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Working Paper
The Anatomy of Out-of-Sample Forecasting Accuracy
We develop metrics based on Shapley values for interpreting time-series forecasting models, including“black-box” models from machine learning. Our metrics are model agnostic, so that they are applicable to any model (linear or nonlinear, parametric or nonparametric). Two of the metrics, iShapley-VI and oShapley-VI, measure the importance of individual predictors in fitted models for explaining the in-sample and out-of-sample predicted target values, respectively. The third metric is the performance-based Shapley value (PBSV), our main methodological contribution. PBSV measures the ...
Journal Article
Is the Last Mile More Arduous?
US inflation surged starting in spring 2021, with Consumer Price Index (CPI) inflation reaching a 40-year high of 9 percent in mid-2022. Together with improving supply-chain conditions, policy tightening by the Fed decreased inflation to within 1 to 2 percentage points of its 2 percent target by late 2023 without a significant increase in unemployment. However, concerns have been raised that the last mile of disinflation to reduce inflation consistently to its 2 percent target will be more arduous than the previous miles. Close examination of such concerns indicates that they do not receive ...
Journal Article
Forecasting real housing price growth in the Eighth District states
The authors consider forecasting real housing price growth for the individual states of the Federal Reserve's Eighth District. They first analyze the forecasting ability of a large number of potential predictors of state real housing price growth using an autoregressive distributed lag (ARDL) model framework. A number of variables, including the state housing price-to-income ratio, state unemployment rate, and national inflation rate, appear to provide information that is useful for forecasting real housing price growth in many Eighth District states. Given that it is typically difficult to ...
Working Paper
Metro Business Cycles
We construct monthly economic activity indices for the 50 largest U.S. metropolitan statistical areas (MSAs) beginning in 1990. Each index is derived from a dynamic factor model based on twelve underlying variables capturing various aspects of metro area economic activity. To accommodate mixed-frequency data and differences in data-publication lags, we estimate the dynamic factor model using a maximum- likelihood approach that allows for arbitrary patterns of missing data. Our indices highlight important similarities and differences in business cycles across MSAs. While a number of MSAs ...
Working Paper
Out-of-sample equity premium prediction: economic fundamentals vs. moving-average rules
This paper analyzes the ability of both economic variables and moving-average rules to forecast the monthly U.S. equity premium using out-of-sample tests for 1960?2008. Both approaches provide statistically and economically significant out-of-sample forecasting gains, which are concentrated in U.S. business-cycle recessions. Nevertheless, economic variables and moving-average rules capture different sources of equity premium fluctuations: moving average rules detect the decline in the average equity premium early in recessions, while economic variables more readily pick up the rise in the ...
Journal Article
Real interest rate persistence: evidence and implications
The real interest rate plays a central role in many important financial and macroeconomic models, including the consumption-based asset pricing model, neoclassical growth model, and models of the monetary transmission mechanism. The authors selectively survey the empirical literature that examines the time-series properties of real interest rates. A key stylized fact is that postwar real interest rates exhibit substantial persistence, shown by extended periods when the real interest rate is substantially above or below the sample mean. The finding of persistence in real interest rates is ...
Journal Article
Common Fluctuations in OECD Budget Balances
The authors use a dynamic latent factor model to analyze comovements in OECD surpluses. The world factor underlying common fluctuations in budget surpluses across countries explains an average of 28 to 44 percent of the variation in individual country surpluses. The world factor, which can be interpreted as a global budget surplus index, declines substantially in the 1980s, rises throughout much of the 1990s, peaks in 2000, and declines again after the financial crisis of 2008. The authors then estimate similar world factors in national output gaps, dividend-to-price ratios, and military ...
Working Paper
The Anatomy of Out-of-Sample Forecasting Accuracy
We introduce the performance-based Shapley value (PBSV) to measure the contributions of individual predictors to the out-of-sample loss for time-series forecasting models. Our new metric allows a researcher to anatomize out-of-sample forecasting accuracy, thereby providing valuable information for interpreting time-series forecasting models. The PBSV is model agnostic—so it can be applied to any forecasting model, including "black box" models in machine learning, and it can be used for any loss function. We also develop the TS-Shapley-VI, a version of the conventional Shapley value that ...
Working Paper
Is inflation an international phenomenon?
Common shocks, similarities in central bank reaction functions, and international trade potentially produce common components in international inflation rates. This paper characterizes such links in international inflation rates with a dynamic latent factor model that decomposes inflation for 65 countries into world, regional, and idiosyncratic components. The world component accounts for 34% of inflation variability on average across countries, although the importance of this global factor differs substantially across countries. Variables that reflect policy as well as economic and financial ...