Dynamic Misspecification Research Articles

A Guide to Analyzing Large N, Large T Panel Data

Fixed effects estimation of a static model with robust or panel corrected standard errors is commonly used to model large N, large T panel data. However, this approach is biased and inconsistent in the presence of dynamic misspecification, slope heterogeneity, and cross-sectional dependence. Common correlated effects estimation of a dynamic model has been advanced to address these issues but is rarely used in sociology. Here, I provide an overview of the large N, large T panel data literature, and I conduct an array of Monte Carlo experiments to compare the fixed effects estimator to the common correlated effects estimator regarding the aforementioned issues. I show that fixed effects estimation with robust or panel corrected standard errors do not address these problems, which is most evident with high levels of slope heterogeneity and lag misspecification, and its performance worsens as the time dimension expands. In contrast, the common correlated effects estimator produces superior estimates as T increases and is robust to slope heterogeneity and cross-sectional dependence. Following the experiments, I present an example by examining the drivers of fossil fuel consumption at the U.S. state level from 1960 to 2018, and I conclude by presenting a decision-making framework for researchers to use to make informed decisions when modeling large N, large T panel data.

What Goes Up Might Not Come Down: Modeling Directional Asymmetry with Large-N, Large-T Data

Modeling asymmetric relationships is an emerging subject of interest among sociologists. York and Light advanced a method to estimate asymmetric models with panel data, which was further developed by Allison. However, little attention has been given to the large- N, large- T case, wherein autoregression, slope heterogeneity, and cross-sectional dependence are important issues to consider. The authors fill this gap by conducting Monte Carlo experiments comparing the bias and power of the fixed-effects estimator to a set of heterogeneous panel estimators. The authors find that dynamic misspecification can produce substantial biases in the coefficients. Furthermore, even when the dynamics are correctly specified, the fixed-effects estimator will produce inconsistent and unstable estimates of the long-run effects in the presence of slope heterogeneity. The authors demonstrate these findings by testing for directional asymmetry in the economic development–CO2 emissions relationship, a key question in macro sociology, using data for 66 countries from 1971 to 2015. The authors conclude with a set of methodological recommendations on modeling directional asymmetry.

A specification test for dynamic conditional distribution models with function-valued parameters

This paper proposes a practical and consistent specification test of conditional distribution models for dependent data in a general setting. Our approach covers conditional distribution models indexed by function-valued parameters, allowing for a wide range of useful models for risk management and forecasting, such as the quantile autoregressive model, the CAViaR model, and the distributional regression model. The new specification test (i) is valid for general linear and nonlinear conditional quantile models under dependent data, (ii) allows for dynamic misspecification of the past information set, (iii) is consistent against fixed alternatives, and (iv) has nontrivial power against Pitman deviations from the null hypothesis. As the test statistic is non-pivotal, we propose and theoretically justify a subsampling approach to obtain valid inference. Finally, we illustrate the applicability of our approach by analyzing models of the returns distribution and Value-at-Risk (VaR) of two major stock indexes.

Order‐invariant tests for proper calibration of multivariate density forecasts

SummaryEstablished tests for proper calibration of multivariate density forecasts based on Rosenblatt probability integral transforms can be manipulated by changing the order of variables in the forecasting model. We derive order‐invariant tests. The new tests are applicable to densities of arbitrary dimensions and can deal with parameter estimation uncertainty and dynamic misspecification. Monte Carlo simulations show that they often have superior power relative to established approaches. We use the tests to evaluate generalized autoregressive conditional heteroskedasticity‐based multivariate density forecasts for a vector of stock market returns and macroeconomic forecasts from a Bayesian vector autoregression with time‐varying parameters.

LATENT VARIABLE NONPARAMETRIC COINTEGRATING REGRESSION

This article studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspecified through the use of a proxy regressor in place of the true regressor. Such models occur in linear and nonlinear regressions where the regressor suffers from measurement error or where the true regressor is a latent or filtered variable as in mixed-data-sampling. The treatment allows for endogenous regressors as the latent variable and proxy variables that cointegrate asymptotically with the true latent variable, including correctly specified as well as misspecified systems, and is therefore intermediate between nonlinear nonparametric cointegrating regression and completely spurious nonparametric nonstationary regression. The results relate to recent work on dynamic misspecification in nonparametric nonstationary systems and the limit theory accommodates regressor variables with autoregressive roots that are local to unity and whose errors are driven by long memory and short memory innovations, thereby encompassing applications with a wide range of economic and financial time series. Some implications for forecasting under misspecification are also examined.

