Pricing To Habits and the Law of One Price Morten Ravn 1 Stephanie Schmitt-Grohé 2 Martin Uribe 2 1 European University Institute 2 Duke University Izmir, May 18, 27
Stylized facts we wish to address Pricing-to-Market: LOOP fails (even at micro level and even for traded goods) Goldberg and Knetter, JEL 1997. Crucini and Shintani, 26. A rise in government spending leads to a real exchange rate depreciation, Monacelli & Perotti, 26. an increase in private consumption, a trade balance deterioration.
The Observed Effects of Government Spending Shocks 1. Use structural VAR to estimate effects of government purchases shocks. where 2. Four lags, or L = 4; AX t = B(L)X t 1 + u t X t = log g t log y t log c t tb t y t log e t 3. Data: Quarterly data from 1975 to 25 for the UK. 4. Identification: government spending is not affected contemporaneously by structural innovations to any other variable than government spending itself. (Blanchard and Perotti, 22)
Impulse Response To A Unit Innovation in Domestic Government Purchases, UK: 1975-25 1 g t.3 y t.3 c t.8.2.2.6.1.1.4.2 2 4 6 8.1 2 4 6 8.1 2 4 6 8 1.5 rer t.2 nxy t 1.1.5.1.5 2 4 6 8.2 2 4 6 8 Solid line: point estimate Dashed line: point estimate ± 1 std
Theory We abstract from: nontraded goods distribution costs tariffs or quotas rule of thumb consumers non-competitive behavior in the labor market sticky prices or wages nonseparabilities of preferences incomplete asset markets
A Model of Pricing to Habits Two-country production economy without capital Preferences: E t= βt [U(x t ) + v(h t )] Two traded goods: a and b x t = [ ] ωxa,t c 1 1 ξ + (1 ω)xb,t c 1 1 1 1 ξ ξ 1
Habit Formation Existing Literature on Habit Formation: Habits are formed at the level of a composite good (Superficial Habits) This paper: Habits are formed at the level of an individual good. (Deep Habits) as in Ravn, Schmitt-Grohé, and Uribe 26.
Private Households Habit-adjusted consumption of good a [ 1 ] 1 xa,t c = (c i,a,t θsi,a,t 1) c 1 1 1 η 1 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 x c b,t = [ 1 ] 1 (c i,b,t θsi,b,t 1 c 1 1 )1 η 1 η di s c i,b,t = ρsc i,b,t 1 + (1 ρ) c i,b,t
Public sector Habit-adjusted consumption of good a [ 1 ] 1 xa,t g = (g i,a,t θs g 1 1 i,a,t 1 )1 η 1 η di s g i,a,t = ρsg i,a,t 1 + (1 ρ) g i,a,t Habit-adjusted consumption of good b x g b,t = [ 1 ] 1 (g i,b,t θs g 1 1 i,b,t 1 )1 η 1 η di s g i,b,t = ρsg i,b,t 1 + (1 ρ) g i,b,t
Demand Function for variety i of good a Domestic Demand for variety i of good a d i,a,t = ( Pi,a,t P a,t ) η x a,t + θs i,a,t 1 ( Price elasticity = η 1 θ s ) i,a,t 1 d i,a,t Foreign Demand for variety i of good a d i,a,t = ( P i,a,t P a,t Price elasticity = η ) η x a,t + θs i,a,t 1 ( 1 θ s i,a,t 1 d i,a,t )
The firm s pricing problem Firm i faces demand d i,a,t and d i,a,t Firm i is the monopolistic supplier of variety i of good a Price discrimination: P i,a,t need not equal P i,a,t Production Function: y i,a,t = h i,a,t
Deviations from the LOOP The profit maximizing price in eqm, if ρ = : P a,t = 1 Pa,t = 1 ( η ( η 1 1 θ s a,t 1 d a,t 1 1 θ s a,t 1 d a,t markups will be time-varying ) + θω a,t ) + θω a,t 1 1 MC t MC t markups will be destination specific LOOP fails
The Real Exchange Rate Domestic price index: Foreign price index: P t = γp a,t + (1 γ)p b,t P t = γ P a,t + (1 γ )P b,t Real exchange rate, e t : e t = P t P t = f ( Pa,t P a,t, Pb,t P b,t, + + ± P b,t ) P a,t real depreciation in response to a positive domestic demand shock possible
Calibration of Structural Parameters Parameter Value Description β.99 Subjective discount factor (quarterly) σ 1 Intertemporal elasticity of subsitution φ.15 Preference parameter ω.75 Preference parameter ξ 1.5 Elasticity of substitution η 6 Price-elasticity of demand θ.6 Degree of habit persistence ρ.85 Persistence of habit stock ḡ, ḡ.622 Steady-state level of g t, gt ρ g, ρ g.87 Serial correlation of the log of g t
Impulse Response To A Unit Innovation in Domestic Gov t Purchases.2 μ a and μ a *.1 μ b and μ b *.3 e a =P a * /Pa.1.2.1.1.1 μ a μ a *.2 5 1 15.2 μ b μ b *.3 5 1 15.1 5 1 15.3.2 e b =P b * /Pb.2.15 e=p * /P deep habits superficial habits.3.2 W/P deep habits superficial habits.1.1.5.1.1 5 1 15.5 5 1 15.1 5 1 15.6.4 c deep habits superficial habits.1 tb/gdp deep habits superficial habits.2.15 output deep habits superficial habits.2.1.2.1.2.3.5.4 5 1 15.4 5 1 15 5 1 15
Estimation of Model on UK data: 1975-25 Goal: Estimate the preference parameters associated with deep habits: θ, ρ, η Strategy: Pick {θ, ρ, η} so as to minimize the distance between empirical and theoretical impulse responses to a unit innovation in government purchases. Match 9 periods of impulse responses for 5 variables.
Estimation results: θ =.49, ρ =.95, η = 4 Impulse Response To A Unit Innovation in Domestic Gov t Purchases 1 g t.3 y t.8.2.6.1.4.2 2 4 6 8.1 2 4 6 8.3 c t.2 nxy t.2.1.1.1.1 2 4 6 8.2 2 4 6 8 1.5 rer t 1.5.5 2 4 6 8 Source: Explaining the Effects of Government Spending Shocks on Consumption and the Real Exchange Rate, by Ravn, Schmitt-Grohé, and Uribe, 27.
Conclusion: Under Pricing to Habits there are deviations from the LOOP Deviations from the LOOP are time varying Pricing to Habits can explain why in response to a demand shock the real exchange rate depreciates private consumption rises the trade balance deteriorates Estimation of the model yields: θ =.49, ρ =.95, and η = 4