Testing of functional forms of regressions with lagged dependent variable and autocorrelated errors

This paper presents the test statistics for the Maximum Likelihood Ratio, the Lagrange Multiplier and the Wald tests for regressions that involve a lagged dependent variable, autocorrelated errors and the Box–Cox transformation. A computational procedure is suggested.     

Resolving spurious regressions and serially correlated errors

This study investigates the spurious regression phenomenon for two independent stationary and non-stationary processes and illustrates, using a Monte Carlo analysis, that estimation of the spurious regression in first differences or with a lagged dependent variable eliminates the spurious regression problem. Moreover, the results also apply in eliminating the problem of serially correlated errors as well as the problem of ARCH(1) errors.     

A note on spurious significance in regressions involving <Emphasis Type="BoldItalic">I</Emphasis>(0) and <Emphasis Type="BoldItalic">I</Emphasis>(1) variables

We demonstrate that t ratios (the F statistic) for I(1) regressors in a model with an I(0) dependent variable will generally be oversized. This indicates that spurious significance occurs in a situation where it was not previously identified. We also compare the asymptotic rejection rates of t ratios for various combinations of I(1) and I(0) variables in the two-variable linear regression model. These rejection rates systematically increase with the degree of autocorrelation, yielding spurious significance, when both variables are either positively or negatively autocorrelated. In contrast, when one variable is negatively autocorrelated and the other is positively autocorrelated the rejection rates systematically fall and are undersized.     

Health expenditure models: A comparison using panel data

In this article, we focus on the estimation of outpatient expenditures with panel data. We model the logarithm of expenditures and consider five different models. The first two are two-part and sample selection cross-section models. Two-part panel data models turn out to be inappropriate for dealing with expenditures. We thus estimate sample selection models with panel data: one without a lagged dependent variable and two with a lagged dependent variable. These two latter models differ in their assumptions on the variance of the residuals. Modelling heteroscedasticity may indeed be important to avoid the bias due to the retransformation problem. We show that lagged dependent variables are important factors for heteroscedasticity. For the models with state dependence, we provide a new solution to the initial conditions problem by controlling for generalised residuals. We establish that panel data models highly improve the correlation explained by the model in the time-series dimension without damaging the fit in the cross-section dimension. For all indicators of fit, the model with state dependence and heteroscedasticity seems to dominate the others.     

Consistency ofs 2 in the linear regression model with correlated errors

We give a simple sufficient condition for consistency of the standard OLS-based estimate of the disturbance variance in the linear regression model with autocorrelated disturbances.Research supported by Deutsche Forschungsgemeinschaft (DFG). We are grateful to B. M. Poetscher for a generous supply of counterexamples.     

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.     

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。     

The lower bound and the causes of monetary policy inertia: evidence from Sweden

In 2009, in the midst of a global recession, Sweden’s Riksbank approached a lower bound on nominal interest rates. This encounter with the lower bound provides a natural experiment for investigating the causes of monetary policy inertia. To exploit this experiment, we estimate Taylor rules with Tobit specifications that permit both interest rate smoothing and persistent shocks (serial correlation) as explanations for inertia. The interest rate smoothing hypothesis leads to a specification in which lagged actual values of the dependent variable appear on the right-hand side of the Taylor rule, while the persistent shocks hypothesis leads to a specification in which lagged values of an unobserved latent dependent variable appear on the right-hand side of the Taylor rule. The divergence of actual and latent dependent variables that occurs at the lower bound provides leverage in distinguishing the two hypotheses. For a conventional Taylor rule, we find evidence of both sources of inertia. For a modified Taylor rule that includes a measure of financial stress, our evidence suggests that interest rate smoothing is the principal source of monetary policy inertia.     