Not so Harmless After All: The Fixed-Effects Model

The fixed-effects estimator is biased in the presence of dynamic misspecification and omitted within variation correlated with one of the regressors. We argue and demonstrate that fixed-effects estimates can amplify the bias from dynamic misspecification and that with omitted time-invariant variablesanddynamic misspecifications, the fixed-effects estimator can be more biased than the ‘naïve’ OLS model. We also demonstrate that the Hausman test does not reliably identify the least biased estimator when time-invariant and time-varying omitted variables or dynamic misspecifications exist. Accordingly, empirical researchers are ill-advised to rely on the Hausman test for model selection or use the fixed-effects model as default unless they can convincingly justify the assumption of correctly specified dynamics. Our findings caution applied researchers to not overlook the potential drawbacks of relying on the fixed-effects estimator as a default. The results presented here also call upon methodologists to study the properties of estimators in the presence of multiple model misspecifications. Our results suggest that scholars ought to devote much more attention to modeling dynamics appropriately instead of relying on a default solution before they control for potentially omitted variables with constant effects using a fixed-effects specification.

Order Invariant Tests for Proper Calibration of Multivariate Density Forecasts

Established tests for proper calibration of multivariate density forecasts based on Rosenblatt probability integral transforms can be manipulated by changing the order of variables in the forecasting model. We derive order invariant tests. The new tests are applicable to densities of arbitrary dimensions and can deal with parameter estimation uncertainty and dynamic misspecification. Monte Carlo simulations show that they often have superior power relative to established approaches. We use the tests to evaluate GARCH-based multivariate density forecasts for a vector of stock market returns.

Income and democracy: dynamic misspecification due to the presence of serial correlation

ABSTRACTWe address the issue of dynamic misspecification arising from the possible existence of serial correlation when examining the relationship between income and democracy by employing a panel count data estimation method. We find evidence that income per capita systematically predicts democracy, but it does not so in relation to the colonization experience of each country. Our results are robust across model specification and samples.

Latent Variable Nonparametric Cointegrating Regression

This paper studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspecified through the use of a proxy regressor in place of the true regressor. Such regressions arise naturally in linear and nonlinear regressions where the regressor suffers from measurement error or where the true regressor is a latent variable. The model considered allows for endogenous regressors as the latent variable and proxy variables that cointegrate asymptotically with the true latent variable. Such a framework includes correctly specified systems as well as misspecified models in which the actual regressor serves as a proxy variable for the true regressor. The system is therefore intermediate between nonlinear nonparametric cointegrating regression (Wang and Phillips, 2009a, 2009b) and completely misspecified nonparametric regressions in which the relationship is entirely spurious (Phillips, 2009). The asymptotic results relate to recent work on dynamic misspecification in nonparametric nonstationary systems by Kasparis and Phillips (2012) and Duffy (2014). The limit theory accommodates regressor variables with autoregressive roots that are local to unity and whose errors are driven by long memory and short memory innovations, thereby encompassing applications with a wide range of economic and financial time series.

Misspecification and Expectations Correction in New Keynesian DSGE Models

This paper focuses on the dynamic misspecification that characterizes the class of small-scale New Keynesian models currently used in monetary and business cycle analysis, and provides a remedy for the typical difficulties these models have in accounting for the rich contemporaneous and dynamic correlation structure of the data. We suggest using a statistical model for the data as a device through which it is possible to adapt the econometric specification of the New Keynesian model such that the risk of omitting important propagation mechanisms is kept under control. A pseudo-structural form is built from the baseline system of Euler equations by forcing the state vector of the system to have the same dimension as the state vector characterizing the statistical model. The pseudo-structural form gives rise to a set of cross-equation restrictions that do not penalize the autocorrelation structure and persistence of the data. Standard estimation and evaluation methods can be used. We provide an empirical illustration based on USA quarterly data and a small-scale monetary New Keynesian model.

