Dynamic Effects of Consumption Tax Reforms

with Consumer Durables

Qian Li

School of Economics, Shanghai University of Finance and Economics

February 22, 2017

Abstract

This paper evaluates the welfare effects of consumption tax reforms along the transition

paths with consumer durables at present. Major proposals of consumption tax reforms include

consumer durables like housing in the consumption tax base. This paper studies exclusively

how interaction between liquidity constraints and a higher tax on durable consumption can lead

to a welfare loss of young cohorts. This result is in sharp contrast with the existing literature

that a consumption tax reform undoubtedly benefits young generations. The implication of this

study is that a consumption tax system may be a good idea in the long-run steady state, but

switching to such a system may bear a large short-run cost.

Keywords:Incomplete markets, Consumption taxes, Consumer durables, Liquidity constraint,

Transitional dynamics

JEL classification: E2 , D52, H21

1 Introduction

Given the complexity and the cost of the current tax system, tax reforms ignite heated discussion

among politicians and economists. The debates favor consumption taxes over income taxes for

their efficiency and fairness. The principal of consumption taxes is to exempt investment from

taxation, i.e. people should be taxed on what they take out of the economy, instead of what they

put in. A relaxed tax burden promotes capital accumulation, creating a larger economic pie to be

shared its population. At the same time, an increased capital accumulation improves the return

to labor and reduces the return to capital. In other words, prices are tilted in favor of households

with relatively lower wealth and stronger reliance on labor income. Because the economy is more

concentrated by such households, a consumption tax reform creates a positive redistribution effect

(Coleman (1999), Correia (2010)). Taking the transitional dynamics into account, switching to a

consumption tax system benefits younger cohorts. In fact, younger cohorts are more likely to be in

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the group with lower wealth and heavier labor dependence. Moreover, since younger cohorts have

longer life expectancy, they can take into account the full amount of future benefits. As stated in

Seidman (1992), the younger the cohorts are at the time of the consumption tax reform, the larger

the welfare gain they get.

Several proposals regarding consumption tax reforms have been discussed over decades. They

mainly differ in the format of implementation, the items and levels of deduction and the marginal

tax rates. For instance, a national sales tax functions the same as the current state and local sales

tax, but on a national level. It charges a proportional tax on all consumption good. As another

example, the flat tax reform proposed by Hall and Rabushka (1995) intends to remove all current

taxes on income. Instead a flat tax is levied at the firm level on cooperate income net of investment

and the same tax is applied to labor income at the households level with a exemption level of

20% the average labor earning. One common feature of all these proposals is that they involve a

100% write-off of business investment from the tax base. Namely, out of the three categories of

investment, only business and inventory investment are exempted from taxation, while residential

investment is remained in the tax base. Residential investment, mainly composed of housing, is

a one single largest consumption item for over two thirds of the population. Including durables

like housing stock in discussing consumption tax reforms may give extra implication than without.

This is then main motivation of this paper.

From the distribution of housing stock over the life-cycle, we can see that housing stock grows

rather slowly before hitting the age of 25. Then a rapid growth appears between the age of 27

and 46. The average value of housing purchased at different age groups also reflect the fact that

the 27 to 35 year old group has the strongest desire for acquiring housing assets. However, while

the income profile shows that the income remains low before reaching 27, it is likely that these

young households have saved just enough to pay for the down-payment. A sudden switch from the

income tax to a consumption tax regime may aggravate the liquidity constraints of these young

households, such that they either postpone the consumption of housing or downgrade the size of

housing consumption or even worse, slip into the regime of becoming a non-homeowner. From this

standpoint, including durables like housing in evaluating consumption tax reforms adds an extra

interaction term: liquidity constraint. Therefore, this paper studies exclusively the interaction

between liquidity constraints and a higher tax durable consumption that results the tax reform.

I show that even though a consumption tax reform may generate a big welfare gain in a long run,

the existing population, especially younger cohorts may suffer from a large welfare loss. This result

is in contrast with the previous literature. The mechanism lies in the lumpy nature of consumer

durables and liquidity constraints.

This paper contributes several streams of literature regarding taxation and portfolio choice.

