GMM Estimation with Non‐causal Instruments under Rational Expectations*

Lanne and Saikkonen [Oxford Bulletin of Economics and Statistics (2011a) Vol. 73, pp. 581–592], show that the generalized method of moments (GMM) estimator is inconsistent, when the instruments are lags of variables that admit a non‐causal autoregressive representation. This article argues that this inconsistency depends on distributional assumptions, that do not always hold. In particular under rational expectations, the GMM estimator is found to be consistent. This result is derived in a linear context and illustrated by simulation of a nonlinear asset pricing model.     

THE ROLE OF CONDITIONAL HETEROSKEDASTICITY IN IDENTIFYING AND ESTIMATING LINEAR TRIANGULAR SYSTEMS,WITH APPLICATIONS TO ASSET PRICING MODELS THAT INCLUDE A MISMEASURED FACTOR

A new estimator is proposed for linear triangular systems, where identification results from the model errors following a bivariate and diagonal GARCH(1,1) process with potentially time‐varying error covariances. This estimator applies when traditional instruments are unavailable. I demonstrate its usefulness on asset pricing models like the capital asset pricing model and Fama–French three‐factor model. In the context of a standard two‐pass cross‐sectional regression approach, this estimator improves the pricing performance of both models. Set identification bounds and an associated estimator are also provided for cases where the conditions supporting point identification fail. Copyright © 2013 John Wiley & Sons, Ltd.     

ENDOGENEITY IN COUNT DATA MODELS: AN APPLICATION TO DEMAND FOR HEALTH CARE

The generalized method of moments (GMM) estimation technique is discussed for count data models with endogenous regressors. Count data models can be specified with additive or multiplicative errors. It is shown that, in general, a set of instruments is not orthogonal to both error types. Simultaneous equations with a dependent count variable often do not have a reduced form which is a simple function of the instruments. However, a simultaneous model with a count and a binary variable can only be logically consistent when the system is triangular. The GMM estimator is used in the estimation of a model explaining the number of visits to doctors, with as a possible endogenous regressor a self-reported binary health index. Further, a model is estimated, in stages, that includes latent health instead of the binary health index. © 1997 John Wiley & Sons, Ltd.     

GMM with Multiple Missing Variables

We consider efficient estimation in moment conditions models with non‐monotonically missing‐at‐random (MAR) variables. A version of MAR point‐identifies the parameters of interest and gives a closed‐form efficient influence function that can be used directly to obtain efficient semi‐parametric generalized method of moments (GMM) estimators under standard regularity conditions. A small‐scale Monte Carlo experiment with MAR instrumental variables demonstrates that the asymptotic superiority of these estimators over the standard methods carries over to finite samples. An illustrative empirical study of the relationship between a child's years of schooling and number of siblings indicates that these GMM estimators can generate results with substantive differences from standard methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Indirect inference for dynamic panel models

Maximum likelihood (ML) estimation of the autoregressive parameter of a dynamic panel data model with fixed effects is inconsistent under fixed time series sample size and large cross section sample size asymptotics. This paper proposes a general, computationally inexpensive method of bias reduction that is based on indirect inference, shows unbiasedness and analyzes efficiency. Monte Carlo studies show that our procedure achieves substantial bias reductions with only mild increases in variance, thereby substantially reducing root mean square errors. The method is compared with certain consistent estimators and is shown to have superior finite sample properties to the generalized method of moment (GMM) and the bias-corrected ML estimator.     

Regression Discontinuity Applications with Rounding Errors in the Running Variable

Many empirical applications of regression discontinuity (RD) models use a running variable that is rounded and hence discrete, e.g. age in years, or birth weight in ounces. This paper shows that standard RD estimation using a rounded discrete running variable leads to inconsistent estimates of treatment effects, even when the true functional form relating the outcome and the running variable is known and is correctly specified. This paper provides simple formulas to correct for this discretization bias. The proposed approach does not require instrumental variables, but instead uses information regarding the distribution of rounding errors, which is easily obtained and often close to uniform. Bounds can be obtained without knowing the distribution of the rounding error. The proposed approach is applied to estimate the effect of Medicare on insurance coverage in the USA, and to investigate the retirement‐consumption puzzle in China, utilizing the Chinese mandatory retirement policy. Copyright © 2014 John Wiley & Sons, Ltd.     

Exact computation of GMM estimators for instrumental variable quantile regression models

We show that the generalized method of moments (GMM) estimation problem in instrumental variable quantile regression (IVQR) models can be equivalently formulated as a mixed‐integer quadratic programming problem. This enables exact computation of the GMM estimators for the IVQR models. We illustrate the usefulness of our algorithm via Monte Carlo experiments and an application to demand for fish.     

