Capital adjustment cost and inconsistency in income‐based dynamic panel models with fixed effects

After the seminal work of Nickell (1981), a vast literature demonstrates the inconsistency of ‘conditional convergence’ estimator in income‐based dynamic panel models with fixed effects when the time horizon (T) is short but the sample of countries (N) is large. Less attention is given to the economic root of inconsistency of the fixed effects estimator when T is also large. Using a variant of the Ramsey growth model with long‐run adjustment cost of capital, we demonstrate that the fixed effects estimator of such models could be inconsistent when T is large. This inconsistency arises because of the long‐run adjustment cost of capital which gives rise to a negative moving average coefficient in the error term. Income convergence will be thus overestimated. We theoretically characterize the order of this inconsistency. Our Monte Carlo simulation demonstrates that the size of the bias is substantial and it is greater in economies with higher capital adjustment costs. We show that the use of instrumental variables that take into account the presence of the negative moving average term in the error will overcome this bias.     

Hierarchically spatial autoregressive and moving average error model

This paper considers a hierarchically spatial autoregressive and moving average error (HSEARMA) model. This model captures the spatially autoregressive and moving average error correlation, the county-level random effects, and the district-level random effects nested within each county. We propose optimal generalized method of moments (GMM) estimators for the spatial error correlation coefficient and the error components' variances terms, as well as a feasible generalized least squares (FGLS) estimator for the regression parameter vector. Further, we prove consistency of the GMM estimator and establish the asymptotic distribution of the FGLS estimator. A finite-scale Monte Carlo simulation is conducted to demonstrate the good finite sample performances of our GMM-FGLS estimators.     

EFFICIENCY GAINS OF SYSTEM GMM AND MDE OVER INDIVIDUAL EQUATION ESTIMATION*

In the econometric literature it is known that, under certain conditions, estimating a system of equations together is more efficient than estimating each equation separately. This finding has been proved, however, only under the assumption of a known parametric form of heteroskedasticity (including homoskedasticity) or non‐random regressors/instruments. This note shows that an analogous finding holds for GMM under heteroskedasticity of unknown form and random regressors/instruments. Specifically, I provide a necessary condition for the efficiency gain of the system GMM over the single‐equation GMM. An analogous necessary condition for the efficiency gain is also shown to hold for minimum‐distance (or χ2) estimation (MDE).     

The extent of the market and stages of agricultural specialization

Abstract This paper provides empirical evidence of an U‐shaped causal relationship between the extent of the market (size of the relevant urban market) and the pattern of crop specialization in a village economy. We use the recent two‐stage estimator developed by Lewbel (2012) and exploit heteroscedasticity for identification. The results suggest that the portfolio of crops in a village economy becomes more diversified initially as the extent of the market increases. However, after the market size reaches a threshold, the production structure starts to specialize again. This evidence on the stages of agricultural diversification is consistent with the stages of diversification identified in the recent literature for the economy as a whole and also for the manufacturing sector.     

The non-monotonicity of the bias and mean squared error of the two stage least squares estimators of exogenous variable coefficients

Owen (1976) [Owen, A.D., 1976. A proof that both the bias and mean squared error of the two stage least squares estimator are monotonically non-increasing functions of sample size. Econometrica 44, 409–411.] has shown that in a two equation static simultaneous equation model both the bias and mean squared error of the two stage least squares estimator of the endogenous variable coefficient are monotonically non-increasing functions of the sample size. This paper shows that neither property carries over to the exogenous variable coefficient estimator.     

The participation decision versus the level of participation in an environmental treaty: a spatial probit analysis

This paper represents treaty participation as a two-stage game, for which nations first decide whether or not to participate and then they choose their level of participation. The resulting subgame perfect equilibrium is used to derive a reduced-form equation for estimating and separating the influences of the variables at the two decision stages. This spatial probit equation forms the basis for a full-information maximum likelihood estimator that accounts for the simultaneity bias associated with public good spillins at both stages. When the procedure is applied to the Helsinki Protocol, we find that the strategic influence of a variable may drastically differ depending upon which stage is scrutinized.     

RIDGE ESTIMATORS FOR PROBIT REGRESSION: WITH AN APPLICATION TO LABOUR MARKET DATA

In this paper we propose ridge regression estimators for probit models since the commonly applied maximum likelihood (ML) method is sensitive to multicollinearity. An extensive Monte Carlo study is conducted where the performance of the ML method and the probit ridge regression (PRR) is investigated when the data are collinear. In the simulation study we evaluate a number of methods of estimating the ridge parameter k that have recently been developed for use in linear regression analysis. The results from the simulation study show that there is at least one group of the estimators of k that regularly has a lower mean squared error than the ML method for all different situations that have been evaluated. Finally, we show the benefit of the new method using the classical Dehejia and Wahba dataset which is based on a labour market experiment.     

In-house R&D,external R&D and cooperation breadth in Spanish manufacturing firms: is there a synergistic effect on innovation outputs?

