Time Series

Cointegration Tests Using Instrumental Variables with an Example of the U.K. Demand for Money

Walter Enders, Kyung So Im, and Junsoo Lee

Abstract:

In this paper, we propose new cointegration tests based on stationary instrumental variables in a single equation model as well as in a system of equations. An important property of our tests is that the asymptotic distribution is standard normal or chi-square. As such, the asymptotic distribution of the IV tests does not depend on the number of the regressors, differing deterministic terms, structural changes, and even statinary covariates. Thus, our IV cointegration tests have operating advantages in the presence of nuisance parameters. Moreover, we show that including stationary covariates increases considerably the power of the tests without affecting size. We illustrate the use of the tests by examining the demand for money
in the U.K.

The Flexible Fourier Form and Testing for Unit Roots: An Example of the Term Structure of Interest Rates

Walter Enders and Junsoo Lee

Abstract:

We develop a unit-root test that relies on a simple variant of Gallant’s (1981) Flexible Fourier Form. The test is based on the fact that nonlinearities of an unknown form, including structural change, can often be captured using the low frequency components of a Fourier approximation. Hence, instead of modeling the nonlinearities or selecting specific break dates, the specification problem is transformed into selecting the proper frequency components to include in the estimating equation. It is shown that the Fourier approximation does reasonably well for the types of nonlinearities and breaks often used in economic analysis. The appropriate use of the test is illustrated using several interest rate spreads.

A Statistical Investigation of Federal Reserve Behavior with “Opportunistic Disinflation”

Walter Enders and Helle Bunzel

Abstract:

We conduct a thorough statistical analysis of the empirical foundations for the existence of a Taylor rule. We argue that the traditional linear specification is problematic as inflation, the output gap and the federal funds rate appear to be non-stationary or highly persistent variables that are not cointegrated. Although this lack of cointegration could be caused by missing variables or structural breaks, we are unable to ‘salvage’ the rule using several plausible candidate variables and break dates. As such, we investigate the possibility that the Taylor rule should be modeled as a threshold process. Although the standard types of threshold models are reasonable, we find that a modified threshold model that is consistent with “opportunistic disinflation” makes significant progress towards explaining Federal Reserve behavior.

Identifying aggregate demand and supply shocks in a small open economy

Walter Enders & Stan Hurn

Abstract:

The standard Blanchard-Quah (BQ) decomposition forces aggregate demand and supply shocks to be orthogonal. However, for a variety of reasons, this assumption may be problematic. For example, policy actions may cause positive correlation between demand and supply shocks. This paper employs a modification of the BQ procedure that allows for correlated shifts in aggregate supply and demand. The method is demonstrated using Australian data. It is found that shocks to Australian aggregate demand and supply are highly correlated. The estimated shifts in the aggregate demand and supply curves are then used to measure the effects of inflation targeting on the Australian inflation rate and level of GDP.

Whose line is it?: A Survey of Plagiarism in the Economics Profession

Walter Enders & Gary A. Hoover

Abstract:

This paper reports the results of a survey regarding the instances of plagiarism reported by journal editors in the economics profession. The survey finds that nearly 24% of responding editors encounter one case of plagiarism in a typical year. In addition, the survey reveals that less than 19% of responding journals have a formal policy regarding plagiarism. Moreover, there is a great deal of variance in what is considered plagiarism and what an appropriate response to plagiarism should be. A majority of editors believe that the economics profession would benefit from a professional code of ethics.

Testing for a unit root with a nonlinear Fourier function

Walter Enders & Junsoo Lee

Abstract:

The paper develops a unit-root test that allows for an unknown number of structural breaks with unknown functional forms. The test is based on the fact that the behavior of such series can often be captured using a single frequency component of a Fourier approximation. Hence, instead of selecting specific break dates, the number of breaks, and the form of the breaks, the specification problem is transformed into selecting the proper frequency component to include in the estimating equation. Our proposed test does not exhibit any serious size distortions, and shows decent power. The appropriate use of the test is illustrated using real GDP and the interest rate differential.

Using the Aggregate Demand-Aggregate Supply Model to Identify Structural Demand-Side and Supply-Side Shocks: Results Using a Bivariate VAR

James Peery Cover, Walter Enders, & C. James Hueng

Abstract:

This paper uses the short-run restrictions implied by a simple aggregate demand-aggregate supply model as an aid in identifying structural shocks. Combined with the Blanchard-Quah restriction, it allows estimation of the slope of the aggregate supply curve, the variances of structural demand and supply shocks, and the extent to which structural demand and supply shocks are correlated. This paper finds that demand and supply shocks are highly correlated and that demand shocks possibly can account for as much as 82% of the long-run forecast error variance of real U.S. GDP.

A General Test For Time-dependence in Parameters

Ralf Becker, Walter Enders and Stan Hurn

Abstract:

We propose a new test based on a Fourier series to approximate the unknown form of a nonlinear time-series model. The test has good size and power properties to detect structural breaks, seasonal parameters and random coefficients. Moreover, it has reasonable power to discriminate between nonlinearity in variables and nonlinearity in parameters. We use the test to show that U.S. inflation is appropriately estimated with a time-varying intercept that jumps in the late 1960’s, peaks in the early 1980’s and then begins to decline. German income and consumption data is used to illustrate the ability of the test to suggest the form of the nonlinearity.

