Statistical inference of partially linear varying coefficient spatial autoregressive models

This paper proposes a semiparametric partially linear varying coefficient spatial autoregressive model, which is a generalization of standard spatial autoregressive model and partially linear spatial autoregressive model. To estimate the unknown spatial lag parameter, constant coefficients and coefficient functions, a profile quasi-maximum likelihood approach based on the local-linear method is introduced. To test the existence of the spatial effects, a generalized likelihood ratio test statistic is proposed, and a residual-based bootstrap procedure is used to derive the p-value of the test. Some simulations are conducted to examine the performance of our proposed procedures and the results are satisfactory. Furthermore, a real-world example is given to demonstrate the application of the proposed procedures.     

Model Selection in Spatial Autoregressive Models with Varying Coefficients

Spatial autoregressive (SAR) models with varying coefficients are useful for capturing heterogeneous effects of the impacts of covariates as well as spatial interaction in empirical studies, and a wide range of popular models can be seen as its special cases, such as linear SAR models. In this study, we will propose a unified model selection method for the SAR model with varying coefficients to achieve two targets simultaneously: (1) variable selection (eliminate irrelevant covariates), and (2) identification of the covariates with constant effect among the relevant covariates. To do so, we follow the idea of group LASSO to incorporate two penalty functions to simultaneously do model selection and estimation. Monte Carlo experiments show that the proposed method performs well in finite samples. Finally, we illustrate the method with an application to the housing data of Chinese cities.     

Maximum likelihood estimation of time-varying parameters: an application to the Athens Stock Exchange index

The problem of maximum likelihood estimation of time-varying parameters is considered. A hierarchical approach is proposed that involves, first, the estimation of the model order and parameters when they are assumed time-invariant. Second, for each parameter, an autoregressive (AR) model, with constant coefficients, is developed. This allows the parameters to change over time. Finally, the estimates of the AR coefficients for each parameter are used as initial conditions to a time-varying model with AR coefficients, which are allowed to change over time subject to some regularity constraints. This approach is then applied to the Athens Stock Exchange index, where the dominant forces affecting this index are analysed.     

On the flexibility of the Rotterdam model

The Rotterdam model is a discrete approximation to a continuous time model and the approximation errors are known to be small. Unlike other approximations, with fixed parameters at the point of approximation, the Rotterdam model's coefficients differ at each observation, but are treated as constants during estimation. This procedure introduces relatively large approximation errors which are a potential source of bias. In this paper the performance of the Rotterdam model in reproducing the characteristics of four integrable demand systems is assessed. As anticipated, the model's performance is directly related to the variability of the underlying coefficients and the bias in the parameter estimates is minimal if the coefficients are relatively constant. The model can also discriminate well against an invalid alternative hypothesis. However, in the absence of a computationally feasible varying parameter methodology the conclusion has to be that tests of parameter stability are essential when using the Rotterdam model.     

Static and dynamic forecasting of short-run demand for money

Previous studies of static and dynamic out-of-sample simulations of the demand for money have indicated a breakdown in the short-run real money balances over the past 1974 forecast period. Using the varying parameter regression technique, the findings of this paper demonstrate that previous results are misleading because the shift of the money demand is obscured by the constant coefficient estimation technique. Our estimation procedure has not only drastically improved both static and dynamic forecasts but has also solved the missing money puzzle.     

An extension of mixed estimation,with an application to forecasting new product growth

This paper extends the mixed estimation technique to handle a case in which the coefficients of a set of linear constraints are known nonlinear functions of an unknown parameter vector for which an extraneous unbiased estimate is available. This novel form of the mixed estimation technique is illustrated by applying it to the Bass innovation/diffusion model of new product growth. It is suggested that this is superior to the traditional method whereby managerial intuition is incorporated into this type of model, and is an attractive alternative to recently-suggested Bayesian methods.I thank an anonymous referee for helpful comments and references.     

