GENERALIZED INTEGER-VALUED AUTOREGRESSION

The integer-valued AR1 model is generalized to encompass some of the more likely features of economic time series of count data. The generalizations come at the price of loosing exact distributional properties. For most specifications the first and second order both conditional and unconditional moments can be obtained. Hence estimation, testing and forecasting are feasible and can be based on least squares or GMM techniques. An illustration based on the number of plants within an industrial sector is considered.     

Panel data unit roots tests: The role of serial correlation and the time dimension

We investigate the influence of residual serial correlation and of the time dimension on statistical inference for a unit root in dynamic longitudinal data, known as panel data in econometrics. To this end, we introduce two test statistics based on method of moments estimators. The first is based on the generalized method of moments estimators, while the second is based on the instrumental variables estimator. Analytical results for the Instrumental Variables (IV) based test in a simplified setting show that (i) large time dimension panel unit root tests will suffer from serious size distortions in finite samples, even for samples that would normally be considered large in practice, and (ii) negative serial correlation in the error terms of the panel reduces the power of the unit root tests, possibly up to a point where the test becomes biased. However, near the unit root the test is shown to have power against a wide range of alternatives. These findings are confirmed in a more general set-up through a series of Monte Carlo experiments.     

Reduced-rank regression: A useful determinant identity

We formulate an identity for the determinant of a product involving rectangular matrices. The identity can be used to derive the maximum likelihood estimator in reduced-rank regressions with Gaussian innovations. Furthermore, the identity sheds light on the structure of the estimation problem that arises when the reduced-rank parameters are subject to additional constraints.     

A CONSISTENT MODEL SPECIFICATION TEST FOR A REGRESSION FUNCTION BASED ON NONPARAMETRIC WAVELET ESTIMATION

In this paper we present a consistent specification test of a parametric regression function against a general nonparametric alternative. The proposed test is based on wavelet estimation and it is shown to have similar rates of convergence to the more commonly used kernel based tests. Monte Carlo simulations show that this test statistic has adequate size and high power and that it compares favorably with its kernel based counterparts in small samples.     

Inferences on the difference and ratio of the means of two inverse Gaussian distributions

Methods for interval estimation and hypothesis testing about the ratio of two independent inverse Gaussian (IG) means based on the concept of generalized variable approach are proposed. As assessed by simulation, the coverage probabilities of the proposed approach are found to be very close to the nominal level even for small samples. The proposed new approaches are conceptually simple and are easy to use. Similar procedures are developed for constructing confidence intervals and hypothesis testing about the difference between two independent IG means. Monte Carlo comparison studies show that the results based on the generalized variable approach are as good as those based on the modified likelihood ratio test. The methods are illustrated using two examples.     

A SCORE TEST FOR SEASONAL FRACTIONAL INTEGRATION AND COINTEGRATION

This paper develops a time domain score statistic for testing fractional integration at zero and seasonal frequencies in quarterly time series models. Further, it introduces the notion of fractional cointegration at different frequencies between two seasonally integrated, I(1) series. In testing problems involving seasonal fractional cointegration, it is argued that the alternative hypothesis is one-sided for which the usual score test may not be appropriate. Therefore, based on ideas in Silvapulle and Silvapulle (1995), a one-sided score statistic is constructed. A simulation study finds that the score statistic generally has desirable size and power properties in moderately sized samples. The score test is applied to the quarterly Australian consumption function. The income and consumption series are found to be I(1) at zero and seasonal frequencies and these two series are not cointegrated at any frequency.     

Better approximate confidence intervals for a binomial parameter

This paper discusses five methods for constructing approximate confidence intervals for the binomial parameter Θ, based on Y successes in n Bernoulli trials. In a recent paper, Chen (1990) discusses various approximate methods and suggests a new method based on a Bayes argument, which we call method I here. Methods II and III are based on the normal approximation without and with continuity correction. Method IV uses the Poisson approximation of the binomial distribution and then exploits the fact that the exact confidence limits for the parameter of the Poisson distribution can be found through the x² distribution. The confidence limits of method IV are then provided by the Wilson-Hilferty approximation of the x². Similarly, the exact confidence limits for the binomial parameter can be expressed through the F distribution. Method V approximates these limits through a suitable version of the Wilson-Hilferty approximation. We undertake a comparison of the five methods in respect to coverage probability and expected length. The results indicate that method V has an advantage over Chen's Bayes method as well as over the other three methods.     