ABSTRACT

This study explores the nature of relationship between in-house R&D, external R&D and cooperation breadth and their joint impact on patent counts as well as technological, product and process, innovations in Spanish manufacturing firms. With regards to patent counts, empirical findings from a Generalized Method of Moments (GMM) estimator suggest a complementarity effect of internal and external R&D activities conditional on the breadth of R&D cooperation. Concerning technological innovation, results from dynamic random-effects probit models indicate no synergistic effects. In addition, we find evidence of persistence of all three innovation output measures. Our results suggest policy implications in relation to strengthening firms’ absorptive capacity that could have long-run effects.     

Engineering robust instruments for GMM estimation of panel data regression models with errors in variables: a note

Econometricians have long recognized the need to account in some way for measurement errors, specification errors and endogeneity to ensure that the ordinary least squares estimator is consistent. This article introduces a new generalized method of moments estimator that relies on robust instruments to estimate panel data regression models containing errors in variables. We show how this GMM approach can be generalized for the panel data framework using higher moments and cumulants as instruments. The new instruments, engineered for greater robustness, are proposed to tackle the pervasive problem of weak instruments.     

A generalized method of moments estimator for a spatial model with moving average errors, with application to real estate prices

This paper proposes a new GMM estimator for spatial regression models with moving average errors. Monte Carlo results are given which suggest that the GMM estimates are consistent and robust to non-normality, and the Bootstrap method is suggested as a way of testing the significance of the moving average parameter. The estimator is applied in a model of English real estate prices, in which the concepts of displaced demand and displaced supply are introduced to derive the spatial lag of prices, and the moving average error process represents spatially autocorrelated unmodelled variables.      

INTER‐TEMPORAL LABOUR FORCE PARTICIPATION AMONG MARRIED WOMEN IN JAPAN*

This paper investigates the components that affect inter‐temporal labour force participation among married women in Japan. We estimate linear probability models and simple, dynamic probit models with a variety of specifications. We find that serially correlated transitory errors have a significant effect on the participation behaviour of married women, while the first‐order lagged dependent variable has no significant effect. The result that serially correlated transitory errors influence married women's inter‐temporal labour force participation suggests that exogenous rather than endogenous causes have a significant effect on long‐term economic disparity among married women.     

MACROECONOMIC POLICY REFORMS AND PRODUCTIVITY GROWTH IN AFRICAN AGRICULTURE

This article employs a two‐stage procedure to investigate the impact of macroeconomic policy reforms on the agricultural productivity growth of 33 African countries from 1981 to 2001. In the first stage, we measure agricultural productivity using a nonparametric Malmquist productivity index. In the second stage, we build a generalized method of moments (GMM) model with a measure of structural adjustment program (SAP) intensity as a key instrument for macroeconomic policy reforms. We also control for the effects of globalization, civil violence, level of development of physical and financial infrastructure, and other economic variables as well as natural resource factors that directly affect agricultural productivity. Our results indicate a strong positive correlation between the extent of SAP intensity and agricultural productivity, suggesting that the macroeconomic policy reforms improved agricultural productivity growth in the sample countries. (JEL E6, O13, O41)     

Convenient estimators for the panel probit model: Further results

Bertschek and Lechner (1998) propose several variants of a GMM estimator based on the period specific regression functions for the panel probit model. The analysis is motivated by the complexity of maximum likelihood estimation and the possibly excessive amount of time involved in maximum simulated likelihood estimation. But, for applications of the size considered in their study, full likelihood estimation is actually straightforward, and resort to GMM estimation for convenience is unnecessary. In this note, we reconsider maximum likelihood based estimation of their panel probit model then examine some extensions which can exploit the heterogeneity contained in their panel data set. Empirical results are obtained using the data set employed in the earlier study. Helpful comments and suggestions by Irene Bertschek and Michael Lechner are gratefully acknowledged. This paper has also benefited from comments by two anonymous referees and from seminar participants at the Center for Health Economics at the University of York. Any remaining errors are the responsibility of the author.     

A Monte Carlo study of growth regressions

Using Monte Carlo simulations, this paper evaluates the bias properties of estimators commonly used to estimate growth regressions derived from the Solow model. We explicitly allow for measurement error, country-specific fixed effects and regressor endogeneity. An OLS estimator applied to a single cross-section of variables averaged over time (the between estimator) performs best in terms of the extent of bias on each of the estimated coefficients. Fixed-effects and the Arellano–Bond GMM estimator overstate the speed of convergence under a wide variety of assumptions, while the between estimator understates it. Finally, fixed effects and Arellano–Bond bias towards zero the slope estimates on the human and physical capital accumulation variables, while the between estimator and the Blundell–Bond system GMM estimator bias these coefficients upwards.      

