Estimation When a Parameter Is on a Boundary: Theory and Applications

Donald Andrews ()

No 1153, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper establishes the asymptotic distribution of extremum estimators when the true parameter lies on the boundary of the parameter space. The boundary may be linear, curved, and/or kinked. The asymptotic distribution is a function of a multivariate normal distribution in models without stochastic trends and a function of a multivariate Brownian motion in models with stochastic trends. The results apply to a wide variety of estimators and models. Examples treated explicitly in the paper are: (1) quasi-ML estimation of a random coefficients regression model with some coefficient variances equal to zero, (2) LS estimation of a regression model with nonlinear equality and/or inequality restrictions on the parameters and iid regressors, (3) LS estimation of an augmented Dickey-Fuller regression with unit root and time trend parameters on the boundary of the parameter space, (4) method of simulated moments estimation of a multinomial discrete response model with some random coefficient variances equal to zero, some random effect variances equal to zero, or some measurement error variances equal to zero, (5) quasi-ML estimation of a GARCH(1,q*) or IGARCH(1,q*) model with some GARCH MA parameters equal to zero, (6) semiparametric LS estimation of a partially linear regression model with nonlinear equality and/or inequality restrictions on the parameters, and (7) LS estimation of a regression model with nonlinear equality and/or inequality restrictions on the parameters and integrated regressors.

Keywords: Asymptotic distribution; boundary; equality restrictions; extremum estimator; GARCH(1; q*) model; generalized method of moments estimator; inequality restrictions; integrated regressors; least squares estimator; maximum likelihood estimator; locally asymptotically mixed normal; locally asymptotically normal; method of simulated moments estimator; nonlinear equality and inequality restrictions; parameter restrictions; partially linear model; random coefficients regression; quasi-maximum likelihood estimator; restricted estimator; semiparametric estimator; stochastic trends; unit root model (search for similar items in EconPapers)
JEL-codes: C13 (search for similar items in EconPapers)
Pages: 92 pages
Date: 1997-06
Note: CFP 988.
References: View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Published in Econometrica (November 1999), 67(6): 1341-1383

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