A Note on the Performance of Biased Estimators with Autocorrelated Errors

It is a well-established fact in regression analysis that multicollinearity and autocorrelated errors have adverse effects on the properties of the least squares estimator. Huang and Yang (2015) and Chandra and Tyagi (2016) studied the PCTP estimator and the r-(k,d) class estimator, respectively, to deal with both problems simultaneously and compared their performances with the estimators obtained as their special cases. However, to the best of our knowledge, the performance of both estimators has not been compared so far. Hence, this paper is intended to compare the performance of these two estimators under mean squared error (MSE) matrix criterion. Further, a simulation study is conducted to evaluate superiority of the r-(k,d) class estimator over the PCTP estimator by means of percentage relative efficiency. Furthermore, two numerical examples have been given to illustrate the performance of the estimators

Bootstrap Methods for Inference in a SUR model with Autocorrelated Disturbances

Although the Parks (1967) estimator for a SUR model with AR disturbances is efficient both asymptotically and in small samples, Kmenta and Gilbert (1970) and more recently Beck and Katz (1995) note that estimated standard errors tend to be biased downward as compared with the true variability of the estimates. This bias leads to tests that show over-rejection and to confidence intervals that are too small. We suggest bootstrapping the tests to correct this inference problem. After illustrating the over rejection associated with the estimated asymptotic standard errors, we develop a bootstrap approach to inference for this model, illustrate its use, and show using Monte Carlo methods that the bootstrap gives rejection probabilities close to the nominal level chosen by the researcher.

Robust Trend Estimation for AR(1) Disturbances

We discuss the robust estimation of a linear trend if the noise follows an autoregressive process of first order. We find the ordinary repeated median to perform well except for negative correlations. In this case it can be improved by a Prais-Winsten transformation using a robust autocorrelation estimator. -- Wir behandeln die robuste Schätzung eines linearen Trends bei autoregressiven Fehlern erster Ordnung. Die Repeated Median Regression zeigt ein gutes Verhalten bei positiven Korrelationen. Bei negativen Korrelationen ist eine Verbesserung durch eine Prais-Winsten Transformation mittels eines robusten Korrelationsschätzers möglich.Robust Regression,Autocorrelations,Detrending,Cochrane-Orcutt Estimator,Prais-Winsten Estimator

Testing for Spatial Autocorrelation in a Fixed Effects Panel Data Model

This paper derives several Lagrange Multiplier statistics and the correspondinglikelihood ratio statistics to test for spatial autocorrelation in a fixed effectspanel data model. These tests allow discriminating between the two main typesof spatial autocorrelation which are relevant in empirical applications, namelyendogenous spatial lag versus spatially autocorrelated errors. In this paper, fivedifferent statistics are suggested. The first one, the joint test, detects the presenceof spatial autocorrelation whatever its type. Hence, it indicates whetherspecific econometric estimation methods should be implemented to account forthe spatial dimension. In case they need to be implemented, the other four testssupport the choice between the different specifications, i.e. endogenous spatiallag, spatially autocorrelated errors or both. The first two are simple hypothesistests as they detect one kind of spatial autocorrelation assuming the otherone is absent. The last two take into account the presence of one type of spatialautocorrelation when testing for the presence of the other one. We use themethodology developed in Lee and Yu (2008) to set up and estimate the generallikelihood function. Monte Carlo experiments show the good performance ofour tests. Finally, as an illustration, they are applied to the Feldstein-Horiokapuzzle. They indicate a misspecification of the investment-saving regressiondue to the omission of spatial autocorrelation. The traditional saving-retentioncoefficient is shown to be upward biased. In contrast our results favor capitalmobility.Testing ; Spatial ; Autocorrelation ; Fixed ; Effects ; Panel Data Model

ESTIMATION OF EFFICIENT REGRESSION MODELS FOR APPLIED AGRICULTURAL ECONOMICS RESEARCH

This paper proposes and explores the use of a partially adaptive estimation technique to improve the reliability of the inferences made from multiple regression models when the dependent variable is not normally distributed. The relevance of this technique for agricultural economics research is evaluated through Monte Carlo simulation and two mainstream applications: A time-series analysis of agricultural commodity prices and an empirical model of the West Texas cotton basis. It is concluded that, given non-normality, this technique can substantially reduce the magnitude of the standard errors of the slope parameter estimators in relation to OLS, GLS and other least squares based estimation procedures, in practice, allowing for more precise inferences about the existence, sign and magnitude of the effects of the independent variables on the dependent variable of interest. In addition, the technique produces confidence intervals for the dependent variable forecasts that are more efficient and consistent with the observed data. Key Words: Efficient regression models, partially adaptive estimation, non-normality, skewness, heteroskedasticity, autocorrelation.Efficient regression models, partially adaptive estimation, non-normality, skewness, heteroskedasticity, autocorrelation., Research Methods/ Statistical Methods,

