T HE F ISCAL M ULTIPLIER M ORASS : A B AYESIAN P ERSPECTIVE Todd B. Walker (IU) with Eric M. Leeper (IU) and Nora Traum (NC State) May 19, 2011 Bundesbank Spring Conference
F ISCAL M ULTIPLIER ( S ): D EFINITION 1. Present Value Multiplier: �� Q � � Q i =0 R − 1 t =0 E t ∆ Y t + Q t + i Present Value Multiplier(Q) = �� Q � � Q i =0 R − 1 t =0 E t ∆ G t + Q t + i 2. Impact Multiplier: Q = 0
H OW B IG /S MALL A RE F ISCAL M ULTIPLIERS ? IMF Working Paper 10/73 March 2010 1. 17 coauthors: model builders for policy institutions 2. Seven Structural Models: QUEST, GIMF, FRB-US, SIGMA BoC-GEM, OECD Fiscal, NAWM. 3. Conclude: “Robust finding across all models that fiscal policy can have sizeable output multipliers.”
R EPRESENTATIVE IMF M ULTIPLIER EC's QUEST ECB's NAWM Fed's SIGMA IMF's GIMF Fed's FRB-US BoC's GEM 2 2 1 1 0 0 0 1 2 3 4 5 1 Year of Monetary Accommodation F IGURE 1: Estimated Impact on GDP of Increase in Government Purchases of 1 Percent of GDP
R OBUST F INDING ? • Cogan, Cwik, Taylor and Wieland (2010), Cwik and Wieland (2010) • Multipliers less than 1 • Uhlig (2010) • Long-run multipliers negative
U HLIG (2010) I MPULSE R ESPONSE 1 output gov.spending 0.5 0 % output −0.5 −1 −1.5 2000 2010 2020 2030 2040 2050 Figure 5. Output and Government Spending: 40 years.
M OTIVATION Why do policy models yield very different conclusions for multipliers even when conditioning on same data set? Answer: Multipliers are conditional statistics, so different specifications → different multipliers
M OTIVATION Why do policy models yield very different conclusions for multipliers even when conditioning on same data set? Answer: Multipliers are conditional statistics, so different specifications → different multipliers IMF WP10/73’s Response to Uhlig (2010) and Cogan et al. (2010): • include hand-to-mouth agents • focus on short-run & temporary stimulus • model different types of fiscal-monetary interactions (Davig-Leeper (2009))
T HIS P APER Open Question: To what extent does a DSGE model force a particular multiplier on the data? • “black box” problem of DSGE models • use Bayesian methodology to address issue
O UR C ONTRIBUTION • Build suite of nested models to determine important elements for multipliers. • Use modified prior predictive analysis (PPA) to understand a priori what restrictions are generated by DSGE model • More general message: What does it mean for a prior to be “flat”? • Distribution of object of interest should be “flat” relative to economic question at hand
F INDINGS • Model restrictions impose tight ranges on multipliers • Rigidities and hand-to-mouth agents key for long run multipliers > 0 • Most important features for multiplier variation: • gov. spending process • hand-to-mouth agents • monetary-fiscal interactions
R EVIEW OF PPA • Standard Exercise [Lancaster (2004), Geweke (2010)]: used to evaluate model’s adequacy for given feature of data before estimation stage (model evaluation) • θ parameters, y data, ω vector of interest θ ( m ) ∼ p ( θ ) y ( m ) p ( y | θ ( m ) ) ∼ ω ( m ) p ( ω | y ( m ) , θ ( m ) ) ∼ • Compare distribution of ω to data
R EVIEW OF PPA • Standard Exercise [Lancaster (2004), Geweke (2010)]: used to evaluate model’s adequacy for given feature of data before estimation stage (model evaluation) • θ parameters, y data, ω vector of interest θ ( m ) ∼ p ( θ ) y ( m ) p ( y | θ ( m ) ) ∼ ω ( m ) p ( ω | y ( m ) , θ ( m ) ) ∼ • Compare distribution of ω to data • compuationally inexpensive
M ODIFIED PPA • Issue: What is multiplier in data? Requires model and identification • A j DSGE model, θ parameters of DSGE, ω = multipliers Draw θ ( m ) ∼ p ( θ ) Solve DSGE Model Calculate ω m | θ ( m ) Form p ( ω | A j )
M ODIFIED PPA • Issue: What is multiplier in data? Requires model and identification • A j DSGE model, θ parameters of DSGE, ω = multipliers Draw θ ( m ) ∼ p ( θ ) Solve DSGE Model Calculate ω m | θ ( m ) Form p ( ω | A j ) • PPA gives entire range of possible multipliers
O UR M ODEL 1. forward-looking, optimizing agents 2. utility from consumption and leisure 3. capital and labor inputs in production 4. monopolistic competition 5. nominal & real frictions 6. fiscal and monetary policy 7. open economy features