SIMULATED MAXIMUM LIKELIHOOD ESTIMATION BASED ON FIRST‐ORDER CONDITIONS*

I describe a strategy for structural estimation that uses simulated maximum likelihood (SML) to estimate the structural parameters appearing in a model's first‐order conditions (FOCs). Generalized method of moments (GMM) is often the preferred method for estimation of FOCs, as it avoids distributional assumptions on stochastic terms, provided all structural errors enter the FOCs additively, giving a single composite additive error. But SML has advantages over GMM in models where multiple structural errors enter the FOCs nonadditively. I develop new simulation algorithms required to implement SML based on FOCs, and I illustrate the method using a model of U.S. multinational corporations.     

Grouped coefficients to reduce bias in heterogeneous dynamic panel models with small T

We propose the grouped coefficients estimator to reduce bias in dynamic panels with small T that have a multilevel structure to the coefficient and factor loading heterogeneity. If groups are chosen such that the within-group heterogeneity is small, then the grouped coefficients estimator can lead to substantial bias reduction compared to pooled GMM dynamic panel estimators. We also propose using a Wald test that can be used to assess whether pooled estimators suffer from heterogeneity bias. We illustrate the usefulness of grouped coefficients with an application to labour demand in which the coefficients are grouped by sub-sector. Our results suggest that the standard pooled estimates are substantially biased.     

Nonparametric methods for estimating and testing for constant betas in asset pricing models

In this article, we study the performance of a smoothing spline method in estimating and testing for constant betas in two well-known asset pricing models, the usual market model and the three-factor model. The spline estimator is computed taking into account the conditional heteroscedasticity of the errors. Using the right model and estimation procedure for the variance term plays a crucial role in gaining efficiency in beta estimators. A simulation study shows the good performance of our method; in all the scenarios simulated, it outperforms the benchmark rolling estimator. The method enables users to obtain confidence intervals and to test for the significance and constancy of betas. Finally, the method is applied to US data, comprising 25 portfolios formed based on size and the ratio of book equity to market equity. The results show that the time-variability of the betas plays an important role, mainly when sensitivity to the HML factor is considered.     

The Impact of Inequality and Redistribution on Growth

In this paper, we reassess the impact of inequality on growth. The majority of previous papers have employed (system) GMM estimation. However, recent simulation studies indicate that the problems of GMM when using non‐stationary data such as GDP have been grossly underestimated in applied research. Concerning predetermined regressors such as inequality, GMM is outperformed by a simple least‐squares dummy variable estimator. Additionally, new data have recently become available that not only double the sample size compared to most previous studies, but also address the substantial measurement issues that have plagued past research. Using these new data and an LSDV estimator, we provide an analysis that both accounts for the conditions where inequality is beneficial or detrimental to growth and distinguishes between market‐driven inequality and redistribution. We show that there are situations where market inequality affects growth positively while redistribution is simultaneously beneficial.     

ENGLE AND YOO THREE STEP ESTIMATION OF CONSUMERS' EXPENDITURE AND HOUSING EQUITY WITHDRAWAL

This paper reports a substantive application of Engle and Yoo's three-step estimator for cointegrated systems. Their estimator was proposed as a computationally convenient alternative to a number of FIML systems estimators. In part this estimator was developed to overcome some drawbacks of the OLS estimator of the first stage Engle-Granger cointegrating regression which, despite its widespread use, is not asymptotically efficient and does not provide (even) asympototically correct ' t ' statistics. Our application, which is of interest in its own right, is to an explanation of expenditure on nondurables and services in the UK. In formulating an empirical explanation for this variable we find it necessary to extend our framework to consider a system of dynamic error correction equations with feedbacks — or error correction mechanisms — from consumption and housing equity withdrawal.     

Unit Root Tests for Dependent Micropanels

This paper proposes a new test for the null hypothesis of panel unit roots for micropanels with short time dimensions (T) and large cross‐sections (N). There are several distinctive features of this test. First, the test is based on a panel AR(1) model allowing for cross‐sectional dependency, which is introduced by a factor structure of the initial condition. Second, the test employs the panel AR(1) model with AR(1) coefficients that are heterogeneous for finite N. Third, the test can be used both for the alternative hypothesis of stationarity and for that of explosive roots. Fourth, the test does not use the AR(1) coefficient estimator. The effectiveness of the test rests on the fact that the initial condition has permanent effects on the trajectory of a time series in the presence of a unit root. To measure the effects of the initial condition, the present paper employs cross‐sectional regressions using the first time‐series observations as a regressor and the last as a dependent variable. If there is a unit root in every individual time series, the coefficient of the regressor is equal to one. The t‐ratios for the coefficient are this paper's test statistics and have a standard normal distribution in the limit. The t‐ratios are based on the OLS estimator and the instrumental variables estimator that uses reshuffled regressors as instruments. The test proposed in this paper makes it possible to test for a unit root even at T = 2 as long as N is large. Simulation results show that test statistics have reasonable empirical size and power. The test is applied to college graduates' monthly real wage in South Korea. The number of time‐series observations for this data is only two. The null hypothesis of a unit root is rejected against the alternative of stationarity.