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Formulating and Estimating a Dynamic, General Equilibrium
Model Useable for Policy Analysis
based on work byAltig, Christiano, Eichenbaum, Linde
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Objectives• Constructing a DSGE Model
– Model Features – Estimation of Model using VAR’s
• Resolve Apparent Conflict Between Macro and Micro Data
– Macro Evidence:• Inflation is Inertial
– Micro Evidence:• Prices Change Frequently
• Indicate by example how macro models can be brought into contact with micro data
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Example of Micro/Macro ‘Conflict’: Analysis with Calvo-Sticky Prices
• Analysis with Aggregate European and US Data (see Smets-Wouters, Gali-Gertler):
– Prices Re-optimized Every 6 Quarters
• Micro Evidence:
– Prices ‘Re-optimized’ Every 1.7 Quarters
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Proposed Resolution of Conflict
• Firms Re-optimize Frequently (As in Micro)
• When Firms Re-optimize, They Change Price By a Small Amount
– Firms’ Short Run Marginal Cost Increasing in Own Output
– Firm-Specific Factors of Production (Capital)– Build on Sbordone, Woodford, others
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Standard Model• Capital Is Homogeneous• Traded in Perfectly Competitive Markets
– Firm Marginal Cost Independent of Own Output
• Assumptions Unrealistic
– Made for Computational Simplicity
– Hope: It Doesn’t Matter
– In Fact: It Matters A Lot!
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QQ0
P0
P1
P2
MC0
MC1
MC0,f
MC1,f
A
B
B
Intuition: Rising Marginal Cost and Incentive to Raise Price
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More Intuition: Rising Marginal Cost and Incentive to Raise Price
• A Firm Contemplates Raising Price– This Implies Output Falls– Marginal Cost Falls– Incentive to Raise Price Falls
• Effect Quantitatively Important When:– Demand Elastic– Marginal Cost Steep
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Strategy for Evaluating Proposed Resolution of Conflict
• Incorporate Idea Into Otherwise Standard Equilibrium Model
• Estimate Model Parameters Using Macro Data (Elasticity of Demand and Slope of Marginal Cost Particularly Important)
• Ask: Is Model Consistent With– Macro Evidence on Inflation Inertia?– Micro Evidence on Price Changes?
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Key results• Make Progress On Macro/Micro Conflict
– Account for Macro Evidence of Inflation Inertia– Prices re-optimized on average once every 1.6 quarters.– This finding depends on the assumption that capital is firm specific.
• Wage-setting Frictions play Important Role.
– Wage contracts re-optimized on average once every 3 quarters.
• Monetary Policy Crucial In Transmission of Technology Shocks
• According to our model, in absence of monetary accommodation,
– Output and hours would fall in the wake of a positive neutral technology shock;– Output and hours worked would rise by much less than they actually do after a
positive capital embodied technology shock.
• Consistent with findings in Gali, Lopez-Salido and Valles (2002).
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Outline
• Model
• Econometric Estimation of Model– Fitting Model to Impulse Response Functions
• Model Estimation Results
• Implications for Micro Data on Prices
• Evaluate the Reliability of VAR Analysis
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Model…• Two Versions of Model
– Homogeneous Capital– Firm-specific Capital
• Describe Model Under Homogeneous Capital Assumption
• What to Change to Obtain Firm-Specific Capital Version
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Description of Model
• Timing Assumptions
• Firms
• Households
• Monetary Authority
• Goods Market Clearing and Equilibrium
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Timing
• Technology Shocks Realized.• Agents Make Price/Wage Setting, Consumption,
Investment, Capital Utilization Decisions.• Monetary Policy Shock Realized.• Household Money Demand Decision Made.• Production, Employment, Purchases Occur, and
Markets Clear. • Note: Wages, Prices and Output Predetermined Relative to Policy
Shock.
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Evidence from Midrigan, ‘Menu Costs, Multi-Product Firms, and Aggregate Fluctuations’
Histograms of log(Pt/Pt-1), conditional on price adjustment, for two data setspooled across all goods/stores/months in sample.
Lot’s ofsmallchanges
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Households: Sequence of Events
• Technology shock realized.
• Decisions: Consumption, Capital accumulation, Capital Utilization.
• Insurance markets on wage-setting open.
• Wage rate set.
• Monetary policy shock realized.