A Monte Carlo Study of Growth Regressions

Using Monte Carlo simulations, this paper evaluates the bias properties of common estimators used in growth regressions derived from the Solow model. We explicitly allow for measurement error in the right-hand side variables, as well as country-specific effects that are correlated with the regressors. Our results suggest that using 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. The fixed-effects estimator and the Arellano-Bond estimator greatly overstate the speed of convergence under a wide variety of assumptions concerning the type and extent of measurement error, while between understates it somewhat. Finally, fixed effects and Arellano-Bond bias towards zero the slope estimates on the human and physical capital accumulation variables.

Robust Standard Errors for Robust Estimators

A regression estimator is said to be robust if it is still reliable in the presence of outliers. On the other hand, its standard error is said to be robust if it is still reliable when the regression errors are autocorrelated and/or heteroskedastic. This paper shows how robust standard errors can be computed for several robust estimators of regression, including MMestimators. The improvement relative to non-robust standard errors is illustrated by means of large-sample bias calculations, simulations, and a real data example. It turns out that non-robust standard errors of robust estimators may be severely biased. However, if autocorrelation and heteroscedasticity are absent, non-robust standard errors are more e.cient than the robust standard errors that we propose. We therefore also present a test of the hypothesis that the robust and non-robust standard errors have the same probability limit.robust regression, robust standard errors, autocorrelation, heteroskedasticity

Is the New Keynesian Phillips curve flat?

Macroeconomic data suggest that the New Keynesian Phillips curve is quite flat - despite microeconomic evidence implying frequent price adjustments. While real rigidities may help to account for the conflicting evidence, we propose an alternative explanation: if price markup/cost-push shocks are persistent and negatively correlated with the labor share, the latter being a widely used measure for marginal costs, the estimated pass-through of measured marginal costs into inflation is limited, even if prices are fairly flexible. Using a standard New Keynesian model, we show that the GMM approach to the New Keynesian Phillips curve leads to inconsistent and upward biased estimates if cost-push shocks indeed are persistent. Monte Carlo experiments suggest that the bias is quite sizeable: we find average price durations estimated as high as 12 quarters, when the true value is about 2 quarters. Moreover, alternative estimators appear to be biased as well, while standard diagnostic tests fail to signal a misspecification of the model. JEL Classification: E30, C15Cost-push shocks, GMM estimation, New Keynesian Phillips curve, Price Rigidities

A Test for Autocorrelation in Dynamic Panel Data Models

This paper presents an autocorrelation test that is applicable to dynamic panel data models with serially correlated errors. Our residual-based GMM t-test (hereafter: t-test) differs from the m2 and Sargan's over-identifying restriction (hereafter: Sargan test) in Arellano and Bond (1991), both of which are based on residuals from the first-difference equation. It is a significance test which is applied after estimating a dynamic model by the instrumental variable (IV) method and is directly applicable to any other consistently estimated residual. Two interesting points are found: the test depends only on the consistency of the first-step estimation, not on its efficiency;and the test is applicable to both forms of serial correlation (i.e., AR(1) or MA(1)). Monte Carlo simulations are also performed to study the practical performance of these three tests, the m2, the Sargan and the t-test for models with first-order auto-regressive AR(1) and first-order moving-average MA(1) serial correlation. The m2 and Sargan test statistics appear to accept too often in small samples even when the autocorrelation coefficient approaches unity in the AR(1) disturbance. Overall, our residual based t-test has considerably more power than the m2 test or the Sargan test.Dynamic panel data, Residual based GMM t-test, m2 and Sargan tests

Panel Regression with Random Noise

The paper explores the effect of measurement errors on the estimation of a linear panel data model. The conventional fixed effects estimator, which ignores measurement errors, is biased. By correcting for the bias one can construct consistent and asymptotically normal estimators. In addition, we find estimates for the asymptotic variances of these estimators. The paper focuses on multiplicative errors, which are often deliberately added to the data in order to minimize their disclosure risk. They can be analyzed in a similar way as additive errors, but with some important and consequential differences.panel regression, multiplicative measurement errors, bias correction, asymptotic variance, disclosure control