I have the following situation. Longitudinal stock price data. Quarterly observations. Of a sample of n individuals for 30 times. In the 30 days I do not always have all the individuals available. This makes it impossible to use a panel approach (strongly unbalanced and with missing data slots in the middle).
I have to estimate two models: one LOGIT and one OLS. I opted for a cross-section approach.
The variable response (ypsilon) if detected daily has serial correlation. Quarterly surveys attenuate this problem. The poor extension of time series does not allow reliable serial correlation testing.
I want to avoid going to a difference in difference model and keeping the dependent variable unaltered (level).
Can I estimate the model with robust standard error? Does this solve or mitigate potential autocorrelation problems?
Thanks for your time, Alberto
Unless the correlation is large enough, it does not matter much whether you use OLS or Robust standard errors. An insignificant serial correlation will not affect the unbiasedness or consistency of OLS estimators, but it does affect their efficiency. With positive serial correlation, the OLS estimates of the standard errors will be smaller than the true standard errors. This will lead to the conclusion that the parameter estimates are more precise than they really are. With negative serial correlation, the OLS standard errors will be big & the robust standard errors will be smaller than OLS standard errors.
If the serial correlation is significant, it affects the OLS standard errors & because the standard error is central to conducting significance tests and calculating confidence intervals, biased standard errors lead to incorrect conclusions about the significance of the regression coefficients. Many statistical programs provide an option of robust standard errors to correct this bias.
You can try a logarithmic transformation of your dependent variable or use a Weighted least squares regression model.
Hope helpful.
Hemlata