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Full-Text Articles in Economics
Pitfalls And Possibilities In Predictive Regression, Peter C.B. Phillips
Pitfalls And Possibilities In Predictive Regression, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Financial theory and econometric methodology both struggle in formulating models that are logically sound in reconciling short run martingale behaviour for financial assets with predictable long run behavior, leaving much of the research to be empirically driven. The present paper overviews recent contributions to this subject, focussing on the main pitfalls in conducting predictive regression and on some of the possibilities offered by modern econometric methods. The latter options include indirect inference and techniques of endogenous instrumentation that use convenient temporal transforms of persistent regressors. Some additional suggestions are made for bias elimination, quantile crossing amelioration, and control of predictive …
Non-Linearity Induced Weak Instrumentation, Ioannis Kasparis, Peter C.B. Phillips, Tassos Magdalinos
Non-Linearity Induced Weak Instrumentation, Ioannis Kasparis, Peter C.B. Phillips, Tassos Magdalinos
Cowles Foundation Discussion Papers
In regressions involving integrable functions we examine the limit properties of IV estimators that utilise integrable transformations of lagged regressors as instruments. The regressors can be either I(0) or nearly integrated (NI) processes. We show that this kind of nonlinearity in the regression function can significantly affect the relevance of the instruments. In particular, such instruments become weak when the signal of the regressor is strong, as it is in the NI case. Instruments based on integrable functions of lagged NI regressors display long range dependence and so remain relevant even at long lags, continuing to contribute to variance reduction …
Cointegrating Rank Selection In Models With Time-Varying Variance, Xu Cheng, Peter C.B. Phillips
Cointegrating Rank Selection In Models With Time-Varying Variance, Xu Cheng, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Reduced rank regression (RRR) models with time varying heterogeneity are considered. Standard information criteria for selecting cointegrating rank are shown to be weakly consistent in semiparametric RRR models in which the errors have general nonparametric short memory components and shifting volatility provided the penalty coefficient C n → infinity and C n /n → 0 as n → ∞. The AIC criterion is inconsistent and its limit distribution is given. The results extend those in Cheng and Phillips (2008) and are useful in empirical work where structural breaks or time evolution in the error variances is present. An empirical application …
Semiparametric Cointegrating Rank Selection, Xu Cheng, Peter C.B. Phillips
Semiparametric Cointegrating Rank Selection, Xu Cheng, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Some convenient limit properties of usual information criteria are given for cointegrating rank selection. Allowing for a nonparametric short memory component and using a reduced rank regression with only a single lag, standard information criteria are shown to be weakly consistent in the choice of cointegrating rank provided the penalty coefficient C n → ∞ and C n /n → 0 as n → ∞. The limit distribution of the AIC criterion, which is inconsistent, is also obtained. The analysis provides a general limit theory for semiparametric reduced rank regression under weakly dependent errors. The method does not require the …
Laws And Limits Of Econometrics, Peter C.B. Phillips
Laws And Limits Of Econometrics, Peter C.B. Phillips
Cowles Foundation Discussion Papers
We start by discussing some general weaknesses and limitations of the econometric approach. A template from sociology is used to formulate six laws that characterize mainstream activities of econometrics and the scientific limits of those activities., we discuss some proximity theorems that quantify by means of explicit bounds how close we can get to the generating mechanism of the data and the optimal forecasts of next period observations using a finite number of observations. The magnitude of the bound depends on the characteristics of the model and the trajectory of the observed data. The results show that trends are more …
Trending Time Series And Macroeconomic Activity: Some Present And Future Challenges, Peter C.B. Phillips
Trending Time Series And Macroeconomic Activity: Some Present And Future Challenges, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Some challenges for econometric research on trending time series are discussed in relation to some perceived needs of macroeconomics and macroeconomic policy making.
Empirical Limits For Time Series Econometric Models, Werner Ploberger, Peter C.B. Phillips
Empirical Limits For Time Series Econometric Models, Werner Ploberger, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper seeks to characterize empirically achievable limits for time series econometric modeling. The approach involves the concept of minimal information loss in time series regression and the paper shows how to derive bounds that delimit the proximity of empirical measures to the true probability measure in models that are of econometric interest. The approach utilizes generally valid asymptotic expressions for Bayesian data densities and works from joint measures over the sample space and parameter space. A theorem due to Rissanen is modified so that it applies directly to probabilities about the relative likelihood (rather than averages), a new way …
Fully Modified Iv, Give And Gmm Estimation With Possibly Non-Stationary Regressions And Instruments, Yuichi Kitamura, Peter C.B. Phillips
Fully Modified Iv, Give And Gmm Estimation With Possibly Non-Stationary Regressions And Instruments, Yuichi Kitamura, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops a general theory of instrumental variables (IV) estimation that allows for both I(1) and I(0) regressors and instruments. The estimation techniques involve an extension of the fully modified (FM) regression procedure that was introduced in earlier work by Phillips-Hansen (1990). FM versions of the generalized instrumental variable estimation (GIVE) method and the generalized method of moments (GMM) estimator are developed. In models with both stationary and nonstationary components, the FM-GIVE and FM-GMM techniques provide efficiency gains over FM-IV in the estimation of the stationary components of a model that has both stationary and nonstationary regressors. The paper …
Comment On ‘To Criticize The Critics’, By Peter C.B. Phillips, Christopher A. Sims
Comment On ‘To Criticize The Critics’, By Peter C.B. Phillips, Christopher A. Sims
Cowles Foundation Discussion Papers
In his paper “To Criticize the Critics” (1991), Peter Phillips discusses Bayesian methodology for time series models. The main point that Uhlig and I set out to make, however, was that careful consideration of the implications of the likelihood principle suggests that much of the recent work under the “unit root” label in the econometrics literature is being incorrectly interpreted in practice. We pointed out that time series models with possible unit roots are one of the few domains within which the implications of a likelihood principle approach to inference are difference, even in the large samples, from those of …
