Testing Multiple Non-Nested Factor Demand Systems

This article explains how to obtain straightforward extensions of the most popular univariate non‐nested statistics, and of the RESET‐test, to a multivariate context and examines how to use these tests to compare alternative factor demand systems. The empirical application involves the classical Berndt–Khaled KLEM data set. A statistically adequate specification is determined for each competing factor demand system. The empirical results are interpreted for each system, the models are compared on the basis of multivariate paired and joint non‐nested procedures and practical indications about what to expect if these tests are applied to alternative factor demand specifications are provided.     

An Artificial Neural Network Test For Structural Change With Unspecified Parametric Form

Tests for a structural change of unknown timing in parameterized regression functions have been introduced previously under the maintained assumption that the models are correctly specified. However, the existing family of tests are unable to discriminate between structural change and misspecification. This paper introduces test statistics which do not require specification of the parametric form of the underlying data-generating process (DGP). I approximate it by a version of artificial neural networks (ANN). My simulation studies indicate that an ANN approximates the DGP quite well and that the derived tests have good power relative to the power envelope.
JEL Classification Numbers: C12, C14, C45.     

An evaluation of excess demand,actual cost and normal cost pricing hypotheses using non-nested tests

This paper has emperically analyzed three versions(zero lag,geometric lag and almon lag) of three price change hypotheses – namely the excess demand, actual cost and the normal cost hypothesis – the goal being to select the hypothesis that describes the underlying price dynamics for manufactured goods. The rival models are specified as non-nested alternatives and each version is estimated by using an efficient estimator. The traditional discrimination criteria which clearly reject the zero lag version, are found to be impotent in discriminating between the dynamic versions of the models. A sequential cross-evaluation of the two dynamic versions using both pairwise and multiple non-nested hypothesis tests proposed by Davidson and MacKinnon reveals a systematic domination by the almon version of normal cost pricing over both the excess demand and the actual cost pricing mechanisms in the Canadian manufacturing sector during the period 1961:1–87:4. This result is robust under alternative specifications of the desired stock of inventories for the excess demand model. The finding implies that short–run variations in demand conditions or in actual unit costs arising from temperoary changes in productivity may not paly a significant role in manufactured goods pricing decisions.     

Simple Procedures for Testing Autoregressive Versus Moving Average Errors in Regression Models

This paper develops several simple separate (or non-nested) procedures for testing autoregressive versus moving average errors in regression models. These asymptotically valid tests are straightforward to calculate: after estimating both models by maximum likelihood methods, the procedure involves testing the significance of variables added to a linearized version of the null model, the added variables being the predictions, or the residuals from the specified alternative model, or the difference of the predictions of the two models. Some small sample evidence on the properties of the tests is presented, as is an empirical application on the Australian unexpected inflation rate series.
JEL Classification Numbers: C12, C22, C52, E31.     

Testing for nonlinear panel unit roots under cross-sectional dependency — With an application to the PPP hypothesis

In this paper we propose a number of nonlinear panel unit root tests that are robust to cross-sectional dependency. These tests may be used to test the null hypothesis of non-stationarity against the alternative that some or all of the time series in the system of equations follow a stationary exponential smooth transition autoregressive (ESTAR) process. In contrast to previous research we relax the assumption that the cross-correlation structure is driven by a common-factor and consider an endogenous correlation structure. Based on the size and power results from the Monte Carlo simulations we recommend using the Wald version of our cross-sectional dependent robust nonlinear panel unit root (CDR-NPU) method.Finally, in an empirical application we demonstrate that our more powerful nonlinear method, in contrast to previous methods, can provide support for PPP even in smaller samples. In consistency with the univariate tests in Bahmani-Oskooee et al. (2008) our CDR-NPU tests support the theory that less industrialized economies exhibit stronger and more distinct nonlinear adjustment patterns towards PPP.     

Testing For Efficient Contracts In Unionized Labour Markets

This paper addresses the design of empirical tests to distinguish between two competing explanations of wage and employment determination in unionized labour markets, the labour-demand and efficient-contract models. We argue that most of the tests employed are restrictive, propose an alternative non-nested approach, a central feature of which is the variation in the set of instrumental variables across the models, and provide an illustration of how it might be implemented, using data from the Workplace Industrial Relations Survey (WIRS) 1984 Panel File. The results demonstrate how the traditional approach can lead to inappropriate conclusions, and thereby emphasize the empirical importance of the specification of the instrumental variables.     

