Inflation, Demand for Liquidity, and Welfare

Transcription

1 Inflation, Demand for Liquidity, and Welfare Shutao Cao Césaire A. Meh José-Víctor Ríos-Rull Yaz Terajima Bank of Canada Bank of Canada University of Minnesota Bank of Canada Mpls Fed, CAERP Sixty Years Since Baumol-Tobin: A Celebration Conference Preliminary September 26, 202 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.

2 Motivation Inflation affects relative prices of holding different types of assets and hence welfare. Most previous studies use representative-agent models and aggregate evidence to measure the cost. Dotsey and Ireland (996), Lucas (2000), among others. Heterogeneous behavior and micro evidence can be important. Inflation, Demand for Liquidity, and Welfare September 26, 202 2/42

3 Motivation Recent work on welfare cost of inflation take into account heterogeneity. Welfare cost varies considerably across households: Mulligan and Sala-i-Martin (2000), Doepke and Schneider (2006), Meh and Terajima (2008), Erosa and Ventura (2002), Chiu and Molico (2008) Aggregate welfare effects can differ when heterogeneity is considered Not much done in the literature: Money holding for transaction purpose varies with age. This is important because Welfare cost of inflation will differ across age groups Potential nonlinear effects of inflation when aggregated Inflation, Demand for Liquidity, and Welfare September 26, 202 3/42

4 Other literature Lucas (2000) points out an importance of using micro data to estimate the gains/costs of inflation. Mulligan and Sala-i-Martin (2000) and Attanasio et al. (2002) use micro data to estimate the welfare cost of inflation. Dotsey and Ireland (996) analyze a general equilibrium model of money demand with an intermediation cost of credit transaction technology. Erosa and Venture (2002) incorporates heterogeneity over household income. Chui and Molico (200) uses a search model of demand for money. Heer and Maussner (202) analyze the effects of inflation on distributions of both income and wealth. Heer et al. (2007) document that the money-age profile is hump-shaped and money is weakly correlated with income and wealth. Ragot (200) documents that the distribution of money across Inflation, Demand for Liquidity, and Welfare September 26, 202 4/42

5 What we do Ask welfare implications of inflation by building an OLG model where money and credit are used for transaction; and calibrating model to capture age, cohort and time effects on money-consumption ratios. 2 Document money-consumption ratios, i.e., liquidity demand for money People are very different between ages and between social classes over money holdings and wealth 3 Use data to disentangle age, cohort and time effects Inflation, Demand for Liquidity, and Welfare September 26, 202 5/42

6 Findings Money-consumption ratio is higher for older and poor households. 5 times higher for old households (aged 76-85) relative to that for young (aged 26-35) 2 times higher for poor households relative to that for rich households These effects do not disappear once we control for cohort and time effects. Age-specific transaction cost captures age profile of money holding. Aggregate welfare effects when inflation from.92% to 0%, Aggregate consumption decreases by 0.83%. Distributional effects are summarize as follows, To be added Inflation, Demand for Liquidity, and Welfare September 26, 202 6/42

7 Data: Two Household Surveys Our main data sources are two household surveys (repeated cross-section) Canadian Financial Monitor (CFM), , by Ipsos Reid money holdings information available for all years consumption information available only for Survey of Household Spending (SHS), , by Statistics Canada no information on money holdings consumption information available for all years Money: checking account and some savings accounts (for transactions) Consumption: durables (excluding housing), non-durables, and service Inflation, Demand for Liquidity, and Welfare September 26, 202 7/42

8 Data: Combining CFM and SHS To separate out age, cohort and time effects, we need data on money-con ratios over a longer period than from CFM. Obtain a -year series by combining CFM and SHS, following Bethencourt and Ríos-Rull (2009): From CFM, calculate a joint distribution (in quintile) of households over money and consumption. 2 For each year over , calculate average money holdings of households in each quintile from CFM and average consumption in each quintile from SHS. 3 Holding fixed the joint distribution from Step (), assign the average money holdings and consumption in the respective quintile in each year over For each year and each consumption quintile, calculate average money-consumption ratios over money quintile using the marginal distribution from Step () as weights. Inflation, Demand for Liquidity, and Welfare September 26, 202 8/42

