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Full-Text Articles in Economics
John Denis Sargan At The London School Of Economics, David F. Hendry, Peter C.B. Phillips
John Denis Sargan At The London School Of Economics, David F. Hendry, Peter C.B. Phillips
Cowles Foundation Discussion Papers
During his period at the LSE from the early 1960s to the mid 1980s, John Denis Sargan rose to international prominence and the LSE emerged as the world’s leading centre for econometrics. Within this context, we examine the life of Denis Sargan, describe his major research accomplishments, recount the work of his many doctoral students, and track this remarkable period that constitutes the Sargan era of econometrics at the LSE.
Functional Coefficient Nonstationary Regression, Jiti Gao, Peter C.B. Phillips
Functional Coefficient Nonstationary Regression, Jiti Gao, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coffiecient components. The model accommodates a cointegrating structure and allows for endogeneity with contemporaneous correlation among the regressors, the varying coefficient drivers, and the residuals. This framework allows for a mixture of stationary and non-stationary data and is well suited to a variety of models that are commonly used in applied econometric work. Nonparametric and semiparametric estimation methods are proposed to estimate the varying coefficient functions. The analytical findings reveal some important differences, including convergence rates, that …
Bootstrapping I(1) Data, Peter C.B. Phillips
Bootstrapping I(1) Data, Peter C.B. Phillips
Cowles Foundation Discussion Papers
A functional law for an I(1) sample data version of the continuous-path block bootstrap of Paparoditis and Politis (2001) is given. The results provide an alternative demonstration that continuous-path block bootstrap unit root tests are consistent under the null.
Bootstrapping Spurious Regression, Peter C.B. Phillips
Bootstrapping Spurious Regression, Peter C.B. Phillips
Cowles Foundation Discussion Papers
The bootstrap is shown to be inconsistent in spurious regression. The failure of the bootstrap is spectacular in that the bootstrap effectively turns a spurious regression into a cointegrating regression. In particular, the serial correlation coefficient of the residuals in the bootstrap regression does not converge to unity, so the bootstrap is not even first order consistent. The block bootstrap serial correlation coefficient does converge to unity and is therefore first order consistent, but has a slower rate of convergence and a different limit distribution from that of the sample data serial correlation coefficient. The analysis covers spurious regressions involving …
The Method Of Simulated Scores For The Estimation Of Ldv Models With An Application To External Debt Crisis, Vassilis A. Hajivassiliou, Daniel Mcfadden
The Method Of Simulated Scores For The Estimation Of Ldv Models With An Application To External Debt Crisis, Vassilis A. Hajivassiliou, Daniel Mcfadden
Cowles Foundation Discussion Papers
The method of simulated scores (MSS) is presented for estimating LDV models with flexible correlation structure in the unobservables. We propose simulators that are continuous in the unknown parameter vectors, and hence standard optimization methods can be used to compute the MSS estimators that employ these simulators. We establish consistency and asymptotic normality of the MSS estimators and derive suitable rates at which the number of simulations must use if biased simulators are used. The estimation method is applied to analyze a model in which the incidence and the extent of debt repayments problems of LDC’s are viewed as optimized …
Tests For Parameter Instability And Structural Change With Unknown Change Point, Donald W.K. Andrews
Tests For Parameter Instability And Structural Change With Unknown Change Point, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper considers tests of parameter instability and structural change with unknown change point. The results apply to a wide class of parametric models including models that satisfy maximum likelihood type regularity conditions and models that are suitable for estimation by generalized method of moments procedures. The paper considers likelihood ratio and likelihood ratio like tests, as well as asymptotically equivalent Wald and Lagrange multiplier tests. Each test implicitly uses an estimate of change point. Tests of both “pure” and “partial” structural change are discussed.
