On estimating long-run effects in models with lagged dependent variables

A common procedure in economics is to estimate long-run effects from models with lagged dependent variables. For example, macro panel studies frequently are concerned with estimating the long-run impacts of fiscal policy, international aid, or foreign investment.Our analysis points out the hazards of this practice. We use Monte Carlo experiments to demonstrate that estimating long-run impacts from dynamic models produces unreliable results.Biases can be substantial, sample ranges very wide, and hypothesis tests can be rendered useless in realistic data environments. There are three reasons for this poor performance. First, OLS estimates of the coefficient of a lagged dependent variable are downwardly biased in finite samples. Second, small biases in the estimate of the lagged, dependent variable coefficient are magnified in the calculation of long-run effects. And third, and perhaps most importantly, the statistical distribution associated with estimates of the LRP is complicated, heavy-tailed, and difficult to use for hypothesis testing. While many of the underlying problems have been long-known in the literature, the continued widespread use of the associated empirical procedures suggests that researchers are unaware of the extent and severity of the estimation problems. This study aims to illustrate their practical importance for applied research.     

Estimating gravity equation models in the presence of sample selection and heteroscedasticity

Gravity models are widely used to explain patterns of trade. However, two stylized features of trade data, sample selection and heteroscedasticity challenge the estimation of gravity models. We propose a two-step method of moments (TS-MM) estimator that deals with both issues. The Monte-Carlo experiments show that the TS-MM estimates are resistant to various combinations of sample selection and heteroscedasticity. Moreover, the TS-MM estimator performs reasonably well even when the data generating process deviates from the TS-MM assumptions. We revisit the world trade in 1990 to illustrate the usefulness of the proposed model, with emphasis on the identification of the extensive margin of trade.     

Lagged duration dependence in mixed proportional hazard models

We study the identification of a mixed proportional hazard model with lagged duration dependence when data provide multiple outcomes per stratum. Within strata variation is exploited to non-parametrically identify lagged duration dependence in more general models than in the literature.     

Panel data inference under spatial dependence

This paper focuses on inference based on the standard panel data estimators of a one-way error component regression model when the true specification is a spatial error component model. Among the estimators considered, are pooled OLS, random and fixed effects, maximum likelihood under normality, etc. The spatial effects capture the cross-section dependence, and the usual panel data estimators ignore this dependence. Two popular forms of spatial autocorrelation are considered, namely, spatial autoregressive random effects (SAR-RE) and spatial moving average random effects (SMA-RE). We show that when the spatial coefficients are large, test of hypothesis based on the standard panel data estimators that ignore spatial dependence can lead to misleading inference.     

Testing for Granger non-causality in heterogeneous panels

This paper proposes a very simple test of Granger (1969) non-causality for heterogeneous panel data models. Our test statistic is based on the individual Wald statistics of Granger non causality averaged across the cross-section units. First, this statistic is shown to converge sequentially to a standard normal distribution. Second, the semi-asymptotic distribution of the average statistic is characterized for a fixed T sample. A standardized statistic based on an approximation of the moments of Wald statistics is hence proposed. Third, Monte Carlo experiments show that our standardized panel statistics have very good small sample properties, even in the presence of cross-sectional dependence.     

Health status and labour market outcome: Empirical evidence from Australia

This paper uses eight waves of Australia Household, Income and Labour Dynamics data to study the issues of state dependence and the short‐run and long‐run response to health shocks on the labour market. We consider six alternative panel data binary dependent variable models with different ways of modelling labour market dynamics and individual heterogeneity. We find that the key results with regard to labour market dependence and the impacts of health shocks are sensitive to model specification and pooling of male and female samples with differences as large as sixfold. Specification analysis is conducted and favours the dynamic fixed effects logit model for separate male and female samples. Methods for evaluating dynamic response paths to a one‐time health shock for binary outcomes are also suggested and results are presented.     

Nonlinear relationship between health care expenditure and its determinants: a panel smooth transition regression model

This paper employs a panel of 16 OECD countries over the period 1975–2009 to reexamine the health care expenditure (HCE)-income relationship by considering a lagged ratio of public expenditures on health as the transition variable in panel smooth transition regression (PSTR) models. PSTR models can capture the heterogeneity of any individual country, provide more detailed information for policy makers of an individual government, and resolve the insufficient observations problem that frequently appears in annual country-level data. Our empirical results indicate that the relationship between HCE and its determinants, including income, time (trend), and age structure variables, is nonlinear and varies with time and across countries. The time (trend) variable—a proxy for technical progress in health care—has a non-linear impact on HCE. Ignoring the variables—technological change of health care and age structure of population—will result in over-estimates of the income elasticities of HCE. Moreover, HCE behaves as a necessity good, and the income elasticity increases when the five-period lagged ratio of public expenditures on health increases. Clearly, the ratio of government financing on health plays an important role in influencing HCE.     

