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Let's say we have House Prices across different cities (Bristol, Brighton, London, Glasgow) across time (Monthly data from 2016-2020) and we're trying to predict it using unemployment and crime.
t = time period (months) i = city HPit = B1crimeit + B2unemit + uit
Would we interpret the beta coefficients differently from a PooledOLS model vs. a Random Effects model vs. a Fixed Effects model?
Thanks, any help would be greatly appreciated. :)
If you use built-in techniques, which usually don't alter the summary regression table, the interpretation is almost the same in those three cases. However, if you explicitly define the fixed effects as city factors or year factors, then the interpretation will change.
For example, if you use city factors as intercept changes (non multiplicative factors), then that coefficient will be read as a greater (+) or lower (-) intercept for that particular city, in respect of the base intercept.
In this example:
The base intercept is 535.2727. So, Sam's intercept is 535.2727+24.9628 and Arnold's intercept is 535.2727+64.42.
If you combine the factors with the variables, then the slopes change, and you'll have a greater (+) or lower (-) slope for that particular city, in respect of the base slope for that variable.
Using the same data as above:
In this case, the base slope is 0.8053, but sam's slope is 0.80 - 0.015 and Arnold's slope is 0.80 + 0.06.
You can use both techniques at the same time (as you see, in the last table, results may change dramatically). Also apply that intuition to the time variable. That intuition is basically the one for dummy variables.
