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Motivation

Motivation. Hard to believe that productivity shocks drive the whole cycle We want to know their importance relative to demand shocks. A traditional approach. Estimate a structural model Recover the supply and demand shocks: money, productivity, etc…

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Motivation

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  1. Motivation • Hard to believe that productivity shocks drive the whole cycle • We want to know their importance relative to demand shocks

  2. A traditional approach • Estimate a structural model • Recover the supply and demand shocks: money, productivity, etc… • Use the model to perform a variance decomposition of GDP • Problem: the results entirely depend on the model’s specification

  3. The semi-structural VAR approach • Shocks are identified by their dynamic effects on the variables of interest • Instead of being driven by one model, identification is driven by a range of models: • Consistent with the class of models that predict the same dynamic effects

  4. A strategy: • One of the most robust predictions across models is that demand shocks have no long-run effect on output • On the other hand, productivity shocks tend to affect output permanently • Furthermore, with an expectational Phillips curve in unemployment, neither demand not supply shocks have a long run effect on unemployment

  5. The VAR method • Take two variables, money and output • Regress them on themselves, lagged • The econometric residuals are not shocks

  6. Recovering the shocks • In general, residuals are related to shocks by some Matrix B • If I know B, I can recover the true shocks from the residuals

  7. Impulse responses • The dynamic responses of m and y to the true shocks can then be recovered.

  8. Example:

  9. Computing B? • We need 4 identifying assumptions to get the 4 coefficients of B • We can normalize the shocks’ variance to 1 and assume that they are uncorrelated • Furthermore, B must match the covariance matrix of residuals • This gives us 3 restrictions on B, one is missing

  10. Bringing economics in • Suppose monetary authorities do not react instantaneously to an output shock: • No contemporaneous effect of the output shock on money

  11. Computing B • B is lower-triangular • As Ω = Eεε’ definite positive, there exists a unique lower-triangular matrix Z such that Ω = ZZ’ and z11 > 0. (Choleski decomposition) • Therefore, B = Z.

  12. Long-run restrictions • We want to transpose this technique to use the fact that supply shocks have permanent effects on output as an identifying assumption • Because of that, output is I(1) and must be filtered to be made stationary. • This guarantees only transitory effects on unemployment of all shocks • Thus we estimate

  13. Again, we want to identify the true shocks • Independence and matching the residual covariance matrix yields three restrictions • How can we express the fourth restriction that demand shocks have no long run impact on output?

  14. The vector Xt has a VMA representation Xt = C(L)vt • The cumulated effect of a shock ηon X is C(1)b • The long-run effect of a shock on y is its cumulated effect on Δy.

  15. For the demand shock to have no long-run effect on output, we thus need that [C(1)B]12= 0 • This Matrix is upper-triangular and we can identify B again, using the Choleski decomposition

  16. Main results • Demand shocks peak after 2-4 quarters • Supply shocks are slightly contractionary on employment upon impact, very small positive effect then • Estimated demand shocks match well NBER peaks and through  suggest they are main source of fluctuations • The oil shocks have both a demand and supply component  casts doubts on independence

  17. Gali (1999) • Takes on BQ by proposing a « better » identifying assumption • Focuses on the employment-reducing effect of technology shocks • Argues that it kills the RBC hypothesis

  18. The Gali critique • In BQ, any permanent shock on output is interpreted as a technology shock • Ex: labor market participation • OK to focus on effects of demand shocks, not great to focus on effects of technology shocks • Gali shows that labor producticity is stationary if ROR on K is pinned down and no technology shock

  19. Methodology • A variant of BQ • The VAR uses the change in labor productivity, and the change in total hours per capita. • Non-productivity shocks have no long-run effect on labor productivity • Estimates of technology are then not polluted by labor hoarding which only affects labor productivity temporarily

  20. Results • Correlation between employment and productivity is negative, contrary to RBC model • Non-productivity shocks have permanent effects on hours • Pattern is robust across countries • Technology shocks alone do not replicate the RBC model’s predictions

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