A Bayesian Nonparametric Investigation of the Predictive Effect of Exchange Rates on Commodity Prices

This study proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates in relation to commodity prices for three commodity-exporting countries: Canada, Australia, and New Zealand. We propose a new time-dependent infinite mixture of a normal linear regression model of the conditional distribution of the commodity price index. The mixing weights follow a set of Probit stick-breaking priors that are time-varying. We find that exchange rates have a positive predictive effect in general, but accounting for time variation does not improve forecasting performance. By contrast, the intercept in the regression and the lagged dependent variable show signs of parameter change over time in most cases, which is important in forecasting both the mean and the density of commodity prices one period ahead. The results also suggest that the variance is a large source of the time variation in the conditional distribution of commodity prices.     

Long-term impact of investments in early schooling — Empirical evidence from rural Ethiopia

We examine the cumulative impact of early schooling investments on later schooling outcomes using enrollment status and relative grade attainment as short-run and long-run measures of schooling. Using a child-level longitudinal data set from rural Ethiopia, we estimate a dynamic conditional schooling demand function where the coefficient estimate on the lagged dependent variable captures the impact of all previous period schooling inputs and resources. We find that a child who is enrolled in the prior period is 33 percentage points more likely to be enrolled currently. These lagged effects are stronger for girls and for children from higher income households.     

Estimating the covariance matrix for regression models with ar(1) errors and lagged dependent variables

We propose a simple procedure, based on an artificial linear regression, for consistently estimating the covariance matrix of the parameter estimates for linear regression models with serially correlated errors and lagged dependent variables.     

A multidimensional spatial lag panel data model with spatial moving average nested random effects errors

This paper focuses on a three-dimensional model that combines two different types of spatial interaction effects, i.e. endogenous interaction effects via a spatial lag on the dependent variable and interaction effects among the disturbances via a spatial moving average (SMA) nested random effects errors. A three-stage procedure is proposed to estimate the parameters. In a first stage, the spatial lag panel data model is estimated using an instrumental variable (IV) estimator. In a second stage, a generalized moments (GM) approach is developed to estimate the SMA parameter and the variance components of the disturbance process using IV residuals from the first stage. In a third stage, to purge the equation of the specific structure of the disturbances a Cochrane–Orcutt-type transformation is applied combined with the IV principle. This leads to the GM spatial IV estimator and the regression parameter estimates. Monte Carlo simulations show that our estimators are not very different in terms of root mean square error from those produced by maximum likelihood. The approach is applied to European Union regional employment data for regions nested within countries.     

Habit,seasonality, and time aggregation in consumer behaviour

Habitual behaviour in consumer demand analysis is generally portrayed via some form of a lagged dependent variable model. The purpose of this paper is to explore the implications for habit behaviour of time aggregation. This is done by specifying both habit and seasonal components in demand relations. The results indicate that much of what has traditionally been identified as habitual behaviour is, in fact, seasonal effects.     

Enhancing the local power of IVX-based tests in predictive regressions

IVX estimation is used increasingly often in predictive regressions with regressors of unknown persistence. While not exhibiting the second-order bias the OLS estimator has in this setup, IVX estimators have reduced rates of convergence when the regressors are highly persistent. The reduced convergence rates may sometimes lead to power losses in finite samples when testing for no predictability, for instance. The note discusses a simple way of improving the local power of IVX-based tests, consisting of augmenting the predictive regression with the lagged dependent variable. This implies a feed-back loop which strengthens the signal of the IVX instrument without changing its dynamic properties. The proposed augmentation works best when the power loss of IVX would have been maximal compared to the infeasible OLS-based test.     

Generalized spatial autocorrelation in a panel-probit model with an application to exporting in China

This paper proposes a generalized spatial panel-data probit model with spatial autocorrelation of the dependent variable, the time-invariant individual shocks, and the remainder disturbances. It proposes its estimation with a Bayesian Markov chain Monte Carlo procedure. Simulation results show that the proposed estimation method performs well in small- to medium-sized samples. This method is then applied to the analysis of export-market participation of 1451 Chinese firms between 2002 and 2006 in the prefecture-level city of Wenzhou in the province of Zhejiang. Empirical results show that two of the three forms of the hypothesized spatial autocorrelation are significant, namely the spatial lag for the dependent variable and the time-invariant firm-specific shocks, but not the time-variant shocks. Ignoring any of these significant spatial effects would lead to misspecification.     