An Improved Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimator, Donald W.K. Andrews, Christopher J. Monahan
An Improved Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimator, Donald W.K. Andrews, Christopher J. Monahan
Cowles Foundation Discussion Papers
This paper considers a new class of heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators. The estimators considered are prewhitened kernel estimators with vetor autoregressions employed in the prewhitening stage. The paper establishes consistency, rate of convergence, and asymptotic truncated mean squared error (MSE) results for the estimators when a fixed or automatic bandwidth procedure is employed. Conditions are obtained under which prewhitening improves asymptotic truncated MSE. Monte Carlo results show that prewhitening is very effective in reducing bias, improving confidence interval coverage probabilities, and rescuing over-rejection of t -statistics constructed using kernel-HAC estimators. On the other hand, prewhitening is …
Generic Uniform Convergence, Donald W.K. Andrews
Generic Uniform Convergence, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper presents several generic uniform convergence results that include generic uniform laws of large numbers. These results provide conditions under which pointwise convergence almost surely or in probability can be strengthened to uniform convergence. The results are useful for establishing asymptotic properties of estimators and test statistics. The results given here have the following attributes, (1) they extend results of Newey to cover convergence almost surely as well as convergence in probability, (2) they apply to totally bounded parameter spaces (rather than just to compact parameter spaces), (3) they introduce a set of conditions for a generic uniform law …
Estimating Long Run Economic Equilibria, Peter C.B. Phillips, Mico Loretan
Estimating Long Run Economic Equilibria, Peter C.B. Phillips, Mico Loretan
Cowles Foundation Discussion Papers
Our subject is econometric estimation and inference concerning long-run economic equilibria in models with stochastic trends. Our interest is focused on single equation specifications such as those employed in the Error Correction Model (ECM) methodology of David Hendry (1987, 1989 inter alia) and the semiparametric modified least squares method of Phillips and Hansen (1989). We start by reviewing the prescriptions for empirical time series research that are presently available. We argue that the diversity of choices is confusing to practitioners and obscures the fact that statistical theory is clear about optimal inference procedures. Part of the difficulty arises from the …
Asymptotics For Linear Processes, Peter C.B. Phillips, Victor Solo
Asymptotics For Linear Processes, Peter C.B. Phillips, Victor Solo
Cowles Foundation Discussion Papers
A method of deriving asymptotics for linear processes is introduced which uses an explicit algebraic decomposition of the linear filter. The method leads to substantial simplifications in the asymptotics and offers a unified approach to strong laws and central limit theory for linear processes. Sample means and sample covariances are covered. The results also accommodate both homogeneous and heterogeneous innovations as well as innovations with undefined means and variances.
Asymptotics For Semiparametric Econometric Models: Iii. Testing And Examples, Donald W.K. Andrews
Asymptotics For Semiparametric Econometric Models: Iii. Testing And Examples, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper considers tests of nonlinear parametric restrictions in semiparametric econometric models. To date, only Wald tests of such restrictions have been considered in the literature. Here, Wald, Lagrange multiplier, and likelihood ratio-like test statistics are considered and are shown to have asymptotic chi-square distributions under the null and local alternatives. The results hold for a wide variety of underlying estimation techniques and in a wide variety of model scenarios. A number of examples are given to illustrate the testing results of this paper and the estimation and stochastic equicontinuity results of the antecedents to this paper, viz. Andrews (1989b, …
Asymptotic Optimality Of Generalized Cl, Cross-Validation, And Generalized Cross-Validation In Regression With Heteroskedastic Errors, Donald W.K. Andrews
Asymptotic Optimality Of Generalized Cl, Cross-Validation, And Generalized Cross-Validation In Regression With Heteroskedastic Errors, Donald W.K. Andrews
Cowles Foundation Discussion Papers
The problem considered here is that of using a data-driven procedure to select a good estimate from a class of linear estimates indexed by a discrete parameter. In contrast to other papers on this subject, we consider models with heteroskedastic errors. The results apply to model selection problems in linear regression and to nonparametric regression estimation via series estimators, nearest neighbor estimators, and local regression estimators, among others. Generalized C L , cross-validation, and generalized cross-validation procedures are analyzed.