Modeling Inflation and Money Demand Using a Fourier-Series Approximation

Ralf Becker, Walter Enders and Stan Hurn

Stationarity tests with unattended nonlinearity

Ralf Becker, Walter Enders and Junsoo Lee

Abstract:

The paper develops a test with the null of stationarity that allows for the possibility of an unknown number of structural breaks, or other nonlinearities, in the data-generating process. The test is based on the fact that the behavior of a breaking process can often be captured using a single frequency component of a Fourier approximation. Hence, instead of selecting specific break dates, the number of breaks, and the form of any nonlinearities, the specification problem is transformed into selecting a low frequency component to include in the estimating equation. Our proposed test does not exhibit any serious size distortions, and shows reasonable power. The appropriate use of the test is illustrated using real exchange rates in the post-Bretton Woods period.

Walter Enders and C. W. J. Granger

Abstract:

This article develops critical values to test the null hypothesis of a unit root against the alternative of stationarity with asymmetric adjustment. Specific attention is paid to threshold and momentum threshold autoregressive processes. The standard Dickey-Fuller tests emerge as a special case. Within a reasonable range of adjustment parameters, the power of the new tests is shown to be greater than that of the corresponding Dickey-Fuller test. The use of the tests is illustrated using the term structure of interest rates. It is shown that the movements toward the long-run equilibrium relationship are best estimated as an asymmetric process.

Plagiarism in the Economics Profession: A Survey

Walter Enders and Gary Hoover

Abstract:

This paper reports the results of a survey regarding academic plagiarism in the economics profession. We received 1208 usable responses from a broad cross-section of economists. As in our previous survey of journal editors, there is substantial variance in what is considered plagiarism and in the appropriate response to a clear case of plagiarism. Many of the respondents are not aware of the distinction between copyright infringement and plagiarism. We also find that risk of damage to ones reputation from plagiarizing is minimal since most cases go unreported. Moreover, a substantial portion of the 295 reported cases of plagiarism could be classified as hierarchal. Hierarchical plagiarism occurs when a superior, such as a major professor or employer, passes off the subordinate’s words or ideas as her/his own.

Forecasting Persistent Data with Possible Structural Breaks: Old School and New School Lessons Using OECD Unemployment Rates

Walter Enders and Ruxandra Prodan

Abstract:

In contrast to recent forecasting developments, Old School forecasting techniques, such as exponential smoothing and the Box-Jenkins methodology, do not attempt to explicitly model or to estimate breaks in a time series. Adherents of the New School methodology argue that once breaks are well-estimated, it is possible to control for regime shifts when forecasting. We compare the forecasts of monthly unemployment rates in 10 OECD countries using various Old School and New School methods. Although each method seems to have drawbacks and no one method dominates the others, the Old School methods often outperform the New School methods for forecasting the unemployment rates.

In-Sample and Out-of-Sample Properties of Linear and Nonlinear Taylor Rules

Walter Enders and Ting Qin

Abstract:

This paper examines the in-sample and out-of-sample properties of linear and nonlinear Taylor rules using real-time U.S. data. We find that (i) in-sample and out-of-sample performance measures generally select the same functional form for the Taylor rule and that (ii) the form of the Taylor rule differs across the pre-Greenspan and Greenspan sample periods. However, when we compare the out-of-sample forecasting performance of the Taylor rules to those of univariate models of the federal funds rate, we find it quite interesting that the univariate models forecast better than the Taylor rules after 1979 (but not before 1979).

Assessing the Importance of Global Shocks versus Country-Specific Shocks

Walter Enders and Kaouthar Souki

Abstract:

A common assumption in the open-economy macroeconomics literature is that global shocks have little influence on current account balances, relative output levels, and real exchange rates. The aim of the paper is to develop an identification scheme that allows for the possibility that global shocks can affect all countries asymmetrically. Toward this end, we use a four-variable structural vector autoregression (VAR) of the Sims-Bernanke type that allows us to obtain a global shock and three country-specific shocks. We find that global shocks explain almost all of the movements in the German/US real exchange rate and sizable portions of the movements in the other real rates. Moreover, global shocks are important in explaining the changes in the bilateral current accounts between the three countries considered. Our decomposition also allows us to measure the extent to which third-country effects are important in explaining bilateral real exchange rates and relative output levels.

Walter Enders, Barry Falk & Pierre L. Siklos

Abstract

We estimate real U.S. GDP growth as a threshold autoregressive process, and construct confidence intervals for the parameter estimates. However, there are various approaches that can be used in constructing the confidence intervals. Specifically, standard-t, bootstrap-t, and bootstrap-percentile confidence intervals are simulated for the slope coefficients and the estimated threshold. However, the results for the different methods have very different economic implications. We perform a Monte Carloexperiment to evaluate the various methods.