Conditional predictive density evaluation in the presence of instabilities

We propose new methods for evaluating predictive densities. The methods include Kolmogorov–Smirnov and Cramér–von Mises-type tests for the correct specification of predictive densities robust to dynamic mis-specification. The novelty is that the tests can detect mis-specification in the predictive densities even if it appears only over a fraction of the sample, due to the presence of instabilities. Our results indicate that our tests are well sized and have good power in detecting mis-specification in predictive densities, even when it is time-varying. An application to density forecasts of the Survey of Professional Forecasters demonstrates the usefulness of the proposed methodologies.

Determinacy, indeterminacy and dynamic misspecification in linear rational expectations models

This paper proposes a testing strategy for the null hypothesis that a multivariate linear rational expectations (LRE) model may have a unique stable solution (determinacy) against the alternative of multiple stable solutions (indeterminacy). The testing problem is addressed by a misspecification-type approach in which the overidentifying restrictions test obtained from the estimation of the system of Euler equations of the LRE model through the generalized method of moments is combined with a likelihood-based test for the cross-equation restrictions that the model places on its reduced form solution under determinacy. The resulting test has no power against a particular class of indeterminate equilibria, hence the non rejection of the null hypothesis can not be interpreted conclusively as evidence of determinacy. On the other hand, this test (i) circumvents the nonstandard inferential problem generated by the presence of the auxiliary parameters that appear under indeterminacy and that are not identifiable under determinacy, (ii) does not involve inequality parametric restrictions and hence the use of nonstandard inference, (iii) is consistent against the dynamic misspecification of the LRE model, and (iv) is computationally simple. Monte Carlo simulations show that the suggested testing strategy delivers reasonable size coverage and power against dynamic misspecification in finite samples. An empirical illustration focuses on the determinacy/indeterminacy of a New Keynesian monetary business cycle model of the US economy.

Dynamic misspecification in the environmental Kuznets curve: Evidence from CO2 and SO2 emissions in the United Kingdom

This study looks at the behaviour of emissions when in disequilibrium with respect to the environmental Kuznets curve (EKC) relationship. We use the non-linear threshold cointegration and error correction methodology and a long dataset beginning in 1830, in an application to the United Kingdom. There is significant evidence that, not only does the ‘inverse-U’ shape hold between per capita CO2 and SO2 emissions and GDP per capita, but we also find that temporary disequilibrium from the long-run EKC is corrected in an asymmetric fashion. This may be due to the historical pressure of environmental regulation in the UK to reduce emissions that are higher than permitted. However further analysis suggests that technological change can partially account for the asymmetric adjustment.

Dynamic misspecification in nonparametric cointegrating regression

Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The limit properties of the Nadaraya–Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent, in general, with a “pseudo-true function” limit that is a local average of the true regression function. In this respect nonlinear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centred on the pseudo-true function and appropriately scaled, the NW estimator still has a mixed Gaussian limit distribution. The convergence rates are the same as those obtained under correct specification (hn, h is a bandwidth term) but the variance of the limit distribution is larger. The practical import of the results for index models, functional regression models, temporal aggregation and specification testing are discussed. Two nonparametric linearity tests are considered. The proposed tests are robust to dynamic misspecification. Under the null hypothesis (linearity), the first test has a χ2 limit distribution while the second test has limit distribution determined by the maximum of independently distributed χ2 variates. Under the alternative hypothesis, the test statistics attain a hn divergence rate.

Conditional Predictive Density Evaluation in the Presence of Instabilities

We propose new methods for evaluating predictive densities. The methods include Kolmogorov-Smirnov and Cramer-von Mises-type tests for the correct specification of predictive densities robust to dynamic mis-specification. The novelty is that the tests can detect mis-specification in the predictive densities even if it appears only over a fraction of the sample, due to the presence of instabilities. Our results indicate that our tests are well sized and have good power in detecting mis-specification in predictive densities, even when it is time-varying. An application to density forecasts of the Survey of Professional Forecasters demonstrates the usefulness of the proposed methodologies.

