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# Re: st: one-sided F test for multiple coefficients

 From Stas Kolenikov To statalist@hsphsun2.harvard.edu Subject Re: st: one-sided F test for multiple coefficients Date Thu, 23 Dec 2010 14:28:15 -0600

```No, if you reject the null, it means that some of the coefficients are
negative. That's not what you want; to reject the null in favor of the
null that all coefficients are negative, the null must be that at
least one of the coefficients is non-negative, and that is the null
space that is very difficult to work with.

You need to read Andrews' papers on estimation on the boundary that
appeared in Econometrica in early 2000s. He did not invent all of the
wheel of course as these questions were first raised in 1950s-60s for
similar issues in ANOVA for agricultural experiments (is it true that
increasing the amount of fertilizer leads to a monotone increase in
yield?)

On Thu, Dec 23, 2010 at 2:19 PM, Chung Choe <Chung.Choe@ceps.lu> wrote:
> Hi Statalisters:
>
> When running wage regressions, I include a set of explanatory variables (X1, X2, and X3) along with other control variables. Suppose that the coefficients associated with those variables are b1, b2, and b3.
>
> In my specific case, the coefficients are supposed to be negative and it turns out that many of them are so. I'd like to conduct a formal test to show the estimates are negative.
>
> I would want to set up a null hypothesis as follows:
>
> H0: b1>=0, b2>=0, and b3>=0.
>
> Hence if I reject the null, I could conclude that a set of X variables is negatively associated with wages.
>
> First, I wonder if it's correct to apply F-test to this case.
> Second, how do we implement this test in Stata?
>
> Many thanks,
>
> Chung
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--
Stas Kolenikov, also found at http://stas.kolenikov.name
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```