with shorter panels with large N (ratio of T/N is small).

  • SCC estimator performs equally well in large N settings.

4.4 Your Roadmap with Panel Data

  • Is it a fixed effects or random effects model?

  • Hausman test. But primarily the choice should be driven by theory!

  • Use robust standard errors, start with HAC.

  • Check whether there is any cross-sectional dependence:

  • If not, you can stick to HAC.

  • If you have cross-sectional dependence, you need to use PCSE or SCC (use SCC).