Parametric and semi-parametric estimation of the binary response model of labour market participation

This paper compares the familiar probit model with three semiparametric estimators of binary response models in an application to labour market participation of married women. This exercise is performed using two different cross-section data sets from Switzerland and Germany. For the Swiss data the probit specification cannot be rejected and the models yield similar results. In the German case the probit model is rejected, but the coefficient estimates do not vary substantially across the models. The predicted choice probabilities, however, differ systematically for a subset of the sample. The results of this paper indicate that more work is necessary on specification tests of semiparametric models and on simulations using these models.     

Conditional empirical likelihood estimation and inference for quantile regression models

This paper considers two empirical likelihood-based estimation, inference, and specification testing methods for quantile regression models. First, we apply the method of conditional empirical likelihood (CEL) by Kitamura et al. [2004. Empirical likelihood-based inference in conditional moment restriction models. Econometrica 72, 1667–1714] and Zhang and Gijbels [2003. Sieve empirical likelihood and extensions of the generalized least squares. Scandinavian Journal of Statistics 30, 1–24] to quantile regression models. Second, to avoid practical problems of the CEL method induced by the discontinuity in parameters of CEL, we propose a smoothed counterpart of CEL, called smoothed conditional empirical likelihood (SCEL). We derive asymptotic properties of the CEL and SCEL estimators, parameter hypothesis tests, and model specification tests. Important features are (i) the CEL and SCEL estimators are asymptotically efficient and do not require preliminary weight estimation; (ii) by inverting the CEL and SCEL ratio parameter hypothesis tests, asymptotically valid confidence intervals can be obtained without estimating the asymptotic variances of the estimators; and (iii) in contrast to CEL, the SCEL method can be implemented by some standard Newton-type optimization. Simulation results demonstrate that the SCEL method in particular compares favorably with existing alternatives.     

Goodness-of-fit tests based on series estimators in nonparametric instrumental regression

This paper proposes several tests of restricted specification in nonparametric instrumental regression. Based on series estimators, test statistics are established that allow for tests of the general model against a parametric or nonparametric specification as well as a test of exogeneity of the vector of regressors. The tests’ asymptotic distributions under correct specification are derived and their consistency against any alternative model is shown. Under a sequence of local alternative hypotheses, the asymptotic distributions of the tests are derived. Moreover, uniform consistency is established over a class of alternatives whose distance to the null hypothesis shrinks appropriately as the sample size increases. A Monte Carlo study examines finite sample performance of the test statistics.     

GMM estimation of social interaction models with centrality

This paper considers the specification and estimation of social interaction models with network structures and the presence of endogenous, contextual, correlated, and group fixed effects. When the network structure in a group is captured by a graph in which the degrees of nodes are not all equal, the different positions of group members as measured by the Bonacich (1987) centrality provide additional information for identification and estimation. In this case, the Bonacich centrality measure for each group can be used as an instrument for the endogenous social effect, but the number of such instruments grows with the number of groups. We consider the 2SLS and GMM estimation for the model. The proposed estimators are asymptotically efficient, respectively, within the class of IV estimators and the class of GMM estimators based on linear and quadratic moments, when the sample size grows fast enough relative to the number of instruments.     

Specification and testing of some modified count data models

This paper explores the specification and testing of some modified count data models. These alternatives permit more flexible specification of the data-generating process (dgp) than do familiar count data models (e.g., the Poisson), and provide a natural means for modeling data that are over- or underdispersed by the standards of the basic models. In the cases considered, the familiar forms of the distributions result as parameter-restricted versions of the proposed modified distributions. Accordingly, score tests of the restrictions that use only the easily-computed ML estimates of the standard models are proposed. The tests proposed by Hausman (1978) and White (1982) are also considered. The tests are then applied to count data models estimated using survey microdata on beverage consumption.     

Estimating Nested Count Data Models

Count data models have found a wide variety of applications not only in applied economics and finance but also in diverse fields ranging from biometrics to political science. Poisson and negative binomial (NB) models have been extensively used in count data analysis. Two particular NB model specifications, NBI and NBII, have been especially popular. However, these models impose arbitrary restrictions on the relation between the conditional mean and variance of the dependent variable, limiting their generality. This study proposes tests for selection among the Poisson and NB models by formally demonstrating that the log likelihood function (LLF) of a general NB model parametrically nests the LLF of the Poisson, NBI and NBII as testable special cases. It also proposes estimation of the general NB model since it allows greater flexibility in the relationship between the mean and variance of the dependent variable than NBI and NBII. The empirical application, which uses micro-level data on recreational boating, provides support for the paper's main theme. Tests clearly reject not only the Poisson, but also NBI and NBII, in favour of a different NB model, underscoring the importance of the general model specification.     

