Pitfalls of testing non-nested hypotheses by the lagrange multiplier method

The paper considers the problem of testing non-nested hypotheses by the application of the Lagrange Multiplier (LM) method to an exponentially combined likelihood function. It shows that the general test statistic derived by Atkinson (1970) and later by Breusch and Pagan (1980) can be regarded as an LM statistic only if it can be assumed that the parameters of the alternative model are known. When none of the parameters are known, the paper shows that a straightforward application of the LM method to testing non-nested hypotheses breaks down and it discusses the reasons for this failure.     

Class Analysis and Earnings Inequality: Nested and Non-Nested Comparisons of Two Class Models in Israel

This paper demonstrates how nesting and non-nesting analytical strategies provide different answers regarding the comparative utility of theoretical models. This paper demonstrates this incompatibility by testing the empirical efficacy of Goldthorpe's and Wright's class schemes in explaining earnings inequality in Israel. These models are non-nested, because while they partially overlap each other conceptually and empirically, neither can be written as a parametric restriction of the other. As they are non-nested, we cannot test each model against the other by using the conventional sociological approach to hypotheses testing. For the sake of demonstration, however, we show results obtained from the conventional Ordinary Least Squares regression models with conventional Baysian Information Coefficient statistic, serving as criterion for a decision rule. Wright's model was found to be more significant in explaining earnings variations in Israeli society. Yet when we used two models of non-nested specification tests (the Cox-Pesaran model and the J test) to examine each model's unique contribution, neither of these models were able to reject the rival hypothesis. This revised version was published online in June 2006 with corrections to the Cover Date.     

Testing panel data regression models with spatial error correlation

This paper derives several lagrange multiplier (LM) tests for the panel data regression model with spatial error correlation. These tests draw upon two strands of earlier work. The first is the LM tests for the spatial error correlation model discussed in Anselin (Spatial Econometrics: Methods and Models, Kluwer Academic Publishers, Dordrecht; Rao's score test in spatial econometrics, J. Statist. Plann. Inference 97 (2001) 113) and Anselin et al. (Regional Sci. Urban Econom. 26 (1996) 77), and the second is the LM tests for the error component panel data model discussed in Breusch and Pagan (Rev. Econom. Stud. 47(1980) 239) and Baltagi et al. (J. Econometrics 54 (1992) 95). The idea is to allow for both spatial error correlation as well as random region effects in the panel data regression model and to test for their joint significance. Additionally, this paper derives conditional LM tests, which test for random regional effects given the presence of spatial error correlation. Also, spatial error correlation given the presence of random regional effects. These conditional LM tests are an alternative to the one-directional LM tests that test for random regional effects ignoring the presence of spatial error correlation or the one-directional LM tests for spatial error correlation ignoring the presence of random regional effects. We argue that these joint and conditional LM tests guard against possible misspecification. Extensive Monte Carlo experiments are conducted to study the performance of these LM tests as well as the corresponding likelihood ratio tests.     

On the comprehensive method of testing non-nested regression models

The paper derives the specific form of the exponentially combined likelihood function of two competing multivariate non-linear regression models and shows that the application of the comprehensive approach to testing non-nested regression models will, in general, be indeterminate. It establishes that in the univariate case there exists a large number of tests of non-nested regression models which are consistent in addition to having the same asymptotic distribution under the null hypothesis. The paper then derives a set of conditions under which all these consistent tests are asymptotically equivalent not only under the null hypothesis but also under local alternatives. As an application of this latter result the paper establishes the asymptotic equivalence of the tests recently proposed by Davidson and MacKinnon, and Fisher and McAleer under local alternatives, and shows that within the class of tests considered in the paper these proposed tests possess maximum local power. The latter test has this property only when the number of explanatory variables of the ‘true’ model is not more than that of the ‘false’ model.     

