# Re: st: problems with Murphy-Topel

 From "Austin Nichols" <[email protected]> To [email protected] Subject Re: st: problems with Murphy-Topel Date Mon, 29 Oct 2007 13:45:39 -0400

```Rachel--
I'm not going to address your main question (sorry).

Instead, I want to offer another approach from the literature that may
be closer to what you really want to model.  You measure a trend in
income X to see if there are long-run secular effects of increasing X
on Y and then deviation from trend to see if there are contemporaneous
short-run effects of X on Y, right?

Try taking the first difference of X/2 and the two-period moving average of X:
g dx=(x-l.x)/2
g ax=(x+l.x)/2
which two terms sum to X in the model (x=ax+dx) but decompose the
effect of X into a short-run effect (the coef on dx) and a long-run
effect (the coef on ax).

This idea (among others) is from
Michael Baker; Dwayne Benjamin; Shuchita Stanger
"The Highs and Lows of the Minimum Wage Effect: A Time-Series
Cross-Section Study of the Canadian Law"
Journal of Labor Economics, Vol. 17, No. 2. (Apr., 1999), pp. 318-350.

On 10/29/07, Rachel Bouvier <[email protected]> wrote:
> Hi stata-listers:
>
> I'm working on a problem dealing with the Murphy-Topel procedure as
> outlined in Hardin (2002) and Hole (2006).  Briefly, I have a very large
> stacked model in the first stage, consisting of 31 countries and up to
> 17 years (some countries have a shorter time series).  It is stacked so
> that the intercepts and the coefficients can vary for each country,
> rather than "pooling" them all.  (I posted a question about this
> quite a while ago, so it may seem familiar to some.)
>
> I use OLS to predict the trend of income over time for each country,
> and call this variable "new_predict", and its square,
> "new_pred2."  I also generate another variable, called
> "new_flux," which is made up of the residuals from the first
> stage (or how far income falls from its predicted trend).  I then use
> those three variables from the first stage in my second stage model
> (also using OLS).  I need to adjust the standard errors from the second
> stage model because those three variables were generated in the first
> stage.
>
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