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# Re: Re: st: Regression with different firms

 From Christopher Baum To "statalist@hsphsun2.harvard.edu" Subject Re: Re: st: Regression with different firms Date Fri, 10 Aug 2012 10:42:43 +0000

<>
On Aug 10, 2012, at 2:33 AM, Felix wrote:

> it worked when I used the following command:
> reshape long firm std, i(date) j(firm_id)
>
> When I did the regression: regress firm std market_return, however, it produced an oddly low RÂ” (0.09) and extremely high t-statists (~74.73). Is there a special command for time series regression in this case?

You are estimating a variant of the well-known CAPM (Capital Asset Pricing Model):

>>>>>> return_firm_i = a*std_i + b* market_return

where you are allowing for firm-specific (and time-specific) volatility (of what? stock prices?) to shift the intercept. But you are constraining the CAPM 'beta' to be constant across firms and time. In terms of the CAPM, this makes no sense. The whole point is that firms that are more risky should have a higher return, and v.v. Furthermore, according to the standard CAPM  (r_i - r_f) = alpha_i + beta_i (R - r_f), where r_i, r_f and R are the firm return, risk-free rate and market return, respectively, volatility in R will be magnified for firms with \beta > 1, as they are riskier than the market portfolio. This will cause a firm-specific volatility measure to be correlated with the firm's contemporaneous return, and implies that the errors in the regression you ran cannot be independent of the error term. Ergo, OLS cannot be consistent.

Now that you have solved your data management problem, I think you need to come up with a more coherent explanation of the model you're trying to estimate. Customarily, the CAPM would be estimated for each firm (using, e.g., -statsby-). But your variant on the CAPM causes econometric problems, and I don't know how to interpret your coefficient 'b'.

KIt

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html

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