Testing the specification of multivariate models in the presence of alternative hypotheses

In this paper we propose a non-nested hypothesis test for testing the specification of a multivariate econometric model in the presence of an alternative model which purports to explain the same phenomenon. We demonstrate that the new test statistic tends to minus the same random variable as the CPD test statistic introduced by Pesaran and Deaton (1978), provided that the truth is ‘close’ to the null hypothesis. Since the new test is simpler to compute than the multivariate CPD test, it would seem to be the procedure of choice.     

Testing non-nested semiparametric models: an application to Engel curves specification

This paper proposes a test statistic for discriminating between two partly non-linear regression models whose parametric components are non-nested. The statistic has the form of a J-test based on a parameter which artificially nests the null and alternative hypotheses. We study in detail the realistic case where all regressors in the non-linear part are discrete and then no smoothing is required on estimating the non-parametric components. We also consider the general case where continuous and discrete regressors are present. The performance of the test in finite samples is discussed in the context of some Monte Carlo experiments. The test is well motivated for specification testing of Engel curves. We provide an application using data from the 1980 Spanish Expenditure Survey. © 1998 John Wiley & Sons, Ltd.     

Bootstrap J-Test for Panel Data Models with Spatially Dependent Error Components,a Spatial Lag and Additional Endogenous Variables

We develop a bootstrap J-test method for testing a panel model against one non-nested alternative when the competing specifications are estimated by Feasible Generalised Spatial Two Stage Least Squares/Generalised Method of Moments (FGS2SLS/GMM). Both models incorporate spatially correlated error components, thus accounting for spatial heterogeneity via random effects, and accommodate endogenous regressors other than the spatially lagged dependent variable. The proposed scheme is applied to a testing problem involving non-nested wage equations as motivated by the Wage Curve literature and the New Economic Geography theory. Results show that our bootstrap test is a reliable and effective procedure for correcting asymptotic reference critical values and distinguishing between the two rival hypotheses.     

Testing nested or non-nested hypotheses

This paper presents a test procedure for nested or non-nested hypotheses. The test statistic is based on the difference between two estimators of the pseudo-true value as defined for instance by Sawa. This statistic is similar to the usual Wald statistic in the case of nested hypotheses and it can be replaced by an asymptotically equivalent one deduced from the score function.     

Testing for autoregressive against moving average errors in the linear regression model

This paper presents a new approach to hypotheses testing problems which are non-nested in the classical sense and which concern the covariance matrix of the disturbance vector of the linear regression model. In particular, the application of the approach to testing for AR(1) disturbances against MA(1) disturbances is explored in some detail. Practical difficulties are discussed and selected upper bounds for the test's five percent significance points are tabulated. The small sample power of four versions of the new test are compared empirically and a clear conclusion is made in regard to the best overall test.     

Diagnostic Tests of Cross‐section Independence for Limited Dependent Variable Panel Data Models*

This article considers the problem of testing for cross‐section independence in limited dependent variable panel data models. It derives a Lagrangian multiplier (LM) test and shows that in terms of generalized residuals of Gourieroux et al. (1987) it reduces to the LM test of Breusch and Pagan (1980) . Because of the tendency of the LM test to over‐reject in panels with large N (cross‐section dimension), we also consider the application of the cross‐section dependence test (CD) proposed by Pesaran (2004) . In Monte Carlo experiments it emerges that for most combinations of N and T the CD test is correctly sized, whereas the validity of the LM test requires T (time series dimension) to be quite large relative to N. We illustrate the cross‐sectional independence tests with an application to a probit panel data model of roll‐call votes in the US Congress and find that the votes display a significant degree of cross‐section dependence.     

Testing for serial correlation,spatial autocorrelation and random effects using panel data

