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…

• Use the model to perform a variance decomposition of GDP

• Problem: the results entirely depend on the model’s specification

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

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

The VAR method

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

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

Impulse responses

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

Example:

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

Bringing economics in

• Suppose monetary authorities do not react instantaneously to an output shock:

• No contemporaneous effect of the output shock on money

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.

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

• 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?

• The vector Xt has a VMA representation Xt = C(L)vt

• The cumulated effect of a shock η on X is C(1)b• The long-run effect of a shock on y is its

cumulated effect on Δy.

• 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

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

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

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

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

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