Working Paper: NBER ID: w23186
Authors: Ulrich K. Müller; Mark W. Watson
Abstract: We develop inference methods about long-run comovement of two time series. The parameters of interest are defined in terms of population second-moments of lowfrequency trends computed from the data. These trends are similar to low-pass filtered data and are designed to extract variability corresponding to periods longer than the span of the sample divided by q/2, where q is a small number, such as 12. We numerically determine confidence sets that control coverage over a wide range of potential bivariate persistence patterns, which include arbitrary linear combinations of I(0), I(1), near unit roots and fractionally integrated processes. In an application to U.S. economic data, we quantify the long-run covariability of a variety of series, such as those giving rise to the “great ratios”, nominal exchange rates and relative nominal prices, unemployment rate and inflation, money growth and inflation, earnings and stock prices, etc.
Keywords: longrun comovement; statistical inference; economic time series
JEL Codes: C22; C53; E17
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Consumption (E21) | Income (D31) |
| Nominal Exchange Rates (F31) | Relative Nominal Prices (E30) |
| Relative Nominal Prices (E30) | Nominal Exchange Rates (F31) |
| Inflation Rates (E31) | Unemployment Rate (J64) |
| GDP (E20) | Consumption (E21) |
| Short-term Interest Rates (E43) | Long-term Interest Rates (E43) |