9 Data: Joint distribution of Money and Consumption CFM contain household-level information regarding money and consumption. Hence, we can construct a joint distribution of households over money and consumption: Marginal Dist. w. w.2 w.3 w.4 w.5 5th w 5 w 52 w 53 w 54 w 55 w 5. Money 4th w 4 w 42 w 43 w 44 w 45 w 4. Quintile 3rh w 3 w 32 w 33 w 34 w 35 w 3. 2nd w 2 w 22 w 23 w 24 w 25 w 2. st w w 2 w 3 w 4 w 5 w. st 2nd 3rd 4th 5th Marginal Consumption Distribution Quintile Inflation, Demand for Liquidity, and Welfare September 26, 202 9/42

10 Data: Joint distribution of Money and Consumption For each year over the period, CFM has information on money, {w.,..., w 5. }, and we can calculate average money holdings in each quintile. SHS has information on consumption, {w.,..., w.5 }, and we can calculate average consumption in each quintile. Use these information to approximate money-consumption ratios in each consumption quintile. Inflation, Demand for Liquidity, and Welfare September 26, 202 0/42

11 Data: Combining CFM and SHS Do this for six age groups: Aged 26-35, 36-45, 46-55, 56-65, and Inflation, Demand for Liquidity, and Welfare September 26, 202 /42

12 Money-Consumption Ratio by Consumption Money-consumption ratio declines as consumption increases. Inflation, Demand for Liquidity, and Welfare September 26, 202 2/42

13 Money-Consumption Ratio Money-Consumption Ratio by Consumption Consumption Inflation, Demand for Liquidity, and Welfare September 26, 202 3/42

14 Money-Consumption Ratio by Consumption and Age Money-consumption ratio rises with household age. Inflation, Demand for Liquidity, and Welfare September 26, 202 4/42

15 Money-Consumption Ratio by Consumption and Age Money consumption ratio, CFM age< Consumption Inflation, Demand for Liquidity, and Welfare September 26, 202 5/42

16 Money-Consumption Ratio by Cohort Money-consumption ratio declines for newer cohorts. Older cohorts have higher money-consumption ratios given consumption. Inflation, Demand for Liquidity, and Welfare September 26, 202 6/42

17 Money-Consumption Ratio Money-Consumption Ratio by Cohort Age Data Inflation, Demand for Liquidity, and Welfare September 26, 202 7/42

18 Money-Consumption Ratio Over Time Aggregate money-consumption ratios change over time with the macroeconomic environment. Inflation, Demand for Liquidity, and Welfare September 26, 202 8/42

19 Average Money-Consumption Ratio Money-Consumption Ratio Over Time 2.00 consumpreal moneyreal Year Inflation, Demand for Liquidity, and Welfare September 26, 202 9/42

20 $ Money and Consumption Over Time Year consumpreal moneyreal Inflation, Demand for Liquidity, and Welfare September 26, /42

21 Empirical Analysis on Money-Consumption Ratios by Age, Cohort and Time It is difficult to separate out these three effects. Our identification strategy and assumptions are: Three effects are independent Cohort effects are assumed to be exponential with respect to the differences in birth year (µ birth year/0 ) Time effects are time-specific (λ time ) Age effects are age-specific (αage ) Estimate µ, λ t and α i using annual data on money-consumption ratios from 999 to 2009, with six 0-year age groups. Inflation, Demand for Liquidity, and Welfare September 26, 202 2/42

22 Estimation of cohort, time and age effects Use the following moment conditions: ( m c ( m c ( m c ( m c ) ) ),999 = α ( m c 2,999 = α2 µ. = α i,999 i ). = α I,999 I ( m c ( m µ i c ( m µ I c ),2000 = αµ 0 λ2000 )2,2000 = α2 λ µ ). ) i,2000 = α i. I,2000 = α I µ i 0 µ I 0 λ 2000 λ 2000 ( m c ( m c ( m c ( m c ) ) ),2009 = αµλ2009 ) 2,2009 = α2λ2009. i,2009 = α i. J,2009 = α I λ µ i λ µ I This gives us I equations and I + parameters. Inflation, Demand for Liquidity, and Welfare September 26, /42

23 Estimation of cohort, time and age effects Additional assumptions we make are: Cohort effects reduce the demand for money over time: µ (0, ) Inflation, Demand for Liquidity, and Welfare September 26, /42

