Dynamic quantile causal inference and forecasting

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.