Publication: Dynamic quantile causal inference and forecasting
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Publication date
2021-04
Defense date
2021-06-28
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Abstract
Standard impulse response functions measure the average effect of a shock on a response
variable. However, different parts of the distribution of the response variable may react
to the shock differently.
The first chapter, “Quantile Structural Vector Autoregression”, introduces a framework
to measure the dynamic causal effects of shocks on the entire distribution of response
variables, not just on the mean. Various identification schemes are considered: shortrun
and long-run restrictions, external instruments, and their combinations. Asymptotic
distribution of the estimators is established. Simulations show our method is robust to
heavy tails. Empirical applications reveal causal effects that cannot be captured by the
standard approach. For example, the effect of oil price shock on GDP growth is statistically
significant only in the left part of GDP growth distribution, so a spike in oil price may
cause a recession, but there is no evidence that a drop in oil price may cause an expansion.
Another application reveals that real activity shocks reduce stock market volatility.
The second chapter, “Quantile Local Projections: Identification, Smooth Estimation,
and Inference”, is devoted to an increasingly popular method to capture heterogeneity of
impulse response functions, namely to local projections estimated by quantile regression.
We study their identification by short-run restrictions, long-run restrictions, and external
instruments. To overcome their excessive volatility, we introduce two novel estimators:
Smooth Quantile Projections (SQP) and Smooth Quantile Projections with Instruments
(SQPI). The SQPI inference is valid under weak instruments. We propose information criteria
for optimal smoothing and apply the estimators to shocks in financial conditions and
monetary policy. We demonstrate that financial conditions affect the entire distribution
of future GDP growth and not just its lower part as previously thought.
The third chapter, “Smooth Quantile Projections in a Data-Rich Environment”, modifies
the estimator from the second chapter to construct distribution forecasting in a setting
with potentially many variables. To this end we introduce a novel estimator, Smooth Quantile
Projections with Lasso. The estimator involves two penalties, one controlling roughness
of the forecasts over forecast horizons, while the other penalty selects the most informative
set of predictors. We also introduce information criteria to guide the optimal choice of
the two penalties and represent the problem as a linear program in standard form.
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Keywords
Asymmetry, Causal inference, Impulse response, Instrumental variables, Quantile regression, Regularization, Shocks, Treatment effects, Vector autoregression