Investment In The Greek Processing Of Agricultural Products And Food: A Panel Data Approach

<p class="MsoBodyText" style="line-height: normal; margin: 0in 35.4pt 0pt 35.45pt;"><span style="font-size: 10pt; mso-bidi-font-style: italic; mso-ansi-language: EN-US;"><span style="font-family: Times New Roman;"><span style="mso-tab-count: 1;">                </span>The aim of this research is to quantify Greek investors’ behaviour in the industry of processing agricultural products and food at the aggregate level for all sectors and all regions over the period 1981-1999. The focus of this study is to investigate empirically the effectiveness of the EU and national policies concerning investment incentives in the processing of Greek agricultural products. Investors’ behaviour is examined by employing a synthesized traditional model. The dynamic model is estimated using alternative dynamic panel data methods, GMM and ML techniques. EU and national subsidies are instrumental in stimulating agricultural investments in the past decades, followed by investors’ expectations and, in most of the cases, investment lagged by one year. The empirical results obtained by ML by GMM are very similar, with the exception that the t-statistics are higher in the former case. Moreover, there is no evidence for autocorrelation or dynamic misspecification. </span></span></p>

Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes

This article develops nonparametric tests of independence between two stochastic processes satisfying β-mixing conditions. The testing strategy boils down to gauging the closeness between the joint and the product of the marginal stationary densities. For that purpose, we take advantage of a generalized entropic measure so as to build a whole family of nonparametric tests of independence. We derive asymptotic normality and local power using the functional delta method for kernels. As a corollary, we also develop a class of entropy-based tests for serial independence. The latter are nuisance parameter free, and hence also qualify for dynamic misspecification analyses. We then investigate the finite-sample properties of our serial independence tests through Monte Carlo simulations. They perform quite well, entailing more power against some nonlinear AR alternatives than two popular nonparametric serial-independence tests.

An Analysis of Investment Activity in the Greek Agricultural Products and Food Manufacturing Sector

The food and drinks sector occupy first place in Greek manufacturing industry. This paper aims to quantify Greek investors' behavior in processing agricultural products at the sectoral level, to investigate empirically the effectiveness of the EU and national policies concerning investment incentives, by employing a synthesized traditional model. The dynamic model is estimated using alternative panel data methods, GMM and ML. The results are for 1981–1999, for all regions and for nine agricultural sectors. EU and national subsidies exert strong influence on investment decisions. The estimates obtained by ML and GMM are almost identical and there is no evidence for autocorrelation or dynamic misspecification.

A bootstrap-based non-parametric forecast density

Interest in density forecasts (as opposed to solely modeling the conditional mean) arises from the possibility of dynamics in higher moments of a time series, as well as in forecasting the probability of future events in some applications. By combining the idea of Markov bootstrapping with that of kernel density estimation, this paper presents a simple non-parametric method for estimating out-of-sample multi-step density forecasts. The paper also considers a host of evaluation tests for examining the dynamic misspecification of estimated density forecasts by targeting autocorrelation, heteroskedasticity and neglected non-linearity. These tests are useful, as a rejection of the tests gives insight into ways to improve a particular forecasting model. In an extensive Monte Carlo analysis involving a range of commonly used linear and non-linear time series processes, the non-parametric method is shown to work reasonably well across the simulated models for a suitable choice of the bandwidth (smoothing parameter). Furthermore, an application of the method to the U.S. Industrial Production series provides multi-step density forecasts that show no sign of dynamic misspecification.

Bootstrap conditional distribution tests in the presence of dynamic misspecification

Abstract In this paper, we show the first order validity of the block bootstrap for Kolmogorov-type conditional distribution tests under dynamic misspecification and parameter estimation error. Our approach is unique because we construct statistics that allow for dynamic misspecification under both hypotheses. We consider two tests; the CK test of Andrews [1997. A conditional Kolmogorov test, Econometrica 65, 1097–1128], and a version of the DGT test of Diebold, Gunther and Tay [1998a. Evaluating density forecasts with applications to finance and management. International Economic Review 39, 863–883]. Test limiting distributions are Gaussian processes with covariance kernels that reflect dynamic misspecification and parameter estimation error. Critical values are based on an extension of the empirical process version of the block bootstrap to the case of nonvanishing parameter estimation error. Monte Carlo experiments are also carried out.