A martingale approach for testing diffusion models based on infinitesimal operator

I develop an omnibus specification test for diffusion models based on the infinitesimal operator. The infinitesimal operator based identification of the diffusion process is equivalent to a “martingale hypothesis” for the processes obtained by a transformation of the original diffusion model. My test procedure is then constructed by checking the “martingale hypothesis” via a multivariate generalized spectral derivative based approach that delivers a N(0,1) asymptotical null distribution for the test statistic. The infinitesimal operator of the diffusion process is a closed-form function of drift and diffusion terms. Consequently, my test procedure covers both univariate and multivariate diffusion models in a unified framework and is particularly convenient for the multivariate case. Moreover, different transformed martingale processes contain separate information about the drift and diffusion specifications. This motivates me to propose a separate inferential test procedure to explore the sources of rejection when a parametric form is rejected. Simulation studies show that the proposed tests have reasonable size and excellent power performance. An empirical application of my test procedure using Eurodollar interest rates finds that most popular short-rate models are rejected and the drift misspecification plays an important role in such rejections.     

The impact of purchasing power parity on auto foreign trade

In this study, the validity of the assumption saying that the import and export are a function of prices as in the classical, neo-classical approaches is studied within the framework of the import and export of automobile vehicles between 1997 and 2003 in Turkey and the EU countries which are automobile manufacturers. The price here is considered as the purchasing power parity. The effect of the purchasing power parity on the automobile import and export is determined by using classical models with constant coefficients, and fixed and random effects models with constant slope coefficients and a constant term differing according to units and/or time. The models comprise balanced linear panel data models. The likelihood ratio test and F-test are used in the selection of fixed effects and classical models; and the Lagrange multiplier test is used in the selection of random effects and classical models. As for the selection of fixed and random effects models, the Hausman test is used. As a result of these tests, the fixed effects models covering both individual and time effects are selected as the most appropriate import and export models.     

Estimation and testing of stochastic frontier models using variational Bayes

We show how a wide range of stochastic frontier models can be estimated relatively easily using variational Bayes. We derive approximate posterior distributions and point estimates for parameters and inefficiency effects for (a) time invariant models with several alternative inefficiency distributions, (b) models with time varying effects, (c) models incorporating environmental effects, and (d) models with more flexible forms for the regression function and error terms. Despite the abundance of stochastic frontier models, there have been few attempts to test the various models against each other, probably due to the difficulty of performing such tests. One advantage of the variational Bayes approximation is that it facilitates the computation of marginal likelihoods that can be used to compare models. We apply this idea to test stochastic frontier models with different inefficiency distributions. Estimation and testing is illustrated using three examples.     

A general dependence test and applications

We describe a test, based on the correlation integral, for the independence of a variable and a vector that can be used with serially dependent data. Monte Carlo simulations suggest that the test has good power to detect dependence in several models, performing nearly as well or better than the BDS test in univariate time series and complementing the BDS test in distributed lag models. Finally, we apply our test in conjunction with the BDS test to examine models of US unemployment rates. © 1998 John Wiley & Sons, Ltd.     

What model for entry in first-price auctions? A nonparametric approach

We develop a selective entry model for first-price auctions that nests two polar models often estimated in the empirical literature on auctions, Levin and Smith (1994), and Samuelson (1985). The selective entry model features a pro-competitive selection effect. The selection effect is shown to be nonparametrically identifiable, and a nonparametric test for its presence is proposed. This test can be used to discriminate between the two polar models.     

Predicting the portfolio risk of high-dimensional international stock indices with dynamic spatial dependence

The spatial dependence of assets, which relates to similarities in economic, political, or cultural systems and other aspects, has been confirmed through empirical research; however, spatial dependence has rarely been applied to financial risk measurement. To fill this gap in the literature, a dynamic spatial GARCH-copula (sGC) model is proposed in this paper to evaluate the portfolio risk of international stock indices. In this model, a spatial GARCH is used as the marginal distribution and vine copula is adopted as the joint distribution of indices. Then, the proposed model is applied empirically to assess portfolio risk. Results show that, first, the proposed risk prediction model with spatial dependence outperforms a model neglecting spatial effects per the Kupiec test, Z test and Christoffersen test. Risk prediction during periods of economic stability is also more accurate than during times of crisis. Second, risk measures for models with spatial dependence are higher than those without such dependence but lower than for vine copula models. Third, models including either spatial dependence or vine copulas alone exhibit relatively poor performance. Fourth, the model involving extreme value theory (EVT) generates the greatest value at risk to pass the Kupiec test, Z test and Christoffersen test; however, this model is not suitable for characterizing international indices with EVT based on negative values of the shape parameters of estimates. Findings offer important implications for personal investors, institutional investors, and national regulatory authorities.     