Description of purchase incidence by multivariate heterogeneous Poisson processes

In this paper the application of bivariate Poisson heterogeneous models to budget data is studied. This study was motivated from inconsistencies that we encountered when univariate Poisson based models were applied to cumulative data sets. Application of a multivariate Poisson based model is a possible solution to this problem. In this paper we will study the feasibility of estimators based on these models.     

Testing a linear dynamic panel data model against nonlinear alternatives

The most popular econometric models in the panel data literature are the class of linear panel data models with unobserved individual- and/or time-specific effects. The consistency of parameter estimators and the validity of their economic interpretations as marginal effects depend crucially on the correct functional form specification of the linear panel data model. In this paper, a new class of residual-based tests is proposed for checking the validity of dynamic panel data models with both large cross-sectional units and time series dimensions. The individual and time effects can be fixed or random, and panel data can be balanced or unbalanced. The tests can detect a wide range of model misspecifications in the conditional mean of a dynamic panel data model, including functional form and lag misspecification. They check a large number of lags so that they can capture misspecification at any lag order asymptotically. No common alternative is assumed, thus allowing for heterogeneity in the degrees and directions of functional form misspecification across individuals. Thanks to the use of panel data with large $N$ and $T$, the proposed nonparametric tests have an asymptotic normal distribution under the null hypothesis without requiring the smoothing parameters to grow with the sample sizes. This suggests better nonparametric asymptotic approximation for the panel data than for time series or cross sectional data. This is confirmed in a simulation study. We apply the new tests to test linear specification of cross-country growth equations and found significant nonlinearities in mean for OECD countries’ growth equation for annual and quintannual panel data.     

The Relative Performance of Poisson and Negative Binomial Regression Estimators

Negative binomial estimators are commonly used in estimating models with count‐data dependent variables. In this paper, sampling experiments are used to evaluate the performance of these estimators relative to the simpler Poisson estimator in finite‐sample situations. The results do not suggest a clear preference for negative binomial estimators in situations in which the underlying dependent variables are overdispersed, unless the researcher is comfortable in assumptions about the precise form of the overdispersion.     

Relative efficiencies of some simple Bayes estimators of coefficients in a dynamic equation with serially correlated errors - II

Generalized least squares estimators, with estimated variance-covariance matrices, and maximum likelihood estimators have been proposed in the literature to deal with the problem of estimating autoregressive models with autocorrelated disturbances. In this paper we compare the small sample efficiencies of these estimators with those of some approximate Bayes estimators. The comparison is done with the help of a sampling experiment applied to a model specification. Though these Bayes estimators utilize very weak prior information, they out-perform the sampling theory estimators in every case we consider.     

Instrumental variable estimation based on grouped data

The paper considers the estimation of the coefficients of a single equation in the presence of dummy intruments. We derive pseudo ML and GMM estimators based on moment restrictions induced either by the structural form or by the reduced form of the model. The performance of the estimators is evaluated for the non-Gaussian case. We allow for heteroscedasticity. The asymptotic distributions are based on parameter sequences where the number of instruments increases at the same rate as the sample size. Relaxing the usual Gaussian assumption is shown to affect the normal asymptotic distributions. As a result also recently suggested new specification tests for the validity of instruments depend on Gaussianity. Monte Carlo simulations confirm the accuracy of the asymptotic approach.     

Model specification tests: A simultaneous approach

In econometrics, specification tests have been constructed to verify the validity of one specification at a time. It is argued that most of these tests are not, in general, robust in the presence of other misspecifications, so their application may result in misleading conclusions. Using the Lagrange Multiplier principle we develop efficient test procedures that are capable of testing a number of specifications simultaneously. These tests will ‘confirm’ the validity (or invalidity) of a general model requiring the estimates of the restricted model only. Through an extensive Monte Carlo experiment we study the performance of these tests and some commonly used one-directional tests. We also suggest a Multiple Comparison Procedure, to identify different sources of errors. This, we hope, will lead to a better specification of econometric models.     

Cross-sectional tests of asset pricing models with full-rank mimicking portfolios

In the standard tests of asset pricing models, factor risk premia are estimated on a test asset span so that models are tested with degrees of freedom reduced by the number of factors. Risk premia of traded factors can be further restricted to be equal to their expected returns, but such restrictions cannot be imposed on models with nontraded factors, which may create a problem of testing without full restrictions or on unequal asset spans across models. We propose a full-rank mimicking portfolio approach by projecting nontraded factors onto a combined span of test assets and benchmark traded factors. Under the Hansen-Jagannathan distance framework, we demonstrate that full-rank mimicking portfolios can provide improved power and fair performance comparison against a benchmark model in both specification and model comparison tests.     