24 Estimation results α α 2 α 3 α 4 α 5 α 6 µ (0.00) (0.00) 0.002) (0.002) (0.003) (0.007) (0.864) λ 00 λ 0 λ 02 λ 03 λ 04 λ 05 λ 06 λ 07 λ 08 λ (0.04) (0.03) (0.03) (0.04) (0.05) (0.06) (0.05) (0.05) (0.03) (0.007) λ 99 by normalization Use the estimates to calibrate the following model. For calibration, the averages over λ 99 λ 04 and λ 05 λ 09 are used as the time effects since the model period is 0 years. Inflation, Demand for Liquidity, and Welfare September 26, /42

25 We build on Erosa and Ventura (2002) Seminal work on distribution of welfare cost of inflation: An infinitely-lived agent model with costly credit transaction. Study distribution of welfare cost over income. But abstract from life-cycle effects of inflation which is our focus. Inflation, Demand for Liquidity, and Welfare September 26, /42

26 Model Build an OLG model Consumption can be purchased with money and costly credit Agents live for I = 7 periods Agents differ in income profile (J = 5 exogenous income groups) Focus on transaction demand for money, and abstract from other roles of money such as hedging for liquidity risks Exogenous labour endowments and supply Inflation, Demand for Liquidity, and Welfare September 26, /42

27 Household s problem max {c ij,s ij,m i+,j,a i+,j } I i= β i c σ ij σ s.t. c ij ( s ij ) m ij ; sij c ij + w γ j (x)dx +a i+,j + ( + π)m i+,j 0 }{{} transaction cost [ + r( τ a )]a ij + m ij + ( τ z )w z ij ; a,j = 0, m,j = m Inflation, Demand for Liquidity, and Welfare September 26, /42

28 Government Budget Constraint and Inflation Government budget constraint (G exogenous government spending): All money is held by households. G = π M/P + τ l w L + τ a r A I,J i=,j= µ ij m i+,j = M/P There is a constant inflation rate. M t+ = ( + π) M t Inflation, Demand for Liquidity, and Welfare September 26, /42

29 Transaction technology ( ) x θi γ i (x) = γ i η ti x Fixed cost with respect to consumption and variable with respect to money-credit ratios Age effects: γ i and θ i Cohort effects (new): we assume cohort effects (η ti ) on transaction costs to vary with cohort (indexed by t i ) Use data to discipline γ i, θ i, η ti Inflation, Demand for Liquidity, and Welfare September 26, /42

30 Calibration strategy Household money demand for consumption ( m ij c ij ) are different in age (i), income (j) and time (t). Assume that time effects are driven by macroeconomic parameters such as tax rates, inflation and interest rates. Our focus will be on matching money-consumption ratios and consumption from the model to those in the data. Data: ( m ijt c ijt ) = f ijt (α i, µ, λ t ) and c ijt Model: ( m ijt c ijt ) = +[ R tc ijt /(wγ i η ti )] /θ i and c ijt Dynamically calibrate along a transition where macroeconomic parameters are changing. Use τ zt to balance the government budget. Inflation, Demand for Liquidity, and Welfare September 26, /42

31 Dimension of calibration Household groups: Age, I = 7 (We will not target i = HHs for calibration as their portfolio is fixed by assumption.) Income (and consumption class), J = 5 Total 35 groups (30 groups without i = HHs) Time periods: 2 periods, 999 and 2009 Inflation, Demand for Liquidity, and Welfare September 26, 202 3/42

32 Calibration: Data 2 periods x 35 household labour income, {zijt data } I,J,T i=,j=,t= 2 periods x 30 household consumption, {cijt data } I,J,T i=2,j=,t= 2 periods x 30 household money-consumption ratios, { mdata ijt } I,J,T cijt data i=2,j=,t= Out of these, estimate 6 α data i s (age), µ data (cohort) and λ data (time) 2 periods x 5 aggregate moments: π data t, rt data data, R t, τ data at and Gt data Inflation, Demand for Liquidity, and Welfare September 26, /42