Heteroscedasticity diagnostics for <Emphasis Type="Italic">t</Emphasis> linear regression models

The t regression models provide a useful extension of the normal regression models for datasets involving errors with longer-than-normal tails. Homogeneity of variances (if they exist) is a standard assumption in t regression models. However, this assumption is not necessarily appropriate. This paper is devoted to tests for heteroscedasticity in general t linear regression models. The asymptotic properties, including asymptotic Chi-square and approximate powers under local alternatives of the score tests, are studied. Based on the modified profile likelihood (Cox and Reid in J R Stat Soc Ser B 49(1):1–39, 1987), an adjusted score test for heteroscedasticity is developed. The properties of the score test and its adjustment are investigated through Monte Carlo simulations. The test methods are illustrated with land rent data (Weisberg in Applied linear regression. Wiley, New York, 1985). The project supported by NSFC 10671032, China, and a grant (HKBU2030/07P) from the Grant Council of Hong Kong, Hong Kong, China.     

Canonical forms and tests of hypotheses Part II: Multivariate mixed linear models

Abstract  In the literature on multivariate analysis of variance, exact test procedures are restricted to linear models with fixed effects only. In this paper tests are presented for multivarite linear hypotheses with respect to mixed models, which constitude a generalization of (univariate) regular models described by R oebruck (1982). Furthermore it is shown, that the matrices, which are used to compute the test statistics, can be derived from the univariate "sums of squares" in the same manner as in the case of fixed models. The applicability of this theory is demonstrated by two examples.     

A simple test for regression specification with non-nested alternatives

In this paper, I introduce a simple test for the presence of the data-generating process among several non-nested alternatives. The test is an extension of the classical J test for non-nested regression models. I also provide a bootstrap version of the test that avoids possible size distortions inherited from the J test.     

Exact linear rank tests for two‐sample equivalence problems with continuous data

The present paper introduces a methodology for the semiparametric or non‐parametric two‐sample equivalence problem when the effects are specified by statistical functionals. The mean relative risk functional of two populations is given by the average of the time‐dependent risk. This functional is a meaningful non‐parametric quantity, which is invariant under strictly monotone transformations of the data. In the case of proportional hazard models, the functional determines just the proportional hazard risk factor. It is shown that an equivalence test of the type of the two‐sample Savage rank test is appropriate for this functional. Under proportional hazards, this test can be carried out as an exact level α test. It also works quite well under other semiparametric models. Similar results are presented for a Wilcoxon rank‐sum test for equivalence based on the Mann–Whitney functional given by the relative treatment effect.     

An automatic Portmanteau test for serial correlation

This article introduces a data-driven Box–Pierce test for serial correlation. The proposed test is very attractive compared to the existing ones. In particular, implementation of this test is extremely simple for two reasons: first, the researcher does not need to specify the order of the autocorrelation tested, since the test automatically chooses this number; second, its asymptotic null distribution is chi-square with one degree of freedom, so there is no need of using a bootstrap procedure to estimate the critical values. In addition, the test is robust to the presence of conditional heteroskedasticity of unknown form. Finally, the proposed test presents higher power in simulations than the existing ones for models commonly employed in empirical finance.     

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.     

An unbiased model comparison test using cross-validation

Social scientists often consider multiple empirical models of the same process. When these models are parametric and non-nested, the null hypothesis that two models fit the data equally well is commonly tested using methods introduced by Vuong (Econometrica 57(2):307–333, 1989) and Clarke (Am J Political Sci 45(3):724–744, 2001; J Confl Resolut 47(1):72–93, 2003; Political Anal 15(3):347–363, 2007). The objective of each is to compare the Kullback–Leibler Divergence (KLD) of the two models from the true model that generated the data. Here we show that both of these tests are based upon a biased estimator of the KLD, the individual log-likelihood contributions, and that the Clarke test is not proven to be consistent for the difference in KLDs. As a solution, we derive a test based upon cross-validated log-likelihood contributions, which represent an unbiased KLD estimate. We demonstrate the CVDM test’s superior performance via simulation, then apply it to two empirical examples from political science. We find that the test’s selection can diverge from those of the Vuong and Clarke tests and that this can ultimately lead to differences in substantive conclusions.     

