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Heterogeneous Consumers and Consumption-Real Exchange Rate Anomaly Izzet Yildiz November 2008

Heterogeneous Consumers and Consumption-Real Exchange Rate Anomaly Izzet Yildiz November 2008 Research Proposal. Motivation. Both country specific crisis and global crisis change the risk perception of investors for the countries which makes exchange rates volatile

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Heterogeneous Consumers and Consumption-Real Exchange Rate Anomaly Izzet Yildiz November 2008

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  1. Heterogeneous Consumers and Consumption-Real Exchange Rate Anomaly Izzet Yildiz November 2008 Research Proposal

  2. Motivation • Both country specific crisis and global crisis change the risk perception of investors for the countries which makes exchange rates volatile • Theory says that there should be close relation between fluctuations in consumption ratios and bilateral exchange rates • (Backus Smith (1993)) • However it is rejected in the data

  3. Question • How can we set up a model which gives plausible correlation of exchange rates and consumption while preserving other properties of exchange rate such as volatility and persistency?

  4. Contribution • Introducing heterogeneous consumers with limited participation to asset markets by defining two different agents; wage earners and investors • Simpler mechanism than endogenous segmentation • No fix costs of entering to the asset markets

  5. Data

  6. Data

  7. Data

  8. Data • Observations 1-Data shows that there is no systematic cross correlation between exchange rate and consumption (consumption real exchange rate anomaly, CKM(2002)): Cross correlation (data)=-0.35 Cross 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

  9. Data 3-Limited participation among the consumers Family holdings of financial assets, by selected characteristics of families and type of asset, 2004 SCF survey

  10. Data Percentage of Family holdings in total financial assets in the economy,2004 SCF survey

  11. Literature • Backus Smith(1993): -Endowment economy with and without non-traded goods - point out consumption real exchange rate anomaly in both models • Chari, Kehoe, McGrattan (2002): -Two country general equilibrium model -Exclude non-traded goods ( explain only 2 percent of variations in exchange rate) -Monetary shocks, calvo style sticky prices, separable preferences in leisure -real exchange rate is equal to ratio of marginal utilities of consumption of households in two countries

  12. Literature -exchange rate is as volatile as in data (by high risk aversion=5) but has lower persistency (by price stickiness) -point out persistence and consumption anomaly -introduce different preferences and two asset market frictions to solve consumption-exchange rate anomaly 1-nonseparable preferences 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”

  13. Literature • Steinsson (2008) -focus on persistency 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”

  14. Literature • Alvarez, Atkeson and Kehoe(2008): -Endogenously segmented asset markets -Household should pay randomly assigned fixed cost to transfer money between good and asset markets -Household with low fixed cost enter to the asset market -Focused on time varying risk premium, no quantitative results for consumption-exchange rate anomaly

  15. HOME FOREIGN Intermediate good firms (monopolistic) Intermediate good firms (monopolistic) profit Wage -labor Final good firms (competitive) Final good firms (competitive) Wage earner Investor Model

  16. Model • Final Good Firms: In home country each period t, choose the allocation of domestic and foreign input, yH(i, st) and yF(i, st) to maximize its profit by producing final good y(st) subject to

  17. Model • FOCs and Solution: • From zero profit condition

  18. Model • Intermediate good firms: -monopolistic market -Prices are sticky ( calvo style). Firm should hold prices fix for N periods. In each period t, 1/N of the firms can optimize their prices. Prices are optimized before the realization of shocks - 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 homogenous factor model in 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.

  19. Model • Problem subject to

  20. Model • FOCs and solution for prices give optimal prices for τ=0, N, 2N …; ,

  21. Model • Wage Earners -For simplification I assumed there is no money growth and money supply is constant -Households can not issue and trade bonds. -They can only supply labor and consume. -Their total share in population is 1-α.

  22. Model • Problem: subject to • FOCs

  23. Model • Investors -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 -State contingent bonds, markets are complete. -For simplicity I assumed the only traded asset in markets is bonds.

  24. Model • Problem subject to • FOCs Home Country Bonds: Foreign Country Bonds:

  25. Model • Market Clearing Conditions: Bond markets Final Goods and Labor markets

  26. Model Equilibrium

  27. Results • No model output yet… • Comparison with CKM(2002): Real exchange rate depends on only the consumption of investor not aggregate consumption

  28. Results Empirical Check: • Potential problem: Investor consumption’s moments can be similar to aggregate consumption, so anomaly can still exist. • Need top 20 income percentile’s (investors) consumption data for two countries • Candidates are Italy and UK -Consumption Insurance and Entrepreneurial Risk: Evidence from Italian Micro-Data” Declich and Ventura(2003)- Italy data • US: CEX(consumer expenditure survey) UK: FES(family expenditure survey) Italy: SHIW(Survey on Household Income and Wealth)

  29. Results-CEX • The Interview sample is in the form of a rotating panel, and it follows survey households for a maximum of five quarters, although only inventory and basic sample data are collected in the first quarter (these data are not publicly available). • Annual data(1984-2006) is available in the web. Moments of the log consumption for different income percentiles are as given

  30. Roadmap • Calculating the output of model • Finding the consumption data for two countries • Including monetary and other real shocks ( in Steinsson (2008)) • Introducing different risk aversion parameters for investors and wage earners • Comparing different utility forms( wealth in investors’ utility)

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