Second-Generation RCMs
As previously noted, second-generation RCMs are concerned with relaxing the usual restrictions concerning the direct effects of explanatory variables on the explained variables, functional forms, measurement errors, and use of …
Sampling Theory Inference with Known Covariance Matrix
Writing y{ = x'в + eі so that all N observations are included yields the familiar matrix expression y = XP + e, (4.2) where y and e are of …
Solutions to the Measurement Error Problem
In Section 2, it was shown that in the linear regression model with measurement errors, the OLS estimators are biased and inconsistent. There is no "quick fix" since the inconsistency …
The Nature and Statistical Consequences of Collinearity
Consider first a linear regression model with two explanatory variables, У t = P1 + P2X2 + P3X3 + e, Assume that the errors are uncorrelated, with mean zero and …
Spatial stochastic process models
The most often used approach to formally express spatial autocorrelation is through the specification of a functional form for the spatial stochastic process (14.1) that relates the value of a …
Qualitative Response. Models
G. S. Maddala and A. Flores-Lagunes* 1 Introduction This chapter deals with regression models when the dependent variable is qualitative. There are many situations in economics where the dependent variable …
Computational matters
With the continuing increase in computer power it may appear strange to be concerned with computational matters. However, the need to use computationally intensive methods, such as the bootstrap, in …
Basic Elements of. Asymptotic Theory
Benedikt M. Potscher and Ingmar R. Prucha 1 Introduction Consider the estimation problem where we would like to estimate a parameter vector 0 from a sample Y1, ..., Yn. Let …
Methods for introducing inexact nonsample information
Economists usually bring general information about parameters to the estimation problem, but it is not like the exact restrictions discussed in the previous section. For example, we may know the …
Essentials of Count. Data Regression
A. Colin Cameron and Pravin K. Trivedi 1 Introduction In many economic contexts the dependent or response variable of interest (y) is a nonnegative integer or count which we wish …
Estimation of simultaneous equation sample selection model
A two-stage estimation method can be easily generalized for the estimation of a simultaneous equation model. Consider the linear simultaneous equation y* = y*B + xC + u, which can …
The Neyman-Pearson lemma and the Durbin-Watson test
The first formal specification test in econometrics, the Durbin-Watson (DW) (1950) test for autocorrelation in the regression model has its foundation in the UMP test principle via a theorem of …
The Gauss-Newton Regression
Associated with every nonlinear regression model is a somewhat nonstandard artificial regression which is probably more widely used than any other. Consider the univariate, nonlinear regression model yt = vt(P) …
Hypothesis Testing with Artificial Regressions
Artificial regressions like the GNR are probably employed most frequently for hypothesis testing. Suppose we wish to test a set of r equality restrictions on 9. Without loss of generality, …
The OPG Regression
By no means all interesting econometric models are regression models. It is therefore useful to see if artificial regressions other than the GNR exist for wide classes of models. One …
An Artificial Regression for GMM Estimation
Another useful artificial regression, much less well known than the OPG regression, is available for a class of models estimated by the generalized method of moments (GMM). Many such models …
Artificial Regressions and HETEROsKEDASTiciTy
Covariance matrices and test statistics calculated via the GNR (1.7), or via artificial regressions such as (1.35) and (1.36), are not asymptotically valid when the assumption that the error terms …
Double-Length Regressions
Up to this point, the number of observations for all the artificial regressions we have studied has been equal to n, the number of observations in the data. In some …
An Artificial Regression for Binary Response Models
For binary response models such as the logit and probit models, there exists a very simple artificial regression that can be derived as an extension of the Gauss - Newton …
General Hypothesis. Testing
Anil K. Bera and Gamini Premaratne* 1 Introduction The history of statistical hypothesis testing is, indeed, very long. Neyman and Pearson (1933) traced its origin to Bayes (1763). However, systematic …
A COMPANION TO THEORETICAL ECONOMETRICS
This is the first companion in econometrics. It covers 32 chapters written by international experts in the field. The emphasis of this companion is on "keeping things simple" so as …
Some Test Principles Suggested in the Statistics Literature
We start by introducing some notation and concepts. Suppose we have n independent observations y1, y2,..., yn on a random variable Y with density function f(y; 0), where 0 is …
Artificial Regressions
Russell Davidson and James G. MacKinnon 1 Introduction All popular nonlinear estimation methods, including nonlinear least squares (NLS), maximum likelihood (ML), and the generalized method of moments (GMM), yield estimators …
Neyman-Pearson generalized lemma and its applications
The lemma can be stated as follows: Let g1, g,..., gm, gm+1 be integrable functions and ф be a test function over S such that 0 < ф < 1, …
The Concept of an Artificial Regression
Consider a fully parametric, nonlinear model that is characterized by a parameter vector 0 which belongs to a parameter space 0 C R k and which can be estimated by …