Modelling Category Inflation with Multiple Inflation Processes: Estimation,Specification and Testing1

Zero-inflated ordered probit (ZIOP) and middle-inflated ordered probit (MIOP) models are finding increasing favour in the discrete choice literature. We propose generalizations to these models – which collapse to their ZIOP/MIOP counterparts under a set of simple parameter restrictions – with respect to the inflation process. These generalizations form the basis of a new specification test of the inflation process in ZIOP and MIOP models. Support for our generalization framework is principally demonstrated by revisiting a key ZIOP application from the economics literature, and reinforced by the reassessment of an important MIOP application from political science. Our specification test supports the generalized models over the original ZIOP/MIOP ones, suggesting an important role for it in modelling zero- and middle-inflation processes.     

Modelling Category Inflation with Multiple Inflation Processes: Estimation,Specification and Testing1

Zero‐inflated ordered probit (ZIOP) and middle‐inflated ordered probit (MIOP) models are finding increasing favour in the discrete choice literature. We propose generalizations to these models – which collapse to their ZIOP/MIOP counterparts under a set of simple parameter restrictions – with respect to the inflation process. These generalizations form the basis of a new specification test of the inflation process in ZIOP and MIOP models. Support for our generalization framework is principally demonstrated by revisiting a key ZIOP application from the economics literature, and reinforced by the reassessment of an important MIOP application from political science. Our specification test supports the generalized models over the original ZIOP/MIOP ones, suggesting an important role for it in modelling zero‐ and middle‐inflation processes.     

Do dropouts suffer from dropping out? Estimation and prediction of outcome gains in generalized selection models

In this paper we describe methods for predicting distributions of outcome gains in the framework of a latent variable selection model. We describe such procedures for Student‐t selection models and a finite mixture of Gaussian selection models. Importantly, our algorithms for fitting these models are simple to implement in practice, and also permit learning to take place about the non‐identified cross‐regime correlation parameter. Using data from High School and Beyond, we apply our methods to determine the impact of dropping out of high school on a math test score taken at the senior year of high school. Our results show that selection bias is an important feature of this data, that our beliefs about this non‐identified correlation are updated from the data, and that generalized models of selectivity offer an improvement over the ‘textbook’ Gaussian model. Further, our results indicate that on average dropping out of high school has a large negative impact on senior‐year test scores. However, for those individuals who actually drop out of high school, the act of dropping out of high school does not have a significantly negative impact on test scores. This suggests that policies aimed at keeping students in school may not be as beneficial as first thought, since those individuals who must be induced to stay in school are not the ones who benefit significantly (in terms of test scores) from staying in school. Copyright © 2004 John Wiley & Sons, Ltd.     

Testing for Misspecification in Binary Response Models with Competing Distributions*

In empirical studies, the probit and logit models are often used without checks for their competing distributional specifications. It is also rare for econometric tests to be focused on this issue. Santos Silva [Journal of Applied Econometrics (2001 ), Vol. 16, pp. 577–597] is an important recent exception. By using the conditional moment test principle, we discuss a wide class of non‐nested tests that can easily be applied to detect the competing distributions for the binary response models. This class of tests includes the test of Santos Silva (2001 ) for the same task as a particular example and provides other useful alternatives. We also compare the performance of these tests by a Monte Carlo simulation.     

Marriage Market,Parents’ Bargaining Powers,and Children's Nutrition and Education*

Test of resource pooling and test of effect of sex ratio in the marriage market on intrahousehold resource allocation are combined to test the unitary household model. The consistency condition between the two tests is derived to test the Nash household bargaining and Pareto‐efficient household models. I examine intrahousehold resource allocation to children's nutrition and education in Indonesia. For children's nutrition, the unitary household model is rejected in favour of the non‐unitary models. The results for investment in education are mixed. The decision‐making process may differ depending on the type of decision being made.     

Testing for correlation in error-component models

This paper concerns linear models for grouped data with group-specific effects. We construct a portmanteau test for the null of no within-group correlation beyond that induced by the group-specific effect. The approach allows for heteroskedasticity and is applicable to models with exogenous, predetermined, or endogenous regressors. The test can be implemented as soon as three observations per group are available and is applicable to unbalanced data. A test with such general applicability is not available elsewhere. We provide theoretical results on size and power under asymptotics where the number of groups grows but their size is held fixed. Extensive power comparisons with other tests available in the literature for special cases of our setup reveal that our test compares favorably. In a simulation study we find that, under heteroskedasticity, only our procedure yields a test that is both size correct and powerful. In a large data set on mothers with multiple births we find that infant birthweight is correlated across children even after controlling for mother fixed effects and a variety of prenatal care factors. This suggests that such a strategy may be inadequate to take care of all confounding factors that correlate with the mother's decision to engage in activities that are detrimental to the infant's health, such as smoking.