heterogeneous consumers and consumption real exchange rate anomaly izzet yildiz april 2009 n.
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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):

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Presentation Transcript
  • 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)
this paper proposes
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
  • 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?
  • 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/δ for mean and std. dev. and with tangent 1 for auto correlation
  • 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 GDP=0.83

Stdev of Real Exch. Rate/Stdev GDP=4.36


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

Participation rate of families by asset types, 2004 SCF survey


Percentage of Family holdings in total value of asset markets 2004 SCF survey

  • 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


-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

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”

  • 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”

  • 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

model overview



Intermediate good firms (monopolistic)

Intermediate good firms (monopolistic)


Wage -labor

Final good firms


Final good firms





Model Overview
model sticky price
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.
model intermediate good firms
Model-Intermediate Good Firms
  • Intermediate good firms:

-monopolistic market

- 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).

model intermediate good firms1
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.
model final good firms
Model-Final Good Firms
  • Final good firms solve static problem in competitive markets each period t
  • Their production function is;
  • Θ gives mark up, p and Θ 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
model wage earners
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-α.

-The budget constraint is;

model wage earners1
Model-Wage Earners
  • They choose consumption, labor and real money to maximize utility function;
  • FOCs for labor is;
model investors
  • 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. 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

model investors1
  • Their budget constraint;
  • Investor choose bonds for st+1, consumption and real money to maximize
  • FOCs

Home Country Bonds:

  • No model output yet…
  • Comparison with CKM(2002):

Real exchange rate depends on only the consumption of investor not aggregate consumption

empirical evidence
Empirical Evidence

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


  • Does the top 20 (investors) and low 20 (wage earners) income percentile’s 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?
empirical evidence1
Empirical Evidence

First Country: Italy


  • 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.
empirical evidence2
Empirical Evidence


  • 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.
empirical evidence3
Empirical Evidence
  • Italy consumption data for investors and wage earners
empirical evidence4
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 year’s 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.
empirical evidence5
Empirical Evidence
  • Consumption Aggregation method:
empirical evidence6
Empirical Evidence


  • 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.
empirical evidence7
Empirical Evidence
  • US consumption data for investors and wage earners
empirical evidence8
Empirical Evidence
  • Comparison of two countries data( ci-cj)

-Variance and autocorrelation of wage earner and average consumer is lower than investor

empirical evidence9
Empirical Evidence

Comparison of US-Italy consumption growth data( ci-cj) over years

data problems
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.
  • There is difference between wage earners and investor data moments. Variance of investor’s 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

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