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Heterogeneous Consumers and Consumption-Real Exchange Rate Anomaly Izzet Yildiz April 2009. Motivation. Theory says that there should be close relation between fluctuations in consumption ratios and bilateral exchange rates Backus Smith (1993):
1-Data shows that there is no systematic correlation between exchange rate and consumption (consumption real exchange rate anomaly, CKM(2002)):
correlation (data, US-EU)=-0.35
correlation (theory)= 1.00
2-Consumption ratios are more stable than real exchange rates,CKM(2002)
Stdev of consumption/Stdev GDP=0.83
Stdev of Real Exch. Rate/Stdev GDP=4.36
3-Limited participation among the consumers
Participation rate of families by asset types, 2004 SCF survey
Percentage of Family holdings in total value of asset markets 2004 SCF survey
-Endowment economy with and without non-traded goods
- point out consumption real exchange rate anomaly in both models
-Two country general equilibrium model
-Exclude non-traded goods ( explain only 2 percent of variations in exchange rate)
-Monetary shocks, sticky prices, separable preferences in leisure
-real exchange rate is equal to ratio of marginal utilities of consumption of households in two countries
-exchange rate is as volatile as in data (by high risk aversion=5) but has lower persistence (by price stickiness)
-point out persistence and consumption anomaly
-introduce different preferences and two asset market frictions to solve consumption-exchange rate anomaly
2-different interest rate rules
3-incomplete asset markets (uncontingent bonds)
4-Habit persistence ( external habit)
Both ways couldn’t solve the anomaly.
“The main failing of our model is the consumption-real exchange rate anomaly”
-focus on persistence and hump shaped dynamics of real exchange rates
-introduce real shocks (phillips curve shocks) to CKM model (labor supply, productivity, government spending, demand , cost-push)
-match the persistence of real exchange rate (persistence anomaly)
-with habit formation and phillips curve shocks, find lower but still positive correlation of real exchange rate and consumption (0.45)
“At present there are no fully satisfactory solution to this problem in the literature”
-Two country pure exchange economy
-Focus on creating time varying risk premia and forward premium anomaly
-Endogenously segmented asset markets: household should pay randomly assigned fixed cost to transfer money between good and asset markets
“Our model provides potential resolution to the Backus Smith (1993 ) puzzle …”
-No quantitative results and empirical evidence for consumption-exchange rate anomaly
- For simplification I assume that intermediate firms have fix capital stock( k=1) with no depreciation. So I eliminate investment and adjustment cost from the equations as in homogenous factor model of Steinsson(2008)
-Production function is cobb-douglas, e is the nominal exchange rate and Q(st) is the price of one unit of home currency in st at time 0 (discount factor).
-Wage earners can not issue and trade bonds.
-They can only supply labor and consume.
-Their total share in population is 1-α.
-The budget constraint is;
-their total share in population is α.
-consume but they don’t supply labor to production.
-shareholders of intermediate firms, and their earnings are the profits of monopolistic intermediate firms.
-Investors have access to asset markets. They can hold both domestic and foreign bonds under no arbitrage condition
-For simplicity I assumed the only traded asset in markets is state contingent bonds and markets are complete
Home Country Bonds:
Real exchange rate depends on only the consumption of investor not aggregate consumption
First Country: Italy
Second Country: United States
-Variance and autocorrelation of wage earner and average consumer is lower than investor
Comparison of US-Italy consumption growth data( ci-cj) over years
1-Calculating correlation of real exchange rates and consumption from micro surveys
2-With respect to results, completing model and getting output by trying to match the statistical properties from micro survey
3-Looking at other countries consumer surveys( emerging countries)
4-If heterogeneity is not adequate to explain the anomaly,try alternative approaches
-Motivation: Investors maximize also their wealth not only their consumption while giving investment decision.