Demand Shocks and Open Economy Puzzles Yan Bai and Jos´ e-V´ ıctor R´ ıos-Rull University of Rochester, University of Minnesota CSWEP 2015 Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 1 / 21
Motivation A standard international real business cycle model with technology shocks fails to generate the following stylized facts International consumption correlation is small than output correlation (Quantity anomaly) The real exchange rate (RER) is negatively correlated with relative consumption (Backus-Smith puzzle) ◮ corr ( RER , cH / cF ) < 0; Agents consume more of domestic goods when they are more expensive A model with demand shocks has the potential to solve these puzzles, but it fails to produce the observed comovement of output and TFP Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 2 / 21
This paper We pose a standard two-country real business cycle model with goods market friction With only demand shocks, the model can account for simultaneously, ◮ Quantity anomaly ◮ Backus-Smith puzzle ◮ Comovements of output and TFP Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 3 / 21
The logic Demand shocks like productivity shocks ◮ In order to transform produced goods into used goods, households must exert (search) e ff ort ◮ Such e ff orts are not accounted for in NIPA ◮ Increase in search e ff ort implies increased measured productivity Solving international puzzles in a two-country, two-good setup: increase in domestic demand leads to ◮ Domestic boom: output and TFP increase ◮ Increase in domestic consumption and consumer prices ◮ Appreciation of real exchange rate ◮ Foreign output and TFP also increase Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 4 / 21
Literature Backus-Smith puzzle: ◮ Demand shocks (Stockman and Tesar 1995) ◮ Endogenous discount factor and low elasticity between home and foreign goods (Corsetti, Dedola, and Leduc 2008) ◮ Non-tradable goods (Engel and Wang 2011) ◮ Labor wedge from home production (Karabarbounis 2012) . ◮ Capacity utilization: (Ra ff o (2010)) Search frictions in international setup: (Alessandria (2009) and Drozd and Nosal (2012)) Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 5 / 21
A two-country, two-good economy with shopping friction Two countries j = 1 , 2 each with a continuum of firms, measure one Firms in country j produces F j = z j f ( n j ) Current utility of households � c jj , c jj ∗ , d jj , d jj ∗ , n j , θ j � u ◮ Consumption from home c jj and from foreign c jj ∗ ◮ Search shopping e ff ort for home good d jj and for foreign good d jj ∗ ◮ θ j is a preference shock Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 6 / 21
Search friction Households have to send costly shoppers to search for goods from each country; Unfound goods perish Competitive search: agents choose which market to search A market is characterized by ( p , Q , F ) • Price p • Market tightness Q : average measure of firms per shoppers • Output F Aggregate state S = ( θ, B ) θ = { ( θ j , z j ) j = 1 , 2 } denotes shocks B is the share of mutual fund held by country 1. Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 7 / 21
Matching technology Matching of country j households with country i firms M ji = A ( D ji ) α ( T ji ) 1 − α ◮ D ji : measure of country j shoppers for country i firms ◮ T ji : measure of country i firms found by country j shoppers Probability that a firm is matched with a shopper � � − α Ψ T ( Q ji ) ≡ A ( D ji ) α ( T ji ) 1 − α T ji ≡ A ( Q ji ) − α = A T ji D ji Probability that a shopper is matched with a firm � � 1 − α Ψ d ( Q ji ) ≡ A ( D ji ) α ( T ji ) 1 − α T ji ≡ A ( Q ji ) 1 − α = A D ji D ji Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 8 / 21
