Octo ber 16.

Notes on the Oct15best.do regressions results.

  We drop the top 5% of districts by population.  This was not
datamining-- they are just too different for it to make sense to
include them. If you do include them, everything is insignficant.

First,let's think about explaining the number of prosecutions. We'll
look at the number rather than the prosecution rate, since the
prosecution rate we have used before is really an index, the number of
prosecutions divided by the crime rate, and that is artificial.
Instead, we'll regress the number of prosecutions on the  number of
crimes and see how it changes.

We do OLS as  a robustness check. This regression says the number of
prosecutions rises with the budget and with the population, but not
with the amount of crime.

Next, we instrument for both crime and the proseuction budget. Neither
comes in significant, nor does population.

  The R2 of 1st stage regressions for crime and th budget both are
prety good-- around .5.  But I am dubious taht crime needs
instrumenting. It isn't even signfiicant in the first regression.

 If we instrument for just the budget, then we get nice results.
Budget is signficant at the 8.9% level, at least,  and so is
population, but not crime.

 If we look at marginal effect in this last regression, budget has an
elasticity of .54 and population has an elasiticty of .43.

   The referee worried taht the results might depend on size. We
should do the weighted regressions he wanted, but I haven't yet. Here,
POPulation has been in the regressions, so we are adjusting for size
and by construction  teh residuals won't be correlated with
population.

 Next, we try to explain the win rate of prosecutors, regressing win
rate (which really does have a 0 to 100% meaning, unlike our
prosecution rate) on the level of crime, the budget, and so forth.

First, use tobit, not instrumenting for anything.

The result is that neither budget nor crime is significant, but more
felclosed does mean a lower win rate.

     Instrumenting for both budget and crime, the IVTOBIT maximum
likelihood doesn't converge. Thus, I used the two-step estimator. This
is worse, becasue we can't interpret the coefficients or have robust
standard errors. IT is OK, though, for testing whether we need to use
IV, and for statistical signfiicance of variables. What happens is
that nothing is signficant. But the Wald test says that we can't
reject exogeneity of crime.

.Instrumenting for just budget, and using maximum likelihood, the win
rate rises in budget, falls in crime, and falls in proseuction. The
Wald test rejects exogeneity of Budget too.

 The elasticy of budget is .10, which is reasonable. The elatisicites
of crime and proseuctions are -.04 and -.03, very small desptie their
signficaance.

   The residuals are uncorrelated with population.

 Third, let's see whether   win rate actually is negatively correlated
with budget , as we point out is a theoretical possibility. If we
correlate budget per population and the win rate, it indeed is
negative, but tiny.  Budget per crime and th ewin rate have a small
positive correlation.  If we run the same IVTOBIT regression as before
with only budget instrumented, then  budget comes in positive and
significant, as before. That makes sense, since the effect of the
number of proseuctions is so tiny, an elastiicty of 3%.