Kenneth D. West’s research while affiliated with University of Wisconsin–Madison and other places

We study long-run correlations between safe real interest rates in the United States and over 30 variables that have been hypothesized to influence real rates. The list of variables is motivated by an intertermporal IS equation, by models of aggregate savings and investment, and by reduced-form studies. We use annual data, mostly from 1890 to 2016. We find that safe real interest rates are correlated as expected with demographic measures. For example, the long-run correlation with labor force hours growth is positive, which is consistent with overlapping generations models. For another example, the long-run correlation with the proportion of 40 to 64 year-olds in the population is negative. This is consistent with standard theory where middle-aged workers are high savers who drive down real interest rates. In contrast to standard theory, we do not find productivity to be positively correlated with real rates. Most other variables have a mixed relationship with the real rate, with long-run correlations that are statistically or economically large in some samples and by some measures but not in others. (JEL E21, E22, E24, E43, E52)

Long horizon regressions that rely on linear models are common in many applied fields. Examples from economics include forecasting inflation 12 quarters ahead (Crone et al., 2013) and relating 120 month ahead changes in exchange rates to current period variables (Snaith et al., 2013). We describe R code to implement recently developed procedures that adjust long horizon regressions to lessen bias in parameter estimates (West, 2016).

We examine the behavior, determinants, and implications of the equilibrium level of the real federal funds rate, interpreted as the long run or steady state value of the real funds rate. We draw three main conclusions. First, the uncertainty around the equilibrium rate is large, and its relationship with trend GDP growth much more tenuous than widely believed. Our narrative and econometric analysis using cross-country data and going back to the 19th century supports a wide range of plausible estimates for the current level of the equilibrium rate, from a little over 0 per cent to the pre-crisis consensus of 2 per cent. Second, a bivariate vector error correction model that looks only to U.S. and world real rates well captures the behavior of U.S. real rates. The model treats real rates as cointegrated unit root processes. As of the end of our sample (2014), the model forecasts the real rate in the U.S. will asymptote to an equilibrium value of a little less than half a percent by 2021. Consistent with our first point, however, confidence intervals around this point estimate are huge. Third, the uncertainty around the equilibrium rate argues for more “inertial” monetary policy than implied by standard versions of the Taylor rule. Our simulations using the Fed staff’s FRB/US model show that explicit recognition of this uncertainty results in a later but steeper normalization path for the funds rate compared with the median “dot” in the FOMC’s Summary of Economic Projections.

We consider tests of equal population forecasting ability when mean squared prediction error is the metric for forecasting ability, the two competing models are nested, and the iterated method is used to obtain multistep forecasts. We use Monte Carlo simulations to explore the size and power of the MSPE-adjusted test of Clark and West (2006, 2007) (CW) and the Diebold-Mariano-West (DMW) test. The empirical size of the CW test is almost always tolerable: across a set of 252 simulation results that span 5 DGPs, 9 horizons, and various sample sizes, the median size of nominal 10% tests is 8.8%. The comparable figure for the DMW test, which is generally undersized, is 2.2%. An exception for DMW occurs for long horizon forecasts and processes that quickly revert to the mean, in which case CW and DMW perform comparably. We argue that this is to be expected, because at long horizons the two competing models are both forecasting the process to have reverted to its mean. An exception for CW occurs with a nonlinear DGP, in which CW is usually oversized. CW has greater power and greater size adjusted power than does DMW in virtually all DGPs, horizons and sample sizes. For both CW and DMW, power tends to fall with the horizon, reflecting the fact that forecasts from the two competing models both converge towards the mean as the horizon grows. Consistent with these results, in an empirical exercise comparing models for inflation, CW yields many more rejections of equal forecasting ability than does DMW, with most of the rejections occurring at short horizons.

We construct an example in which the least squares estimator has unbounded bias and no moments, even though the regressor and disturbance have moments of all orders and are independently distributed across observations.

We fit a factor model to two monthly panels of deflated prices of energy, metals and agricultural commodities. Prices consistently display a tendency to revert towards the factor, though the speed of reversion to the factor is slow. Using both in- and out-of-sample metrics, we compare the factor model to that of a “no change” model and to two simple models that tie changes in commodity prices to percentage change in either global industrial production or the U.S. dollar. The factor model does relatively well at long (12 month) horizons. In terms of commodities, the factor model's performance is best for energy prices, worst for metals, with agricultural prices falling in between.