Specification tests and tests for overidentifying restrictions in panel data models with selection

Standard tests are generally not applicable in panel data models with selection. The paper shows how the Hausman specification test and the Sargan-Hansen test for overidentifying restrictions can be generalized to panel data models with unobserved heterogeneity and sample selection.     

基金业绩与资金流量:我国基金市场存在“赎回异象”吗?

近年来,国内学者普遍使用基金短期(季度)回报率作为解释变量,基于平衡面板数据样本对我国基金"业绩—资金流量关系"进行实证检验,得出我国基金市场存在"赎回异象"的结论。本文分别以基金中长期(年度)的原始回报率、市场模型及Fama-French三因子模型调整后的回报率作为解释变量,运用固定效应的非平衡面板数据回归模型,实证发现:基金滞后年度回报率对资金净流量产生显著的正面影响,投资者总体上"追逐业绩"而非"反向选择","赎回异象"不过是一种假象。与此相关,本文还发现,与海外研究结论明显不同,我国明星基金不能获得超额的资金流入,投资者并不热衷于"追星"。最后,本文运用"委托—代理"理论对实证结果进行了理论分析,并提出了完善我国基金市场业绩激励机制的建议。     

Health care expenditure and income in the OECD reconsidered: Evidence from panel data

This paper reconsiders the long-run economic relationship between health care expenditure and income using a panel of 20 OECD countries observed over the period 1971–2004. In particular, the paper studies the non-stationarity and cointegration properties between health care spending and income. This is done in a panel data context controlling for both cross-section dependence and unobserved heterogeneity. Cross-section dependence is modelled through a common factor model and through spatial dependence. Heterogeneity is handled through fixed effects in a panel homogeneous model and through a panel heterogeneous model. Our findings suggest that health care is a necessity rather than a luxury, with an elasticity much smaller than that estimated in previous studies.     

Non-linear adjustment of real wages,employment and output in the UK

We employ the Brock, Dechert and Scheinkman statistic to investigate non-linearity in conditional mean in UK real wages, employment and output, and to fit threshould regression models to the series. The latter porvide reasonable representations for thenon-lineraity in real wages and output but the residuals from the threshold autoregressive model for employment still contain a non-linear component. In a forecast comparison the TAR models performed better than simple autoregressions. Using the lagged share of wages as an error-correction term we find evidence that all three series respond asymmetrically to lagged changes in wage share and other variables. Fore-casts of real wages and employment derived from these models were superior to those derived from standard, symmetric, ECMs.     

Estimation of Dynamic Panel Data Sample Selection Models

This paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule, when the latent equations contain strictly exogenous variables, lags of the dependent variables, and unobserved individual effects. We derive a set of conditional moment restrictions which are then exploited to construct two-step GMM-type estimators for the parameters of the main equation. In the first step, the unknown parameters of the selection equation are consistently estimated. In the second step, these estimates are used to construct kernel weights in a manner such that the weight that any two-period individual observation receives in the estimation varies inversely with the relative magnitude of the sample selection effect in the two periods. Under appropriate assumptions, these "kernel-weighted" GMM estimators are consistent and asymptotically normal. The finite sample properties of the proposed estimators are investigated in a small Monte-Carlo study.     

STABILITY OF THAI BAHT: TALES FROM THE TAILS

We demonstrate how the EVT‐based signalling approach for currency crises can be applied to an individual country with a small sample size. Using Thai historical data, first, we study the tail characteristics of the distributions of two Thai baht instability measures and 21 economic fundamentals. Then, we test asymptotic dependence between the currency instability measures and lagged economic fundamentals. Empirically, we find that the distributions of both currency instability measures and economic variables are heavy tailed. Assuming a normal distribution for the variables tends to underestimate the probability of extreme events. Furthermore, most of the economic variables which are usually used as signalling indicators for currency crises are asymptotically independent of the currency instability measures. Signals issued by these variables are thus not reliable. Nevertheless, the non‐parametric EVT approach facilitates the selection of economic indicators with credible signals and high crisis prediction success.     

A COMPUTATIONALLY PRACTICAL SIMULATION ESTIMATION ALGORITHM FOR DYNAMIC PANEL DATA MODELS WITH UNOBSERVED ENDOGENOUS STATE VARIABLES*

This article develops a simulation estimation algorithm that is particularly useful for estimating dynamic panel data models with unobserved endogenous state variables. Repeated sampling experiments on dynamic probit models with serially correlated errors indicate the estimator has good small sample properties. We apply the estimator to a model of female labor supply and show that the rarely used Polya model fits the data substantially better than the popular Markov model. The Polya model also produces far less state dependence and many fewer race effects and much stronger effects of education, young children, and husband's income on female labor supply decisions.     