ESTIMATION OF THE VECTOR MOVING AVERAGE MODEL BY VECTOR AUTOREGRESSION

We examine a simple estimator for the multivariate moving average model based on vector autoregressive approximation. In finite samples the estimator has a bias which is low where roots of the characteristic equation are well away from the unit circle, and more substantial where one or more roots have modulus near unity. We show that the representation estimated by this multivariate technique is consistent and asymptotically invertible. This estimator has significant computational advantages over Maximum Likelihood, and more importantly may be more robust than ML to mis-specification of the vector moving average model. The estimation method is applied to a VMA model of wholesale and retail inventories, using Canadian data on inventory investment, and allows us to examine the propagation of shocks between the two classes of inventory.     

Monte carlo sampling approach to testing nonnested hypothesis: monte carlo results

Alternative ways of using Monte Carlo methods to implement a Cox-type test for separate families of hypotheses are considered. Monte Carlo experiments are designed to compare the finite sample performances of Pesaran and Pesaran's test, a RESET test, and two Monte Carlo hypothesis test procedures. One of the Monte Carlo tests is based on the distribution of the log-likelihood ratio and the other is based on an asymptotically pivotal statistic. The Monte Carlo results provide strong evidence that the size of the Pesaran and Pesaran test is generally incorrect, except for very large sample sizes. The RESET test has lower power than the other tests. The two Monte Carlo tests perform equally well for all sample sizes and are both clearly preferred to the Pesaran and Pesaran test, even in large samples. Since the Monte Carlo test based on the log-likelihood ratio is the simplest to calculate, we recommend using it.     

A CONSISTENT MODEL SPECIFICATION TEST BASED ON THE KERNEL SUM OF SQUARES OF RESIDUALS

This paper constructs a consistent model specification test based on the difference between the nonparametric kernel sum of squares of residuals and the sum of squares of residuals from a parametric null model. We establish the asymptotic normality of the proposed test statistic under the null hypothesis of correct parametric specification and show that the wild bootstrap method can be used to approximate the null distribution of the test statistic. Results from a small simulation study are reported to examine the finite sample performance of the proposed tests.     

Power kurtosis transformations: Definition, properties and ordering

Summary Heavy tail distributions can be generated by applying specific non-linear transformations to a Gaussian random variable. Within this work we introduce power kurtosis transformations which are essentially determined by their generator function. Examples are theH-transformation of Tukey (1960), theK-transformation of MacGillivray and Cannon (1997) and theJ-transformation of Fischer and Klein (2004).Furthermore, we derive a general condition on the generator function which guarantees that the corresponding transformation is actually tail-increasing. In this case the exponent of the power kurtosis transformation can be interpreted as a kurtosis parameter. We also prove that the transformed distributions can be ordered with respect to the partial ordering of van Zwet (1964) for symmetric distributions.     

BAYESIAN ANALYSIS OF A FRACTIONAL COINTEGRATION MODEL

The concept of fractional cointegration, whereby deviations from an equilibrium relationship follow a fractionally integrated process, has attracted some attention of late. The extended concept allows cointegration to be associated with mean reversion in the error, rather than requiring the more stringent condition of stationarity. This paper presents a Bayesian method for conducting inference about fractional cointegration. The method is based on an approximation of the exact likelihood, with a Jeffreys prior being used to offset identification problems. Numerical results are produced via a combination of Markov chain Monte Carlo algorithms. The procedure is applied to several purchasing power parity relations, with substantial evidence found in favor of parity reversion.     

A BAYESIAN INTERPRETATION OF MULTIPLE POINT ESTIMATES

Consider a large number of econometric investigations using different estimation techniques and/or different subsets of all available data to estimate a fixed set of parameters. The resulting empirical distribution of point estimates can be shown - under suitable conditions - to coincide with a Bayesian posterior measure on the parameter space induced by a minimum information procedure. This Bayesian interpretation makes it easier to combine the results of various empirical exercises for statistical decision making. The collection of estimators may be generated by one investigator to ensure the satisfaction of our conditions, or they may be collected from published works, where behavioral assumptions need to be made regarding the dependence structure of econometric studies.     

Dynamic factor models

Summary Factor models can cope with many variables without running into scarce degrees of freedom problems often faced in a regression-based analysis. In this article we review recent work on dynamic factor models that have become popular in macroeconomic policy analysis and forecasting. By means of an empirical application we demonstrate that these models turn out to be usefu in investigating macroeconomic problems.     