Maximum likelihood estimation and Lagrange multiplier tests for panel seemingly unrelated regressions with spatial lag and spatial errors: An application to hedonic housing prices in Paris

This paper proposes maximum likelihood estimators for panel seemingly unrelated regressions with both spatial lag and spatial error components. We study the general case where spatial effects are incorporated via spatial errors terms and via a spatial lag dependent variable and where the heterogeneity in the panel is incorporated via an error component specification. We generalize the approach of Wang and Kockelman (2007) and propose joint and conditional Lagrange multiplier tests for spatial autocorrelation and random effects for this spatial SUR panel model. The small sample performance of the proposed estimators and tests are examined using Monte Carlo experiments. An empirical application to hedonic housing prices in Paris illustrate these methods. The proposed specification uses a system of three SUR equations corresponding to three types of flats within 80 districts of Paris over the period 1990-2003. We test for spatial effects and heterogeneity and find reasonable estimates of the shadow prices for housing characteristics.     

Estimation with overidentifying inequality moment conditions

This paper derives limit distributions of empirical likelihood estimators for models in which inequality moment conditions provide overidentifying information. We show that the use of this information leads to a reduction of the asymptotic mean-squared estimation error and propose asymptotically uniformly valid tests and confidence sets for the parameters of interest. While inequality moment conditions arise in many important economic models, we use a dynamic macroeconomic model as a data generating process and illustrate our methods with instrumental variable estimators of monetary policy rules. The results obtained in this paper extend to conventional GMM estimators.     

Exact permutation tests for non-nested non-linear regression models

This paper proposes exact distribution-free permutation tests for the specification of a non-linear regression model against one or more possibly non-nested alternatives. The new tests may be validly applied to a wide class of models, including models with endogenous regressors and lag structures. These tests build on the well-known J test developed by Davidson and MacKinnon [1981. Several tests for model specification in the presence of alternative hypotheses. Econometrica 49, 781–793] and their exactness holds under broader assumptions than those underlying the conventional J test. The J-type test statistics are used with a randomization or Monte Carlo resampling technique which yields an exact and computationally inexpensive inference procedure. A simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions. The test procedure developed is illustrated by an application to inflation dynamics.     

Seemingly Unrelated Negative Binomial Regression

This paper discusses the specification and estimation of seemingly unrelated multivariate count data models. A new model with negative binomial marginals is proposed. In contrast to a previous model based on the multivariate Poisson distribution, the new model allows for over-dispersion, a phenomenon that is frequently encountered in economic count data. Semi-parametric estimation is possible if some of the assumption of the fully specified model are violated.     

Forecasting economic time series using flexible versus fixed specification and linear versus nonlinear econometric models

Nine macroeconomic variables are forecast in a real-time scenario using a variety of flexible specification, fixed specification, linear, and nonlinear econometric models. All models are allowed to evolve through time, and our analysis focuses on model selection and performance. In the context of real-time forecasts, flexible specification models (including linear autoregressive models with exogenous variables and nonlinear artificial neural networks) appear to offer a useful and viable alternative to less flexible fixed specification linear models for a subset of the economic variables which we examine, particularly at forecast horizons greater than 1-step ahead. We speculate that one reason for this result is that the economy is evolving (rather slowly) over time. This feature cannot easily be captured by fixed specification linear models, however, and manifests itself in the form of evolving coefficient estimates. We also provide additional evidence supporting the claim that models which ‘win’ based on one model selection criterion (say a squared error measure) do not necessarily win when an alternative selection criterion is used (say a confusion rate measure), thus highlighting the importance of the particular cost function which is used by forecasters and ‘end-users’ to evaluate their models. A wide variety of different model selection criteria and statistical tests are used to illustrate our findings.     

A model of labour supply with job offer restrictions

We specify a model of labour supply with job offer restrictions. A job offer is defined by a wage rate and working hours. The number of job offers is restricted, and follows a Poisson distribution. Individuals choose the alternative with the highest utility level. Three specifications are estimated: a basic specification, a specification in which the number of job offers depends on characteristics, and a specification in which the wage rate depends on working hours. Although the properties of the sample distribution of hours observed are replicated well for all of the specifications, the implications for the underlying behaviour are different.     

Partial rank estimation of duration models with general forms of censoring

In this paper we propose estimators for the regression coefficients in censored duration models which are distribution free, impose no parametric specification on the baseline hazard function, and can accommodate general forms of censoring. The estimators are shown to have desirable asymptotic properties and Monte Carlo simulations demonstrate good finite sample performance. Among the data features the new estimators can accommodate are covariate-dependent censoring, double censoring, and fixed (individual or group specific) effects. We also examine the behavior of the estimator in an empirical illustration.