Semiparametric efficiency bound and semiparametric MLE
On asymptotic efficiency for semiparametric estimation, Chamberlain (1986) derived an asymptotically lower bound for variances of - ft - consistent regular semiparametric estimators for the sample selection model (18.1). The …
Serial correlation in the disturbances of the linear regression model
The seminal work of Cochrane and Orcutt (1949) alerted the econometric profession to the difficulties of assuming uncorrelated disturbances in time series applications of the linear regression model. It soon …
Prior Information
The information on the parameters can come from two sources. One is from the observations, which are informative about о(0). But we may also have a priori information. Let this …
The Optimal Two-step or Iterated GMM Estimator
It is remarked in Section 3 that if q = p then GMM is equivalent to the MM estimator based on E[f(vt, 0o)] = o and so the estimator does …
The encompassing approach
This approach generalizes Cox's original idea and asks whether model Hf can explain one or more features of the rival model Hg. When all the features of model Hg can …
Multivariate data
In some data sets more than one count is observed. For example, data on the utilization of several different types of health service, such as doctor visits and hospital days, …
Concluding Remarks
Recent sampling theory research on heteroskedastic models seems to be concentrated on methods for estimation and hypothesis testing that do not requirespecification of a particular parametric form of heteroskedasticity. They …
Factor analysis
A generalization of the model discussed above is the factor analysis model. It is written, in a somewhat different notation, as Уп = Л£ n + Є n, where £n …
The Variance Decomposition of Belsley, Kuh, and Welsch (1980)
A property of eigenvalues is that tr( X'X) = XK=1 . This implies that the sizes of the eigenvalues are determined in part by the scaling of the data. Data …
Spatial dependence in panel data models
When observations are available across space as well as over time, the additional dimension allows the estimation of the full covariance of one type of association, using the other dimension …
Simulation Methods
In binary QRM there is little basis to choose between the logit and probit models because of the similarity of the cumulative normal and the logistic distributions. In the multinomial …
Limited-Information Estimators of Structural Parameters
We now consider the estimation of an equation in the linear simultaneous system. Note that the ith rows of B and Г contain the coefficients in the ith structural equation …
Orders of magnitude
In determining the limiting behavior of sequences of random variables it is often helpful to employ notions of orders of relative magnitudes. We start with a review of the concepts …
Collinearity in nonlinear regression models
When examining Z(P) for collinearity a problem arises. That is, Z(P) depends not only on the data matrix X but also on the parameter values p. Thus collinearity changes from …
Overdispersion
The Poisson regression model is usually too restrictive for count data, leading to alternative models as presented in Sections 3 and 4. The fundamental problem is that the distribution is …
Semiparametric IV estimation and conditional moments restrictions
Simultaneous equation models with selectivity can also be estimated by semiparametric methods. Semiparametric IV methods for the estimation of sample selection models are considered in Powell (1987) and Lee (1994b). …
Maximum likelihood estimation
An n x 1 vector y generated by the linear regression model (3.12) with an ARMA(p, q) disturbance process with normal errors, i. e. et ~ IN(0, a2), can be …
Handling the Rank in Practice
The question is how one should apply this theorem in practice. Since 00 is an unknown parameter vector it is not yet clear how one should compute the rank of …
The Overidentifying Restrictions Test
The asymptotic theory so far has been predicated on the assumption that the model is correctly specified in the sense that E[f(vt, 00)] = 0. If this assumption is false …
Power and finite sample properties
A number of studies have examined the small sample properties of nonnested tests. For a limited number of cases it is possible to determine the exact form of the test …
Practical Considerations
Those with experience of nonlinear least squares will find it easy to use packaged software for Poisson regression, which is a widely available option in popular econometrics packages like LIMDEP, …
Seemingly Unrelated. Regression
Denzil G. Fiebig* 1 Introduction Seemingly unrelated regression (SUR) is one of the econometric developments that has found considerable use in applied work. Not all theoretical developments find their way …
MIMIC and reduced rank regression
Above, we considered elaborations of equation (8.18), which offered additional information about the otherwise unidentified parameters in the form of an additional indicator. The latent variable appeared once more as …
Other Diagnostic Issues and Tools
There are a number of issues related to the diagnosis of collinearity, and other diagnostic tools. In this section we summarize some of these. 1.2 The centering issue Eigenvalue magnitudes …
Spatial dependence in models for qualitative data
Empirical analysis of interacting agents requires models that incorporate spatial dependence for discrete dependent variables, such as counts or binary outcomes (Brock and Durlauf, 1995). This turns out to be …
Self-Selection
Lung-fei Lee* 1 Introduction This paper provides some account on econometric models and analysis of sample selection problems. The paper is divided into three parts. The first part considers possible …
Full Information Methods
In this section, we change the notation somewhat and write the jth equation as Vj = Yj в + Xj Yj + U = Zj 8j + U (6-16) Here, …
Independent processes
In this subsection we discuss LLNs for independent processes. Theorem 18.12 (Kolmogorov's strong LLN for iid random variables) Let Zt be a sequence of identically and independently distributed (iid) random …
Collinearity in maximum likelihood estimation
Collinearity in the context of maximum likelihood estimation is similarly diagnosed. Instead of minimizing the sum of squared errors we maximize the loglikelihood function. Standard gradient methods for numerical maximization …
Other Parametric Count Regression Models
Various models that are less restrictive than Poisson are presented in this section. First, overdispersion in count data may be due to unobserved heterogeneity. Then counts are viewed as being …
Estimation of the intercept
The semiparametric estimation of sample selection models described has focused on the estimation of regression coefficients in outcome and selection equations. The intercept of the outcome equation has been absorbed …
Maximum marginal likelihood estimation
There is a mounting literature that suggests that the method of maximum likelihood estimation as outlined in Section 3.1 can lead to biased estimates and inaccurate asymptotic test procedures based …
The Classical Simultaneous Equations Model
We now turn to identification in the classical simultaneous equations model. Estimation in this model is comprehensively reviewed in chapter 6 by Mariano. The model is By + Гх = …
Other Estimators as Special Cases of GMM
It is remarked in the introduction that GMM estimation encompasses many estimators of interest in econometrics, and so provides a very convenient framework for the examination of various issues pertaining …
Measures of Closeness and Vuong’s Approach
So far the concepts of nested and nonnested hypotheses have been loosely defined, but for a more integrated approach to nonnested hypothesis testing and model selection a more formal definition …
