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Working Paper
Significance Bands for Local Projections
An impulse response function describes the dynamic evolution of an outcome variable following a stimulus or treatment. A common hypothesis of interest is whether the treatment affects the outcome. We show that this hypothesis is best assessed using significance bands rather than relying on commonly displayed confidence bands. Under the null hypothesis, we show that significance bands are trivial to construct with standard statistical software using the LM principle, and should be reported as a matter of routine when displaying impulse responses graphically.
Working Paper
Disasters Everywhere: The Costs of Business Cycles Reconsidered
Business cycles are costlier and stabilization policies more beneficial than widely thought. This paper shows that all business cycles are asymmetric and resemble mini “disasters”. By this we mean that growth is pervasively fat-tailed and non-Gaussian. Using long-run historical data, we show empirically that this is true for all advanced economies since 1870. Focusing on the peacetime sample, we develop a tractable local projection framework to estimate consumption growth paths for normal and financial-crisis recessions. Using random coefficient local projections we get an easy and ...
Working Paper
The Long-Run Effects of Monetary Policy
Is the effect of monetary policy on the productive capacity of the economy long lived? Yes, in fact we find such impacts are significant and last for over a decade based on: (1) merged data from two new international historical databases; (2) identification of exogenous monetary policy using the macroeconomic trilemma; and (3) improved econometric methods. Notably, the capital stock and total factor productivity (TFP) exhibit hysteresis, but labor does not. Money is non-neutral for a much longer period of time than is customarily assumed. A New Keynesian model with endogenous TFP growth can ...
Working Paper
Impulse Response Functions for Self-Exciting Nonlinear Models
We calculate impulse response functions from regime-switching models where the driving variable can respond to the shock. Two methods used to estimate the impulse responses in these models are generalized impulse response functions and local projections. Local projections depend on the observed switches in the data, while generalized impulse response functions rely on correctly specifying regime process. Using Monte Carlos with different misspecifications, we determine under what conditions either method is preferred. We then extend model-average impulse responses to this nonlinear ...
Working Paper
Local Projections
A central question in applied research is to estimate the effect of an exogenous intervention or shock on an outcome. The intervention can affect the outcome and controls on impact and over time. Moreover, there can be subsequent feedback between outcomes, controls and the intervention. Many of these interactions can be untangled using local projections. This method’s simplicity makes it a convenient and versatile tool in the empiricist’s kit, one that is generalizable to complex settings. This article reviews the state-of-the art for the practitioner, discusses best practices and ...
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
State-Dependent Local Projections: Understanding Impulse Response Heterogeneity
An impulse response is the dynamic average effect of an intervention across horizons. We use the well-known Kitagawa-Blinder-Oaxaca decomposition to explore a response’s heterogeneity over time and over states of the economy. This can be implemented with a simple extension to the usual local projection specification that nevertheless keeps the model linear in parameters. Using our new decomposition-based approach, we show how to unpack heterogeneity in the fiscal multiplier, an object that at any point in time may depend on a number of potentially correlated factors, including existing ...
Report
Disasters Everywhere: The Costs of Business Cycles Reconsidered
Business cycles are costlier and stabilization policies more beneficial than widely thought. This paper shows that all business cycles are asymmetric and resemble mini “disasters.” By this we mean that growth is pervasively fat-tailed and non-Gaussian. Using long-run historical data, we show empirically that this is true for all advanced economies since 1870. Focusing on the peacetime sample, we develop a tractable local projection framework to estimate consumption growth paths for normal and financial-crisis recessions. Using random coefficient local projections we get an easy and ...
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 ...
Working Paper
A Local Projections Approach to Difference-in-Differences Event Studies
Many of the challenges in the estimation of dynamic heterogeneous treatment effects can be resolved with local projection (LP) estimators of the sort used in applied macroeconometrics. This approach provides a convenient alternative to the more complicated solutions proposed in the recent literature on Difference in-Differences (DiD). The key is to combine LPs with a flexible ‘clean control’ condition to define appropriate sets of treated and control units. Our proposed LP-DiD estimator is clear, simple, easy and fast to compute, and it is transparent and flexible in its handling of ...