Multivariable linear regression for data with multiple time points

[#1]

I'm measuring the garbage output of various cities in my country. I have five independent variables as predictors measured at 4-time points (same for the outcome).

I'm not interested in the effects of time. I want to know the regression coefficients for each of my variables. To find that out, I could do four separate multiple regressions, one for each time point. But that wouldn't summarize the data well since I would have four sets of results. So my question is, is there a way to enter the data for all four-time points and get one set of regression coefficients?

[#2]

There are many options:

1. First evaluate the consistency of the within country (the 4 time points), and if this is reasonably consistent, you can take the mean and standard deviation (or some other appropriate enumerative statistic) of those 4 points.  You will be able to model the 5 independent variable effects on the mean and on variation.

2. As you suggest, you can model each time separately and compare the 4 models.

3. Do you predict any of the 5 independent variables will have a latent or lagged effect?  If so you might want to look at the slope of the 4 points in time series and use that as a response variable.