Category A COMPANION TO Theoretical Econometrics

Parametric and. Nonparametric Tests. of Limited Domain and. Ordered Hypotheses. in Economics

Esfandiar Maasoumi*

1 Introduction

In this survey, technical and conceptual advances in testing multivariate linear and nonlinear inequality hypotheses in econometrics are summarized. This is discussed for economic applications in which either the null, or the alternative, or both hypotheses define more limited domains than the two-sided alternatives typically tested. The desired goal is increased power which is laudable given the endemic power problems of most of the classical asymptotic tests. The impedi­ments are a lack of familiarity with implementation procedures, and characteri­zation problems of distributions under some composite hypotheses.

Several empirically important cases are identified in which practical "one-sided" tests can be conducted by either the %2-distribution, or th...

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Basic duration distributions

In this section we introduce some parametric families of duration distributions. Exponential family

The exponentially distributed durations feature no duration dependence. In consequence of the time-independent durations, the hazard function is constant, X(y) = X. The cdf is given by the expression F(y) = 1 – exp(-Xy), and the survivor function is S( y) = exp(-Xy).

The density is given by:

f(У) = X exp^Xy^ У > °. (21.5)

This family is parametrized by the parameter X taking strictly positive values.

An important characteristic of the exponential distributions is that the mean and standard deviation are equal, as implied by EY = |, VY = ^ ...

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Nonlinear production frontiers

The previous models both assumed that the production frontier was log-linear. However, many common production functions are inherently nonlinear in the parameters (e. g. the constant elasticity of substitution or CES or the asymptoti­cally ideal model or AIM, see Koop et al., 1994). However, the techniques outlined above can be extended to allow for an arbitrary production function. Here we assume a model identical to the stochastic frontier model with common effi­ciency distribution (i. e. m = 1) except that the production frontier is of the form:12

Подпись: (24.16)Уі = /X; P) + Vi _ Zi.

The posterior simulator for everything except в is almost identical to the one given above. Equation (24.10) is completely unaffected, and (24.9) and (24...

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Extending the autoregressive AR(1) model

The probabilistic reduction (PR) perspective, as it relates to respecification, pro­vides a systematic way to extend AR(1) in several directions. It must be empha­sized, however, the these extensions constitute alternative models. Let us consider a sample of such statistical models.

AR(p) model

The extension of the AR(1) to the AR(p) model amounts to replacing the Markov (reduction) assumption with that of Markov of order p, yields:


Vt = a0 + £ akyt-k + ut, f О T,


with the model assumptions 1c-5c modified accordingly.


Extending the AR(1) model in order to include a trend, amounts to replacing the reduction assumption of mean stationarity E(yt) = p, for all f О T, with a particu­lar form of mean-heterogeneity, say E(yf) = pf, for all f О T...

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Extensions to the HEGY approach

Ghysels, Lee, and Noh (1994), or GLN, consider further the asymptotic distribu­tion of the HEGY test statistics for quarterly data and present some extensions. In particular, they propose the joint test statistics F(l 1 П 12 П 13 П l4) and F(l 2 П 13 П l4), the former being an overall test of the null hypothesis yt ~ SI(1) and the latter a joint test of the seasonal unit roots implied by the summation operator 1 + L + L2 + L3. Due to the two-sided nature of all F-tests, the alternative hypoth­esis in each case is that one or more of the unit root restrictions is not valid. Thus, in particular, these tests should not be interpreted as testing seasonal integration against stationarity for the process. From the asymptotic independence of t*., i =

1,. ....

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Simulation Based. Inference for. Dynamic Multinomial. Choice Models

John Geweke, Daniel Houser,
and Michael Keane

multinomial choice histories and partially observed payoffs. Many general sur­veys of simulation methods are now available (see Geweke, 1996; Monfort, Van Dijk, and Brown, 1995; and Gilks, Richardson, and Spiegelhalter, 1996), so in our view a detailed illustration of how to implement such methods in a specific case has greater marginal value than an additional broad survey. Moreover, the techniques we describe are directly applicable to a general class of models that includes static discrete choice models, the Heckman (1976) selection model, and all of the Heckman (1981) models (such as static and dynamic Bernoulli models, Markov models, and renewal processes)...

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