Presence Of Conditional Heteroskedasticity Research Articles

Estimating the returns to education using a parametric control function approach: evidences for a developing country

This paper investigates the causal effect of education on earnings in Brazil by employing a new method proposed by Klein and Vella (2010) that obtains identification on the presence of conditional heteroskedasticity. In contrast to traditionally used IV methods, this approach yields unbiased estimates in the absence of instruments. Results indicate that the average return to education in Brazil was relatively stable at around 14% from 1995 to 2003, declined afterwards reaching 10.7% in 2014, but has bounced back to 11.8% after the economic crisis in 2015. The results suggest that the OLS estimations are downward biased and we interpret this as a sign of under-education premiums that are likely to occur in environments where the more talented ones are dropped from school and moved into the labor market earlier in life.

Improving Weighted Least Squares Inference

In the presence of conditional heteroskedasticity, inference about the coefficients in a linear regression model these days is typically based on the ordinary least squares estimator in conjunction with using heteroskedasticity consistent standard errors. Similarly, even when the true form of heteroskedasticity is unknown, heteroskedasticity consistent standard errors can be used to base valid inference on a weighted least squares estimator. Using a weighted least squares estimator can provide large gains in efficiency over the ordinary least squares estimator. However, intervals based on plug-in standard errors often have coverage that is below the nominal level, especially for small sample sizes. In this paper, it is shown that a bootstrap approximation to the sampling distribution of the weighted least squares estimate is valid, which allows for inference with improved finite-sample properties. Furthermore, when the model used to estimate the unknown form of the heteroskedasticity is misspecified, the weighted least squares estimator may be less efficient than the ordinary least squares estimator. To address this problem, a new estimator is proposed that is asymptotically at least as efficient as both the ordinary and the weighted least squares estimator. Simulation studies demonstrate the attractive finite-sample properties of this new estimator as well as the improvements in performance realized by bootstrap confidence intervals.

Estimation of Seasonal Cointegration under Conditional Heteroskedasticity

We consider the estimation of seasonal cointegration in the presence of conditional heteroskedasticity (CH) using a feasible generalized least squares method. We capture cointegrating relationships and time-varying volatility for long-run and short-run dynamics in the same model. This procedure can be easily implemented using common methods such as ordinary least squares and generalized least squares. The maximum likelihood (ML) estimation method is computationally difficult and may not be feasible for larger models. The simulation results indicate that the proposed method is superior to the ML method when CH exists. In order to illustrate the proposed method, an empirical example is presented to model a seasonally cointegrated times series under CH.

Inference in VARs with conditional heteroskedasticity of unknown form

We consider a framework for asymptotically valid inference in stable vector autoregressive (VAR) models with conditional heteroskedasticity of unknown form. A joint central limit theorem for the LS estimators of both the VAR slope parameters as well as the unconditional innovation variance parameters is obtained from a weak vector autoregressive moving average model set-up recently proposed in the literature. Our results are important for correct inference on VAR statistics that depend both on the VAR slope and the variance parameters as e.g. in structural impulse responses. We also show that wild and pairwise bootstrap schemes fail in the presence of conditional heteroskedasticity if inference on (functions) of the unconditional variance parameters is of interest because they do not correctly replicate the relevant fourth moments’ structure of the innovations. In contrast, the residual-based moving block bootstrap results in asymptotically valid inference. We illustrate the practical implications of our theoretical results by providing simulation evidence on the finite sample properties of different inference methods for impulse response coefficients. Our results point out that estimation uncertainty may increase dramatically in the presence of conditional heteroskedasticity. Moreover, most inference methods are likely to understate the true estimation uncertainty substantially in finite samples.

Estimating Heterogeneous Returns to Education in Germany Via Conditional Heteroskedasticity

In this paper I investigate the causal returns to education for different educational groups in Germany by employing a new method by Klein and Vella (2010) that bases identification on the presence of conditional heteroskedasticity. Compared to IV methods, key advantages of this approach are unbiased estimates in the absence of instruments and parameter interpretation that is not bounded to local average treatment effects. Using data from the German Socio-Economic Panel Study (SOEP) I find that the causal return to education is 8.5% for the entire sample, 2.3% for graduates from the basic school track and 11% for graduates from a higher school track. Across these groups the endogeneity bias in simple OLS regressions varies significantly. This confirms recent evidence in the literature on Germany. Various robustness checks support the findings.

