Cowles Foundation

About: Cowles Foundation is a based out in . It is known for research contribution in the topics: Estimator & Nonparametric statistics. The organization has 139 authors who have published 1660 publications receiving 119633 citations.

Testing for a Unit Root in Time Series Regression

Abstract: SUMMARY This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey & Fuller. Simulations are reported on the performance of the new tests in finite samples.

Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis

Abstract: Recently, Perron has carried out tests of the unit-root hypothesis against the alternative hypothesis of trend stationarity with a break in the trend occurring at the Great Crash of 1929 or at the 1973 oil-price shock. His analysis covers the Nelson–Plosser macroeconomic data series as well as a postwar quarterly real gross national product (GNP) series. His tests reject the unit-root null hypothesis for most of the series. This article takes issue with the assumption used by Perron that the Great Crash and the oil-price shock can be treated as exogenous events. A variation of Perron's test is considered in which the breakpoint is estimated rather than fixed. We argue that this test is more appropriate than Perron's because it circumvents the problem of data-mining. The asymptotic distribution of the estimated breakpoint test statistic is determined. The data series considered by Perron are reanalyzed using this test statistic. The empirical results make use of the asymptotics developed for the test stati...

Statistical Inference in Instrumental Variables Regression with I(1) Processes

Abstract: This paper studies the asymptotic properties of instrumental variable (IV) estimates of multivariate cointegrating regressions and allows for deterministic and stochastic regressors as well as quite general deterministic processes in the data-generating mechanism. It is found that IV regressions are consistent even when the instruments are stochastically independent of the regressors. This phenomenon, which contrasts with traditional theory for stationary time series, is a beneficial artifact of spurious regression theory whereby stochastic trends in the instruments ensure their relevance asymptotically. Problems of inference are also addressed and some promising new theoretical results are reported. These involve a class of Wald tests which are modified by semiparametric corrections for serial correlation and for endogeneity. The resulting test statistics which we term fully-modified Wald tests have limiting x2 distributions, thereby removing the obstacles to inference in cointegrated systems that were presented by the nuisance parameter dependencies in earlier work. Some simulation results are reported which seek to explore the sampling behaviour of our suggested procedures. These simulations compare our fully modified (semiparametric) methods with the parametric error-correction methodology that has been extensively used in recent empirical research and with conventional least squares regression. Both the fully-modified and errorcorrection methods work well in finite samples and the sampling performance of each procedure confirms the relevance of asymptotic distribution theory, as distinct from super-consistency results, in discriminating between statistical methods.

Cointegration and Tests of Present Value Models

Abstract: In a model where a variable Y[sub t] is proportional to the present value, with constant discount rate, of expected future values of a variable y[sub t] the "spread" S[sub t]= Y[sub t] - [theta sub t] will be stationary for some [theta] whether or not y[sub t]must be differenced to induce stationarity. Thus, Y[sub t] and y[sub t] are cointegrated. The model implies that S[sub t] is proportional to the optimal forecast of [delta Y{sub t+1}] and also to the optimal forecast of S*[sub t], the present value of future [delta y{sub t}]. We use vector autoregressive methods, and recent literature on cointegrated processes, to test the model. When Y[sub t] is the long-term interest rate and y[sub t] the short-term interest rate, we find in postwar U.S. data that S[sub t] behaves much like an optimal forecast of S*[sub t] even though as earlier research has shown it is negatively correlated with [delta Y{sub t+1}]. When Y[sub t] is a real stock price index and y[sub t] the corresponding real dividend, using annual U.S. data for 1871-1986 we obtain less encouraging results for the model, al-though the results are sensitive to the assumed discount rate.

Firms in International Trade

Abstract: Despite the fact that importing and exporting are extremely rare firm activities, economists generally devote little attention to the role of firms when discussing international trade. This paper summarizes key differences between trading and non-trading firms, demonstrates how these differences present a challenge to standard trade models and shows how recent "heterogeneous-firm" models of international trade address these challenges. We then make use of transaction-level U.S. trade data to introduce a number of new stylized facts about firms and trade. These facts reveal that the extensive margins of trade -- that is, the number of products firms trade as well as the number of countries with which they trade -- are central to understanding the well-known role of distance in dampening aggregate trade flows.