From the aspect of taxation, this paper extends the previous discussion of consumption taxes

from non-durables to consumer durables. For example, Correia (2010), Coleman (2000), Ventura

(1999), Altig et al. (2001), Hall and Rabushka(1995), Seidman (1984) and Li (2016), etc. From the

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perspective of portfolio choice, this paper relates to Luengo-Prado (2006), who studies the exces-

sive smoothness and excessive sensitivity of consumption toward income; Diaz and Luengo-Prado

(2010), the wealth composition; Yang (2009), the life-cycle pattern of housing stock; Villaverde

and Krueger (2011), the life-cycle profile of non-durable and durable consumption; etc. This paper

also contributes to the discussion of the relationship between taxation and housing tenure decision.

For example, studies like Gervais (2002), Garria and Schlagehauf (2007), Berkovec and Fullerton

(1992) adn Rosen and Rosen (1980) investigate the relationship between the unfair tax treatment

of owner occupied houses and the homeownership rate. The current paper studies specifically how

the switch from a tax on income to a tax on housing would affect the housing tenureship.

The rest of the paper is structured as follows. Section 2 presents some empirical facts regarding

the life-cycle profile of income, consumption and assets holding. This part serves as a motivation

for the paper and as targets for calibrating the benchmark economy. The model is described in

Section 3, with the characterization of equilibrium along the transition paths. Section 4 explains

the calibration strategy. In Section 5, consumption tax reform will be expressed in detail. Three ex-

periments will be conducted in attempt to compare with the existing literature, to provide intuition

and to evaluate the effects of consumption tax reforms in the real economy. Section 6 concludes

the paper

2 Emperical Facts

In this section, I present the facts of portfolio choice over the life-cycle and statistics of main vari-

ables in the paper. Following Fernandez-Villaverde and Krueger [2011] and Yang [2009], I construct

the flow of total expenditures, non-durable consumption and durable consumption from CEX data,

and wealth, net worth and stock of housing assets from SCF data. Throughout the paper, I de-

fine durable consumption as consumption on vehicle, home appliances, furniture, jewelries, etc,

following the definition of NIPA. Housing consumption is the net inflow of houses,

2.1 Life-cycle income and consumption profile

CEX is a rotating panel containing 5000 households, each household is interviewed every three

months for 5 quarters, and 20% of the households are replaced by new sample during each quarter.

The interview questions covers households income, expenditure, financial statues with focus on con-

sumer expenditure flows. The dataset provides detailed infomation of households total expenditure,

non-durable consumption, durable consumption and purchasing of housing.

I use dataset of 1996 to 2006 for construct a pseudo-panel. I define 16 cohorts with 5 year

difference ranging from 21 years old to 85 years old. For example, a households who was born

between 1981 and 1985 are defined as the youngest cohort with the mean age of 23 at the year

2006; a households who was born between 1911 and 1915 is defined as the oldest cohort with the

mean age of 83 at 1996. After constructing the pseudo-panel data, I follow Fernandez-Villaverde

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and Krueger [2011] using semi-nonparametric regression to control for the time and cohort effects

and obtain the life-cycle profile of income, total expenditure, durable consumption and housing

consumption. The definition of each entry, construction method and the regression algorithm are

shown in Appendix.

Fifure 2 and Fifure ?? portraits the life-cycle income and earning pattern. As expected, they

both monotonically increases until 45 years old before decreasing. After age 65, earning is flatter

than income. Figure 3 and Figure 4 plot the life-cycle profile of total expenditure, durable con-

sumption in 2013 dollars. They are almost the same as Fernandez-Villaverde and Krueger [2011] .

Because of the liquidity constraint while young, both expenditures exhibit a hump shape over the

life-cycle.

In addition to the previous literature, I also construct the consumption flow of housing over

the life-cycle from CEX data. Because major proposed consumption tax reforms exempt businiess

investment from taxation while remaining residential investment in the tax base, housing become

the largest consumption item to be taxed. Understanding the pattern of housing consumption is

crucial for analysing the effect of such tax reforms. Since CEX data does not directly ask questions

of housing consumption each quarter, I calculated such flow by constructing the net inflow of

housing over the life cycle. More specifically, CEX asks homeowners the year and the price when

they purchase the house. This information serves as the inflow of the housing consumption of

the same cohort as the interviewee and at the age when he/she bought the house, not the age

he/she is interviewed. Moreover, CEX also interviews the disposal of housing, and this information

is regarded as the outflow of the housing consumption. I construct two pseudo-panels of inflow

and outflow of housing respectively, then subtract outflow from the inflow panel. The reason of

constructing two pseudo-panel is that the two interview questions might be answered by different

individuals. Figure 5 shows the average consumption flow of housing for all households and Figure

?? for homeowner only. These two figures reflect the fact that first, most households purchase their

houses before 40, namely young households saving in the form of durables; Second, the housing

consumption is much higher than other durable consumptions.