This paper considers a spatial panel data regression model with serial correlation on each spatial unit over time as well as spatial dependence between the spatial units at each point in time. In addition, the model allows for heterogeneity across the spatial units using random effects. The paper then derives several Lagrange multiplier tests for this panel data regression model including a joint test for serial correlation, spatial autocorrelation and random effects. These tests draw upon two strands of earlier work. The first is the LM tests for the spatial error correlation model discussed in Anselin and Bera [1998. Spatial dependence in linear regression models with an introduction to spatial econometrics. In: Ullah, A., Giles, D.E.A. (Eds.), Handbook of Applied Economic Statistics. Marcel Dekker, New York] and in the panel data context by Baltagi et al. [2003. Testing panel data regression models with spatial error correlation. Journal of Econometrics 117, 123–150]. The second is the LM tests for the error component panel data model with serial correlation derived by Baltagi and Li [1995. Testing AR(1) against MA(1) disturbances in an error component model. Journal of Econometrics 68, 133–151]. Hence, the joint LM test derived in this paper encompasses those derived in both strands of earlier works. In fact, in the context of our general model, the earlier LM tests become marginal LM tests that ignore either serial correlation over time or spatial error correlation. The paper then derives conditional LM and LR tests that do not ignore these correlations and contrast them with their marginal LM and LR counterparts. The small sample performance of these tests is investigated using Monte Carlo experiments. As expected, ignoring any correlation when it is significant can lead to misleading inference.     

The combined equilibrium of travel networks and residential location markets

The combined ‘user’ equilibrium of travel networks and residential location markets is shown to exist and to be unique in the expected allocation of households to residential locations and to the routes and links of the network, in the vacancies and rents of residential locations and in the congested travel time and cost of each network link. The formulation combines a multinomial logit model of households' location and route choices derived from utility maximization, a binary logit model of house owners' offer decisions derived from profit maximization and the standard model of network congestion. A travel disutility measure (consistent with utility maximization) replaces the standard ‘generalized cost function’. The proof utilizes a non-linear programming formulation which reproduces the simultaneous equilibrium conditions of the behavioral formulation. The stability of the unique equilibrium position is briefly discussed, a computational algorithm is proposed and hints for generalized formulations are provided.     

Some comparisons of tests for a shift in the slopes of a multivariate linear time series model

Our objective is to find a simple, robust, reasonably powerful test for a shift in one or more of the slopes in a linear time series model at some unknown point of time. Two such tests are ‘Chow's test’ (1960) for a shift at the midpoint of the record and the ‘Farley-Hinich test’ (1970b); both can be performed easily with standard regression programs. In section 2, we compare the asymptotic properties of these tests when the disturbance variance is known. As expected, Chow's test is superior when the true shift is near the middle of the record; with a single, uniformly-distributed explanatory variable, the Farley-Hinich tests dominates over the remaining eighty-four percent of the record. In section 3, we describe the results of some Monte Carlo experiments with a finite sample, which can be summarized as follows. (i) The asymptotic results of section 2 were appropriate for finite sample power comparisons. (ii) The relative performance of the two tests does not depend appreciably on whether the variance is known. (iii) The likelihood ratio test, which is far more costly to perform than the other two tests, does not dominate either Chow's test or the Farley-Hinich test; it has moderately more power at the ends of the record, moderately less in the middle. The conclusion is clear: at low cost (in terms of computer cost and lost power), one can reduce the probability of over- looking a structural shift by routinely performing Chow's test or the Farley-Hinich test.     

ON COMPARING MACROECONOMIC MODELS USING FORECAST ENCOMPASSING TESTS

ABSTRACT It is clearly of interest to macroeconomists to be able to evaluate whether one large-scale macroeconometric model ‘is better’ than another. Although comparisons between models are sometimes invidious, because the purposes for which the models were built differ, it is the case that formal comparisons of two models' statistical properties are rare. This is in spite of considerable theoretical advances in the econometric methodology, namely the development and use of non-nested and encompassing tests. Chong and Hendry (1986) advocate the use of the forecast encompassing regressions, where the outturns are regressed on competing (one-step-ahead) forecasts. This paper reports the findings of applying this rather easy-to-use method of comparing large scale macroeconometric models. The forecast data we use are those published by three macroeconometric modelling groups, namely: Liverpool; the National Institute; and The London Business School. Forecasts for up to three years ahead are published for unemployment, growth, and inflation, throughout the 1980's. Forecast encompassing tests fail to separate one model from another, based on one-year-ahead forecasts. Each model ‘wins’ once. However, the conclusions are not the same as using root-mean-square-forecast-error criteria, illustrating Clements and Hendry's (1994) observation that minimum root-mean-square-forecast-error is neither necessary nor sufficient for a model to have constant parameters, to provide accurate forecasts, or to encompass its rivals.     