Generalized Method of Moment estimation of multivariate multifractal models

Multifractal processes have recently been introduced as a new tool for modeling the stylized facts of financial markets and have been found to consistently provide certain gains in performance over basic volatility models for a broad range of assets and for various risk management purposes. Due to computational constraints, multivariate extensions of the baseline univariate multifractal framework are, however, still very sparse so far. In this paper, we introduce a parsimoniously designed multivariate multifractal model, and we implement its estimation via a Generalized Methods of Moments (GMM) algorithm. Monte Carlo studies show that the performance of this GMM estimator for bivariate and trivariate models is similar to GMM estimation for univariate multifractal models. An empirical application shows that the multivariate multifractal model improves upon the volatility forecasts of multivariate GARCH over medium to long forecast horizons.     

Testing for PPP: Should we use panel methods?

A common finding in the empirical literature on the validity of purchasing power parity (PPP) is that it holds when tested for in panel data, but not in univariate (i.e. country-specific) analysis. The usual explanation for this mismatch is that panel tests for unit roots are more powerful than their univariate counterparts. In this paper we suggest an alternative explanation. Existing panel methods assume that cross-unit cointegrating relationships, that would tie the units of the panel together, are not present. Using simulations, we show that if this important underlying assumption of panel unit root tests is violated, the empirical size of the tests is substantially higher than the nominal level, and the null hypothesis of a unit root is rejected too often even when it is true. More generally, this finding warns against the automatic use of panel methods for testing for unit roots in macroeconomic time series.First version received: November 2001/Final version received : October 2003     

Can we reject linearity in an HAR-RV model for the S&P 500? Insights from a nonparametric HAR-RV

This article tests the linearity assumption underlying the popular heterogeneous autoregressive model for realized volatility (HAR-RV). We implement a consistent model specification test that is robust to both distributional and model misspecification. We find that, using a nonparametric HAR-RV (NPHAR-RV), we are unable to reject the null of linearity.     

Nonlinear Mean-Reversion in Real Exchange Rates: Toward a Solution To the Purchasing Power Parity Puzzles

We fit nonlinearly mean-reverting models to real dollar exchange rates over the post-Bretton Woods period, consistent with a theoretical literature on transactions costs in international arbitrage. The half lives of real exchange rate shocks, calculated through Monte Carlo integration, imply faster adjustment speeds than hitherto recorded. Monte Carlo simulations reconcile our results with the large empirical literature on unit roots in real exchange rates by showing that when the real exchange rate is nonlinearly mean reverting, standard univariate unit root tests have low power, while multivariate tests have much higher power to reject a false null hypothesis.     

Testing for deterministic and stochastic cycles in macroeconomic time series

In this paper we use a statistical procedure which is appropriate to test for deterministic and stochastic (stationary and nonstationary) cycles in macroeconomic time series. These tests have standard null and local limit distributions and are easy to apply to raw time series. Monte Carlo evidence shows that they perform relatively well in the case of functional misspecification in the cyclical structure of the series. As an example, we use this approach to test for the presence of cycles in US real GDP.      

Consumer allocation models: Choice of functional form

The functional form of consumer allocation models should be able to satisfy theoretical properties derived from the theory of consumer demand. The paper sketches four approaches that meet this condition. Of course, also empirical performance matters. Next to naive goodness-of-fit comparison, non-nested hypothesis testing can be employed. The latter technique is applied to a comparison of four versions of differential demand systems: the Rotterdam system, a version of the Almost Ideal Demand (AID) system, the CBS system and the NBR system. These systems are artificially nested in a more general model using scalar weights in contrast to Barten and McAleer (1991) who use matrix weights for this purpose. Annual data over the period 1921–1981 for The Netherlands for four major groups of consumer expenditure have been used for the empirical application. The CBS system dominates the others.     

Forecasting stock returns: Do less powerful predictors help?

This paper proposes a simple but efficient way to improve the predictability of stock returns. Instead of torturously constructing new powerful predictors, we readily select existing predictors that have low correlations and thus provide complementary information. Our forecasting strategy is to use the selected predictors based on a multivariate regression model. In our forecasting strategy, less powerful predictors are also useful for forecasting stock returns if they could provide complementary information. The empirical results show that our forecasting strategy outperforms not only the univariate regression models that use each predictor's information separately but also combination approaches that use all predictors jointly. We also document that our strategy extracts significantly more useful information from the complementary predictors than the competing models. In addition, from an asset allocation perspective, a mean-variance investor realizes substantial economic gains. Furthermore, the evidence based on Monte Carlo simulations supports the feasibility of our forecasting strategy.     

Parameter constancy in cointegrating regressions

This paper proposes an approach to testing for coefficient stability in cointegrating regressions in time series models. The test statistic considered is the one-sided version of the Lagrange Multiplier (LM) test. Its limit distribution is non-standard but is nuisance parameter free and can be represented in terms of a stochastic bridge process which is tied down like a Brownian bridge but relies on a random rather than a deterministic fraction to do so. The approach provides a test of the null hypothesis of cointegration against specific directions of departure from the null; subset coefficient stability tests are also available. A small simulation studies the size and power properties of these tests and an empirical illustration to Australian data on consumption, disposable income, inflation and money is provided.     

