I have a question in the area of meta research. I have a dataset that consists of regression data of several economics papers. More explicitly, I have the values of the regression coefficients, the standard errors, the sample sizes and the significance levels.

My research question is: Do the effect sizes get smaller over the years? This has to do with the fact that by now we have Big Data which yields smaller effect sizes but more significance.

Unfortunately, I don't know if the coefficients are standardized. Is there a method or a formula that allows to pool the different regression coefficients and somehow measure their magnitude over the years? I know that usually one would use Cohen's Kappa in meta research in order to compare effect sizes. But since this is no test between two samples but rather a regression, Cohen's Kappa is not applicable.

This is what I have so far: Considering that I have the unstandardized coefficients and standard errors, I have the respective t-values by dividing the two values. These values have to be the same as for the quotient of the standardized coefficients and standard errors:

$\frac{b_1}{se_{x_1}} = t = \frac{\hat{b_1}}{\hat{se_{x_1}}}$

Also, the standardized coefficient can be derived by the unstandardized coefficient and the sample deviations of y and x_1 (which are unfortunately unknown):

$\hat{b_1}= b \frac{\sigma_y}{\sigma_{x_1}}$

Lastly, I know that the mean of the standardized variables is 0 and the standard deviation is 1. Any ideas on how to proceed or on a new approach are welcome! Thanks in advance!