After adjusting for the family size, Figure 6, Figure 7, Figure 8 and Figure ?? are the corre-

sponding total expenditure, durable consumption, housing consumption over the life cycle for all

households and for homeowners respectively. The adjustment of family scales differentiated in non-

housing consumption and housing consumption consumption, following Yang (2009). The specific

numbers are presented in Table 1. As studied in Fernandez-Villaverde and Krueger [2011], after

controlling for the family size, the hump shape of total expenditure and durable consumption still

present.

In order to capture the life-cycle durable and housing stock, I turn to SCF data to construct

a pseudo-panel using five waves of survey from 1992 to 2004. One thing has to pay attention is

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Figure 1: Total income Figure 2: Total earning

Figure 3: Total expenditure

Figure 4: Consumption on durables Figure 5: Consumption on housing

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Figure 6: Life-cycle total expenditure,

adult equivalent

Figure 7: Life-cycle expenditure on durables,

adult equivalentFigure 8: Housing consumption, adult equivalent

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Table 1: Equivalence scales

Family size 1 2 3 4 5 6 7+

Non-housing 1 1.34 1.65 1.97 2.27 2.57 2.87

Housing 1 1.1 1.2 1.3 1.4 1.5 1.6

Figure 9: Life cycle durable stock Figure 10: Life cycle housing stock

that SCF might under-represent the durable stock. SCF does not ask for the value of all durable

possessions, but rather it collects data on vehicles and the three most valuable durables assets,

such as furniture, jewelries, equipments and collections, etc. The results are plotted in Figure

9, Figure 10 and Figure 11, Figure 12 after controlling for the family size, in 2013 dollars. The

comparison between durable and housing stock shows that durable consists a small portion of the

entire households durable possession. Moreover, housing stock grows relatively slowly between age

21 and 25, reflecting the fact that young households have to save up for the down-payment before

purchasing. A rapid growth appears between age 26 and 46, echoing the finding from CEX data

that most housing consumption occurs between 25 and 35 years old. After age 57, the housing

stock slightly decreases. There is some extent of inconsistency with Yang [2009] who documents

that housing stock flattens out after 65. One possible source of this inconsistency might stem

from our definition of housing values. Yang [2009] includes both shelter services and consumption

of other goods for which the house provides access to in the measure of housing value. In my

statistics, I consider only the market value of housing reported in the survey, without taking into

account the fringe benefit associated with the house.

2.2 Liquidity constraint

Documented in literature, young households as negative networth up to around age 30, the main

saving in durable and housing assets. Figure 13 and Figure 14 show the total wealth and the

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Figure 11: Life cycle durable stock, adult equiv-

alent

Figure 12: Life cycle housing stock, adult equiv-

alent

Figure 13: Life cycle total assets Figure 14: Life-cycle net worth

networth over the life-cycle. Both peak between age 56 and 60.

2.3 Distribution of durable and housing assets

This part presents some facts about the distribution of durables and housing assets. Three reasons

motivate me to focus on such a distribution. First, I do not tend to explain how the tax reform

would affect the housing market, but rather, i focus on the entire durable assets. Second, there

is strict difference in distribution of durable-housing and financial assets. More specific, financial

assets highly concentrate at the lower end, while we can see later that durable-housing concentrates

at 0 and somewhere in the middle, reflecting the fact that there is considerable non-homeowners

and that housing is much more valuable than other durables. The last reason is for the purpose

of calibration: in other to capture the preference in consuming other durable to housing, or vice

verse, the choice of grid points should enable the model to match certain moments and statistics.