Conditional and unconditional food demand elasticities in a dynamic multistage demand system

This paper estimates conditional and unconditional demand elasticities in a three stage analysis of consumer demand for food and non-food items in Greece. A dynamic version of the AIDS model is specified and estimated, and full system misspecification tests applied. Correction formulas for price and expenditure elasticities are used to calculate unconditional elasticities from conditional demand sub-systems. All food items rank as price inelastic. Deviations between the calculated conditional and unconditional price and expenditure elasticities are found to be significant, demonstrating the importance of correcting conditional elasticities before they can be used for policy purposes or welfare analyses.     

Numeraire choice in normalized quadratic functional forms

A semi-nested test procedure is developed for choosing the numeraire for a normalized quadratic profit function when too few observations exist for nested hypothesis testing and when too many alternatives exis for conventional non-nested testing. Sensitivity of empirical results to choice of numeraire price is examined using agricultural data for the US and ten multistate regions. Few test conclusions vary by numeraire but own price input demand elasticities differ greatly.     

Heteroskedasticity testing through a comparison of Wald statistics

This paper shows that a test for heteroskedasticity within the context of classical linear regression can be based on the difference between Wald statistics in heteroskedasticity-robust and nonrobust forms. The test is asymptotically distributed under the null hypothesis of homoskedasticity as chi-squared with one degree of freedom. The power of the test is sensitive to the choice of parametric restriction used by the Wald statistics, so the supremum of a range of individual test statistics is proposed. Two versions of a supremum-based test are considered: the first version does not have a known asymptotic null distribution, so the bootstrap is employed to approximate its empirical distribution. The second version has a known asymptotic distribution and, in some cases, is asymptotically pivotal under the null. A simulation study illustrates the use and finite-sample performance of both versions of the test. In this study, the bootstrap is found to provide better size control than asymptotic critical values, namely with heavy-tailed, asymmetric distributions of the covariates. In addition, the use of well-known modifications of the heteroskedasticity consistent covariance matrix estimator of OLS coefficients is also found to benefit the tests’ overall behaviour.     

The analysis of consumer demand in Greece. Model selection and dynamic specification

The paper analyses the pattern of consumer demand in Greece exploring systematically the questions of the functional form of demand that best fits the data, the appropriate dynamic structure and the empirical validity of the constraints of demand theory. A general dynamic Almost Ideal demand model for four categories of consumer non-durables for the period 1958–1994 is estimated. The maintained specification rejects the static AI, its counterparts implied by the partial adjustment and autoregressive disturbances models and, upon applying a non-nested test, the Rotterdam specification. However, it cannot reject homogeneity and symmetry nor the hypothesis of structural stability.     

Nonparametric neural network modeling of hedonic prices in the housing market

This article addresses the contribution to hedonic modeling of a nonparametric approach based on artificial neural network (ANN) regressions. ANNs provide consistent estimates for the hedonic price of each attribute and permit a number of hypotheses on the hedonic price relationship to be tested nonparametrically. In particular, we exploit results by Stinchcombe and White (Econom Theory 14:295?C324, 1998) in order to carry out misspecification testing in linear and semiloglinear hedonic models. The same approach directly applies to testing misspecification of any parametric specification for the hedonic relationship. A nonparametric significance test for the variables in the hedonic model is also proposed. The test extends the approach developed by Racine (J Bus Econ Stat 15(3):369?C378, 1997) in kernel-based nonparametric testing to ANN-based inference. The finite sample performance of the proposed tests is analyzed through Monte Carlo experiments, and simulation-based algorithms for computation of the null distribution of the tests are proposed. Then, the performance of three classes of regression models??linear, semi-log, and ANNs??applied to hedonic price modeling in a Spanish regional housing market is compared. Our results indicate the presence of nonlinear behavior, as predicted by economic theory, with the ANN-based tests detecting statistically significant evidence of misspecification??both in the linear and the semilog specifications??and ANN regressions providing moderate improvement of predictive performance.     

Dynamic specification and misspecification in systems of demand equations: a testing strategy for model selection

The purpose of this study is to describe a misspecification testing strategy that is designed to ensure the appropriateness of the statistical assumptions underlying a system of equations. A systemwise test approach is used to test the statistical assumptions. The systemwise tests take into account information in, and interaction between, all equations in the system and can be used in a wide variety of applications where systems of equations are estimated. If the systemwise test leads to rejection, single equation F-test will then be used to help identify specific problems. The systemwise testing approach is illustrated by modelling Swedish consumer demand for milk. The example illustrates how the approach can be used to solve issues regarding dynamic specification of models, structural change and other forms of model misspecification.