Nonlinearity in dynamic adjustment: Semiparametric estimation of panel labor supply

We estimate a semiparametric dynamic panel data model by the local linear kernel method and we interpret the slope of the nonparametric component function as a varying slope coefficient. Thus, the slope coefficient is a smooth, but otherwise unknown, function of some of the regressors. A Monte Carlo experiment is reported to examine the finite sample performance of the local linear estimator. We apply the estimation method to a labor supply equation for men from the triannual Survey of Income and Program Participation (SIPP). Specification tests based on the estimated labor supply elasticities, partial adjustment coefficients, and residuals demonstrate the improvements from a semiparametric partially linear model. Our empirical results point to a need by economists to revisit the issue of the speed of labor market adjustment to policy induced shifts in labor demand and to take more formal econometric account of heterogeneity in wage effects when studying the distributional consequences of tax reforms for labor supply earnings. First version received: July 2000/Final version received: January 2001     

A new estimator for trade costs and its small sample properties

This paper discusses the estimation of parameters of a traditional transportation model, as it is typically present in so-called Takayama–Judge type spatial price equilibrium models. In contrast to previously used estimation methods, observations of regional prices as well as of trade costs are used in a direct estimation of the first order conditions. The proposed method uses bi-level programming techniques to minimize a weighted least squares criterion under the restriction that the estimated parameters satisfy the Kuhn–Tucker conditions for an optimal solution of the transport model. A penalty function and a smooth reformulation are used to iteratively approximate the complementary slackness conditions. Monte-Carlo simulations are used to trace out some properties of the estimator and compare it with a traditional calibration method. The analysis shows that the proposed technique estimates prices as well as trade costs more precisely than the traditional calibration method. It is suggested to apply the same method to a range of linear and quadratic models.     

THE KNOWLEDGE-CAPITAL MODEL OF FDI: A TIME VARYING COEFFICIENTS APPROACH

The present article reexamines some of the issues regarding the Knowledge-Capital Model that encompasses both horizontal and vertical Foreign Direct Investment. The empirical support for this model is however mixed. This article proposes a new way of estimating coefficients by allowing them to vary over time. The estimation results obtained using data from 30 OECD countries for the period from 1982 to 2003 confirm that these coefficients cannot be considered as constant over time and that the vertical component of the Knowledge-Capital Model is relevant.     

Small Sample Properties Of Existing And New Estimators Of The Autocorrelation Coefficient And Regression Coefficients In The Context Of Ar(1) Errors

This study systematically and comprehensively investigates the small sample properties of the existing and some new estimators of the autocorrelation coefficient and of the regression coefficients in a linear regression model when errors follow an autoregressive process of order one. The new estimators of autocorrelation coefficient proposed here are based on the jackknife procedure. The jackknife procedure is applied in two alternative ways: first to the regression itself, and second to the residuals of the regression model. Next, the performance of the existing and new estimators of autocorrelation coefficient (thirty-three in total) is investigated in terms of bias and the root mean squared errors. Finally, we have systematically compared all of the estimators of the regression coefficients (again thirty-three) in terms of efficiency and their performance in hypothesis testing. We observe that the performance of the autocorrelation coefficient estimators is dependent upon the degree of autocorrelation and whether the autocorrelation is positive or negative. We do not observe a direct link between the bias and efficiency of an estimator. The performance of the estimators of the regression coefficients also depends upon the degree of autocorrelation. If the efficiency of regression estimator is of concern, then the iterative Prais-Winsten estimator should be used since it is most efficient for the widest range of independent variables and values of the autocorrelation coefficient. If testing of the hypothesis is of concern, then the estimators based on jackknife technique are certainly superior and are highly recommended. However, for negative values of the autocorrelation coefficient, the estimators based on Quenouille procedure and iterative Prais-Winsten estimator are comparable. But, for computational ease iterative Prais-Winsten estimator is recommended.

     

What Drove the Massive Hoarding of International Reserves in Emerging Economies? A Time‐varying Approach

Existing empirical models fail to explain the surge in the accumulation of foreign exchange reserves by emerging countries during the last decade. This paper provides an estimate of the demand for international reserves on a panel of emerging countries using a time‐varying panel smooth transition regression (TV‐PSTR) model to relax the assumption of coefficient stability in the relationship. Evidence is dound that the parameters are not constant. In addition, it is observed that the coefficients remained relatively stable until 2000 and then increased gradually and strongly thereafter. The specification provided here accounts for an acceleration that linear specifications fail to explain. Finally, it is found that mercantilist motives are the major driver of this acceleration.     

TESTING THE STRUCTURE OF CONDITIONAL CORRELATIONS IN MULTIVARIATE GARCH MODELS: A GENERALIZED CROSS‐SPECTRUM APPROACH*

We introduce a class of generally applicable specification tests for constant and dynamic structures of conditional correlations in multivariate GARCH models. The tests are robust to the presence of time‐varying higher‐order conditional moments of unknown form and are pure significance tests. The tests can identify linear and nonlinear misspecifications in conditional correlations. Our approach does not necessitate a particular parameter estimation method and distributional assumption on the error process. The asymptotic distribution of the tests is invariant to the uncertainty in parameter estimation. We assess the finite sample performance of our tests using simulated and real data.     