• Household allocates beginning of period cash between deposits at financial intermediary and cash to be used in consumption transactions.
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Dynamic Response of Consumption to Monetary Policy Shock
• In Estimated Impulse Responses:– Real Interest Rate Falls
– Consumption Rises in Hump-Shape Pattern:
R t/ t 1
c
t
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Consumption ‘Puzzle’
• Intertemporal First Order Condition:
• With Standard Preferences:
c t 1 c t
MUc,tMUc,t 1
R t/ t 1‘Standard’ Preferences
t
c
t
c
Data!
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One Resolution to Consumption Puzzle• Concave Consumption Response Displays:
– Rising Consumption (problem)– Falling Slope of Consumption
• Habit Persistence in Consumption
– Marginal Utility Function of Slope of Consumption– Hump-Shape Consumption Response Not a Puzzle
• Econometric Estimation Strategy Given the Option, b>0
Uc logc b c 1
Habit parameter
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Dynamic Response of Investment to Monetary Policy Shock
• In Estimated Impulse Responses:
– Investment Rises in Hump-Shaped Pattern:
I
t
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Investment ‘Puzzle’• Rate of Return on Capital
• Rough ‘Arbitrage’ Condition:
• Positive Money Shock Drives Real Rate:
• Problem: Burst of Investment!
R tk MP t 1
k Pk ,t 11 Pk ,t
,
Pk ,t ~ consumption price of installed capital
MP tk ~marginal product of capital
0,1 ~depreciation rate.
R t t 1 R tk .
R tk
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One Solution to Investment Puzzle• Adjustment Costs in Investment
– Standard Model (Lucas-Prescott)
– Problem: • Hump-Shape Response Creates Anticipated
Capital Gains
t
I
t
I
Data!
k 1 k F IkI.
Pk ,t 1Pk ,t
1
Optimal Under Standard Specification
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One Solution to Investment Puzzle…
• Cost-of-Change Adjustment Costs:
• This Does Produce a Hump-Shape Investment Response– Other Evidence Favors This Specification– Empirical: Matsuyama, Smets-Wouters.– Theoretical: Matsuyama, David Lucca
k 1 k F II 1
I
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Wage Decisions
• Households supply differentiated labor.
• Standard Calvo set up as in Erceg, Henderson and Levin and CEE.
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Contemporaneous Impact of Positive Monetary Shock
• Quantities and Prices Don’t Move
• Money Market:
Supply of Funds:Households
Deposits vs Cash
Monetary Authority
Demand for FundsFirm Wages
Money Injection
Financial Intermediary
Deposits Loans
R Drops
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Implications for Wage and Price Re-Optimization
• Our benchmark estimates imply that wage decisions are re-optimized on average 3.6 quarters.
• The implication of our estimate of gamma for how frequently firms re-optimize prices depends critically on whether we assume capital is firm specific or homogeneous.
– If capital is homogeneous, firms re-optimize prices on average once every 6 quarters,
– If capital is firm specific, firms re-optimize prices once every 1.6 quarters.
– At a broad level, this is consistent with micro evidence from Bils and Klenow, Lucas and Golosov and Klenow and Kryvtsov.
• I’ll provide intuition for this in a moment.
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Monetary Policy and Technology Shocks
• Policy Issue:
– How would the economy have responded to technology shocks if monetary policy had not been accommodative?
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• Cross Sectional Implications For Production Not Extreme
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Micro Findings
• Homogeneous and Firm-Specific Capital Models are Indistinguishable from the Point of View of Aggregate Data
• Very Different Implications for – Degree of Price Stickiness in Micro Data– Dispersion of Prices and Output Across Firms
• Firm-Specific Capital Model Seems to Have Better Micro Implications
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Summary• We constructed a dynamic GE model of cyclical fluctuations.
• Given assumptions satisfied by our model, we identified dynamic response of key US economic aggregates to 3 shocks
– Monetary Policy Shocks– Neutral Technology Shocks– Capital Embodied Technology Shocks
• These shocks account for substantial cyclical variation in output.
• Estimated GE model does a good job of accounting for response functions (However, Misses on Inflation Response to Neutral Shock)
• Have Made Progress on Micro/Macro Conflict– But, Need to Further Investigate Cross-Sectional Implications of Model
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Summary…
• Calvo Sticky Prices and Wages Seems Like Good Reduced Form
– What is the Underlying Structure?