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# st: Instrumental variables with estimates from odd and even months

 From Adrian Stork To "statalist@hsphsun2.harvard.edu" Subject st: Instrumental variables with estimates from odd and even months Date Wed, 5 Feb 2014 22:22:27 +0100

```Dear all

I'm trying to use an instrumental variables estimator to mitigate the
Errors-in-Variables (EIV) issue but I'm a bit confused how to get there.
So, my dependent variable is actually estimated from time-series
regressions. Here I rergess the time-series of 50 stocks against a market
index, thus resulting in 50 coefficients for each of the 50 stocks.
However, to solve the EIV-issue it is argued to run these time-series
regressions separately for odd and even months. I did that, so far so good,
but I don't know how to implement the next step.
This instrumental variables estimator is defined as:

b=(^B_odd' ^B_even)^(-1) ^B' R

this is almost identical to the OLS-estimator, where ^B_odd' is the
transposed matrix of coefficients estimated over odd months, ^B_even is the
matrix of coefficients estimated over even months. (-1) is the inverse of
the resulting matrix and ^B' is B_odd'  if month t is even or B_even' if
month t is odd (the last point is actually the most confusing one). R is
the dependet variable, i.e. again the stock return of stock i.
Having said all that, the tricky part in my opinion is the ^B' which
changes in odd and even months depending on t. My rather naive approach is
to run the following regression in Stata to implement this instrumental
approach:

.ivregress 2sls R (betaeven=betaodd)

I get a result and it makes very much sense, but I'm not 100% sure whether
my solution is correct (especially given the changing nature of B'). Could
anyone confirm that what I did (i.e. the ivregress command) is in line with
above formula? From the Stata Manual I can't say for sure. Any
help/suggestions are much appreciated.

Best,