Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households Shutao Cao C´ esaire A. Meh Jos´ e-V´ ıctor R´ ıos-Rull Yaz Terajima Bank of Canada Bank of Canada University of Minnesota Bank of Canada Mpls Fed, CAERP Seminar at GRIPS Preliminary July 16, 2013 The views expressed are those of the authors and not of the Bank of Canada, the Federal Reserve Bank of Minneapolis or the Federal Reserve System.
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Demand for Liquidity and Welfare Cost of Inflation byCohort and Age of Households
Shutao Cao Cesaire A. Meh Jose-Vıctor Rıos-Rull Yaz Terajima
Bank of Canada Bank of Canada University of Minnesota Bank of CanadaMpls Fed, CAERP
Seminar at GRIPS
Preliminary
July 16, 2013
The views expressed are those of the authors and not of the Bank of Canada, the
Federal Reserve Bank of Minneapolis or the Federal Reserve System.
Introduction – Inflation, Money and Welfare
Money demand and welfare cost of long-run inflation have receivedattention for a long time.
I Cost: Money is subject to inflation tax.
I Benefit: Money provides liquidity in transactions.
Hence, important to capture endogenous demand for money.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 2/35
Introduction – Inflation, Money and Welfare
Most studies focus on aggregate evidence to measure the cost:
I Dotsey and Ireland (1996), Lucas (2000), and many more.
Heterogeneous behavior and micro evidence can be important:
I Mulligan and Sala-i-Martin (2000), Doepke and Schneider (2006), Meh andTerajima (2008), Erosa and Ventura (2002), Chiu and Molico (2008).
I Welfare cost varies considerably across households.
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Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 3/35
What we do
We focus on two issues:
I Transaction demand for money
I Heterogeneity over household age
Document transaction demand for money by household type,especially, across age groups.
I Cross-sectional data on money and consumption
I Money-consumption ratios as transaction demand for money
Construct a structural model where
I households differ by age and class, and
I choose to use money and credit for consumption based on credit-transactiontechnology.
Calibrate the model to the data.
Simulate with different inflation rates to derive welfare implications.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 4/35
Issues with cross-sectional data
Age and cohort effects are mixed in observed money demand.
Example: Old households have high demand for money because:
I they are old (i.e., age effects) or
I they were born earlier (i.e., cohort effects)?
Dynamic macroeconomic environments (i.e., time effects) add to thecomplexity.
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Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 5/35
Then, our identification strategy for the three effects is
We build an OLG model with within-age heterogeneity where moneyand credit are used for transactions;
Credit-transaction technology is specific to age and cohort;
Time effects are captured by macroeconomic environments: inflation,interest and tax rates; and
Calibrate model parameters to cross-sectional data across two timeperiods.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 6/35
Findings: Data on Money Holdings
Money-consumption ratio is higher for older and poor households:
I 4 times higher for old households (aged 76-85) relative to that foryoung (aged 26-35), and
I 3.5 times higher for the poorest 20% of households relative to therichest 20%.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 7/35
Findings: Model Calibration and the Three Effects
Age- and cohort-specific transaction cost captures age profile ofmoney holdings well.
Breakdown of differences in money-consumption ratios into threeeffects:
I Cohort effects generate increasing money-consumption ratios with age,
I Age effects imply decreasing money-consumption ratios with age, and
I Time effects account little.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 8/35
Findings: Cost of Inflation
Inflation ↑ from 1.92% to 10% ⇒ aggregate consumption ↓ by 0.47%
I Cohort effects of lower credit-transaction costs over time dampenswelfare loss.
Distributional effects are summarized as follows,
I Cohorts who are alive at the time of the increase in inflation bear twoto three times larger welfare loss than those that are born later.
I Poor households bear three times as large welfare loss than their richpeers.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 9/35
Other literature
Lucas (2000) points out an importance of using micro data to estimate the gains/costs ofinflation.
Mulligan and Sala-i-Martin (2000) and Attanasio et al. (2002) use micro data to estimatethe welfare cost of inflation.
Dotsey and Ireland (1996) analyze a general equilibrium model of money demand with anintermediation cost of credit transaction technology.
Erosa and Ventura (2002) incorporates heterogeneity over household income.
Chui and Molico (2010) uses a search model of demand for money.
Heer and Maussner (2012) analyze the effects of inflation on distributions of both incomeand wealth.
Heer et al. (2007) document that the money-age profile is hump-shaped and money isweakly correlated with income and wealth.
Ragot (2010) documents that the distribution of money across households is more similarto that of financial assets than of consumption.
Alvarez and Lippi (2009) introduce precautionary motives to the Baumol-Tobin model ofcash-inventory management.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 10/35
Data: Two Household Surveys
Canadian Financial Monitor (CFM), 1999-2010, by Ipsos Reid
I “Money” holdings information available for all years
I Consumption information available only for 2008-2010
Survey of Household Spending (SHS), 1999-2009, by StatisticsCanada
I no information on money holdings
I consumption information available for all years
Money: checking account and some savings accounts (fortransactions)
Consumption: durables (excluding housing), non-durables, and service
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
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Money-Cons Ratio by Consumption & Age, CFM 2008-10
0.5 1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
Consumption
Money−consumption ratio, CFM 2008−2010
age<3536−4546−5556−6566−7576−85
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
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Why does Money-Consumption ratio increase with age?
