Identification of simultaneous equation models with measurement error

This paper establishes identification conditions for a simultaneous equation model in which some of the exogenous variables are measured with error. It is assumed that observational information is confined to the covariance matrix of the observed variables and that prior information on the structural coefficients and error variances takes the form of zero restrictions. The primary result is an easily-applied assignment condition for checking whether or not there are an adequate number and variety of prior restrictions to identify the structural parameters.     

Well-posedness of measurement error models for self-reported data

This paper considers the widely admitted ill-posed inverse problem for measurement error models: estimating the distribution of a latent variable $X^1$ from an observed sample of $X$, a contaminated measurement of $X^1$. We show that the inverse problem is well-posed for self-reporting data under the assumption that the probability of truthful reporting is nonzero, which is supported by empirical evidences. Comparing with ill-posedness, well-posedness generally can be translated into faster rates of convergence for the nonparametric estimators of the latent distribution. Therefore, our optimistic result on well-posedness is of importance in economic applications, and it suggests that researchers should not ignore the point mass at zero in the measurement error distribution when they model measurement errors with self-reported data. We also analyze the implications of our results on the estimation of classical measurement error models. Then by both a Monte Carlo study and an empirical application, we show that failing to account for the nonzero probability of truthful reporting can lead to significant bias on estimation of the latent distribution.     

Assessing the importance of measurement error in capital investment models

New developments in the economics of capital investment emphasize the role of financial variables. Econometric evidence on these hypotheses is potentially compromised by measurement error due to accounting conventions. The paper reviews new capital investment models and considers ways in which accounting procedures might lead to measurement error biases. Advances in errors-in-variables econometric models are employed to gauge the impact of measurement error on estimates of financial influences on capital investment. Cash-flow models appear to be especially susceptible to measurement error but q models seem fairly insensitive to measurement problems.     

Identification of simultaneous equation models with measurement error: a computerized evaluation

Rank conditions for identification in structural models are often difficult evaluate. Here we consider simultaneous equation models with measurement error and we show that previously published rank conditions for identification are not well-suited for evaluation. An alternative rank condition is derived and a computer algebra program is presented that takes care of both the construction and the computation of the rank of the relevant Jacobian matrix. It uses the parameter restrictions as input in order to characterize the identification situation of the individual parameters in the output.     

Maximum likelihood estimation of random effects models

Iterated GLS has a remarkable property when applied to the random effects model in its usual parameterization. The values for the parameter that measures relative variance, obtained through successive iterations, form a monotonic sequence. This property provides convenient checks for multiple maxima of the likelihood function and for existence of a local maximum that satisfies the non-negativity condition.     

Fixed and random effects models: making an informed choice

This paper assesses the options available to researchers analysing multilevel (including longitudinal) data, with the aim of supporting good methodological decision-making. Given the confusion in the literature about the key properties of fixed and random effects (FE and RE) models, we present these models’ capabilities and limitations. We also discuss the within-between RE model, sometimes misleadingly labelled a ‘hybrid’ model, showing that it is the most general of the three, with all the strengths of the other two. As such, and because it allows for important extensions—notably random slopes—we argue it should be used (as a starting point at least) in all multilevel analyses. We develop the argument through simulations, evaluating how these models cope with some likely mis-specifications. These simulations reveal that (1) failing to include random slopes can generate anti-conservative standard errors, and (2) assuming random intercepts are Normally distributed, when they are not, introduces only modest biases. These results strengthen the case for the use of, and need for, these models.

     

Variable selection for additive partially linear models with measurement error

Variable selection for additive partially linear models with measurement error is considered. By the backfitting technique, we first propose a variable selection procedure for the parametric components based on the smoothly clipped absolute deviation (SCAD) penalization, and one-step spare estimates for parametric components are also presented. The resulting estimates perform asymptotic normality as well as an oracle property. Then, two-stage backfitting estimators are also presented for the nonparametric components by using the local linear method, and the structures of asymptotic biases and covariances of the proposed estimators are the same as those in partially linear model with measurement error. The finite sample performance of the proposed procedures is illustrated by simulation studies.     

Measuring welfare effects in models with random coefficients

In economic research, it is often important to express the marginal value of a variable in monetary terms. In random coefficient models, this marginal monetary value is the ratio of two random coefficients and is thus random itself. In this paper, we study the distribution of this ratio and particularly the consequences of different distributional assumptions about the coefficients. It is shown that important characteristics of the distribution of the marginal monetary value may be sensitive to the distributional assumptions about the random coefficients. The median, however, is much less sensitive than the mean. Copyright © 2006 John Wiley & Sons, Ltd.     

A characterization of admissible linear estimators of fixed and random effects in linear models

In the paper the problem of simultaneous linear estimation of fixed and random effects in the mixed linear model is considered. A necessary and sufficient conditions for a linear estimator of a linear function of fixed and random effects in balanced nested and crossed classification models to be admissible are given.     

A note on autoregressive error components models

The purpose of this paper is to shed some light on the asymptotic behavior of a wide class of estimators for a dynamic error components model when only the number of individuals tends to infinity, the number of time periods being kept fixed. In particular, it is shown that this asymptotic behavior is highly dependent on the assumption about the initial observations and that it offers very good approximations to the small sample behavior of the various estimators under consideration.     

