In cointegrated vector autoregressive (VAR) analyses various nonlinear functions of the coefficients are of interest. Notable examples are impulse responses. A general theory for asymptotic inference on such functions is developed under the assumption that the actual data generation process (DGP) is of potentially infinite VAR order although finite order VAR models are fitted to the data and are used for computing the quantities of interest. In the asymptotic theory the VAR order is assumed to grow with the sample size albeit at a smaller rate. Both authors gratefully acknowledge financial support by the DFG, Sonderforschungsbereich 373. This research was partly carried out while the first author was visiting the Institute of Statistics and Econometrics at the Humboldt University and partly while the second author was a Visiting Research Fellow at the Australian National University in Canberra. We thank Kirstin Hubrich for comments. The paper was printed using funds made available b...

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This paper considers alternative methods of testing cointegration in fractionally integrated processes, using the bootstrap. The special feature of the fractional case is the dependence of the asymptotic null distributions of conventional statistics on the fractional integration parameter. Such tests are said to be asymptotically non-pivotal, and conventional asymptotic tests are therefore not available. Bootstrap tests can be constructed, although these may be less reliable in small samples than in the case of asymptotically pivotal statistics. Bias correction techniques, including the double bootstrap of Beran (#988) and the fast double bootstrap of Davidson and MacKinnon (2000) are considered. The investigation focuses on the issues of (a) choice of statistic, (b) bias correction, and also (c) designing the simulation of the null hypothesis. The latter consideration is crucial for ensuring tests are both correctly sized and powerful. Three types of test are considered, all based on residuals from a putative cointegrating regression. Two are of the null hypothesis of non-cointegration; a conventional residual-based test using the Durbin-Watson statistic, and a test based on the F -statistic, as proposed in Davidson (200#). The third is the Shin (#994) residual-based test of the null hypothesis that cointegration exists. The tests are compared in Monte Carlo experiments whose main object is to throw light on the relative roles of issues (a), (b) and (c) in test performance. 1

Saikkonen (1991) developed an asymptotic optimality theory for the estimation of cointegrated regressions. He proposed the dynamic OLS estimator obtained by augmenting the static cointegrating regression with leads and lags of the first differences of the I(1) regressors. However, the assumptions imposed preclude the use of information criteria such as the AIC and BIC to select the number of leads and lags. We show that his results remain valid under weaker conditions which permit the use of such data dependent rules. Simulations show that, relative to sequential general to specific testing procedures, the use of such information criteria can indeed produce estimates with smaller mean squared errors and confidence intervals with better coverage rates. 1

We study estimation and inference in cointegrated regression models with multiple structural changes allowing both stationary and integrated regressors. Both pure and partial structural change models are analyzed. We derive the consistency, rate of convergence and the limit distribution of the estimated break fractions. Our technical conditions are considerably less restrictive than those in Bai, Lumsdaine and Stock (1998) who considered the single break case in a multi-equations system, and permit a wide class of practically relevant models. Our analysis is, however, restricted to a single equation framework. We show that if the coefficients of the integrated regressors are allowed to change, the estimated break fractions are asymptotically dependent so that confidence intervals need to be constructed jointly. If, however, only the intercept and/or the coefficients of the stationary regressors are allowed to change, the estimates of the break dates are asymptotically independent as in the stationary case analyzed by Bai and Perron (1998). We also show that our results remain valid, under very weak conditions, when the potential endogeneity of the nonstationary regressors is accounted for via an increasing sequence of leads and lags of their first-differences as additional regressors. Simulation evidence is presented to assess the adequacy of the asymptotic approximations in finite samples.

The macroeconomics literature has recently witnessed a resurgence of interest in issues related to nominal price rigidities. In particular, advances in computational methods have allowed for the analysis of fully articulated quantitative general equilibrium models with inflexible prices. 1 Because nominal price rigidities create predictable variations in sales, these models provide a natural setting for the study of inventory behavior. Specifically, firms that face increasing marginal costs wish to smooth production and, given predictable variations in sales, can naturally use inventories to accommodate any difference between a smooth production volume and sales. Hornstein and Sarte (1998) study the implications of sticky prices for inventory behavior under different assumptions about the nature of the driving process. Regardless of whether the economy is driven by nominal demand or real supply shocks, the authors find that an equilibrium model with inflexible prices can replicate the main stylized facts of inventory behavior. Namely, production is more volatile than sales while inventory investment is positively correlated with sales at business cycle frequencies. More importantly, their study also makes specific predictions about the dynamic adjustment of inventories and sales to these shocks. In response to a permanent positive money growth Pierre.Sarte@rich.frb.org. I wish to thank Andreas Hornstein and Mark Watson for helpful discussions. I also wish to thank Yash Mehra, Wenli Li, and Roy Webb for thoughtful comments. The opinions expressed herein are the author’s and do not necessarily represent those of the Federal Reserve Bank of Richmond or the Federal Reserve System. Any errors are, of course, my own. 1 See Goodfriend and King (1997) for a survey of recent work.

∗ Canada Research Chair Holder (Econometrics). Centre interuniversitaire de recherche en analyse des organisations (CIRANO), Centre interuniversitaire de recherche en économie quantitative (CIREQ), and Département de sciences

In this paper we study some aspects of North Korean economy through her import behavior. We have found that for North Korean economy some non-market factors are important determinants of the import behavior. Those non-market factors are the country's political situations, its political relation with two communist superpowers, and its relation with the Western industrialized countries especially through foreign debt problems with the Western countries. Only after incorporating those non-market factors, we have a stable import demand function implied in the concept of cointegration. Also, by applying inference procedures for a cointegration model, we have found that most of those non-market factors are statistically significant. However, the impacts of those nonmarket factors are different for different countries and for different commodity groups, which has some interesting implications on the North Korean economy. Key Words: Determinants of Imports, Non-market factors, Stable dynamic s...

This paper analyzes nonlinear cointegrating regressions as have been recently analyzed in a paper by Park and Phillips in Econometrica. I analyze the consequences of removing Park and Phillips' exogeneity assumption, which for the special case of a linear model would imply the asymptotic validity of the least squares estimator for linear cointegrating regressions. For the linear model, the unlikeliness of such an exogeneity assumption to hold in practice has inspired the "fully modified" technique, the "leads and lags" technique, and Park's "canonical regressions". In this paper, a "fully modified" type technique is proposed for nonlinear cointegrating regressions. The mathematical tool for proving this result is a new so-called "convergence to stochastic integrals" result. This result is proven for objects that are summations of a stationary random variable times an asymptotically homogeneous function of an integrated process.

This paper provides a review of the literature on unit roots and cointegration in panels where the time dimension (T), and the cross section dimension (N) are relatively large. It distinguishes between the first generation tests developed on the assumption of the cross section independence, and the second generation tests that allow, in a variety of forms and degrees, the dependence that might prevail across the different units in the panel. In the analysis of cointegration the hypothesis testing and estimation problems are further complicated by the possibility of cross section cointegration which could arise if the unit roots in the different cross section units are due to common random walk components.