Identification approaches

• Narrative approach– Look for exogenous movements in spending– Many of issues of timing, endogeneity with

monetary policy and tax dates do not arise– Build-up dummies can be included directly as

shocks in single equation or systems

Identification approaches

• VAR approach– “Structural approach”

•Wold causal chain• Caution: Testing of identifying restrictions a no-no•Need to maintain causal ordering

– Identifying restriction•Government spending does not respond

contemporaneously to other variables•Mechanically: Ordered “first” in VAR

Identification approaches

• Exogenous variation, final form regression– Aggregate, esp. miliary spending

•Hall, Barro, etc

– State/regional/small country• Flurry of recent work

• Estimating equation

1 1

1 1

t t t tt

t t

z z g g

y y

Review of VAR

• Recursive ordering• Instrumental variables interpretation

VAR example

11 1 12 2 1 21 1 22 2 2... ...t t t k t k t t k t k gtg a g a g a g a y a y a y

11 1 12 2 1 21 1 22 2 2... ...t t t k t k t t k t k g gt yty b g b g b g b y b y b y

Estimate equation by equation

Orthogonalize by putting residual from first equation into second equation (“Cholesky decomposition”)

Economics/Identification: Government spending does not respond contemporaneously to output

VAR with exogenous variable example

Ramey-Shapiro dummy (exogenous)td

10 11 1 12 2 1 21 1 22 2 2... ...t t t t k t k t t k t k yty c d c d c d c d c y c y c y

Identification approaches

• Narrative approach– Look for exogenous movements in spending– Many of issues of timing, endogeneity with

monetary policy and tax dates do not arise– Build-up dummies can be included directly as

shocks in single equation or systems

Identification approaches

• VAR approach– “Structural approach”

•Wold causal chain• Caution: Testing of identifying restrictions a no-no•Need to maintain causal ordering

– Identifying restriction•Government spending does not respond

contemporaneously to other variables•Mechanically: Ordered “first” in VAR

Identification approaches

• Exogenous variation, final form regression– Aggregate, esp. miliary spending

•Hall, Barro, etc

– State/regional/small country• Flurry of recent work

• Estimating equation

1 1

1 1

t t t tt

t t

z z g g

y y

Source: Hall (2009)

Source:

Ramey 2011

Response to spending shocks:

VAR versus Ramey-Shapiro

Source:

Ramey 2011

Source:

Ramey 2011