Testing For A Unit Root By Generalized Least Squares Methods In The Time And Frequency Domains, In Choi, Peter C.B. Phillips
Testing For A Unit Root By Generalized Least Squares Methods In The Time And Frequency Domains, In Choi, Peter C.B. Phillips
Cowles Foundation Discussion Papers
New time and frequency domain tests for the presence of a unit root are developed. The tests are based on generalized least squares (GLS) methods in both the time and the frequency domains. For the time domain tests, moving average processes are assumed for the error terms on the autoregression. For the frequency domain tests, general assumptions are made which allow for stationary and weakly dependent error processes. The limiting distributions of feasible GLS tests are derived under MA(1) errors in the time domain. This theory is extended to higher order moving average processes under an invertibility condition. The limiting …
The Durbin-Watson Ratio Under Infinite Variance Errors, Peter C.B. Phillips, Mico Loretan
The Durbin-Watson Ratio Under Infinite Variance Errors, Peter C.B. Phillips, Mico Loretan
Cowles Foundation Discussion Papers
This paper studies the properties of the von Neumann ratio for time series with infinite variance. The asymptotic theory is developed using recent results on the weak convergence of partial sums of time series with infinite variance to stable processes and of sample serial correlations to functions of stable variables. Our asymptotics cover the null of iid variates and general moving average (MA) alternatives. Regression residuals are also considered. In the static regression model the Durbin-Watson statistic has the same limit distribution as the von Neumann ratio under general conditions. However, the dynamic models, the results are more complex and …
Estimation And Inference In Models Of Cointegration: A Simulation Study, Bruce E. Hansen, Peter C.B. Phillips
Estimation And Inference In Models Of Cointegration: A Simulation Study, Bruce E. Hansen, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies the finite sample distributions of estimators of the cointegrating vector of linear regression models with I(1) variables. Attention is concentrated on the least squares (OLS) and instrumental variables (IV) methods analyzed in other recent work (Phillips and Hansen (1988)). The general preference of OLS to IV techniques suggested by asymptotic theory is reinforced by our simulations. An exception arises for cases of low signal to noise, where spurious IV techniques (so named for their use of instruments that are structurally unrelated to the model) outperform uncorrected least squares. We verify the presence of a small sample estimation …
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 …
Partially Identified Econometric Models, Peter C.B. Phillips
Partially Identified Econometric Models, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies a class of models where full identification is not necessarily assumed. We term such models partially identified. It is argued that partially identified systems are of practical importance since empirical investigators frequently proceed under conditions that are best described as apparent identification. One objective of the paper is to explore the properties of conventional statistical procedures in the context of identification failure. Our analysis concentrates on two major types of partially identified model: the classic simultaneous equations model under rank condition failures; and time series spurious regressions. Both types serve to illustrate the extensions that are needed …
Asymptotic Properties Of Residual Based Tests For Cointegration, Peter C.B. Phillips, Sam Ouliaris
Asymptotic Properties Of Residual Based Tests For Cointegration, Peter C.B. Phillips, Sam Ouliaris
Cowles Foundation Discussion Papers
This paper develops an asymptotic theory for residual based tests for cointegration. These tests involve procedures that are designed to detect the presence of a unit root in the residuals of (cointegrating) regressions among the levels of economic time series. Attention is given to the augmented Dickey-Fuller (ADF) test that is recommended by Engle-Granger (1987) and the Z(a) and Z(t) unit root tests recently proposed by Phillips (1987). TWo new tests are also introduced, one of which is invariant to the normalization of the cointegrating regression. All of these tests are shown to be asymptotically similar and simple representations of …
Understanding Spurious Regressions In Econometrics, Peter C.B. Phillips
Understanding Spurious Regressions In Econometrics, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper provides an analytical study of spurious regressions involving the levels of economic time series. As asymptotic theory is developed for regressions that relate independent random walks. It is shown that the usual t ratio significance tests do not possess limiting distributions but actually diverge as the sample size T approaches infinity. The Durbin-Watson statistic, on the other hand, converges in probability to zero. An alternative asymptotic theory is also analyzed. An alternative asymptotic theory is developed based on the concept of continuous data recording. This theory together with the large sample asymptotics that we present go a long …