← Research Replication

Vulnerable Growth

Do financial conditions help predict the whole distribution of future GDP growth, and not only its mean? The paper's answer gave rise to Growth-at-Risk.

Tobias Adrian, Nina Boyarchenko and Domenico Giannone, American Economic Review 109(4), 2019

Replication by Lorenzo Giordani.

Quantile regression Skewed t Growth-at-Risk Density forecasts
Code → The paper (working-paper version) →
Predictive density 
 
 
 
 
 
 
 
 
 
 
What I did
 
     
  1. Quantile regressions
    Future GDP growth, one quarter and one year ahead, on current growth and the Chicago Fed’s financial conditions index (NFCI), 1973–2015. Nineteen quantiles, solved exactly as linear programmes, with bands from a Gaussian VAR(4) bootstrap.
    2.  
  2. Predictive densities
    A skewed t fitted every quarter to the predicted 5th, 25th, 75th and 95th percentiles, which turns the quantiles into a full distribution.
    3.  
  3. Measures of vulnerability
    Downside and upside entropy, expected shortfall, and a recursive out-of-sample exercise from 1993, scored by predictive score and PIT.
    4.  
  4. Alternatives
    The paper’s maximum-likelihood and kernel estimators, and its evidence on how the mean and the volatility of growth move together.
    5.  
 
 
 
What I found
 
Financial conditions move the left tail of future growth; the centre moves less and the right tail hardly at all.
 
 
−2.52 / 0.03
NFCI coefficient at the 5th and 95th percentile, one quarter ahead: a one-s.d. tightening lowers the bad case by 2.5 points and leaves the good case where it is.
 
−5.5%
5th percentile of growth for 2008Q4, estimated in real time on data up to the crisis (in-sample: −5.9%).
 
−0.9
Correlation between the mean of the predictive distribution and its standard deviation: weak expected growth comes with high uncertainty.
 
 
Downside risk spikes in 1974–75, 1980–82 and 2008–09, while upside risk stays flat. The predicted quantiles coincide with the authors’ replication files to 10−5, and the fitted skewed-t parameters agree in almost every quarter.
 
CaveatOut of sample (1993–2015) the densities were somewhat too optimistic around the centre. The left tail, which is what the model is built for, is well calibrated.