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Nonlinearity and flight to safety in the risk-return trade-off for stocks and bonds
Vogt, Erik; Adrian, Tobias; Crump, Richard K. (2015-04-01)
We document a highly significant, strongly nonlinear dependence of stock and bond returns on past equity market volatility as measured by the VIX. We propose a new estimator for the shape of the nonlinear forecasting relationship that exploits additional variation in the cross section of returns. The nonlinearities are mirror images for stocks and bonds, revealing flight to safety: expected returns increase for stocks when volatility increases from moderate to high levels, while they decline for Treasury securities. These findings provide support for dynamic asset pricing theories where the ...
Staff Reports , Paper 723

Discussion Paper
Discounting the Long-Run
Diamond, Peter A.; Yu, Rui; Adrian, Tobias; Crump, Richard K. (2015-08-31)
Expectations about the path of interest rates matter for many economic decisions. Three sources for obtaining information about such expectations are available. The first is extrapolation from historical data. The second consists of surveys of expectations. The third are expectations drawn from financial market prices, often referred to as market expectations. The last are usually considered to be model-based expectations, because, generally, a model is needed to reliably extract expectations from current prices. In this post, we explain the need for and usage of term structure models for ...
Liberty Street Economics , Paper 20150831

Discussion Paper
Changing Risk-Return Profiles
Crump, Richard K.; Hundtofte , Sean; Giannone, Domenico (2018-10-04)
Are stock returns predictable? This question is a perennially popular subject of debate. In this post, we highlight some results from our recent working paper, where we investigate the matter. Rather than focusing on a single object like the forecasted mean or median, we look at the entire distribution of stock returns and find that the realized volatility of stock returns, especially financial sector stock returns, has strong predictive content for the future distribution of stock returns. This is a robust feature of the data since all of our results are obtained with real-time analyses ...
Liberty Street Economics , Paper 20181004

Discussion Paper
Treasury Term Premia: 1961-Present
Moench, Emanuel; Mills, Benjamin; Adrian, Tobias; Crump, Richard K. (2014-05-12)
Treasury yields can be decomposed into two components: expectations of the future path of short-term Treasury yields and the Treasury term premium. The term premium is the compensation that investors require for bearing the risk that short-term Treasury yields do not evolve as they expected. Studying the term premium over a long time period allows us to investigate what has historically driven changes in Treasury yields. In this blog post, we estimate and analyze the Treasury term premium from 1961 to the present, and make these estimates available for download here.
Liberty Street Economics , Paper 20140512

Discussion Paper
Forecasting Interest Rates over the Long Run
Diamond, Peter A.; Yu, Rui; Adrian, Tobias; Crump, Richard K. (2016-07-18)
In a previous post, we showed how market rates on U.S. Treasuries violate the expectations hypothesis because of time-varying risk premia. In this post, we provide evidence that term structure models have outperformed direct market-based measures in forecasting interest rates. This suggests that term structure models can play a role in long-run planning for public policy objectives such as assessing the viability of Social Security.
Liberty Street Economics , Paper 20160718

Report
A Jackknife Variance Estimator for Panel Regressions
Lopez Gaffney, Ignacio; Crump, Richard K.; Gospodinov, Nikolay (2024-10-01)
We introduce a new jackknife variance estimator for panel-data regressions. Our variance estimator can be motivated as the conventional leave-one-out jackknife variance estimator on a transformed space of the regressors and residuals using orthonormal trigonometric basis functions. We prove the asymptotic validity of our variance estimator and demonstrate desirable finite-sample properties in a series of simulation experiments. We also illustrate how our method can be used for jackknife bias-correction in a variety of time-series settings.
Staff Reports , Paper 1133

Discussion Paper
A Bayesian VAR Model Perspective on the Lagged Effect of Monetary Policy
Crump, Richard K.; Del Negro, Marco; Dogra, Keshav; Gundam, Pranay; Lee, Donggyu; Nallamotu, Ramya; Pacula, Brian (2023-11-21)
Over the last few years, the U.S. economy has experienced unusually high inflation and an unprecedented pace of monetary policy tightening. While inflation has fallen recently, it remains above target, and the economy continues to expand at a robust pace. Does the resilience of the U.S. economy imply that monetary policy has been ineffectual? Or does it reflect that policy acts with “long and variable lags” and so we haven’t yet observed the full effect of the monetary tightening that has already taken place? Using a Bayesian vector autoregressive (BVAR) model, we show that economic ...
Liberty Street Economics , Paper 20231121a

Report
Fundamental Disagreement about Monetary Policy and the Term Structure of Interest Rates
Moench, Emanuel; Eusepi, Stefano; Cao, Shuo; Crump, Richard K. (2020-07-01)
Using a unique data set of individual professional forecasts, we document disagreement about the future path of monetary policy, particularly at longer horizons. The stark differences in short rate forecasts imply strong disagreement about the risk-return trade-off of longer-term bonds. Longer-horizon short rate disagreement co-moves with term premiums. We estimate an affine term structure model in which investors hold heterogeneous beliefs about the long-run level of rates. Our model fits Treasury yields and the short rate paths predicted by different groups of investors and thus matches the ...
Staff Reports , Paper 934

Discussion Paper
A Look at the Accuracy of Policy Expectations
Moench, Emanuel; Eusepi, Stefano; Crump, Richard K. (2011-08-22)
Since the 1980s, the primary policy tool of the Federal Reserve has been the federal funds rate. Because expectations of the future path of the funds rate play a central role in the term structure of interest rates and thus the monetary transmission mechanism, it is important to know how accurate these expectations are in predicting the funds rate. In this post, we investigate this issue using a well-known survey of private sector forecasters. We find that forecasts tend to over-predict the funds rate in easing cycles and under-predict it in tightening cycles. In addition, while forecasts ...
Liberty Street Economics , Paper 20110822

Discussion Paper
Real Inventory Slowdowns
Lucca, David O.; McQuillan, Casey; Crump, Richard K. (2019-11-18)
Inventory investment plays a central role in business cycle fluctuations. This post examines whether inventory investment amplifies or dampens economic fluctuations following a tightening in financial conditions. We find evidence supporting an amplification mechanism. This analysis suggests that inventory accumulation will be a drag on economic activity this year but provide a boost in 2020.
Liberty Street Economics , Paper 20191118

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