N ESTED S PECIFICATIONS • Model 1: Basic RBC
N ESTED S PECIFICATIONS • Model 1: Basic RBC • Model 2: RBC with real frictions
N ESTED S PECIFICATIONS • Model 1: Basic RBC • Model 2: RBC with real frictions • Model 3: NK model with sticky prices and wages
N ESTED S PECIFICATIONS • Model 1: Basic RBC • Model 2: RBC with real frictions • Model 3: NK model with sticky prices and wages • Model 4: NK model with hand-to-mouth agents
N ESTED S PECIFICATIONS • Model 1: Basic RBC • Model 2: RBC with real frictions • Model 3: NK model with sticky prices and wages • Model 4: NK model with hand-to-mouth agents • Model 5: NK model with open economy features
M ODEL 1: B ASIC RBC • CRRA, time-separable utility � � 1 − γ − L 1+ ξ C 1 − γ ∞ � t t β t E t 1 + ξ t =0 • Cobb-Douglas production t L 1 − α Y t = A t K α t • Law of motion for capital: K t = I t + (1 − δ ) K t − 1
M ODEL 1: B ASIC RBC • GBC: B t + τ K t R K t K t − 1 + τ L t W t L t + τ C t C t = R t − 1 B t − 1 + G t + Z t • capital tax, labor tax, government consumption, transfers follow X t = ρ x ˆ ˆ s b t − 1 + ǫ x X t − 1 + (1 − ρ x ) γ x ˆ t where s b t − 1 = B t − 1 /Y t − 1
M ODEL 1: B ASIC RBC • 5,000 draws from priors: γ ∼ N + (2 , 0 . 6) , ξ ∼ N + (2 , 0 . 6) , ρ x ∼ B (0 . 5 , 0 . 2) , γ x ∼ N + (0 . 2 , 0 . 05) • Priors similar to Smets and Wouters (2003) and others • Other parameters fixed at well known values (e.g., β = 0 . 99 )
M ODEL 1: B ASIC RBC Variable Impact 4 quart. 10 quart. 25 quart. ∞ PV ∆ Y � � Prob ∆ G > 1 0.00 0.00 0.00 0.00 0.00 PV ∆ C � � Prob 0.00 0.00 0.00 0.00 0.00 ∆ G > 0 PV ∆ I � � Prob ∆ G > 0 < 0.01 < 0.01 < 0.01 < 0.01 0.00
M ODEL 1: B ASIC RBC Total Output PV Total Consumption PV 2 0.5 0 1 −0.5 0 −1 −1 −1.5 −2 −2 −3 −2.5 0 50 100 150 200 0 50 100 150 200 Wealth Consumption PV Subst. Consumption PV 1.5 0 1 0.5 −0.5 0 −1 −0.5 −1 −1.5 −1.5 −2 −2 0 50 100 150 200 0 50 100 150 200
M ODEL 1: B ASIC RBC Intuition Straightforward: • Baxter-King (1993) Monacelli-Perotti (2008) + distortionary fiscal financing • ↑ G → negative wealth and substitution effects, crowding out • Consumption, Investment falls • Increase in public demand cannot offset decrease in private demand
M ODEL 2: RBC WITH R EAL F RICTIONS Add to Model 1 • Habit formation in utility � � ∞ − L 1+ ξ ( c t − θC t − 1 ) 1 − γ � β t t E t 1 − γ 1 + ξ t =0 θ ∼ B (0 . 5 , 0 . 2) • Capacity utilization: ψ ( v t ) cost per unit of K v = 1 , ψ (1) = 0 , ψ ′′ (1) ψ ψ ′ (1) = 1 − ψ , ψ ∼ B (0 . 6 , 0 . 15)
M ODEL 2: RBC WITH R EAL F RICTIONS • Investment adjustment costs � I t � �� K t = (1 − δ ) K t − 1 + 1 − s I t I t − 1 where s (1) = s ′ (1) = 0 , and s ′′ (1) = s > 0 , s ∼ N (6 , 1 . 5)
M ODEL 2: RBC WITH R EAL F RICTIONS • Investment adjustment costs � I t � �� K t = (1 − δ ) K t − 1 + 1 − s I t I t − 1 where s (1) = s ′ (1) = 0 , and s ′′ (1) = s > 0 , s ∼ N (6 , 1 . 5) • Aggregate resource constraint: Y t = C t + G t + I t + ψ ( v t ) K t − 1
M ODEL 2: RBC WITH R EAL F RICTIONS Variable Impact 4 quart. 10 quart. 25 quart. ∞ PV ∆ Y � � Prob ∆ G > 1 0.01 0.00 0.00 0.00 < 0.01 PV ∆ C � � Prob 0.00 0.00 0.00 0.00 < 0.01 ∆ G > 0 PV ∆ I � � Prob ∆ G > 0 < 0.01 < 0.01 < 0.01 < 0.01 < 0.01
M ODEL 2: RBC WITH R EAL F RICTIONS Total Output PV Total Consumption PV 2 0.5 0 1 −0.5 0 −1 −1 −1.5 −2 −2 −3 −2.5 0 50 100 150 200 0 50 100 150 200 Wealth Consumption PV Subst. Consumption PV 1.5 0 1 0.5 −0.5 0 −1 −0.5 −1 −1.5 −1.5 −2 −2 0 50 100 150 200 0 50 100 150 200
M ODEL 2: RBC WITH R EAL F RICTIONS Total Output PV Total Consumption PV 2 0.5 0 1 −0.5 0 −1 −1 −1.5 −2 −2 −3 −2.5 0 50 100 150 200 0 50 100 150 200 Wealth Consumption PV Subst. Consumption PV 1.5 0 1 0.5 −0.5 0 −1 −0.5 −1 −1.5 −1.5 −2 −2 0 50 100 150 200 0 50 100 150 200
M ODEL 2: RBC WITH R EAL F RICTIONS • More dispersed range of multipliers • Agents and firms want to smooth consumption and investmtent • Smaller wealth effects (agents care about c t , c t − 1 ), larger substitution effects (more sensitive to price changes) • Same policy implications
M ODEL 3: S TICKY P RICE & W AGE Add to Model 2 • Monopolistically competitive intermediate goods & labor services �� 1 � 1+ η p 1 1+ ηp di Y t = y t ( i ) 0 • Price & wage stickiness via Calvo (1983)
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