Is it an age effect?
I Households may become worse with age at using credit.
Or a cohort effect?
I New cohorts may be better at using credit.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 13/35
In addition, Time Effects mixed with Cohort Effects
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 14/35
Our Model: Overlapping Generations
We build on Erosa and Ventura (2002) who did the seminal work ondistribution of welfare cost of inflation, but abstract from life-cycleaspects.
Households differ in
I age: i ∈ {1, · · · I = 7} (i.e., a model period is 10 yrs),
I cohort: h ∈ {1, · · · } and
I earnings: j ∈ {1, · · · , J = 5}.
Consumption can be purchased with money and costly credit. Onlytransaction demand for money.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 15/35
Household’s Problem
max{chij ,shij ,mh,i+1,j ,ah,i+1,j}
I∑i=1
βijc1−σhij
1− σ
s.t.
chij(1− shij) ≤ mhij ,
chij + wt ·∫ shij
0
γhi (x)dx︸ ︷︷ ︸credit-transaction cost
+ah,i+1,j + (1 + πt)mh,i+1,j ≤
[1 + rt(1− τat)]ahij + mhij + (1− τzt)wt zij ;
ah,1,j = 0, mh,1,j = m.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 16/35
Transaction Technology: γhi (.)
γhi (x) = γi · ηh ·(
x1−x
)θiFixed cost with respect to consumption and variable with respect tomoney-credit ratio.
I Rich households tend to use more credit than money, relative to theirpoor peers.
Age effects: γi and θi .
Cohort effects: we assume cohort effects (ηh) on credit transactioncosts to proportionally change with cohort.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 17/35
Government Budget Constraint and Inflation
Government budget constraint (G –exogenous government spending):
Gt = (1 + πt) Mt+1 −Mt + τzt wt Z + τat rt At
Exogenous inflation rates {πt} and capital income tax rates {τat}.
Money supply is set to satisfy aggregate money demand.
Labour income tax rates {τzt} are endogenous to balance the budget.
Aggregate consistency:
Mt =IJ∑ij
mhijt , At =IJ∑ij
ahijt and Z =IJ∑ij
zij .
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 18/35
Equilibrium
Exogenous macroeconomic variables are Rt , πt and τat . Real interestrates, rt , are implied by Rt and πt . An equilibrium of our economy isdefined by a set of variables,{τzt ,Kt ,Mt ,At ,Z , chij , shij , ah,i ,j+1,mh,i ,j+1,wt} ∀h, i , j , t, such that
Each cohort of households, h, optimally choose chij , shij , ah,i ,j+1 andmh,i ,j+1 by solving the HH problem;
τzt is set to balance the government budget;
Mt =∑IJ
ij mhijt , At =∑IJ
ij ahijt and Z =∑IJ
ij zij hold;
Kt is implied by rt = α(
ZKt
)1−α; and
Wage rates are determined by wt = (1− α)(KtZ
)α.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 19/35
More on our identification strategy
Assume that time effects are captured by changes in money demandwith respect to inflation, interest and tax rates;
Assume that age and cohort effects are captured by credit-transactiontechnology that is specific to age and cohort; and
Calibrate model parameters to cross-sectional data across two timeperiods:
I Given households of a same age between two periods, credit-transactiontechnology differs only by a cohort-specific parameter.
I Conditional on existing cohorts in 2009, use age-specific parameters incredit-transaction technology to match money-consumption ratios byage.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 20/35
Calibration Strategy
Two parts to the equilibrium path of this model:
1 Before 2009, capital tax, inflation and interest rates vary as in thedata, and labour income tax rates balance government budget.
2 After 2009, constant capital tax, inflation and interest rates at the 2009levels, but labour income tax rates still balance government budget.
Calibrating the model requires a long period before and after 2009:
I Cohorts born between 1939 to 2179 with a 10-year model period, andtwo steady states to which the economy starts from and converges to,respectively.
Shutao Cao, Cesaire A. Meh, Jose-Vıctor Rıos-Rull, Yaz Terajima GRIPS
Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 21/35
Calibration Strategy
We want the model economy to replicate some key patterns of 2009:
Consumption age-class distribution: 30 βij ’s.
Money-consumption ratio within-age average: 6 γi ’s.
Money-consumption ratio within-age across-class change: 6 θi ’s.
Overall change in average money-consumption ratio between 1999and 2009: η.
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Demand for Liquidity and Welfare Cost of Inflation by Cohort and Age of Households July 16, 2013 22/35
Calibration Strategy
Use the money-consumption ratio derived from the model as moments tobe matched with data:
mhij
chij=
1
1 +[Rtchij/(wtγiηh)
]1/θi
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