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st: Re: Asking about how to run nonlinear ML with STATA

From   Kit Baum <>
To   "BOONYAWAT K." <>
Subject   st: Re: Asking about how to run nonlinear ML with STATA
Date   Sun, 14 Mar 2010 08:28:35 -0400

On Mar 14, 2010, at 7:53 AM, BOONYAWAT K. wrote:

> I have some problem about the methodology that I plan to use in my research, the Mishkin Test. I am not sure whether or not STATA support for "a nonlinear maximum likelihood estimation procedure".
> Refer to Kraft et al (2007), the Mishkin test jointly estimates a linear forecasting equation and a model of market equlibrium pricing. 
> Forecasting equation:  Earningst+1 = α0 + α1Earningst + vt+1                                                                                  
> Pricing equation:            Returnt+1 = β(Earningst+1 - α0 - α1*Earningst)+ εt+1
> Under Mishkin, I have to test whether  α1 = α1*(efficient market hypotheisis) by using the likelihood ratio test,  2n*In(SSRc/SSRu), suggested by Mishkin (1983).
> Note: If α1 = α1* then the sum of squared residuals from the estimation constraining α1 = α1*(SSRc) should not be different from the sum of squared residuals from the estimation allowing α1≠ α1*  (SSRu)
> Previous research, they normally run Mishkin test by SAS using PROC NLIN. However, I am familiar with STATA rather than SAS, so I hope that STATA can do this task as well. I wonder if your could  kindly give me some suggestion about how to do the test with STATA, please.

I do not believe any nonlinear estimation is required. A Wald-type test statistic may be computed using a nonlinear test procedure, employing the delta method:

set obs 1000
g t = _n
tsset t
set seed 20100314
loc lagearncoef 0.92
g double earnings = 0
g double returns = 0
replace earnings = 0.03 + 0.9 * L.earnings + rnormal(0, 0.1) in 2/l
replace returns = 1.5 * earnings - 1.5 * `lagearncoef' * L.earnings + rnormal(0, 0.1) in 2/l
qui reg earnings L.earnings
est store earn
qui reg returns earnings L.earnings
est store rets
suest earn rets
testnl [earn_mean]L.earnings = -1 * [rets_mean]L.earnings / [rets_mean]earnings

I believe this nonlinear Wald test should be asymptotically equivalent to the likelihood ratio test that you cite. If lagearncoef is closer to 0.9, the test will not reject.

Best wishes

Kit Baum   |   Boston College Economics & DIW Berlin   |
                              An Introduction to Stata Programming  |
   An Introduction to Modern Econometrics Using Stata  |

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