Nonlinear models,composite longer leading indicator and forecasts for UK real GDP

This paper examines the role of the Office for National Statistics Composite Longer Leading Indicator, in nonlinear business cycle models for growth rates of UK real gross domestic product (GDP). These models are of the smooth transition regression class, with the transition between “regimes” expressed as functions of lagged changes in the leading indicator. In general, evidence is found of business cycle regime asymmetries, with increases and decreases in the leading indicator implying distinct responses for the dependent variable. Single transition function appears to capture these asymmetries satisfactorily. Nonlinear models provide more accurate one-step ahead forecasts than corresponding linear leading indicator models.     

Outside the box: using synthetic control methods as a forecasting technique

We introduce synthetic control methods (SCM) as a forecasting technique. Using (i) as economic predictors solely the outcome itself, i.e. lagged values of the dependent variable, and (ii) lagged time series of the outcome to build the donor pool, we let SCM choose and weight appropriate values in order to come up with a sensible forecast of the US GDP growth. This procedure performs competitively viable compared with alternative forecasting methods.     

THE LEAD–LAG RELATION BETWEEN THE S&P500 SPOT AND FUTURES MARKETS: AN INTRADAY-DATA ANALYSIS USING A THRESHOLD REGRESSION MODEL

In this paper we examine the lead–lag interaction between the futures and spot markets of the S&P500 using the threshold regression model on intraday data. The use of threshold variables to model the changes in the regression structure with respect to different market conditions enables us to investigate the lead–lag interaction in a data-based approach and avoid stratifying the data arbitrarily. Using the basis as the threshold variable, we find that the short-selling restrictions in the spot market reduce the effect of the spot index as the leading variable. To study the effect of market-wide information on the interaction between the spot and futures markets, we use the coefficient of determination in the regression of the S&P500 on the Morgan–Stanley Composite Index-US and the Major Market Index as the threshold variable. We find that the lead effect of the futures market over the spot market is stronger when there is more market-wide information. On the other hand, the lead effect of the cash market over the futures market is weaker when there is more market-wide information. In addition, we also use the lagged 45-min return of the spot market as the threshold variable. We find that the lead effect of the spot market is stronger in periods of directionless trading than in periods of good or bad markets.     

The impact of collinearity on regression analysis: the asymmetric effect of negative and positive correlations

The purpose of this paper is to ascertain how collinearity in general, and the sign of correlations in specific, affect parameter inference, variable omission bias, and their diagnostic indices in regression. It is found that collinearity can reduce parameter variance estimates and that positive and negative correlation structures have an asymmetric effect on variable omission bias. It is also shown that the effects of collinearity are moderated by the relationship between the dependent variable and the regressors, a consideration not incorporated into most commonly used collinearity diagnostics. The formulae derived enable researchers to assess the sensitivity of regression results to the underlying correlation structure in the data.     

Testing poolability in a system of dynamic regressions with nonspherical disturbances

This study analyzes the testing of cross-equation restrictions within a set of regression equations. Through Monte Carlo experiments we examine the actual size of various asymptotic procedures for testing the poolability hypothesis, i.e., equal slope vectors across individual equations. Regression models with both lagged dependent variable regressors and nonspherical disturbances are considered. In these models we find that the performance in finite samples of classical asymptotic test procedures using critical values from either or ² approximations is often rather poor. However, employing the original test statistics with bootstrapped critical values leads to much more accurate inference in finite samples. In an empirical analysis of panel data on GDP growth and unemployment rates in OECD countries it is shown that classical asymptotic tests and bootstrap procedures may lead to conflicting test outcomes. I am indebted to Peter Boswijk, Jan Kiviet, Peter Vlaar, the associate editor and 2 anonymous referees for their constructive comments. I want to thank Geoffrey Garrett for kindly making available his data.