Residual‐based IV estimation of dynamic panel data models with fixed effects

In dynamic panel regression, when the variance ratio of individual effects to disturbance is large, the system‐GMM estimator will have large asymptotic variance and poor finite sample performance. To deal with this variance ratio problem, we propose a residual‐based instrumental variables (RIV) estimator, which uses the residual from regressing Δy_i,t?1 on as the instrument for the level equation. The RIV estimator proposed is consistent and asymptotically normal under general assumptions. More importantly, its asymptotic variance is almost unaffected by the variance ratio of individual effects to disturbance. Monte Carlo simulations show that the RIV estimator has better finite sample performance compared to alternative estimators. The RIV estimator generates less finite sample bias than difference‐GMM, system‐GMM, collapsing‐GMM and Level‐IV estimators in most cases. Under RIV estimation, the variance ratio problem is well controlled, and the empirical distribution of its t‐statistic is similar to the standard normal distribution for moderate sample sizes.     

Regression Models with Data‐based Indicator Variables*

Ordinary least squares estimation of an impulse‐indicator coefficient is inconsistent, but its variance can be consistently estimated. Although the ratio of the inconsistent estimator to its standard error has a t‐distribution, that test is inconsistent: one solution is to form an index of indicators. We provide Monte Carlo evidence that including a plethora of indicators need not distort model selection, permitting the use of many dummies in a general‐to‐specific framework. Although White's (1980) heteroskedasticity test is incorrectly sized in that context, we suggest an easy alteration. Finally, a possible modification to impulse ‘intercept corrections’ is considered.     

Straight-line models in star-shaped mixtures

Normal-theory inferences are validated in part for straight-line models having star-contoured errors. Adverse effects for the intercept include inconsistent estimation and disturbances in levels of the standard tests. Tests for slope remain exact in level; they are unbiased; and their power through mixing typically dominates the standard Gaussian case. Bounds on level, and envelopes for power curves, are given for certain ensembles and mixtures of distributions, and these are evaluated numerically for selected cases. Effects of mixtures on model diagnostics are examined further.     

The method of elimination and substitution in the GMM estimation of mixed regressive,spatial autoregressive models

This paper proposes a computationally simple GMM for the estimation of mixed regressive spatial autoregressive models. The proposed method explores the advantage of the method of elimination and substitution in linear algebra. The modified GMM approach reduces the joint (nonlinear) estimation of a complete vector of parameters into estimation of separate components. For the mixed regressive spatial autoregressive model, the nonlinear estimation is reduced to the estimation of the (single) spatial effect parameter. We identify situations under which the resulting estimator can be efficient relative to the joint GMM estimator where all the parameters are jointly estimated.     

Evaluating asset‐pricing models using the Hansen–Jagannathan bound: a Monte Carlo investigation

We use recent statistical tests, based on a ‘distance’ between the model and the Hansen–Jagannathan bound, to compute the rejection rates of true models. For asset‐pricing models with time‐separable preferences, the finite‐sample distribution of the test statistic associated with the risk‐neutral case is extreme, in the sense that critical values based on this distribution deliver type I errors no larger than intended—regardless of risk aversion or the rate of time preference. We also show that these maximal‐type‐I‐error critical values are appropriate for both time and state non‐separable preferences and that they yield acceptably small type II error rates. Copyright © 2002 John Wiley & Sons, Ltd.     

Feasible estimation of firm‐specific allocative inefficiency through Bayesian numerical methods

Both the theoretical and empirical literature on the estimation of allocative and technical inefficiency has grown enormously. To minimize aggregation bias, ideally one should estimate firm and input‐specific parameters describing allocative inefficiency. However, identifying these parameters has often proven difficult. For a panel of Chilean hydroelectric power plants, we obtain a full set of such parameters using Gibbs sampling, which draws sequentially from conditional generalized method of moments (GMM) estimates obtained via instrumental variables estimation. We find an economically significant range of firm‐specific efficiency estimates with differing degrees of precision. The standard GMM approach estimates virtually no allocative inefficiency for industry‐wide parameters. Copyright © 2009 John Wiley & Sons, Ltd.     

Weak Identification of Forward‐looking Models in Monetary Economics*

Recently, single‐equation estimation by the generalized method of moments (GMM) has become popular in the monetary economics literature, for estimating forward‐looking models with rational expectations. We discuss a method for analysing the empirical identification of such models that exploits their dynamic structure and the assumption of rational expectations. This allows us to judge the reliability of the resulting GMM estimation and inference and reveals the potential sources of weak identification. With reference to the New Keynesian Phillips curve of Galí and Gertler [Journal of Monetary Economics (1999) Vol. 44, 195] and the forward‐looking Taylor rules of Clarida, Galí and Gertler [Quarterly Journal of Economics (2000) Vol. 115, 147], we demonstrate that the usual ‘weak instruments’ problem can arise naturally, when the predictable variation in inflation is small relative to unpredictable future shocks (news). Hence, we conclude that those models are less reliably estimated over periods when inflation has been under effective policy control.     

