Averaging regression coefficients for 50 regression , how to report t statistic? I am estimating a regression like
Yit = a +b1 Xit +b2 Zit +b3 Rit + e 
where i = 1 to 100
Now I get coefficient estimates for all 100 i, i.e. 100 values of b1, 100 values of b2 and so on.
For reporting purposes I have calculated a cross-sectional average of b estimates, i.e to get one value of b1 and one vane of b2 and so on.
But how do I report the t statistic for these averages I have calculated.
I can see in many papers they have reported the cross-sectional average as I am calculating, but with this average, they report the t statistic too, I am confused how to calculate that t statistic. should I average the individual t statistic too??
Any help would be highly appreciated
 A: If you have 100 separate analyses you can investigate using the methods of meta-analysis for your problem. If you just want to do this for one coefficient you extract from each regression the estimate and its standard error. You then combine them using inverse variance weighting. This is fairly standard and you can do it in standard software like Stata or R and there are also a number of stand-alone programs. If you want to combine more than one coefficient from each regression life becomes more complicated as you need the variance-covariance matrix of the coefficients from each regression to do a multivariate meta-analysis. This is certainly available in Stata or R.
A: From the way you wrote the equation, it follows that you pool time series and cross sectional data together, therefore combine all data, run the regression and report t-stats.
Say you have 100 companies with 3 measures and an outcome which you assume is linearly dependent on the measures. You take measures in time, thus you also have say 12 monthly measures. 
Now you are asking:
1) What is the influence of each measure on the outcome in time for a particular company? Well, it is b1_hat_i, b2_hat_i, b3_hat_i, given they are significant (p-values are less than 0.05 for each). I am assuming away autocorrelation which is quite likely with time-series that usually require a different technique, not OLS, but ARMA, etc.
2) Now you are asking what is the overall effect for a company, of measures 1,2,3 on the outcome? Well, pool companies and answer in a joint regression. However, one regression for all companies may be a wrong model like an average temperature for a hospital -- it matters WHAT is the company.
Now, if you want to average individual coefficients, because it is your theoretical belief, you can test whether coefficients of the pooled model are different from the estimated value of the average of the individual coefficients. If they are, most likely averaging was not a good idea.