Households in country j First choose which markets to shop for V j ( S , b ) = { p j ℓ , Q j ℓ , F ℓ } ℓ = j , j ∗ w j ( S , b ; { p j ℓ , Q j ℓ , F ℓ } ℓ = j , j ∗ ) max Then choose allocations � c jj , c jj ∗ , d jj , d jj ∗ , n j , θ j � � � w j ( S , b ; { p j ℓ , Q j ℓ , F ℓ } ℓ = j , j ∗ ) = max u V j ( S ′ , b ′ ) | θ + β E j ∗ � p j ℓ c j ℓ + b ′ = [1 + R ( S )] b + w j n j ℓ = j c j ℓ = d j ℓ Ψ d ( Q j ℓ ) F ℓ for ℓ = j , j ∗ S ′ = G ( S ) • Search friction: ℓ = { 1 , 2 } c j ℓ = d j ℓ Ψ d ( Q j ℓ ) F ℓ ���� ���� � �� �� �� � shoppers sent fruits found when matched prob. of finding a firm Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 9 / 21
Firm’s problem First choose which markets to serve � � j ∗ Π j ( S ) = max Π j ℓ ( S ) ℓ = j Then choose ( p , Q , F ) to post Π j ℓ ( S ) = max p , Q , F , n p Ψ T ( Q ) F − w ( S ) n subject to F ≤ z j f ( n ) w ℓ ( S , B ℓ ; p , Q , F , p ℓℓ ∗ ( S ) , Q ℓℓ ∗ ( S ) , F ℓℓ ∗ ( S )) ≥ V ℓ ( S , B ℓ ) (households’ participation constraint) Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 10 / 21
Equilibrium Market clearing conditions C j ℓ = A ( D j ℓ ) α ( T j ℓ ) 1 − α z ℓ f ( N ℓ ) T jj + T j ∗ j = 1 B ′ j + B ′ j ∗ = 2 Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 11 / 21
Example • Endowment economy, symmetric equilibrium • Utility � ( c jj ) µ ( c jj ∗ ) 1 − µ � � d jj + d jj ∗ � u ( c jj , c jj ∗ , d jj , d jj ∗ , θ ) = θ j log − µ : home bias parameter, µ ≥ 1 2 Elasticity of substitution between home and foreign goods is 1 Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 12 / 21
Demand shocks as productivity shocks • Let ¯ x denote steady state of variable x and ˆ x ≡ ( x − ¯ x ) / ¯ x • Definition: TFP of country j is p j ∗ j ¯ Y j ∗ j TFP j Y jj = + ���� ���� p jj ¯ ���� production for home production for foreign relative price �� 1 − T jj � 1 − α � D jj � α � T jj � 1 − α + ¯ p j ∗ j � D j ∗ j � α � Az j = p jj ¯ • Demand for goods has a productivity role � θ j ∗ � � z j + α θ j + (1 − µ ) ˆ TFP j = ˆ µ ˆ Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 13 / 21
Real exchange rate and relative consumption • Real exchange rate (RER) j = − (2 µ − 1) 2 (1 − α )( ˆ � θ j − ˆ θ j ∗ ) + (2 µ − 1)(ˆ z j − ˆ z j ∗ ) RER θ j but RER appreciates under a positive demand shock ˆ z j depreciates under a positive productivity shock ˆ • Relative consumption � � c j ∗ = c j − ˆ θ j − ˆ z j − ˆ θ j ∗ ) + (2 µ − 1)(ˆ z j ∗ ) ( ˆ 1 − (2 µ − 1) 2 (1 − α ) ˆ θ j and Domestic consumption increases with both demand shock ˆ z j productivity shock ˆ Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 14 / 21
Real exchange rate, relative consumption and TFP • Under productivity shocks j = ˆ c j − ˆ � c j ∗ RER j − � j ∗ 1 c j − ˆ � c j ∗ ) TFP TFP = 2 µ − 1(ˆ Backus-Smith puzzle: the observed correlation between RER and relative consumption is small and mostly negative; the model, however, generates perfectly correlated relationship. Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 15 / 21
Real exchange rate, relative consumption and TFP • Under demand shocks � � (2 µ − 1) 2 (1 − α ) j = − c j − ˆ � c j ∗ ) (ˆ RER 1 − (2 µ − 1) 2 (1 − α ) j − � α (2 µ − 1) j ∗ c j − ˆ � c j ∗ ) TFP TFP = 1 − (2 µ − 1) 2 (1 − α )(ˆ When α = 0, we have the standard IRBC model which accounts for Backus-Smith puzzle but TFP and consumption are uncorrelated Our shopping model with demand shock can account for both correlations: negatively correlated RER and relative consumption, and positively correlated TFP and consumption. Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 16 / 21
Putting the model to work Preferences � � η 1 − σ η − 1 η − 1 η − 1 η + (1 − µ )( c ∗ ) µ c η − χ n 1 + 1 ν u ( c , c ∗ , d , d ∗ , n , θ ) = θ − ( d + d ∗ ) 1 − σ 1 + 1 ν Production function F ( n ) = z ( n ) γ n Shocks v t ∼ N (0 , Σ 2 ) log( θ t ) = ρ θ log( θ t − 1 ) + v t , Bai, R´ ıos-Rull (Rochester, Minnesota) Demand Shocks and Open Economy Puzzles CSWEP 2015 17 / 21
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