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st: Instrumental variables with estimates from odd and even months


From   Adrian Stork <storkadrian@googlemail.com>
To   "statalist@hsphsun2.harvard.edu" <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,
 Adrian
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