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Figure 15: Distribution of durables

The distribution of other durable possessions such as vehicle, furniture, home appliances, col-

lections etc. are displayed in Figure 15. The left panel of 15 are the distribution of durable stock

for all households, the right panel is for the ones with positive durable possession. We can see

that a considerable amount of households do not possess any durable stock and the distribution

concentrates at the lower end, very similar to the distribution of financial assets. More detailed

statistics are present in the first line of Table 2. The interpretation of the table is as following:

if the value of other durable is below $2, 754, then she is in the lowers quintile of other durable

distribution. We can see from the table that 95% of the population with other durable assets less

than $65, 750. The average value of other durables is $25, 876 and $33, 846

Figure 16 exhibits the distribution of housing assets.The left panel are housing stock for all

households, the right panel for homeowner only. The (positive) value with the highest density

is around $120, 000. The second line of Table 2 shows the statistics of housing assets. First of

all, the homeowenship rate is roughly 63.4%, this number is obtained by defining homeowners as

ones with housing asset over $5, 000. This is definition is consistent with the screen question of

SCF, which imposes a lower bound of the housing value, i.e. $5, 000. The table shows that only

3.4% (40%− (100%− 63.4%)) of the population have houses with values lower than $54, 340. The

percentage of the population with a house value lower than $65, 750 is roughly 5%. The average

value of housing is $156, 788 and $24, 7287 for homeowners.

Table 2: Statistics of other durables and housing assets

Population percentage 20 40 60 80 90 95

Other durables($) 6,811 9,438 18,360 32,012 46,698 65,750

Housing - 54,340 135,300 239,850 369,000 528,000

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Figure 16: Distribution of housing

Because throughout the paper, I consider other durables and housing asset as a entire category

of durables, the left panel of Figure 17 plots the distribution of this category for all households,

the right panel for for positive possessions only. For the entire category of durables, there are two

center: one is 0 reflecting the fact that there is considerable amount of non-homeowners; the other

one at roughly $140, 000 reflecting that housing is more evaluable tha other durables. Second,

comparison between the two figures tells us that for non-homeowners, the have a stronger reliance

on other durables than homeowners do.

More statistics are shown in Table 3. There are 38% of the households are with the value of

durables and housing below $50, 000. The concentration of durables is the highest, nearly 13%.

The homeowners in this group is only 2% of the entire population. As the value of durables and

housing surpasses $100, 000, almost every households in these ranges are homeowners because the

number homeowners within this range is roughly the same as the number of population within these

ranges. Moreover, when the values of durables and housing assets are beyond $100, 000, the ratio

of the value of durable to housing becomes increasingly small, reflecting that the values of durables

are much less than housing and are more concentrated at the lower end. The other durables are

far less spreaded than housing assets.

Table 3: Statistics of durables and housing

Durable and housing value ($e3) <50 (50,100] (100,150] (150,200] (200,500] (500,1000,] 1000+

Percentage of population(%) 37.8 7.5 12.7 11.0 24.2 5.1 1.6

Average value of durables($) 8,839 15,141 17,313 23,460 32,412 61,708 346,482

Percentage as total value of durables(%) 12.9 4.4 8.5 1.0 30.6 12.0 21.6

Average value of housing($) 1,367 63,086 108,415 150,322 268,129 605,302 1,555,794

Homeowner as a percenrage of the population(%) 2.1 6.9 12.6 11.0 24.3 5.1 1.6

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Figure 17: Distribution of durables and housing

3 The Model

The three subscripts t, i, j are the natural time, the individual index and her age.

3.1 Demographics

Each period a continuum of households are born and immediately join the labor market. Each

household works Tr years and lives J years. Households are facing an exogenous shock of death at

each period with the probability of 1 − φj for j < J and the probability of 1 at the year J . The

population is growing at a constant rate of n.

3.2 Preference

Individual derives utility from non-durable consumption cijt, durable stock dijt and leisure lijt. The

future utility is discounted at rate β. The objective function of a new born household i is

EJ∑j=0

βjφju(cijt, dijt, lijt)

Moreover, the durable goods depreciate at the rate of δd.

3.3 Endowment

At the time of birth, each household is endowed with a certain amount of financial assets k0 and

durable goods d0. Each period, household is endowed with one unit of time. At the working age,

the time is divided between working and leisure; after the retirement, households enjoy full-time

leisure.

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3.4 Earning process

During the working age, households receive labor income according to wage wt, age-dependent

labor efficiency ej , idiosyncratic shock θijt and labor hour hijt.

After the retirement, households receive a social security benefit. Throughout the paper, I

assume the social security system is self-financed.

