demand for liquidity and welfare cost of inflation by...

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.



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.



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.



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.



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%.



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.



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.



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.



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



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



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.



In addition, Time Effects mixed with Cohort Effects

2004

2500

3000

3500

4000

4500

5000

5500

6000

6500

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

$

Year

Real Average Consumption Real Average Money



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.



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.



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.



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 .



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.



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.



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.




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.




Use the money-consumption ratio derived from the model as moments tobe matched with data:

mhij

chij=

1

1 +[Rtchij/(wtγiηh)

]1/θi



Calibration of macroeconomic parameters

5 agg. parameters: πt = πdatat , rt = rdatat , Rt = Rtdata

, τat = τdataat ,and Gt = Gdata

t over time:

1939 1949 1959 1969 1979 1989 1999 2009

Inflation (%) 2.37 4.00 1.75 5.60 8.11 3.36 2.02 1.92Nominal interest rate (%) 4.96 4.50 5.60 7.53 12.50 9.70 5.50 4.11Government expenditure (% of GDP) 26 26 26 27 26 25 22 24Capital income tax rate 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

Labour tax rate 0.30 0.38 0.31 0.36 0.27 0.24 0.24 0.30

After that these also remain constant at their 2009 level.



Calibration results

Parameter Value Target Data Model

γ2 0.0180 Average(mc

)i=2

0.1455 0.1584γ3 0.0187 Average

(mc

)i=3

0.1747 0.1799γ4 0.0187 Average

(mc

)i=4

0.2304 0.2529γ5 0.0220 Average

(mc

)i=5

0.2869 0.3121γ6 0.0238 Average

(mc

)i=6

0.4117 0.4361γ7 0.0333 Average

(mc

)i=7

0.6069 0.5482

θ2 1.900 Slope of(mc

)i=2

-0.1021 -0.1109θ3 1.806 Slope of

(mc

)i=3

-0.1231 -0.1184θ4 1.760 Slope of

(mc

)i=4

-0.1970 -0.1788θ5 1.600 Slope of

(mc

)i=5

-0.2557 -0.2623θ6 1.507 Slope of

(mc

)i=6

-0.4615 -0.4422θ7 1.196 Slope of

(mc

)i=7

-0.9359 -0.8479

η 0.5014 m1999c1999

/m2009c2009

0.96 0.9871



Calibration results: Money-consumption ratios

0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1M

oney

-con

sum

ptio

n ra

tioAge < 35

ModelData

0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1Age 36 - 45

ModelData

0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Mon

ey-c

onsu

mpt

ion

ratio

Age 46 - 55

ModelData

0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1Age 56 - 65

ModelData

0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Consumption

Mon

ey-c

onsu

mpt

ion

ratio

Age 66 - 75

ModelData

0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Consumption

Age > 75

ModelData



Calibration results: η

η = 0.501 implies that credit-transaction technology improves byabout 50% for each new cohort every 10 years.

A measure of financial innovation.



Taking out each effect

Credit-transaction technology: γhi (x) = γi · ηh ·(

x1−x

)θi1 Taking out Cohort effects (ηh):

Set h to be the same for all cohorts as that of “Age >75” in 2009.

2 Taking out Age effects (γi and θi ):

Set γi = γ7 and θi = θ7 for all i , the value for “Age >75”.

3 Taking out Time effects (interest, inflation and tax rates):

Set them constant at their 2009 values.

Simulate the model and observe money-consumption ratios in 2009.



MC ratios without cohort effects in 2009

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2M

oney

-con

sum

ptio

n ra

tioAge < 35

BaselineFixed

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2Age 36 - 45

BaselineFixed

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

Mon

ey-c

onsu

mpt

ion

ratio

Age 46 - 55

BaselineFixed

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2Age 56 - 65

BaselineFixed

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

Consumption

Mon

ey-c

onsu

mpt

ion

ratio

Age 66 - 75

BaselineFixed

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

Consumption

Age > 75

BaselineFixed



MC ratios without age (γi and θi ) effects in 2009

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1M

oney

-con

sum

ptio

n ra

tioAge < 35

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Age 36 - 45

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Mon

ey-c

onsu

mpt

ion

ratio

Age 46 - 55

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Age 56 - 65

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Consumption

Mon

ey-c

onsu

mpt

ion

ratio

Age 66 - 75

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Consumption

Age > 75

BaselineFixed &

BaselineFixed &

BaselineFixed &

BaselineFixed &

BaselineFixed &

BaselineFixed &



MC ratios without time effects in 2009

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Mon

ey-c

onsu

mpt

ion

ratio

Age < 35

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Age 36 - 45

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Mon

ey-c

onsu

mpt

ion

ratio

Age 46 - 55

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Age 56 - 65

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2

Consumption

Mon

ey-c

onsu

mpt

ion

ratio

Age 66 - 75

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2

Consumption

Age > 75

BaselineNo Time effect (fixed tauntr)








MC ratios breakdown into three effects in 2009

Cohort effects widen money-consumption ratios across age groups.

I Generate the observed across-age gaps.

I Large improvements in transaction technology over time.

Age effects narrow them.

I People face lower credit-transaction costs and use more credit with age.

Little time effects.

I Past macroeconomic conditions do not appear to influencemoney-consumption ratios much.



Welfare Calculation

Changes in consumption needed to make a household equally happybefore and after inflation changes.

Value before: V 0hj =

∑7i=2 βiju(c0

hij).

Value after plus a constant consumption change over lifecycle of λhj :

V 1hj(λhj) =

∑7i=2 βiju(c1

hij + λhj).

Derive λhj such that V 0hj = V 1

hj(λhj).



Welfare Analysis

Inflation permanently increases from 1.92% in 2009 to 10% in 2019.

Welfare losses (% of consumption) are:

Aggregate Erosa-Ventura (2002) Lucas (2000)0.47 1.44% of income <1% of income

In 200980-y.o. 70–y.o. 60-y.o. 50-y.o. 40-y.o. 30-y.o. 20-y.o. 10-y.o.0.000 0.96 1.07 0.96 0.78 0.63 0.41 0.28

Poor Poor-Middle Middle Middle-Rich Rich0.92 0.69 0.56 0.43 0.32



Conclusion

We revisited one of the oldest questions in Economics.

We paid attention to money demand of households, and theircross-sectional and aging patterns.

We took seriously how technical change in credit transaction overgenerations of households or household aging shape the answer.

We found an answer smaller than that from the previous literatureand that long-run inflation is less painful than previously found.

Still, the pain is not shared equally among household: more by the oldand the poor households.



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