OLS interpretation

[Ali Taleb]

Hi everyone, I am trying just to see the impact of "policy" on the cost of KW ("cost_kw"). I would need to OLS regression. Is the code correct? and Can anyone just help to interpret the coefficient?

   

#delimit;
regress cost_KW policy other_rebates pop median_age unemployment  
;


Source |       SS           df       MS      Number of obs   =       452
-------------+----------------------------------   F(23, 428)      =     12.42
       Model |  .084621209        23  .003679183   Prob > F        =    0.0000
    Residual |  .126826328       428  .000296323   R-squared       =    0.4002
-------------+----------------------------------   Adj R-squared   =    0.3680
       Total |  .211447537       451  .000468842   Root MSE        =    .01721

-----------------------------------------------------------------------------------------
                cost_KW |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
                   policy|   .0135504   .0022828     5.94   0.000     .0090635    .0180372
          other_rebates |  -1.31e-08   6.09e-09    -2.15   0.032    -2.51e-08   -1.13e-09
                    pop |   6.18e-09   3.98e-09     1.55   0.121    -1.64e-09    1.40e-08
             median_age |   .0000222    .000285     0.08   0.938     -.000538    .0005825
           unemployment |  -.0012747   .0003196    -3.99   0.000     -.001903   -.0006465
           
-----------------------------------------------------------------------------------------

Best

[Clyde Schechter]

Well, assuming for the moment that this is a reasonable model for your question, and that the policy variable is coded 0/1 to distinguish those who are not subject to the policy from those who are, the interpretation would be that two entities (regions, whatever the observation unit in your data is) one of which is subject to the policy and the other is not, the expected difference in their cost_KW values is 0.0135504, with a 95% CI from 0.0090635 to 0.0180372, higher for the one subject to the policy. (In reporting these results you will probably want to round these to 2 or 3 places at most.)

That said, this kind of simple model can be very misleading. Unless the policy was imposed on units of analysis by randomization, it may well be that the groups that are subject to the policy and the groups that are not subject to it may differ in relevant ways. In particular, they may have had different cost_KW even before the policy went into effect. For this reason, to try to estimate causal effects, stronger designs are usually needed, such as a difference-in-differences estimation or using instrumental variables, depending on what kind of data you might be able to gather.

[Ali Taleb]

thank you so much, Clyde. I have done a Diff-inDiff and RDD analysis, but I was just trying to know if the results would change or would have significant differences between the two models. However, of course, DD or RDD are better and more feasible to use.

Best

[Nick Cox]

I'd guess that cost is necessarily positive. When that is so, a model of the form used may not be appropriate as positive predictions can't be guaranteed even within the range of the data. Make sure that you look at the usual diagnostic plots, e.g. residual versus fitted, added variable plots.

[Ali Taleb]

Thank you Nick for your reply. I'll check that!

However, the reason why I am using the OLS beside Diff-in-Diff (that is used to examine the impact of the policy on solar adoption) is that I need to see the subsidy pass-through rate (The policy subsidy would be passing to customers rather than to supplier of solar panels if I get for example a coefficient =-1.02; which means that I am having a subsidy passing to the customer).

Frankly, when taking the Log of the Cost (or the price) the results gives me a negative and significant coefficient (which is true based on my theoretical argument). If I use the dependent variable (cost_KW) it will give a positive and non-significant coeff.

Best
Ali

[Nick Cox]

Sometimes, the point is that a theory doesn't apply or does apply but other factors are more important.