The diffusion of successive generations of a technology: A more general model

In many cases of technological development, successive generations of a technology evolve, each more efficient than its predecessor. It has been assumed when modeling and forecasting the adoption of these technologies that the market reaction to each generation was similar. Using the terminology of the Bass model, this similarity is encapsulated in the assumption that the coefficients of innovation and imitation are constant. New data for two and three generations of mobile telephone technology from eleven countries are modeled. The modeling framework used—simultaneous estimation for successive generations using a full information maximum likelihood procedure—demonstrates that, in most cases, the hypothesis of constant coefficients can be rejected. Use of a model with changing coefficients is shown to considerably improve forecasting performance. These results were reinforced by analysis of data for four generations of IBM mainframes.     

ESTIMATION AND INFERENCE BY THE METHOD OF PROJECTION MINIMUM DISTANCE: AN APPLICATION TO THE NEW KEYNESIAN HYBRID PHILLIPS CURVE*

The stability of the solution path in a macroeconomic model implies that it admits a Wold representation. This Wold representation can be estimated semi‐parametrically by local projections and used to estimate the model's parameters by minimum distance techniques even when the stochastic process for the solution path is unknown or unconventional. We name this two‐step estimation procedure “projection minimum distance” and investigate its statistical properties for the broad class of models where the mapping between Wold coefficients and parameters is linear. This includes many situations with likelihood score functions nonlinear in the parameters that would otherwise require numerical optimization routines.     

EFFECT OF OIL PRICES ON STOCK MARKETS: EVIDENCE FROM NEW GENERATION OF STAR MODEL

This paper aims to introduce an evidence of new generations of smooth transition regression model (STAR). It proposes two different forms of STAR model. First: a time varying STAR model (TVSTAR), which identify the estimated coefficients at each point of time. Second: a full specification STAR model (FSSTAR) which provides a consistent estimate even in the existence of some measurement errors, omitted variables and even if the true functional form is unknown. This study will consider the two proposed models and the traditional STAR model to examine the nonlinear relation between oil price and stock market index for two countries (Egypt and Turkey). Our results confirm the existing of a non‐linear relation between oil prices and stock return for both countries. The suggested models gives more accurate information about the time varying effect of oil price changes on stock markets and robust forecasts.     

Measurement Error with Accounting Constraints: Point and Interval Estimation for Latent Data with an Application to U.K. Gross Domestic Product

An econometric methodology is proposed for reconciling inaccurate measures of latent data which are subject to accounting constraints. The method deals with the case in which the measurement errors are serially correlated, generalizing previous contributions. A class of efficient estimators are derived for the latent data. Consistent estimators for the weight matrices applied to the observed information based on a linear regression procedure are obtained together with confidence interval estimators for these weight matrices. Approximate confidence intervals are suggested for the latent data themselves together with specification tests for the assumptions underlying the procedure. An application of the proposed method is made to U.K. Gross Domestic Product in constant prices for 1958Q–1989Q4.     

Structural interactions in spatial panels

Until recently, considerable effort has been devoted to the estimation of panel data regression models without adequate attention being paid to the drivers of interaction amongst cross-section and spatial units. We discuss some new methodologies in this emerging area and demonstrate their use in measurement and inferences on cross-section and spatial interactions. Specifically, we highlight the important distinction between spatial dependence driven by unobserved common factors and those based on a spatial weights matrix. We argue that purely factor-driven models of spatial dependence may be inadequate because of their connection with the exchangeability assumption. The three methods considered are appropriate for different asymptotic settings; estimation under structural constraints when N is fixed and T → ∞, whilst the methods based on GMM and common correlated effects are appropriate when T ≫ N → ∞. Limitations and potential enhancements of the existing methods are discussed, and several directions for new research are highlighted.     

Generalized spatial autocorrelation in a panel-probit model with an application to exporting in China

This paper proposes a generalized spatial panel-data probit model with spatial autocorrelation of the dependent variable, the time-invariant individual shocks, and the remainder disturbances. It proposes its estimation with a Bayesian Markov chain Monte Carlo procedure. Simulation results show that the proposed estimation method performs well in small- to medium-sized samples. This method is then applied to the analysis of export-market participation of 1451 Chinese firms between 2002 and 2006 in the prefecture-level city of Wenzhou in the province of Zhejiang. Empirical results show that two of the three forms of the hypothesized spatial autocorrelation are significant, namely the spatial lag for the dependent variable and the time-invariant firm-specific shocks, but not the time-variant shocks. Ignoring any of these significant spatial effects would lead to misspecification.