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From |
Kit Baum <baum@bc.edu> |

To |
"BOONYAWAT K." <karuntarat.boonyawat@durham.ac.uk> |

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: -------------- clear 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 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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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