The earning function for workers and retiree are as following:

yijt =

wtejθijthijt j ≤ Tr

pentij j > Tr

3.5 Borrowing constraint

Because of the bulky and lumpy nature of durables, durable goods can be acquired through a

downpayment, a fraction of the durable θ. The rest of the durable can be served as a collateral

and households can borrow up to 1− θ fraction of the durable. Denote the financial asset by aijt,

then the borrowing constraints is written as

aijt ≥ (1− θ)dijt

3.6 Production

There is a representative firm using the aggregate capital Kt and labor Lt to produce non-durable

goods durable goods and services. Solving firm’s maximization problem, it gives the following

prices:

rt = AFK(Kt, Lt)− δk,

wt = AFL(Kt, Lt)

where δk is the depreciation rate of capital,

3.7 Government and the fiscal policy

Each period, the government finances an exogenous stream of spending Gt by collection taxes from

households and the firm at both federal level and the state and local level. At the the firm level,

a federal level proportional corporate income tax τa is charged every period. At the household

level, a proportional sales tax τ c,state and a proportional property tax τp are collected by the state

and local government; an income tax at the federal level. The individual income tax is written

as T (rτt aijt + yijt), where rτt is the after (cooperate income) tax return on capital, rτt aijt is the

capital income and yijt is the taxable earning. Households at all working age are subjecting to a

social security tax up to a limit ssijt = min{τ ssyijt, y}, where y is the social security cap. All the

retired population are receiving a social security benefit penijt that is a constant fraction of their

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permanent income. This replacement ratio is denoted by λ.. According to the current tax system,

the taxable income for working population exempts half of the social security payment, and the

entire social security benefit for retired population is included in tax base. Moreover, the state and

local level property tax is also deducted from the federal tax payments.

The tax payment is

Taxtij =

{τ c,statecijt + τp(1 − δd)dijt + τaraijt + T (rτt aijt + yijt − 0.5ssijt − τp(1 − δd)dijt) + ssijt j ≤ Tr

τ c,statecijt + τp(1 − δd)dijt + τaraijt + T (rτt aijt + yijt − τp(1 − δd)dijt) j > Tr

3.8 Equilibrium

One goal of this paper is to evaluate the welfare gain along the transition paths, so I define the

equilibrium over the entire time path. That is I include the time subscript t throughout the

definition of the equilibrium. This is actually a generalized form of a static equilibrium. Households

are different in financial asset holding, durable possession and labor income process. I suppress the

households index i.

Definition: Given an initial endowment of financial assets, consumer durables and labor effi-

ciency (a0t0 , d0t0 , θ0t0) ∈ A×D×Θ at the birth time t0, and its initial distribution µ0t0(a0t0 , d0t0 , θ0t0),

an equilibrium is defined as sequences of prices {rt}∞t=t0 and {wt}∞t=t0 , tax policies {τat }∞t=t0 , {τ c,statet }∞t=t0 ,

{τpt }∞t=t0 , {τ sst }∞t=t0 , {λt}∞t=t0 , {Taxt(.)}∞t=t0 , distribution measure {µt(a0t0 , d0t0 , θ0t0)}∞j=0,t=t0, history-

dependent decision rules {cjt(a0t0 , d0t0 , θjt)}∞j=0,t=t0

, {djt(a0t0 , d0t0 , θjt)}∞j=0,t=t0

, {aj+1,t+1(a0t0 , d0t0 , θjt)}∞j=0,t=t0

and {hjt(a0t0 , d0t0 , θjt)}∞j=0,t=t0

, values of aggregate assets, durables and capital {At+1}∞t=0, {Dt+1}∞t=0

and {Kt+1}∞t=0, such that:

1. Given prices and tax policies; {cjt(a0t0 , d0t0 , θjt)}∞j=0,t=t0

, {dj+1,t+1(a0t0 , d0t0 , θjt)}∞j=0,t=t0

,

{aj+1,t+1(a0t0 , d0t0 , θjt)}∞j=0,t=t0

, {hjt(a0t0 , d0t0 , θjt)}∞j=0,t=t0

solve the households maximiza-

tion problem:

max{cjt,dj+1,t+1,aj+1,t+1}

E

J,t0+J∑j=0,t=t0

βjφ(j)u(cjt, djt, 1− ljt)

(1 + τ ct )cjt + dj+1,t+1 + aj+1,t+1 = (1 + rt)ajt + (1− δd)djt + wtljtejθjt − adjustjt− τ sst min{y, wtljtejθjt} − τpt (1− δd)djt− T (rτt ajt + wtljtejθjt − 0.5τ sst min{y, wtljtejθjt} − τpt (1− δd)djt),

if j ≤ Tr

(1 + τ ct )cjt + dj+1,t+1 + aj+1,t+1 = (1 + rt)ajt + (1− δd)djt + ssjt − adjustjts− τpt (1− δd)djt− T (rτajt + ssjt − τpt (1− δd)djt),

if j > Tr

where adjust is the adjustment cost of durables.

