Structural VARs: Applications and Commentaries

1. Structural VARs: celebrated applications and commentaries Revision Lecture for MSc Time Series Econometrics module, Bristol, Spring 2014

2. Overview • Sims on the ‘price puzzle’ • Christianoet al on identifying mon pol shock using Cholesky • Gali on identifying technology shocks using long run restrictions • Francis et al/Barsky-Simson max share restrictions and news shocks • Canova and de Nicoloon identifying the output effects of monetary policy shocks using sign restrictions • Rigobon on identification through heteroskedasticity • Pinter et al [inc me] on sign restrictions, Bayesian VARs, news shocks

3. Overview (2) • Rudebusch vs Sims on monetary policy ‘shocks’. • Romer and Romer: narrative methods for identifying policy shocks. • Stock and Watson on a factor analysis of the financial crisis. [See earlier lecture slides for detailed look].

4. What to get from a paper for the exam [and life!] • What did the authors do and why? What debate were they contributing to? • What did they find? How did this change what we thought about the debate they were contributing to? • What further work did it prompt? What criticisms can be made? What questions did their work beg?

5. Sims and the price puzzle • Cholesky identification often found that rise in rates caused rise in prices. A puzzle from perspective of modern macro models. • Sims puts this down to missing variables, like commodity prices. Fed responding to many variables, not just inflation and GDP. • Rise in rates looks exogenous, uncorrelated with today’s inflation and GDP, but actually responding to commodity prices, which may be a good forecast of future GDP. • Other explanations by later researchers offered too.

6. Sims • Implication was you needed to enlarge VAR [in later work with Zha, he tried 19 variables!]. • This spurs work on techniques to cope with curse of dimensionality: Bayesian VARs, and factor modelling.

7. CEE on cholesky identification of mon pol shocks • Find monetary policy has persistent and hump-shaped responses on real variables, and inflation. • Needs sticky prices/wages, indexation, habits, and other rigidities to match. • Inconsistent with RBC model [mp neutral on output], and with simplest NK models [IRFs not persistent or hump-shaped]. • Issue: indexation not consistent with micro data on prices. • View paper in light of Rotemburg-Woodford’s effort to fit a simpler sticky price model to similarly identified monetary policy shock responses.

8. Gali on technology shocks and long run restrictions • RBC crowd claimed that technology shocks were dominant explanation for business cycles. • Gali used RBC/NK theory to identify technology shocks; should be only thing affecting labour productivity in long run. • Saw that these shocks caused fall in hours work. [=‘relax/don’t make hay while the sun shines’]

9. Gali: ctd… • Implied tech shocks not dominant cause of business cycles: unconditional correlation of GDP and hours was positive. • Or implied prices were not flexible. Note sticky prices means hours fall after positive technology shock. • Prompted furious debate about the efficacy of long run restrictions in US academia.

10. Gali (3) • Christianoet al showed that results depended on the hours worked variable used. Shd it be hours, or hours/head? How should it be de-trended? • Giraitiset alshow that there was time variation in response of hours worked to tech shock. Became more RBC like as time went by. • Debate produced Francis et al’s paper on max-share restrictions. • Controversy over the sign of response of hours worked implies difficult to use sign restrictions [on hours] to identify this shock!

11. Francis et al on max share restrictions • Critics of LR restrictions argued that finite sample not appropriate for identifying the long run. • Recall that LR restrictions built from infinite series sum, involving ever higher powers of VAR coefficients. Estimated with error. • Francis et al suggest identifying shock by ‘rotating’ the Chol factor of the RF VCOV matrix to max the share of variance at some long but finite horizon.

12. Francis et al (2) • They redo Gali’s analysis of technology shocks. • Find that a technology shock increases hours worked, in line with RBC, and contrary to Gali’s original findings. • Idea derives from papers by Faust (1996) and Faust and Leeper (1997), explaining the pitfalls of long run restrictions.

13. Canova and de Nicoloon sign restrictions • Identifies monetary policy shock based on sign restrictions. • Finds these shocks contribute significantly to fluctuations in inflation and output. • Latter indicates sticky prices. • Some evidence of time variation. • Other foundational papers on sign restrictions are Faust (1998) and Uhlig (1999).

14. CN vs Uhlig • CN: use sign of mon pol shock on ir, m/p [real balances] and output. Finds MP contributes great deal to output volatility. [<=60%] • Uhlig: restricts responses of ir, m, p. Finds mon pol shock has no significant effect on output [implies prices are flexible].

15. Barsky-Sims on news shocks • Exploits Francis et al’s idea on max share restrictions. • Find innovation that is i) orthogonal to a proxy for tfp today but ii) contributes maximally to tfp tomorrow. • Depends on having found a proxy for tfp in the first place, which is somewhat dubious. • Find that news shocks are an important driver of the business cycle. • General implication being that business cycle diagnosis can’t focus only on contemporaneously-revealed shocks.

16. Pinter, Theodoridis and Yates on risk news shocks • Study of ‘risk news’ shocks. These are revelations about future changes in the variance of returns across different activities. • Exploits Barsky-Sims’ method. News shock constructed to be orthogonal to today’s risk proxy, but contribute maximally to fluctuations in the future. • Identifies monetary policy, technology shocks using sign restrictions at the same time.

17. Pinter et al (2) • Paper is a VAR-based reflection on Christiano, Motto, Rostagno, which claimed that risk (contemp +news) shocks accounted for 60% of business cycle volatility in output. • Pinter et al find a number like 20%. • Just as with Barsky-Sims, rather depends on having found a good proxy for cross-sectional risk.

18. Pinter et al (3) • PTY use Bayesian methods to estimate the reduced form VAR. • That’s because they have 10 variables, and 3 lags.=300 coefficients. • Modification of ‘Minnesota’ priors due to Doan et al, by Banburra et al. • Idea: ‘twist’ posterior towards model that each series is a random walk. • In original applications, shown to improve forecasting performance of the VAR. • In this application, eradicates volatile IRFs.

19. ‘Narrative measures’ of monetary and fiscal policy shocks • Aims to circumvent problems with VARs, or corroborate their findings. • Romer and Romer: trawl historical records for fiscal policy changes interpreted as exogenous to the business cycle. • Such shocks contractionary, and more so than those estimated using VARs. • RR repeat same exercise for mon pol shocks. • Repeated by Cloyne for UK

20. Sims vs Rudebush on monetary policy shocks • Rudebusch: ‘shocks’ don’t correlate well with ‘surprises’ measured by Fed Funds Futures. • Sims: these surprises mix up forecast errors due to genuine policy shocks, and errors due to other shocks, which prompted a policy response.

21. Stock and Watson very briefly • Study financial crisis using very large panel of 200+ data series. • Estimate that there are about 8 factors. • Not very few as first thought. • Early factor models had made RBC like claims that only needed a few ‘drivers’ to explain business cycle. • No new factors needed to explain post crisis period. • Crisis was larger version of old shocks, not a new shock.