Heterogeneous Consumers and ConsumptionReal Exchange Rate Anomaly

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• Heterogeneous Consumers and Consumption-Real
  Exchange Rate Anomaly
• Izzet Yildiz
• April 2009

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Motivation

• 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 (consumption
  real exchange rate anomaly)

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This paper proposes

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

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Question

• What is the mechanism gives negative correlation
  of real exchange rates and consumption ratios
  while preserving other properties of real
  exchange rate such as volatility and persistence?

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Data

• Updates of Backus Smith(1993) tables (1971-1990)
• Total private consumption Volume and price index
  are from OECD Quarterly National Accounts
  (1978QI-2006QIV), base year 2000, seasonally
  adjusted
• Nominal exchange rates from FED website
• Countries Australia, Canada, France,Germany,
  Japan, Sweden, United Kingdom, United States
• According to theory points should be on the
  linear line with tangent 1/d for mean and std.
  dev. and with tangent 1 for auto correlation

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Data
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Data
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Data
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Data
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Data

• Additional Observations
• 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 GDP0.83
• Stdev of Real Exch. Rate/Stdev GDP4.36

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Data

• 3-Limited participation among the consumers
• My goal is to differentiate consumers as
  investors and wage earners
• I investigate the data who participates and how
  much with respect to income percentiles

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Data

• Participation rate of families by asset
  types, 2004 SCF survey

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Data
Percentage of Family holdings in total value
of asset markets 2004 SCF survey
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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, sticky prices, separable
  preferences in leisure
• -real exchange rate is equal to ratio of
  marginal utilities of consumption of households
  in two countries

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Literature

• -exchange rate is as volatile as in data (by high
  risk aversion5) 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
• 1-nonseparable preferences
• 2-different interest rate rules
• 3-incomplete asset markets (uncontingent
  bonds)
• 4-Habit persistence ( external habit)
• Both ways couldnt solve the anomaly.
• The main failing of our model is the
  consumption-real exchange rate anomaly

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Literature

• Steinsson (2008)
• -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

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Literature

• Alvarez, Atkeson and Kehoe(2008)
• -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

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Model Overview
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Model-Sticky Price

• Intermediate good prices are sticky in a
  staggered way
• Prices are in local currency
• Each period 1/N of the firms set prices fix for N
  periods before the realization of event st. Price
  of these firms are
• So there is no uncertainty and in optimization
  firms in the specific cohort ( 0,1/N,
  1/N,2/N,choose prices for N periods in the
  particular period.

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Model-Intermediate Good Firms

• Intermediate good firms
• -monopolistic market
• - For simplification I assume that intermediate
  firms have fix capital stock( k1) 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).

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Model-Intermediate Good Firms

• They sell both foreign and domestic markets.
  Their production technology is
• They choose prices of input goods for both
  markets and labor
• Choice variables
• They maximize profits subject to input demand
  from final good firms, production technology and
  price constraints.

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Model-Final Good Firms

• Final good firms solve static problem in
  competitive markets each period t
• Their production function is
• T gives mark up, p and T determines elasticity of
  substitution btw. YF and YH
• They choose the allocation of domestic and
  foreign input, yH(i, st) and yF(i, st) to
  maximize the profit

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Model-Wage Earners

• Wage Earners
• -Wage earners can not issue and trade bonds.
• -They can only supply labor and consume.
• -Their total share in population is 1-a.
• -The budget constraint is

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Model-Wage Earners

• They choose consumption, labor and real money to
  maximize utility function
• FOCs for labor is

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Model-Investors

• Investors
• -their total share in population is a.
• -consume but they dont 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

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Model-Investors

• Their budget constraint
• Investor choose bonds for st1, consumption and
  real money to maximize
• FOCs
• Home Country Bonds

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Results

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

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Empirical Evidence

• Empirical Check
• Potential problem Investor consumptions moments
  can be similar to aggregate consumption, so
  anomaly can still exist.
• Need top 20 income percentiles (investors)
  consumption data for two countries
• Questions
• Does the top 20 (investors) and low 20 (wage
  earners) income percentiles consumption data
  have different statistical properties for each
  country?
• Are the consumption growth difference between
  countries of different percentile groups
  different?
• If yes, is it adequate to explain the anomaly?

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Empirical Evidence

• First Country Italy
• Introduction
• Source SHIW (Survey of Household Income and
  Wealth )
• Period Annual data is available from 1980 to
  2006, but only for 16 years.
• Each years survey includes observation of
  households ranging from 4000 to 8000.
• Each household has 3 individuals on average.
• Households defined by identification codes. Since
  codes are changing in each survey, households can
  not be followed among the surveys
• Its format and questionnaire is different before
  and after 1987.

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Empirical Evidence

• Results
• Wage earners (lowest 20 percentile) and
  investors (top 20 percentile) mean consumption
  growth are different, 3.99 and 4.54.
• Their standard deviation and autocorrelations are
  almost same.
• Therefore in Italy different income groups has
  different level of consumption but their change
  over years has similar properties.

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Empirical Evidence

• Italy consumption data for investors and wage
  earners

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Empirical Evidence

• Second Country United States
• Source CEX (consumer expenditure interview
  survey)
• It is more comprehensive survey than the SHIW.
  Number of household varies from 20,000 to 40,000
  in each years surveys.
• Each survey includes about 700,000 observations
  for 620 consumption items classified by universal
  classification mode.
• It has two main components, interview and diary
  surveys
• Interview survey is done every 3 months. Data is
  available in is from 1990 to 2006. In order to be
  compatible with Italy data, I looked at1993,
  1995, 1998, 2000, 2002, 2004, 2006 surveys
• I used income and detailed expenditure surveys. I
  aggregate consumption data over 620 items for
  each quarter.

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Empirical Evidence

• Consumption Aggregation method

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Empirical Evidence

• Results
• Standard deviation and autocorrelation of less
  than 20 percentile ( wage earners) consumption is
  different than total consumption.
• Top 20 percentile (investors) consumption data
  has higher variance than the total consumption.

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Empirical Evidence

• US consumption data for investors and wage earners

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Empirical Evidence

• Comparison of two countries data( ci-cj)
• -Variance and autocorrelation of wage
  earner and average consumer is lower than
  investor

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Empirical Evidence
Comparison of US-Italy consumption growth data(
ci-cj) over years
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Data Problems

• Italy (SHIW) and US(CEX) surveys have different
  format and questionnaire
• Calculation of consumption and income data is
  different in the surveys
• Size of the surveys and periods are different
• Surveys format and reported file types are
  changing over the years. SHIW in 1987 and CEX in
  1991.

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Conclusion

• There is difference between wage earners and
  investor data moments. Variance of investors
  relative consumption growth between US and Italy
  is higher than both wage earners and average
  consumer
• Second question what is the contribution of this
  difference to the consumption anomaly

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Roadmap

• 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
• Comparing different utility forms( wealth in
  investors utility) such as Bakshi Chen (1996)
• -Motivation Investors maximize also their
  wealth not only their consumption while giving
  investment decision.
• Introducing country specific risk parameters