Estimating Heterogeneous Returns to Education in Germany Via Conditional Heteroskedasticity

In this paper I investigate the causal returns to education for different educational groups in Germany by employing a new method by Klein and Vella (2010) that bases identification on the presence of conditional heteroskedasticity. Compared to IV methods, key advantages of this approach are unbiased estimates in the absence of instruments and parameter interpretation that is not bounded to local average treatment effects. Using data from the German Socio-Economic Panel Study (SOEP) I find that the causal return to education is 8.5% for the entire sample, 2.3% for graduates from the basic school track and 11% for graduates from a higher school track. Across these groups the endogeneity bias in simple OLS regressions varies significantly. This confirms recent evidence in the literature on Germany. Various robustness checks support the findings.

OPTIMAL INSTRUMENTS IN TIME SERIES: A SURVEY

Abstract This article surveys estimation in stationary time‐series models using the approach of optimal instrumentation. We review tools that allow construction and implementation of optimal instrumental variables estimators in various circumstances – in single‐ and multiperiod models, in the absence and presence of conditional heteroskedasticity, by considering linear and non‐linear instruments. We also discuss issues adjacent to the theme of optimal instruments. The article is directed primarily towards practitioners, but econometric theorists and teachers of graduate econometrics may also find it useful.

GENERALIZED EMPIRICAL LIKELIHOOD ESTIMATORS AND TESTS UNDER PARTIAL, WEAK, AND STRONG IDENTIFICATION

The purpose of this paper is to describe the performance of generalized empirical likelihood (GEL) methods for time series instrumental variable models specified by nonlinear moment restrictions as in Stock and Wright (2000, Econometrica 68, 1055–1096) when identification may be weak. The paper makes two main contributions. First, we show that all GEL estimators are first-order equivalent under weak identification. The GEL estimator under weak identification is inconsistent and has a nonstandard asymptotic distribution. Second, the paper proposes new GEL test statistics, which have chi-square asymptotic null distributions independent of the strength or weakness of identification. Consequently, unlike those for Wald and likelihood ratio statistics, the size of tests formed from these statistics is not distorted by the strength or weakness of identification. Modified versions of the statistics are presented for tests of hypotheses on parameter subvectors when the parameters not under test are strongly identified. Monte Carlo results for the linear instrumental variable regression model suggest that tests based on these statistics have very good size properties even in the presence of conditional heteroskedasticity. The tests have competitive power properties, especially for thick-tailed or asymmetric error distributions.This paper is a revision of Guggenberger's job market paper “Generalized Empirical Likelihood Tests under Partial, Weak, and Strong Identification.” We are thankful to the editor, P.C.B. Phillips, and three referees for very helpful suggestions on an earlier version of this paper. Guggenberger gratefully acknowledges the continuous help and support of his adviser, Donald Andrews, who played a prominent role in the formulation of this paper. He thanks Peter Phillips and Joseph Altonji for their extremely valuable comments. We also thank Vadim Marner for help with the simulation section and John Chao, Guido Imbens, Michael Jansson, Frank Kleibergen, Marcelo Moreira, Jonathan Wright, and Motohiro Yogo for helpful comments. Aspects of this research have been presented at the 2003 Econometric Society European Meetings; York Econometrics Workshop 2004; Seminaire Malinvaud; CREST-INSEE; and seminars at Albany, Alicante, Austin (Texas), Brown, Chicago, Chicago GSB, Harvard/MIT, Irvine, ISEG/Universidade Tecnica de Lisboa, Konstanz, Laval, Madison (Wisconsin), Mannheim, Maryland, NYU, Penn, Penn State, Pittsburgh, Princeton, Rice, Riverside, Rochester, San Diego, Texas A&M, UCLA, USC, and Yale. We thank all the seminar participants. Guggenberger and Smith received financial support through a Carl Arvid Anderson Prize Fellowship and a 2002 Leverhulme Major Research Fellowship, respectively.

ROBUST ASYMPTOTIC INFERENCE IN AUTOREGRESSIVE MODELS WITH MARTINGALE DIFFERENCE ERRORS

This paper proposes a GMM-based method for asymptotic confidence interval construction in stationary autoregressive models, which is robust to the presence of conditional heteroskedasticity of unknown form. The confidence regions are obtained by inverting the asymptotic acceptance region of the distance metric test for the continuously updated GMM (CU-GMM) estimator. Unlike the predetermined symmetric shape of the Wald confidence intervals, the shape of the proposed confidence intervals is data-driven owing an estimated sequence of nonuniform weights. It appears that the flexibility of the CU-GMM estimator in downweighting certain observations proves advantageous for confidence interval construction. This stands in contrast to some other generalized empirical likelihood estimators with appealing optimality properties such as the empirical likelihood estimator whose objective function prevents such downweighting. A Monte Carlo simulation study illustrates the excellent small-sample properties of the method for AR models with ARCH errors. The procedure is applied to study the dynamics of the federal funds rate.