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2. The measure of distribution evolves according to the Markovian transition matrix

µ(aj+1,t+1, dj+1,t+1, θj+1,t+1) = µt(ajt, djt, θ

jt)π(θjt, θj+1,t+1)

3. The goods market clear

Ct +Kt+1 − (1− δ)Kt +Dt+1 − (1− δ)Dt +G = Yt

where Ct =∑J

j=1

∑θjt∈Θ

∫A×D cjtµt(ajt, djt, θjt)dajtddjt, Dt =

∑Jj=1

∑θjt∈Θ

∫A×D djtµt(ajt, djt, θjt)dajtddjt

and Kt =∑J

j=1

∑θjt∈Θ

∫A×D ajtµt(ajt, djt, θjt)dajtddjt

4. The labor market clear

Lt =

J∑j=1

∑θjt∈Θ

∫A×D

ljtµt(ajt, djt, θjt)dajtddjt

5. The factor market clear

rt = F1(Kt, Lt)− δ

wr = F2(Kt, Lt)

6. The government budget is satisfied

G =J∑j=1

∑θjt∈Θ

∫A×D

Tjt(.)µt(ajt, djt, θjt)dajtddjt

7. The social security system satisfies:

Tr∑j=1

∑θjt∈Θ

∫A×D

ssjtµt(ajt, djt, θjt)dajtddjt =

J∑j=Tr+1

∑θjt∈Θ

∫A×D

penjtµt(ajt, djt, θjt)dajtddjt

4 Calibration

4.1 Data source

The data sources includes CEX, SCF at the households level, NIPA ”GDP and Personal Income”,

”Fixed Assets” and ”Consumer Durable Goods” at the aggregate level. The capital stock is defined

as private nonresidential fixed asset plus governmental nonresidential fixed asset. The durable stock

is defined as private residential fixed asset plus governmental residential fixed asset plus consumer

durables.

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Table 4: Earning process

Earning Process

θ 1.00 5.29 46.55

0.992 0.008 0.000

Π 0.009 0.980 0.011

0.000 0.083 0.917

Π∗ 0.498 0.443 0.059

4.2 Fiscal policy

The cooperate income tax is 10.3% adopted from Vetura(1999). The state and local sales tax is set

at 5.6% as Conesa et al. (2009). The property tax is 1.11%, the weighted average of each state.

The individual income tax function takes the form of T (y) = κ0(y − (y−κ + κ2)−1/κ1) proposed

by Guvia and Strauss (1985). The parameters κ0 and κ1 are taken from Anagnostopoulos et al.

(2010), κ2 is calibrated such that the government spending is 16% of the GDP. The social security

tax is 12.4%, which is equally devided by employers and employees. The replace ratio in this paper

is set to be 57% to insure that the social security system is self-financed. This number is closed to

the actual replacement ratio of 60%.

4.3 Technology

The production functions is assumed to Coob-Douglas Y = AKαL1−α with capital share of output

equals 0.3. The depreciation rate of capital is 0.1143 and that of durable is 0.08923, roughly the

same as Fernandez-Villaverde and Krueger (2001). Following Luengo-Prado (2006), the adjustment

cost is adjust = µ(1−δd)d if d′ 6= (1−δd)d, where µ = 0.5. Following the literature 1, the adjustment

cost is roughly 5% of the remaining durable stock.

4.4 Earning process

The earning process is adopted from Dvila et al. [2012], shown in 4.

4.5 Preference

The households utility function takes the form of CES, u(c, d) = (cγd1−γ)1−σ−11−σ , where σ is the

risk-aversion parameter, γ governs the elasticity of substitution between non-durable consumption

and durable consumption. For simplicity I assume for now that labor supply is constant at the

level of 0.3. In later sections I will show the results with elastic labor. The rationale of assuming

labor to be constant is that how a consumption tax reform affects the intratemporal choice between

1Yang(2009), Luengo-Prado(2006), Luengo-Prado and Diaz(2010), etc.

