Scaling fitted values obtained from first stage of IV

[Devon Smith]

Hi everyone:

I am running the following regression where I instrument my binary endogenous treatment variable adhd_dx with my instrument q.

svy:ivregress 2sls logtot age_6_10 age_10_13 famsz_0_4 rc2 rc3 rc4 rc5 rg2 rg3 rg4 ins2 ins3 (adhd_dx=q)

. However, the coefficient on adhd_dx is too big and doesn't seem reasonable in the context that I am studying (the dependent variable is log of expenditure)

------------------------------------------------------------------------------
             |                 BRR
      logtot |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     adhd_dx |   4.061351    .654874     6.20   0.000     2.765473    5.357228

This means that the treatment effect is 100*(exp^4.06 -1)!

To make sense of the coefficient, I did the following:

svy:reg adhd_dx age_6_10 age_10_13 famsz_0_4 rc2 rc3 rc4 rc5 rg2 rg3 rg4 ins2 ins3 q

Then obtained the fitted values, yhat. Then scaled yhat :

replace yhat=yhat*100

and then used the scaled fitted values in the second stage

svy:reg logtot age_6_10 age_10_13 famsz_0_4 rc2 rc3 rc4 rc5 rg2 rg3 rg4 ins2 ins3 yhat

I get:

------------------------------------------------------------------------------
             |                 BRR
      logtot |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        yhat |   .0463319   .0059718     7.76   0.000     .0345147     .058149

Now, I have two questions:

1. Is scaling like this okay? I mean, if the original yhat is uncorrelated with unobservables, are the scaled yhats too, since the transformation is linear?

2. How would I interpret the new coefficient? A 1pp increase in adhd_dx leads to a 100*(exp^0.46 -1) percent increase in expenditure- is this the correct interpretation?