Further remarks on the Global Newton method

In this work, we are concerned with the behavior of Smale's ‘Global Newton’ process, starting from points not necessarily on the boundary. We find that the process is locally system stable in the sense that, sufficiently near an equilibrium, one is almost always led to some equilibrium of the system. However, the ‘Global Newton’ process is found typically not to be globally stable; instead, families of cycles appear, preventing convergence to equilibrium.     

Exact permutation tests for non-nested non-linear regression models

This paper proposes exact distribution-free permutation tests for the specification of a non-linear regression model against one or more possibly non-nested alternatives. The new tests may be validly applied to a wide class of models, including models with endogenous regressors and lag structures. These tests build on the well-known J test developed by Davidson and MacKinnon [1981. Several tests for model specification in the presence of alternative hypotheses. Econometrica 49, 781–793] and their exactness holds under broader assumptions than those underlying the conventional J test. The J-type test statistics are used with a randomization or Monte Carlo resampling technique which yields an exact and computationally inexpensive inference procedure. A simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions. The test procedure developed is illustrated by an application to inflation dynamics.     

Model specification tests: A simultaneous approach

In econometrics, specification tests have been constructed to verify the validity of one specification at a time. It is argued that most of these tests are not, in general, robust in the presence of other misspecifications, so their application may result in misleading conclusions. Using the Lagrange Multiplier principle we develop efficient test procedures that are capable of testing a number of specifications simultaneously. These tests will ‘confirm’ the validity (or invalidity) of a general model requiring the estimates of the restricted model only. Through an extensive Monte Carlo experiment we study the performance of these tests and some commonly used one-directional tests. We also suggest a Multiple Comparison Procedure, to identify different sources of errors. This, we hope, will lead to a better specification of econometric models.     

Migrants Encounter Migrants in the City: the Changing Context of ‘Home’ for Second‐Generation Greek‐American Return Migrants

This article looks at the ‘return’ migration of second‐generation Greek Americans to their parents’ homeland, Greece. It is based on interviews with, and written accounts supplied by, 40 participants in the research, all now living in the Athens region. The article addresses two main sets of questions. First, why do they relocate to Greece, what are they looking for, and how do they cope with difficulties and disappointments? Second, and more specifically, how do they react to the fact that Greece is no longer a homogenous hellenistic society, but has become in recent years a de facto multicultural one due to the presence of hundreds of thousands of immigrant workers and their families? Three hypotheses are proposed for this inter‐migrant encounter: returnees, shocked by the ‘new immigration’, view it negatively as upsetting the ‘pure Greek’ homeland they had hoped to find; returnees are more sympathetic because of their own families’ history as immigrants in multicultural America; and returnees differentiate themselves as ‘good’ migrants from Greece’s immigrants who are constructed as ‘bad’ migrants. Evidence from the migrants’ testimonies is found to support all three hypotheses; however, there is more support for the second one. In addition, a fourth outcome was voiced: that of discrimination against Greek Americans who are made to feel, in certain circumstances, outsiders by the ‘true’ Greeks. Suggestions are made for further comparative research.     

A way of modelling investment in a multisectoral model

The paper contains an example of how to introduce heterogeneity of capital in the model framework given by Leif Johansen's so called MSG-model. Heterogeneity of capital is in terms of differences among sectors and differences among ‘vintages’ or ‘techniques’ within each sector.     

The location theory of firm revisited impacts of rising energy prices

The impact of rising energy prices on the locational pattern of industries is analyzed by a simple two-firm straight line location model. The concavity of average cost function of final consumer's good with respect to locational variables is proved for the case of linear homogeneous Cobb- Douglas production functions and this leads to the possible three cases of end-point location. The rise in energy prices induces ‘double location at the market’ or ‘double location at the port’ instead of separate location of two industries, i.e., intermediate good industry and consumer's good industry.