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I have a subset of data from a panel covering 100 cities and 20 years but the subset for some reason does not include the time variable or a variable to distinguish one city from another.

What are the implications for OLS? Would this violate some assumptions? How can I get around it (if at all)?

Can I treat the data as cross-sectional data? Even though there are 20 observations per city across the variables.

Additional Info: To be more specific my dependent variable is year-on-year change in population and the main regressors are year-on-year changes in other variables. Does the fact I am using changes get around these problems at all? (I am thinking it would as long as I can assume the city specific factors are constant).

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  • $\begingroup$ You are asking the validity of pooled OLS estimation in panel data model. When the individual or city has unobserved effect that is correlated with the observed covariates, the pooled ols will be biased and inconsistent. If you don't have panel structure, you probably have to find instruments for the endogenous variables. $\endgroup$ – semibruin Jul 24 '13 at 7:23
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No, in general you can not treat time series data as cross sectional.
Furthermore, you can not pool different levels together and treat them as one random sampling. This, at the very least, will give you a biased estimate (except for when the regressor you are looking at is somehow uncorrelated to the identity of the city, which doesn't make sense).
Think about it this way: There is a distinct effect for the samples from the same city: The actual influence of being from the same city.
With pooling, you eliminate the portion our of your model which would take this effect into account. So now the rest of your model will inherit this variation in the data (Your model now assumes there is no difference between the samples as it comes to city). However this biases your estimates: The estimate now includes the true effect (whatever you are researching) as well as the inherited effect which is actually just from sampling from a certain city.
You can no longer distinguish between cities - and any influence that comes from drawing from a certain city will now be attributed to your other factors - if those factors are also correlated with being from a certain city. Which they most likely are.

You'll be introducing two errors. First the bias from just not acknowledging the existence of any effect of drawing from the same city, second the problems you get with just OLSssing over a time-series. Samples from a time series, for example city A, are serially correlated as the previous year will have some sort of relationship with the current year. But this can introduce problems such as autocorrelation, which may make your assumption of exogenity invalid. In other words your error terms may end up (contemporarily) correlated with your regressor / explanatory variables. Then, once again, your estimate is no longer correct.

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  • $\begingroup$ How familiar are you with the mechanics of OLS estimation (the maths)? Search for "missing variable bias" and "strict exogenity" and "autocorrelation" $\endgroup$ – IMA Jul 24 '13 at 12:05
  • $\begingroup$ @John If you lost your login information, please visit our help page to recover your login credentials and merge your accounts. $\endgroup$ – chl Jul 24 '13 at 12:09
  • $\begingroup$ @IMA: To be more specific my dependent variable is year-on-year change in population and the main regressors are year-on-year changes in other variables. Does the fact I am using changes get around these problems at all? (I am thinking it would as long as I can assume the city specific factors are constant). $\endgroup$ – John Jul 26 '13 at 1:03
  • $\begingroup$ When it comes to the time series issues... maybe. Without throughoutly investigating all the issues in a proper manner no one can say. As far as the pooling issue goes, no, it does not affect that issue. $\endgroup$ – IMA Jul 26 '13 at 7:26

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