Bootstrapping autoregressions with conditional heteroskedasticity of unknown form

Conditional heteroskedasticity is an important feature of many macroeconomic and financial time series. Standard residual-based bootstrap procedures for dynamic regression models treat the regression error as i.i.d. These procedures are invalid in the presence of conditional heteroskedasticity. We establish the asymptotic validity of three easy-to-implement alternative bootstrap proposals for stationary autoregressive processes with martingale difference errors subject to possible conditional heteroskedasticity of unknown form. These proposals are the fixed-design wild bootstrap, the recursive-design wild bootstrap and the pairwise bootstrap. In a simulation study all three procedures tend to be more accurate in small samples than the conventional large-sample approximation based on robust standard errors. In contrast, standard residual-based bootstrap methods for models with i.i.d. errors may be very inaccurate if the i.i.d. assumption is violated. We conclude that in many empirical applications the proposed robust bootstrap procedures should routinely replace conventional bootstrap procedures for autoregressions based on the i.i.d. error assumption.

ARCH tests and quantile regressions

We consider a test based on quantile regressions to verify the presence of conditional heteroskedasticity. The test does not rely on distributional assumptions of the errors, nor on a function describing the pattern of heteroskedasticity. It compares the slope coefficients of the regressions computed at different quantiles. Under homoskedasticity, different regression quantiles yield parallel hyperplanes, and the slope coefficients are not significantly different from one quantile to the other. This is not the case when heteroskedasticity occurs. A Monte Carlo study is implemented in order to verify the behavior of this class of tests for conditional heteroskedasticity based on quantile regressions.

Nonlinear Intraday Dynamics in Eurostoxx50 Index Markets

This paper analyses the nonlinear dynamic behaviour of intraday returns in the Eurostoxx50 cash and futures index which, given their relatively recent appearance, have not yet been analysed. We find that both return series show nonlinear individual dynamics that cannot exclusively be explained by the presence of conditional heteroskedasticity. Our findings also indicate nonlinear dynamic relationships between both market prices. The adjustment process to mispricing errors is nonlinear and shows periods of explosive behaviour. Finally, we distinguish between linear and nonlinear Granger causality and establish that the information flow is bi-directional both in the linear as well as in the nonlinear sphere.

Testing for Autocorrelation and Unit Roots in the Presence of Conditional Heteroskedasticity of Unknown Form

The presence of conditional heteroskedasticity invalidates standard autocorrelation tests such as the Durbin-Watson statistic and its many variants, and reduces the power of standard unit root tests like the Dickey-Fuller test. This paper addresses the problem of testing for AR(1) and AR(p) alternatives in the presence of conditional heteroskedasticity, constructs new autocorrelation tests (called g- and gl- tests), and derives an asymptotic theory for the new statistics. The g test is shown to be robust to any form of conditional heteroskedasticity, while the gl test is robust to the joint presence of conditional heteroskedasticity and lagged dependent variables. The paper also develops a GLS-type unit root test that allows for conditional heteroskedasticity. Its limit distribution turns out to be a convex mixture of the Dickey-Fuller distribution and the standard normal distribution. It is shown that the GLS statistic improves the power of the Dickey-Fuller test under condictional heteroskedasticity. Some Monte Carlo simulations with the new tests are reported.

THE FORM OF THE OPTIMAL NONLINEAR INSTRUMENT FOR MULTIPERIOD CONDITIONAL MOMENT RESTRICTIONS

We present the form of the optimal instrument in a system of multiperiod conditional moment restrictions in the presence of conditional heteroskedasticity. Using Hansen's ( 1985 , Journal of Econometrics 30, 203–228) and Hansen, Heaton, and Ogaki's ( 1988 , Journal of the American Statistical Association 83, 863–871) work on efficiency bounds for generalized method of moments estimators, we show that this form is an autoregressive recurrence parametrized by a few auxiliary processes that are defined through a system of nonlinear stochastic restrictions, with a stability condition among them. In general, the system does not allow inversion and obtaining an explicit solution for the auxiliary parameters. This is a part of my Ph.D. dissertation ( Anatolyev, 2000 ). I am grateful to Kenneth West for introducing me to the subject and providing advice and encouragement. I also thank Bruce Hansen, Yuichi Kitamura, seminar participants at Indiana University, Pennsylvania State University, Rutgers University, University of British Columbia, University of Virginia, and University of Wisconsin, the co-editor Richard Smith, and two referees for helpful comments and suggestions. Research for this paper was supported in part by a fellowship from the Economics Education and Research Consortium, with funds provided by the government of Sweden through the Eurasia Foundation. The opinions expressed in this paper are those of the author and do not necessarily reflect the views of the government of Sweden, the Eurasia Foundation, or any other member of the Economics Education and Research Consortium.

Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form

Conditional heteroskedasticity is an important feature of many macroeconomic and financial time series. Standard residual-based bootstrap procedures for dynamic regression models treat the regression error as i.i.d. These procedures are invalid in the presence of conditional heteroskedasticity. We establish the asymptotic validity of three easy-to-implement alternative bootstrap proposals for stationary autoregressive processes with m.d.s. errors subject to possible conditional heteroskedasticity of unknown form. These proposals are the fixed-design wild bootstrap, the recursive-design wild bootstrap and the pairwise bootstrap. In a simulation study all three procedures tend to be more accurate in small samples than the conventional large-sample approximation based on robust standard errors. In contrast, standard residual-based bootstrap methods for models with i.i.d. errors may be very inaccurate if the i.i.d. assumption is violated. We conclude that in many empirical applications the proposed robust bootstrap procedures should routinely replace conventional bootstrap procedures based on the i.i.d. error assumption.

Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form

Conditional heteroskedasticity is an important feature of many macroeconomic and financial time series. Standard residual-based bootstrap procedures for dynamic regression models treat the regression eroor as i.i.d. These procedures are invalid in the presence of conditional heteroskedasticity. We establish the asymptotic validity of three easy-to-implement alternative bootstrap proposals for stationary autoregressive processes with m.d.s. errors subject to possible conditional heteroskedasticity of unknown form. These proposals are the fixed-design wild bootstrap, the recursive design wild bootstrap and the pairwise bootstrap. In a simulation study all three procedures tend to be more accurate in small samples than the conventional large-sample approximation based on robust standard errors. In contrast, standard residual-based bootstrap methods for models with i.i.d. errors may be very inaccurate if the i.i.d. assumption is violated. We conclude that in many empirical applications the proposed robust bootstrap procedures should routinely replace conventional bootstrap procedures based on the i.i.d. error assumption. JEL Classification: C15, C22, C52

EXCESS RETURNS AND RISK AT THE LONG END OF THE TREASURY MARKET: AN EGARCH‐M APPROACH

AbstractIn this paper we model weekly excess returns of ten‐year Treasury notes and long‐term Treasury bonds from 1968 through 1993 using an exponential generalized autoregressive conditional heteroskedasticity in mean (EGARCH‐M) approach. The results indicate the presence of conditional heteroskedasticity and a strong tendency for the ex‐ante volatility of excess returns to increase more following negative excess return innovations compared with positive innovations of equal magnitude. In addition, increases in ex‐ante volatility are associated in some subperiods with rising excess returns on longer‐term instruments, although the slope of the yield curve and lagged excess returns generally remain significant predictors of excess returns.

A test for the presence of conditional heteroskedasticity within arch-m framework

This paper is concerned with testing the presence of ARCH within the ARCH-M model as the alternative hypothesis. Standard testing procedures are inapplicable since a nuisance parameter is unidentified under the null hypothesis. Nonetheless, the diagnostic tests for the presence of the conditional variance is very important since any misspecification in the conditional variance equation leads to inconsistent estimates of the conditional mean parameters. BTo resolve the problem of unidentified nuisance parameter, ‘Ne apply Davies’ approach, and investigate its finite sample performance through a Monte Carlo study.

A Monte Carlo Investigation of the Box-Cox Model and a Nonlinear Least Squares Alternative

This paper reports a Monte Carlo study of the Box-Cox model and a nonlinear least squares alternative. Key results include the following: the transformation parameter in the Box-Cox model appears to be inconsistently estimated in the presence of conditional heteroskedasticity; the constant term in both the Box-Cox and the nonlinear least squares models is poorly estimated in small samples; conditional mean forecasts tend to underestimate their true value in the Box-Cox model when the transformation parameter is not equal to one; and conditional heteroskedasticity tends to worsen the bias in the Box-Cox predicted values. Copyright 1994 by MIT Press.

The Effect of Money Shocks on Interest Rates in the Presence of Conditional Heteroskedasticity

The Effect of Money Shocks on Interest Rates in the Presence of Conditional Heteroskedasticity