SIZE CHARACTERISTICS OF TESTS FOR SAMPLE SELECTION BIAS: A MONTE CARLO COMPARISON AND EMPIRICAL EXAMPLE

The t-test of an individual coefficient is used widely in models of qualitative choice. However, it is well known that the t-test can yield misleading results when the sample size is small. This paper provides some experimental evidence on the finite sample properties of the t-test in models with sample selection biases, through a comparison of the t-test with the likelihood ratio and Lagrange multiplier tests, which are asymptotically equivalent to the squared t-test. The finite sample problems with the t-test are shown to be alarming, and much more serious than in models such as binary choice models. An empirical example is also presented to highlight the differences in the calculated test statistics.     

The microeconometric estimation of treatment effects—An overview

Summary The need to evaluate the performance of active labour market policies is not questioned any longer. Even though OECD countries spend significant shares of national resources on these measures, unemployment rates remain high or even increase. We focus on microeconometric evaluation which has to solve the fundamental evaluation problem and overcome the possible occurrence of selection bias. When using non-experimental data, different evaluation approaches can be thought of. The aim of this paper is to review the most relevant estimators, discuss their identifying assumptions and their (dis-)advantages. Thereby we will present estimators based on some form of exogeneity (selection on observables) as well as estimators where selection might also occur on unobservable characteristics. Since the possible occurrence of effect heterogeneity has become a major topic in evaluation research in recent years, we will also assess the ability of each estimator to deal with it. Additionally, we will also discuss some recent extensions of the static evaluation framework to allow for dynamic treatment evaluation. The authors thank Stephan L. Thomsen, Christopher Zeiss and one anonymous referee for valuable comments. The usual disclaimer applies.     

Estimation of the number of vertices of different degrees in a graph

An unknown graph is partially observed by selecting a vertex sample and observing the edges in the subgraph induced by the sample. The sample is selected by either simple random sampling or Bernoulli sampling. We consider the problem of estimating the numbers of vertices of different degrees in the unknown graph by using the sample information. Unbiased estimators are given and their variance-covariance matrix is shown to depend on a set of intrinsic graph parameters which can hardly be satisfactorily estimated from the sample information without further assumptions. In particular, the problem of estimating the number of isolates (vertices of degree zero) is considered in some detail.     

Using HP Filtered Data for Econometric Analysis: Some Evidence from Monte Carlo Simulations

Summary: The Hodrick-Prescott (HP) filter has become a widely used tool for detrending integrated time series. Even if the methodological literature sums up an extensive catalogue of severe criticism against an econometric analysis of HP filtered data, the original Hodrick and Prescott (1980, 1997) suggestion to measure the strength of association between economic variables by a regression analysis of corresponding HP filtered time series appears to be very popular. This might be justified if HP induced distortions were quantitatively negligible in empirical applications. However, the simulated regression analyses presented in our paper demonstrate that any attempts of inference based on HP prefiltered series are challenged by a serious risk of spurious regression results. We would like to thank the participants of the Fourth Workshop in Macroeconometrics at the Halle Institute for Economic Research for their comments on a preliminary version of this paper. We are also indebted to the participants of the Thirtieth Macromodels International Conference, in particular David Hendry, S?ren Johansen, Katarina Juselius and Helmut Lütkepohl, for stimulating discussions and fruitful suggestions which helped to improve our paper. Finally, Larry Arnoldy helped to improve the final version of the paper.     

Comparing variances and means when distributions have non-identical shapes

The paper compares several methods for computing robust 1-α confidence intervals for σ ₁ ²-σ ₂ ², or σ ₁ ²/σ ₂ ², where σ ₁ ² and σ ₂ ² are the population variances corresponding to two independent treatment groups. The emphasis is on a Box-Scheffe approach when distributions have different shapes, and so the results reported here have implications about comparing means. The main result is that for unequal sample sizes, a Box-Scheffe approach can be considerably less robust than indicated by past investigations. Several other procedures for comparing variances, not based on a Box-Scheffe approach, were also examined and found to be highly unsatisfactory although previously published papers found them to be robust when the distributions have identical shapes. Included is a new result on why the procedures examined here are not robust, and an illustration that increasing σ ₁ ²-σ ₂ ² can reduce power in certain situations. Constants needed to apply Dunnett’s robust comparison of means are included.     

消费者在C2C交易中的信任模型与数据检验

为了探究个体消费者怎样在C2C交易中形成对个体卖方的信任,提出了消费者的信任结构方程模型,并通过情景泛义模拟实验采集的数据进行检验。文章得出：消费者的感知网站质量是最主要因素,信任机制至关重要,C2C平台市场比个体卖方作用更大,声誉的影响强于规模,买卖方的交互比较关键等结论。