Cointegration analysis for cross-sectionally dependent panels: The case of regional production functions

This paper employs recently developed non-stationary panel methodologies that assume cross-section dependence to estimate a production function for Italian regions over the 1970–2003 period. The analysis consists of three steps. First, unit root tests for cross-sectionally dependent panels are applied. Second, the existence of a cointegrating relationship among value added, physical capital and human capital-augmented labour is investigated, fully allowing for cross-section dependence. Then, the appropriate Fully Modified Ordinary Least Square estimators developed by Bai and Kao [Bai, J., Kao, C. 2006. On the Estimation and Inference of a Panel Cointegration Model with Cross-Sectional Dependence. In: B.H. Baltagi (Ed) Panel Data Econometrics: Theoretical Contributions and Empirical Applications, Elsevier Science: Amsterdam; 2006, pp.3–30.] are used to estimate the long-run relationship. We find that neglecting cross-section dependence can have a strong impact on the estimated long-run input elasticities, generally imparting them an upward bias.     

An augmented autoregressive distributed lag bounds test for cointegration

An augmented autoregressive distributed lag (ARDL) bounds test for cointegration involves an extra F-test on the lagged levels of the independent variable(s) in the ARDL equation. Originally, this testing strategy was introduced using the bootstrap procedure. This paper provides both the small sample and asymptotic critical values for easier implementation of the test, making it applicable for a broader range of researchers. Two advantages of this augmented ARDL bounds test are that the assumption of an I(1) dependent variable is not necessary, and a clear conclusion on the cointegration status is provided by the three tests. The augmented ARDL bounds test is demonstrated using an empirical study on government taxation and expenditures. The tests support the tax-and-spend hypothesis of the budgetary policy for the US, the UK, and France.     

Teaching Regressions with a Lagged Dependent Variable and Autocorrelated Disturbances

The author attempts to rectify the unsatisfactory textbook treatment of the finite-sample properties of estimators of regression models with a lagged dependent variable and autocorrelated disturbances. He contends that the bias of the OLS estimator of a regression model with a lagged dependent variable and autocorrelated disturbances is determined by two effects, the dynamic effect and the correlation effect, which may be reinforcing or offsetting. The implications of these two effects are explored within a theoretical and a Monte Carlo framework.     

CHARTER SCHOOL COMPETITION AND ITS IMPACT ON EMPLOYMENT SPENDING IN MICHIGAN'S PUBLIC SCHOOLS

This paper seeks to determine how competition from charter schools affects a broad range of employees including instructors, administrators, and support personnel. Three empirical models are estimated utilizing a panel data from Michigan: a fixed effect model, a fixed effect model with lagged dependent variable, and an instrumental variable model. The key findings are that when a school district faces competition from charter schools they spend a larger percentage on instructors (most likely most of this is going toward teachers and not teacher aides), while spending a smaller percentage on employees that support instructors. The models seem to imply that the increased spending on teachers may not be reflected in a salary increase. (JEL H52, H75, I21, I22)     

Education and religious participation: city-level evidence from Germany’s secularization period 1890–1930

Why did substantial parts of Europe abandon the institutionalized churches around 1900? Empirical studies using modern data mostly contradict the traditional view that education was a leading source of the seismic social phenomenon of secularization. We construct a unique panel dataset of advanced-school enrollment and Protestant church attendance in German cities between 1890 and 1930. Our cross-sectional estimates replicate a positive association. By contrast, in panel models where fixed effects account for time-invariant unobserved heterogeneity, education—but not income or urbanization—is negatively related to church attendance. In panel models with lagged explanatory variables, educational expansion precedes reduced church attendance, while the reverse is not true. Dynamic panel models with lagged dependent variables and instrumental-variable models using variation in school supply confirm the results. The pattern of results across school types is most consistent with a mechanism of increased critical thinking in general rather than specific knowledge of natural sciences.     

Testing for structural breaks in panel varying coefficient models: with an application to OECD health expenditure

In this article, we propose a model selection approach for testing structural breaks in a semiparametric panel varying coefficient model. Monte Carlo evidence shows that the proposed model selection approach performs well in finite sample settings. Applying the method to an empirical data, we find evidence of structural breaks in Organisation for Economic Co-operation and Development (OECD) health expenditure data by allowing for income elasticity to be state (income)-dependent. The relationship between health expenditure and income is subject to two types of structural changes: smooth changes over income and structural breaks in the time dimension. The findings hold for both foreign exchange rate-converted and Purchasing Power Parity-converted expenditure and GDP.