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Working Paper
Distributions of error correction tests for cointegration
This paper provides cumulative distribution functions, densities, and finite sample critical values for the single-equation error correction statistic for testing cointegration. Graphs and response surfaces summarize extensive Monte Carlo simulations and highlight simple dependencies of the statistic's quantiles on the number of variables in the error correction model, the choice of deterministic components, and the estimation sample size. The response surfaces provide a convenient way for calculating finite sample critical values at standard levels; and a computer program, freely available ...
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
Testing the expectations hypothesis when interest rates are near integrated
Nominal interest rates are unlikely to be generated by unit-root processes. Using data on short and long interest rates from eight developed and six emerging economies, we test the expectations hypothesis using cointegration methods under the assumption that interest rates are near integrated. If the null hypothesis of no cointegration is rejected, we then test whether the estimated cointegrating vector is consistent with that suggested by the expectations hypothesis. The results show support for cointegration in ten of the fourteen countries we consider, and the cointegrating vector is ...
Working Paper
International Evidence on Long-Run Money Demand
We explore the long-run demand for M1 based on a data set that has comprised 32 countries since 1851. In many cases, cointegration tests identify a long-run equilibrium relationship between either velocity and the short rate or M1, GDP, and the short rate. Evidence is especially strong for the United States and the United Kingdom over the entire period since World War I and for moderate and high-inflation countries. With the exception of high-inflation countries?for which a ?log-log? specification is preferred?the data often prefer the specification in the levels of velocity and the short ...
Report
Online Appendix for: International Evidence on Long-Run Money Demand
This appendix supports Staff Report 587. An earlier version of this Staff Report circulated as Working Paper 738.
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
Non-Stationary Dynamic Factor Models for Large Datasets
We study a Large-Dimensional Non-Stationary Dynamic Factor Model where (1) the factors Ft are I (1) and singular, that is Ft has dimension r and is driven by q dynamic shocks with q less than r, (2) the idiosyncratic components are either I (0) or I (1). Under these assumption the factors Ft are cointegrated and modeled by a singular Error Correction Model. We provide conditions for consistent estimation, as both the cross-sectional size n, and the time dimension T, go to infinity, of the factors, the loadings, the shocks, the ECM coefficients and therefore the Impulse Response Functions. ...
Working Paper
Maximum-likelihood estimation of fractional cointegration with application to the short end of the yield curve
We estimate a multivariate autoregressive fractionally-integrated moving-average (ARFIMA) model to illustrate a cointegration testing methodology based on joint estimates of the fractional orders of integration of a cointegrating vector and its parent series. Although previous work has recognized that deviations from long-run relationships could exhibit long memory and go undetected in traditional 1(1)/i (0) cointegration analysis, previous tests for fractional cointegration relied on a two-step testing procedure and maintained the assumption in the second step that the parent series were ...
Working Paper
Cointegration: how short is the long run?