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labor and consumption depends on whether income or substitution effect dominates. σ takes the

value of 2, γ, β and the grid points of durables are calibrated together to match the homeownership

rate, nondurable consumption to durable consumption ratio and the capital to output ratio. More

details of chooing the grid point of durables are layout in the next subsection.

4.6 Grid points of duable assets

Figure 17 shows that there are two centers for durables, 0 and $14, 000, which is roughly twice the

annual earning. Thus, the grid points of durables are chosen to reflect this feature. The results of

such grids points have to match the distribution of durables in Table 2. Moreover, Table 2 shows

that when the values of durables are betlow $50, 000, the number of homeowners is only 2% of the

total households. In the same table, majority of the households in the range of ($50, 100]K are

homeowners and almost all households with durables more than $100K are homeowners. These

facts are convincing enough to regard households with total value of durables beyond $50, 000 (75%

of the average annual earning) are in the housing market, namely homeowners.

Table 5: Parameters

Parameter Name V alue Targets

Technology

α capital share of output 0.3

δk capital depreciate rate 0.0892 Ik/K

δd durable depreciate rate 0.0943 Id/D

µ adjustment cost 0.05

No durable Single durable Multi durables

θ down payment - 1.0 0.2

Government

κ0 average tax rate 0.258

κ1 progressivity 0.768

κ2 1.4 G/Y = 15.9%

y SS contribution limit 2.46× average labor income

τss Social security tax 0.124

b Retired replacement ratio 0.06

5 Numerical Results

In this section, I numerically analyse the effect of consumption tax reforms taking the transitional

dynamics into consideration. The consumption tax reform in mind is Hall and Rabuska’s flat tax

reform. The reason of choosing such a format of consumption tax is towfold. One is because this

proposal has gained wide popularity among the economist and commentators for its simplicity in

16

Table 6: Parameters

Parameter Name V alue Targets

Demographics

g population growth rate 0.011

φ conditional survival rate Bell and Miller(2002)

T maximum age 100

Tr retirement age 65

T0 initial age 20

Labor income process

ρ persistence 0.98 Davila et al.(2012)

σ standard deviation 0.061

e age efficiency Hanson(1993)

Preference

σ relative risk aversion 2

No durable Single durable Multi durables

β discount factor 0.965 0.958 ? K/Y = 1.86

γ substitution between D and C - 0.80 ? D/C = 2.55

dmax the uniform durable size - 0.74 -

dgrid the grid points of durables - - Distribution of durables

carrying out. The other reason is for its delusional treatment of consumer durables.

The flat tax reform removes all the current federal level cooperate income tax and individual

income tax. Instead, at firm level, the flat tax system levy a proportional tax on income net of

investment; on households level, the new tax system charge a proportional tax on earnings that

exceeds the deduction level. According to the proposal, the deduction level is 20% the average

earning. Moreover, the flat tax reform removes social security benefit from the tax base, eliminates

the deduction on property tax payments and half of the social security payments that is paid by

individual. One key feature of this proposal is that it completely writes off the business investment

from taxation, while leaving residential investment remaining in the tax base. This motivates the

discussion of what would happen if consumer durables, especially housing are subject to such a

consumption tax.

The households tax payment at time t become: The tax payment is

Taxtij =

{τ c,statecijt + τp(1− δd)dijt + τaraijt + T (rτt aijt + yijt) + ssijt j ≤ Tr

τ c,statecijt + τp(1− δd)dijt + τaraijt + T (rτt aijt) j > Tr

I present two experiments. To compare with the literature, the first experiment is the case

without consumer durables. In the last experiment, I return to the reality, adopting a 20% down-

payment and a continuous value of durable goods. In all these experiment, households preference

parameter are re-calibrated to match the data. I will explain the adjustment of the specific param-

eters in details in their corrosponding sections.

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5.1 Without duralbes

First consider the case without consumer durables. This is the standard discussion of the effect of

consumption tax reform in a OLG model. The discount parameter is re-calibrated such that the

capital to output ratio equals 1.86 as in the benchmark case.

