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From |
Christopher F Baum <baum@bc.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Re: coeffs across equations |

Date |
Fri, 27 Jun 2003 06:25:07 -0400 |

On Friday, June 27, 2003, at 02:33 AM, Scott wrote in response to Bersant:

Date: Thu, 26 Jun 2003 21:00:53 -0500This is a FAQ on Statalist. One cannot in general test coefficients from separate estimations. Pooling the data and estimating a single, fully interacted model, as suggested, is probably the most sensible approach, although it does then assume homoskedasticity across the 5 categories, which 5 separate regressions will not. Thus, one may want to test for groupwise heteroskedasticity if the est. sigma^2 from the category regressions are very different.

From: "Scott Merryman" <smerryman@kc.rr.com>

Subject: Re: st: test coefficients across equations [was: Re: sample selection bias]

- ----- Original Message -----

From: "Bersant Hobdari" <bh.cees@cbs.dk>

To: <statalist@hsphsun2.harvard.edu>

Sent: Thursday, June 26, 2003 11:51 AM

Subject: Re: st: Re: sample selection bias

Hi Everyone,

I had a question on testing coefficient across separately estimated

samples. The problem is the following: I estimate firm-level production

function where I divide the sample in 5 sub-samples defined by majority

owner: I.e., if majority owner is the State I classify the firm in that

group, if it is a financial institution I classify it in that group and

so on. After estimating regressions I would like to test the equality of

coefficients across equations.

Any suggestion how this could be implemented is highly appreciated.

Sincerely,

Bersant Hobdari

You could create a dummy variable on majority owner then interact it with

your other variables and test the coefficients on the fully interacted model

(see the Stata FAQ on Chow tests). Example using the auto dataset.

Equation 1: mpg = b0 + b1*price (if domestic)

Equation 2: mpg = b0' + b1'*price (if foreign)

Create the interaction term (if you have more categories -xi- comes in

handy)

gen priceXforeign = price *foreign

Regress the full interacted model

regress mpg = price foreign priceXforeign

A test on foreign will compare common intercepts, a test on priceXforeign

will test common slopes, and a test on both foreign and priceXforeign will

test if they are jointly equal to zero, or if equation 2 differs from

equation 1.

However, if you are concerned about correlation across equation (or wish to

test for it), -reshape- your data into a wide data structure and

use -sureg-.

The suggestion for sureg relaxes that assumption, and handles the separate coefficients (including making it easy to test / constrain across equations). However most implementations of SURE will demand that there are the same number of observations in each equation (a constraint not required by SURE, in that one can calculate consistent estimates of the residual covariance matrix from the dot products of the residuals, whatever their length). I suspect Bersant may not have equal numbers of firms per category.

Kit

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