33 Calibration: List of parameters 35 household labour endowments, {z ij } I,J i=,j= 30 discount factors, {β ij } I,J i=2,j= 2 age-dependent credit-transaction cost parameters: 6 γ i s and 6 θ i s 6 cohort-effects parameter, {η ti } t 7 ti =t 2, t i is the birth year for i = 2,..., 7 0 aggregate parameters: π t, r t, R t, τ at and G t Inflation, Demand for Liquidity, and Welfare September 26, /42

34 Calibration WITHOUT solving the model: Parameters and moments 35 labour endowments: {z ij } I,J i=,j= = T {zdata ijt } I,J,T i=,j=,t= 0 agg. parameters: π t = πt data, r t = rt data, Rt = R data t, τat = τat data, and G t = Gt data for t =, 2 Inflation, Demand for Liquidity, and Welfare September 26, /42

35 Calibration WITH solving the model: Parameters 30 discount factors, {β ij } I,J i=2,j= 2 age-dependent credit-transaction cost parameters: 6 γ i s and 6 θ i s 6 cohort-effects parameter, {η ti } t 7 ti =t 2, t i is the birth year for i = 2,..., 7, and set η t = η t2 =, 2 periods of τ zt, w t Inflation, Demand for Liquidity, and Welfare September 26, /42

36 Calibration WITH solving the model: Moments 30 household consumption at t =, {cij,t= data,j }I i=2,j= = {c ij,t=} I,J i=2,j= 6 age-i average household money-consumption ratios at t =, J j { mdata ij,t= cij,t= data J j } J j= = J j ] /θi +[ R t= c ij /(wγ i η ti ) 6 age-i averaged slope of household money-consumption ratios over consumption at t = (and/or t = 2), [( mi,j+,t= data J j ( c data i,j+,t= mdata ij,t= c data ij,t= ) ( / ci,j+,t= ij,t=) ] data cdata = ) ] /θi ] /θi +[ R t= c i,j+,t= /(wγ i η ti ) +[ R t= c ij,t= /(wγ i η ti ) / (c i,j+,t= c ij,t= ) Inflation, Demand for Liquidity, and Welfare September 26, /42

37 Calibration WITH solving the model: Moments 6 ratios of averaged money-consumption ratios over income; for i = 2 to 7 µ λ = J j= J j= +[ R t= c ij,t= /(w t= γ i ηt i )] /θ i +[ R t=2 c ij,t=2 /(w t=2 γ i η ti + ) ] /θ i 2 periods of government budget equations, G data t = π data t M t + τ data a rt data A t + τ zt w t Zt data 2 periods of labour demand: w t = f L (K t, L t ) Inflation, Demand for Liquidity, and Welfare September 26, /42

38 Calibration results Parameter Value Target Data Model γ γ γ γ γ γ θ θ θ θ θ θ j j j j j ( m ( c m ( c m ( c m ( c m ( c m j c ) ) ) ) ) ) 2,j 3,j 4,j 5,j 6,j 7,j j ( ) m c j ( ) m c j ( ) m c j ( ) m c j ( ) m c j ( ) m c 2,j 3,j 4,j 5,j 6,j 7,j Inflation, Demand for Liquidity, and Welfare September 26, /42

39 Calibration results Parameter Value Target Data Model η η η η η η λ 9904 µ λ λ 9904 µ λ λ 9904 µ λ λ 9904 µ λ λ 9904 µ λ λ 9904 µ λ β i, ,..., c i, ,..., ,...,0.239 β i, ,...,0.767 c i, ,..., ,...,0.47 β i, ,..., c i, ,..., ,...,0.630 β i, ,..., c i,4.270,..., ,..., β i, ,..., c i, ,..., ,...,.8499 Inflation, Demand for Liquidity, and Welfare September 26, /42

40 Calibration results - Money-consumption ratios.4.2 age=30 age=40 age=50 age=60 age=70 age= Consumption Inflation, Demand for Liquidity, and Welfare September 26, /42

41 Calibration results - Money-consumption ratios Money consumption ratio Age < 35 Model Data Age Model Data Money consumption ratio Age Model Data Age Model Data Money consumption ratio Age Model Data Consumption Age > 75 Model Data Consumption Inflation, Demand for Liquidity, and Welfare September 26, 202 4/42

42 Results to be added Inflation, Demand for Liquidity, and Welfare September 26, /42