The Spurious Effect Of Unit Roots On Exogeneity Tests In Vector Autoregressions: An Analytical Study, Hiro Y. Toda, Peter C.B. Phillips
The Spurious Effect Of Unit Roots On Exogeneity Tests In Vector Autoregressions: An Analytical Study, Hiro Y. Toda, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper analyzes whether inclusion of a statistically independent random walk in a vector autoregression can result in spurious inference. The problem was raised originally by Ohanian (1988). In a Monte Carlo simulation based on the VAR’s estimated by Sims (1980b, 1982), Ohanian found that block exogeneity of the genuine variables with respect to an artificially generated random walk variable was rejected too often. In the present paper we attempt a full analytical study of this problem. It can be shown that if the genuine variables are nonstationary, the Wald statistic for testing the block exogeneity hypothesis does not have …
Exactly Unbiased Estimation Of First Order Autoregressive/Unit Root Models, Donald W.K. Andrews
Exactly Unbiased Estimation Of First Order Autoregressive/Unit Root Models, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper is concerned with the estimation of first-order autoregressive/unit root models with independent identically distributed normal errors. The models considered include those without an intercept, those with an intercept, and those with an intercept and time trend. The autoregressive (AR) parameter alpha is allowed to lie in the interval (-1,1], which includes the case of a unit root. Exactly median-unbiased estimators of the AR parameter alpha are proposed. Exact confidence intervals for this parameter are introduced. Corresponding exactly median-unbiased estimators and exact confidence intervals are also provided for the impulse response function and the cumulative impulse response. An unbiased …
Time Series Regression With A Unit Root And Infinite Variance Errors, Peter C.B. Phillips
Time Series Regression With A Unit Root And Infinite Variance Errors, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Chan and Tran give the limit theory for the least squares coefficient in a random walk with the iid errors that are in the domain of attraction of a stable law. This note discusses their results and provides generalizations to the case of I(q) processes with weakly dependent errors whose distributions are in the domain of attraction of a stable law. General unit root tests are also studied. It is shown that the semiparametric corrections suggested by the author for the finite variance case continue to work when the errors have infinite variance. The limit laws are expressed in terms …
Testing For A Unit Root In The Presence Of A Maintained Trend, Sam Ouliaris, Joon Y. Park, Peter C.B. Phillips
Testing For A Unit Root In The Presence Of A Maintained Trend, Sam Ouliaris, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops statistics for detecting the presence of a unit root in time series data against the alternative stationarity. Unlike most existing procedures, the new tests allow for deterministic trend polynomials in the maintained hypothesis. They may be used to discriminate between unit root nonstationarity and processes which are stationary around a deterministic polynomial trend. The tests allow for both forms of nonstationarity under the null hypothesis. Moreover, the tests allow for a wide class of weakly dependent and possibly heterogenously distributed procedures. We illustrate the use of the new tests by applying them to a number a models …
Optimal Inference In Cointegrated Systems, Peter C.B. Phillips
Optimal Inference In Cointegrated Systems, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies the properties of maximum likelihood estimates of co-integrated systems. Alternative formulations of such models are considered including a new triangular system error correction mechanism. It is shown that full system maximum likelihood brings the problem of inference within the family that is covered by the locally asymptotically mixed normal asymptotic theory provided that all unit roots in the system have been eliminated by specification and data transformation. This result has far reaching consequences. It means that cointegrating coefficient estimates are symmetrically distributed and median unbiased asymptotically, that an optimal asymptotic theory of inference applies and that hypothesis …
Multiple Regression With Integrated Time Series, Peter C.B. Phillips
Multiple Regression With Integrated Time Series, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Recent work on the theory of regression with integrated process is reviewed. This work is particularly relevant in economics where many financial series and macroeconomic time series exhibit nonstationary characteristics and are often well modeled individually as simple ARIMA processes. The theory makes extensive use of weak convergence methods and allows for integrated processes that are driven by quite general weakly dependent and possibly heterogeneously distributed innovations. The theory also includes near integrated time series, which have roots near unity, and cointegrated series, which move together over time but are individually nonstationary. A general framework for asymptotic analysis is given …
Statistical Inference In Regressions With Integrated Processes: Part 1, Joon Y. Park, Peter C.B. Phillips
Statistical Inference In Regressions With Integrated Processes: Part 1, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops a multivariate regression theory for integrated processes which simplifies and extends much earlier work. Our framework allows for both stochastic and certain deterministic regressors, vector autoregressions and regressors with drift. The main focus of the paper is statistical inference. The presence of nuisance parameters in the asymptotic distributions of regression F -tests is explored and new transformations are introduced to deal with these dependencies. Some specializations of our theory are considered in detail. In models with strictly exogenous regressors we demonstrate the validity of conventional asymptotic theory for appropriately constructed Wald tests. These tests provide a simple …
Testing The Random Walk Hypothesis: Power Versus Frequency Of Observation, Robert J. Shiller, Pierre Perron
Testing The Random Walk Hypothesis: Power Versus Frequency Of Observation, Robert J. Shiller, Pierre Perron
Cowles Foundation Discussion Papers
Power functions of tests of the random walk hypothesis versus stationary first order autoregressive alternatives are tabulated for samples of fixed span but various frequencies of observation. For a t -test and normalized test, power is found to depend, for a substantial range of parameter values, more on the span of the data in time than on the number of observations. For a runs test, power rapidly declines as the number of observations is increased beyond a certain point.