CFDP 1153

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

Author(s): 

Publication Date: June 1997

Pages: 92

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 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.

See CFP: 988