Pricing to Habits and the Law of One Price Morten Ravn Stephanie - PDF document

Pricing to Habits and the Law of One Price Morten Ravn Stephanie Schmitt-Groh´ e Mart ´ ın Uribe 1

Stylized facts we wish to address • The Law Of One Price fails at the good- by-good level even for highly traded goods. – Goldberg and Knetter, JEL 1997. – Crucini and Shintani, 2006. • A rise in government spending leads to – A real exchange rate depreciation. – An increase in private consumption. – A trade balance deterioration. (Ravn, Schmitt-Groh´ e, and Uribe, 2007; Monacelli and Perotti, 2006; Perotti, 2006; Gali et al., 2006) 2

• Estimation of empirical impulse responses 1. Use structural VAR to estimate effects of government purchases shocks. AX t = B ( L ) X t − 1 + u t where  log g t  log y t     log c t   X t =   tb t     y t   log e t 2. Four lags ( L = 4). 3. Identification: government spending is not affected by structural innovations to any other variable than government spending itself. 4. Panel of Countries: Australia, Canada, U.K., and U.S. 5. Sample: Quarterly data from 1975 to 2005 3

Estimated Impulse Response Functions To A Unit Innovation in Domestic Government Purchases g t y t 1 0.3 0.8 0.2 0.6 0.1 0.4 0 0.2 −0.1 0 2 4 6 8 0 2 4 6 8 c t nxy t 0.3 0.05 0.2 0 0.1 −0.05 0 −0.1 −0.1 −0.15 0 2 4 6 8 0 2 4 6 8 rer t 1.5 1 0.5 0 −0.5 0 2 4 6 8 Solid lines: point estimate Dashed lines: point estimate ± 2 std 4

Theory • We abstract from: – Nontraded goods. – Rule-of-thumb consumers. – Distribution costs. – Sticky prices or wages. – Incomplete asset markets. – Tariffs or quotas. – Nonseparabilities of preferences across consumption and leisure. 5

A Model of Pricing to Habits • Two-country production economy without capital. • Preferences ∞ β t [ φ ln( x t ) + (1 − φ ) ln(1 − h t )] � E 0 t =0 • Two traded goods: a and b 1 1 − 1 1 − 1 1 − 1 � � ωx c ξ + (1 − ω ) x c x t = ξ ξ a,t b,t 6

• External deep habits as in Ravn, Schmitt-Groh´ e, and Uribe ( RES , 2006) – Private Households Habit-adjusted consumption of good a 1 �� 1 � i,a,t − 1 ) 1 − 1 1 − 1 x c 0 ( c i,a,t − θ c s c η a,t = η di s c i,a,t = ρs c i,a,t − 1 + (1 − ρ )˜ c i,a,t Habit-adjusted consumption of good b 1 �� 1 � i,b,t − 1 ) 1 − 1 1 − 1 x c 0 ( c i,b,t − θ c s c η b,t = η di s c i,b,t = ρs c i,b,t − 1 + (1 − ρ )˜ c i,b,t – Public sector 1 �� 1 � i,a,t − 1 ) 1 − 1 1 − 1 x g 0 ( g i,a,t − θ g s g η a,t = η di 1 �� 1 � i,b,t − 1 ) 1 − 1 1 − 1 x g 0 ( g i,b,t − θ g s g η b,t = η di 7

• Domestic Demand for good a � − η � P i,a,t d i,a,t = x a,t + θs i,a,t − 1 P a,t � � 1 − θs i,a,t − 1 Price elasticity = − η d i,a,t • Foreign Demand for good a − η   P ∗  i,a,t d ∗ x ∗ a,t + θs ∗ i,a,t = i,a,t − 1  P ∗ a,t  s ∗  i,a,t − 1 Price elasticity = − η  1 − θ  d ∗ i,a,t 8

Firms • Firms can price discriminate internation- ally. • Production Function: y i,a,t = h i,a,t • Optimal pricing − 1   1 � + θ Ω a,t   P a,t =  1 − MC t   � 1 − θ d a,t − 1  η d a,t − 1   1   P ∗ � + θ Ω ∗ a,t =  1 − MC t   a,t d ∗  �  a,t − 1 1 − θ η  d ∗ a,t ⇒ Time-varying deviation from the Law of One Price ( P ∗ a,t /P a,t � = 1 and moves over time). 9

Calibration Parameter Value Description β 0.99 Subjective discount factor (quarterly) σ 1 Intertemporal elasticity of substitution φ 0.15 Preference parameter ω 0.5 Preference parameter ξ 1.5 Elasticity of substitution composite η 5 Elasticity of substitution varieties s g , s ∗ 0.2 Government shares g 10

Estimation • Goal: Estimate deep-habit parameters: Θ ≡ [ θ c θ g ρ ] • Strategy: Pick Θ to minimize the distance between empirical and theoretical impulse responses. • Match 9 quarters of impulse responses of five variables. Estimated Parameters Point Standard Parameter Estimate Deviation θ c 0.52 0.08 θ g 0.57 0.15 ρ 0.99 0.03 11

Predicted and Estimated Impulse Responses g t y t 1 0.3 0.8 0.2 0.6 0.1 0.4 0 0.2 −0.1 0 2 4 6 8 0 2 4 6 8 c t nxy t 0.3 0.05 0.2 0 0.1 −0.05 0 −0.1 −0.1 −0.15 0 2 4 6 8 0 2 4 6 8 rer t 1.5 —– Data 1 - - - Data ± 2std 0.5 –x—x– Deep Habits 0 −0.5 0 2 4 6 8 12

Response of the Domestic and Foreign Markups to a One-Percent Government Spending Shock 0.1 0.05 Foreign Markup 0 Percent deviation from trend −0.05 −0.1 −0.15 Domestic Markup −0.2 −0.25 −0.3 0 1 2 3 4 5 6 7 8 Quarters after the shock 13

Response of the Real Exchange Rate to a Government Spending Shock 1.2 1 Data +2 std 0.8 Percent deviation from trend 0.6 Data 0.4 Deep 0.2 Data −2 std 0 Superficial −0.2 0 1 2 3 4 5 6 7 8 Quarters after the shock 14

Response of Private Consumption to a Gov- ernment Spending Shock 0.2 Data +2 std 0.15 Percent deviation from trend Data 0.1 Deep 0.05 Data −2 std 0 Superficial −0.05 0 1 2 3 4 5 6 7 8 Quarters after the shock 15

Response of the Real Wage to a Govern- ment Spending Shock 0.3 0.25 0.2 Percent deviation from trend Domestic Wage 0.15 0.1 0.05 0 Foreign Wage −0.05 −0.1 0 1 2 3 4 5 6 7 8 Quarters after the shock 16

Conclusion: • Under Pricing to Habits there are devia- tions from the LOOP • Deviations from the LOOP are time vary- ing • Pricing to Habits can explain why in re- sponse to a demand shock – the real exchange rate depreciates – private consumption rises – the trade balance deteriorates • Estimation of the model yields: θ c = 0 . 52, θ g = 0 . 57, and ρ = 0 . 99 17