A semiparametric random effects approach to unobserved heterogeneity in count data models of organizational founding

The paper discusses a semiparametric random-effects approach to the problem of unobserved population heterogeneity in organizational research based on models for pooled cross-sectional time series count data. The analytical value of this approach rests in its ability to produce estimates of the structural parameters that do not depend on any specific assumption about the distribution of the heterogeneity components in the population. The practical value of the method proposed is illustrated in an empirical application to processes of organizational founding, and to the relation between density dependence and unobserved heterogeneity in spatially distributed organizational populations. The empirical evidence produced suggests that future studies of organizational founding at the population level will have to account for variation in observed as well as unmeasured (or unobservable) variables.     

Testing for random effects in panel models with spatially correlated disturbances

In the empirical analysis of panel data the Breusch–Pagan (BP) statistic has become a standard tool to infer on unobserved heterogeneity over the cross-section. Put differently, the test statistic is central to discriminate between the pooled regression and the random effects model. Conditional versions of the test statistic have been provided to immunize inference on unobserved heterogeneity against random time effects or patterns of spatial error correlation. Panel data models with spatially correlated error terms are typically set out under the presumption of some known adjacency matrix parameterizing the correlation structure up to a scaling factor. This paper delivers a bootstrap scheme to generate critical values for the BP statistic allowing robust inference under misspecification of the adjacency matrix. Moreover, asymptotic results are derived for the case of a finite cross-section and infinite time dimension. Finite sample simulations show that misspecification of spatial covariance features could lead to large size distortions, while the robust bootstrap procedure retains asymptotic validity.     

A link between random coefficient autoregressive models and some agent based models

An agent based model (ABM), where each agent makes decisions by using the sum of two signals, is proposed. The first is related to the fundamental information while the second comes from trader’s idiosyncratic noise. This model entails the switching between two groups called fundamentalist and noise traders. Additionally, if the price impact function is log-linear, then the dynamic of log asset prices belongs to the class of random coefficient autoregressive RCA(p) models, which are known to share important stylized facts of financial prices.     

A simple estimator for nonlinear error in variable models

We propose a simple estimator for nonlinear method of moment models with measurement error of the classical type when no additional data, such as validation data or double measurements, are available. We assume that the marginal distributions of the measurement errors are Laplace (double exponential) with zero means and unknown variances and the measurement errors are independent of the latent variables and are independent of each other. Under these assumptions, we derive simple revised moment conditions in terms of the observed variables. They are used to make inference about the model parameters and the variance of the measurement error. The results of this paper show that the distributional assumption on the measurement errors can be used to point identify the parameters of interest. Our estimator is a parametric method of moments estimator that uses the revised moment conditions and hence is simple to compute. Our estimation method is particularly useful in situations where no additional data are available, which is the case in many economic data sets. Simulation study demonstrates good finite sample properties of our proposed estimator. We also examine the performance of the estimator in the case where the error distribution is misspecified.     

Fixed effects instrumental variables estimation in correlated random coefficient panel data models

We provide a set of conditions sufficient for consistency of a general class of fixed effects instrumental variables (FE-IV) estimators in the context of a correlated random coefficient panel data model, where one ignores the presence of individual-specific slopes. We discuss cases where the assumptions are met and violated. Monte Carlo simulations verify that the FE-IV estimator of the population averaged effect performs notably better than other standard estimators, provided a full set of period dummies is included. We also propose a simple test of selection bias in unbalanced panels when we suspect the slopes may vary by individual.     

Average treatment effects for stayers with correlated random coefficient models of panel data

Correlated random coefficient (CRC) models provide a useful framework for estimating average treatment effects (ATE) with panel data by accommodating heterogeneous treatment effects and flexible patterns of selection. In their simplest form, they lead to the well-known difference-in-differences estimator. CRC models yield estimates of ATE for “movers” (i.e., cross-sectional units whose treatment status changed over time) while ATE for “stayers” (i.e., cross-sectional units who retained the same treatment status over time) are not identified. We study additional restrictions on selection into treatment that lead to the identification of ATE for stayers by an extrapolation from quantities identified by the CRC model. We discuss estimation and testing of the extrapolation's validity, then use our results to estimate the returns to agricultural technology adoption among maize farmers in Kenya.     

Estimating time variation in measurement error from data revisions: an application to backcasting and forecasting in dynamic models

Over time, economic statistics are refined. This implies that data measuring recent economic events are typically less reliable than older data. Such time variation in measurement error affects optimal forecasts. Measurement error, and its time variation, are of course unobserved. Our contribution is to show how estimates of these can be recovered from the variance of revisions to data using a behavioural model of the statistics agency. We illustrate the gains in forecasting performance from exploiting these estimates using a real‐time dataset on UK aggregate expenditure data. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimation of error variance in one-way random model

A preliminary-test estimator for the error variance in the one-way random model is considered. The optimum levels of significance for the preliminary test are obtained based on a regret function. A pooling procedure for estimating the error variance, based on weighting functions, is also considered. A comparison of these estimators is made.     

On the existence of maximum likelihood estimates in random effects models for clustered multivariate binary data

We consider a class of random effects models for clustered multivariate binary data based on the threshold crossing technique of a latent random vector. Components of this latent vector are assumed to have a Laird–Ware structure. However, in place of their Gaussian assumptions, any specified class of multivariate distribution is allowed for the random effects, and the error vector is allowed to have any strictly positive pdf. A well known member of this class of models is the multivariate probit model with random effects. We investigate sufficient and necessary conditions for the existence of maximum likelihood estimates for the location and the association parameters. Implications of our results are illustrated through some hypothetical examples.