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Working Paper
State-Dependent Local Projections
Do state-dependent local projections asymptotically recover the population responses of macroeconomic aggregates to structural shocks? The answer to this question depends on how the state of the economy is determined and on the magnitude of the shocks. When the state is exogenous, the local projection estimator recovers the population response regardless of the shock size. When the state depends on macroeconomic shocks, as is common in empirical work, local projections only recover the conditional response to an infinitesimal shock, but not the responses to larger shocks of interest in many ...
Working Paper
Predictable dynamics in the S&P 500 index options implied volatility surface
One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of fitting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time. In this paper we study whether the resulting predictability patterns in the IVS coefficients may be exploited in practice. We propose a two-stage approach to modeling and forecasting the S&P 500 index ...
Working Paper
Impulse Response Analysis for Structural Dynamic Models with Nonlinear Regressors
We study the construction of nonlinear impulse responses in structural dynamic models that include nonlinearly transformed regressors. Such models have played an important role in recent years in capturing asymmetries, thresholds and other nonlinearities in the responses of macroeconomic variables to exogenous shocks. The conventional approach to estimating nonlinear responses is by Monte Carlo integration. We show that the population impulse responses in this class of models may instead be derived analytically from the structural model. We use this insight to study under what conditions ...
Working Paper
Tests of Equal Accuracy for Nested Models with Estimated Factors
In this paper we develop asymptotics for tests of equal predictive ability between nested models when factor-augmented regression models are used to forecast. We provide conditions under which the estimation of the factors does not affect the asymptotic distributions developed in Clark and McCracken (2001) and McCracken (2007). This enables researchers to use the existing tabulated critical values when conducting inference. As an intermediate result, we derive the asymptotic properties of the principal components estimator over recursive windows. We provide simulation evidence on the finite ...
Working Paper
Bootstrapping out-of-sample predictability tests with real-time data
In this paper we develop a block bootstrap approach to out-of-sample inference when real-time data are used to produce forecasts. In particular, we establish its first-order asymptotic validity for West-type (1996) tests of predictive ability in the presence of regular data revisions. This allows the user to conduct asymptotically valid inference without having to estimate the asymptotic variances derived in Clark and McCracken’s (2009) extension of West (1996) when data are subject to revision. Monte Carlo experiments indicate that the bootstrap can provide satisfactory finite sample size ...
Working Paper
When Do State-Dependent Local Projections Work?
Many empirical studies estimate impulse response functions that depend on the state of the economy. Most of these studies rely on a variant of the local projection (LP) approach to estimate the state-dependent impulse response functions. Despite its widespread application, the asymptotic validity of the LP approach to estimating state-dependent impulse responses has not been established to date. We formally derive this result for a structural state-dependent vector autoregressive process. The model only requires the structural shock of interest to be identified. A sufficient condition for the ...