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Report
Aggregate Output Measurements: A Common Trend Approach
We analyze a model for N different measurements of a persistent latent time series when measurement errors are mean-reverting, which implies a common trend among measurements. We study the consequences of overdifferencing, finding potentially large biases in maximum likelihood estimators of the dynamics parameters and reductions in the precision of smoothed estimates of the latent variable, especially for multiperiod objects such as quinquennial growth rates. We also develop an R2 measure of common trend observability that determines the severity of misspecification. Finally, we apply our ...
Working Paper
A residual-based cointegration test for near unit root variables
Methods of inference based on a unit root assumption in the data are typically not robust to even small deviations from this assumption. In this paper, we propose robust procedures for a residual-based test of cointegration when the data are generated by a near unit root process. A Bonferroni method is used to address the uncertainty regarding the exact degree of persistence in the process. We thus provide a method for valid inference in multivariate near unit root processes where standard cointegration tests may be subject to substantial size distortions and standard OLS inference may lead ...
Working Paper
Business Cycles and Low-Frequency Fluctuations in the US Unemployment Rate
I show that business cycles can generate most of the low-frequency movements in the unemployment rate. First, I provide evidence that the unemployment rate is stationary, while its flows have unit roots. Then, I model the log unemployment rate as the error correction term of log labor flows in a vector error correction model (VECM) with intercepts that change over the business cycle. Feeding historical expansions and recessions into the VECM generates large low-frequency movements in the unemployment rate. Frequent recessions from the late 1960s to the early 1980s interrupt labor market ...
Report
Exchange rate cointegration across central bank regime shifts
Foreign exchange rates are examined using cointegration tests over various time periods linked to regime shifts in central bank behavior. The number of cointegrating vectors seems to vary across these regime changes within the foreign exchange market. For example, cointegration is not generally found prior to the Plaza Agreement of September 22, 1985, but it is present after that date. The significance of these changes is evaluated using a likelihood ratio procedure proposed by Quintos (1993). The changing nature of the cointegrating relationships indicate that certain aspects of central bank ...
Report
GDP Solera: The Ideal Vintage Mix
We exploit the information in the successive vintages of gross domestic expenditure (GDE) and gross domestic income (GDI) from the current comprehensive revision to obtain an improved, timely measure of U.S. aggregate output by exploiting cointegration between the different measures and taking their monthly release calendar seriously. We also combine all existing overlapping comprehensive revisions to achieve further improvements. We pay particular attention to the Great Recession and the pandemic, which, despite producing dramatic fluctuations, does not generate noticeable revisions in ...
Working Paper
Linear cointegration of nonlinear time series with an application to interest rate dynamics
We derive a definition of linear cointegration for nonlinear stochastic processes using a martingale representation theorem. The result shows that stationary linear cointegrations can exhibit nonlinear dynamics, in contrast with the normal assumption of linearity. We propose a sequential nonparametric method to test first for cointegration and second for nonlinear dynamics in the cointegrated system. We apply this method to weekly US interest rates constructed using a multirate filter rather than averaging. The Treasury Bill, Commercial Paper and Federal Funds rates are cointegrated, with two ...
Working Paper
Testing for cointegration using the Johansen methodology when variables are near-integrated
We investigate the properties of Johansen's (1988, 1991) maximum eigenvalue and trace tests for cointegration under the empirically relevant situation of near-integrated variables. Using Monte Carlo techniques, we show that in a system with near-integrated variables, the probability of reaching an erroneous conclusion regarding the cointegrating rank of the system is generally substantially higher than the nominal size. The risk of concluding that completely unrelated series are cointegrated is therefore non-negligible. The spurious rejection rate can be reduced by performing additional tests ...
Report
International Evidence on Long-Run Money Demand
We explore the long-run demand for M1 based on a dataset comprising 38 countries and relatively long sample periods, extending in some cases to over a century. Overall, we find very strong evidence of a long-run relationship between the ratio of M1 to GDP and a short-term interest rate, in spite of a few failures. The standard log-log specification provides a very good characterization of the data, with the exception of periods featuring very low interest rate values. This is because such a specification implies that, as the short rate tends to zero, real money balances become arbitrarily ...
Working Paper
Cointegration: how short is the long run?