GMM Estimation with Non‐causal Instruments*

This note provides a warning against careless use of the generalized method of moments (GMM) with time series data. We show that if time series follow non‐causal autoregressive processes, their lags are not valid instruments, and the GMM estimator is inconsistent. Moreover, endogeneity of the instruments may not be revealed by the J‐test of overidentifying restrictions that may be inconsistent and has, in general, low finite‐sample power. Our explicit results pertain to a simple linear regression, but they can easily be generalized. Our empirical results indicate that non‐causality is quite common among economic variables, making these problems highly relevant.     

Land of addicts? an empirical investigation of habit‐based asset pricing models

This paper studies the ability of a general class of habit‐based asset pricing models to match the conditional moment restrictions implied by asset pricing theory. We treat the functional form of the habit as unknown, and estimate it along with the rest of the model's finite dimensional parameters. Using quarterly data on consumption growth, assets returns and instruments, our empirical results indicate that the estimated habit function is nonlinear, that habit formation is better described as internal rather than external, and the estimated time‐preference parameter and the power utility parameter are sensible. In addition, the estimated habit function generates a positive stochastic discount factor (SDF) proxy and performs well in explaining cross‐sectional stock return data. We find that an internal habit SDF proxy can explain a cross‐section of size and book‐market sorted portfolio equity returns better than (i) the Fama and French ( 1993 ) three‐factor model, (ii) the Lettau and Ludvigson ( 2001b ) scaled consumption CAPM model, (iii) an external habit SDF proxy, (iv) the classic CAPM, and (v) the classic consumption CAPM. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimating and Forecasting with a Dynamic Spatial Panel Data Model*

This study focuses on the estimation and predictive performance of several estimators for the dynamic and autoregressive spatial lag panel data model with spatially correlated disturbances. In the spirit of Arellano and Bond (1991) and Mutl (2006) , a dynamic spatial generalized method of moments (GMM) estimator is proposed based on Kapoor, Kelejian and Prucha (2007) for the spatial autoregressive (SAR) error model. The main idea is to mix non‐spatial and spatial instruments to obtain consistent estimates of the parameters. Then, a linear predictor of this spatial dynamic model is derived. Using Monte Carlo simulations, we compare the performance of the GMM spatial estimator to that of spatial and non‐spatial estimators and illustrate our approach with an application to new economic geography.     

Heteroskedasticity-robust semi-parametric GMM estimation of a spatial model with space-varying coefficients

Heteroskedasticity-robust semi-parametric GMM estimation of a spatial model with space-varying coefficients. Spatial Economic Analysis. The spatial model with space-varying coefficients proposed by Sun et al. in 2014 has proved to be useful in detecting the location effects of the impacts of covariates as well as spatial interaction in empirical analysis. However, Sun et al.’s estimator is inconsistent when heteroskedasticity is present – a circumstance that is more realistic in certain applications. In this study, we propose a kind of semi-parametric generalized method of moments (GMM) estimator that is not only heteroskedasticity robust but also takes a closed form written explicitly in terms of observed data. We derive the asymptotic distributions of our estimators. Moreover, the results of Monte Carlo experiments show that the proposed estimators perform well in finite samples.     

Codependence in cointegrated autoregressive models

This paper investigates codependent cycles, i.e., transitory components that react to common stimuli in a similar, although not necessarily synchronous fashion. Unlike previous studies, the methodology of this paper allows FIML estimation of the restricted VAR/VECM and therefore the extraction of the unobserved codependent cyclical components via a Beveridge‐Nelson decomposition. It is further shown that the number and order of cofeature combinations that yield the scalar component models associated with codependence is limited by the dimension of a finite‐order VAR system. Monte Carlo simulations indicate that LR tests based on FIML estimates have higher power than alternative GMM and canonical correlations tests, while maintaining good size properties. An empirical application investigates the presence of codependence in UK consumption data. Copyright © 2007 John Wiley & Sons, Ltd.     

GMM estimators with improved finite sample properties using principal components of the weighting matrix,with an application to the dynamic panel data model

GMM estimators have poor finite sample properties in highly overidentified models. With many moment conditions the optimal weighting matrix is poorly estimated. We suggest using principal components of the weighting matrix. This effectively drops some of the moment conditions. Our simulations, done in the context of the dynamic panel data model, show that the resulting GMM estimator has better finite sample properties than the usual two-step GMM estimator, in the sense of smaller bias and more reliable standard errors.