The steady state results are shown in the first two column of ??. As expected, switching to

a consumption tax regime, capital accumulation increases because investment is exempted from

taxation. Both consumption and aggregate welfare are higher in the new steady state. Figure

18 shows the life-cycle profile of consumption and capital of the two steady states. The capital

accumulation is higher throughout the working age because the investment is untaxed. Toward

the end of the life cycle, capital is lower than the pre-reform level due to the fact that pension is

excluded from the tax base and the return to capitla is lower.

Table 7: Steady sate results

Variables No durable Single durable Continuous durable

∆(%) ∆ ∆

τ c - 0.21 21.3 - 0.22 22.8

r 0.040 0.031 0.040 0.031

w 0.937 0.959 0.93 0.96

K 0.464 0.502 0.50 0.46 0.50 9.8

D - - 0.24 0.22 -7.34

C 0.133 0.134 0.41 0.094 0.097 3.82

K/Y 1.98 2.09 1.96 2.09

D/Y - - 1.03 0.93

G/Y 0.165 0.161 0.164 0.159

C/D investment - - 4.54

Homeownership rate - - 0.33

Welfare -286.48 -278.91 2.71 -2197.1 -2165.7 2.07

However, a higher aggregate welfare in the new steady state is miss leading because the popu-

lation by then is completely different from those today. Figure 19 exhibits the welfare gain of the

existing population at the date of the reform takes place. Being consistent with Seidman (1992),

younger cohort experience a welfare gain. As proofed by Corriea (2010), consumption tax reform

benefit households with relatively low capital income than labor income. Younger cohorts are the

ones mainly rely on their labor income and with relatively lower capital income, so they potentially

benefit from the tax change. The reform take roughly 20 years to converge to the new steady state

(Figure 20), younger cohorts will continue to remain the current income profile throughout the

transition. Thus, the younger the households are, the higher welfare gain they receive.

Households toward retirement are the ones who suffer the most, because they are the main

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Figure 18: Transitional path of variables of interest

Figure 19: Transitional path of variables of interest

19

Figure 20: Transitional path of variables of interest

asset holders. A falling return on capital reduce their wealth tremendously. Even though a higher

wage increases the permanent income and thus the social security payments, the former effect

dominates. And moreover, a consumption tax is newly introduced to the retirement period, thus a

further reduction on their welfare is observed.

Retired households are benefiting and hurting from the following aspects. A falling return on

capital reduces their wealth; a higher wage and thus a higher permanent income increases their

social security benefit; a higher tax on consumption makes purchasing more expensive. However,

everything considered, the retired households are not necessarily lose from this tax change, con-

trasting to the results derived in Seidman (1992). The reason is that I assume a public social

security system while Seidman assumed a private social security system, namely no social security

system. In the economy with no social security system, households have to save a greater deal while

they are working. As a result, once the tax reforms lowers the returns to capital, older generation

get hurt. On contrary, with a public social system, households do not need to save as much as

otherwise, so the falling return to capital will not affect them that much. I also include the case

with no social security system, similar to Seidman(1992) 2 21 confirms the conjecture that the

format of a social security system plays a critical role in determine the welfare gain of retirees.

Evaluating the welfare gain along the income dimension, we will find that middle income house-

holds are the ones who lose the most. Essectially, this is because of their relative lower labor income

as compared to their capital accumulation. The results are presented in Figure 22

2Similar because we both do not have a public social security system, but Seidman’s model does not consider

heterogeneity in households.

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Figure 21: Transitional path of variables of interest

Figure 22: Transitional path of variables of interest

21

5.2 The real economy

6 Conclusion

This paper studies how different the welfare gain would be if we take consumer durables into account

in discussing the effects of consumption tax reforms. Given that major consumption tax reform

proposals treat residential investment such as housing as consumer durables and thus includes it is

the tax base, This study investigates exclusively the interaction between a higher tax on housing

and liquidity constraints. I found that the switch from the current income tax to a consumption tax

regime may cause a short term loss for younger cohorts. This effect has not yet been documented

in existing literature. The reason is that a consumption tax aggravates the liquidity constraint of

young cohorts, such that they either postpone consumption of housing or downgrade their housing

size including the case of becoming a non-homeowner. The policy implication is that even a

consumption tax scheme may generate a welfare gain in the the long run, the short run loss is not

negligible, especially with consumer durable at present.

References

S. R. Aiyagari. Uninsured idiosyncratic risk and aggregate saving. The Quarterly Journal of

Economics, 109(3):659–84, 1994.

A. Anagnostopoulos and Q. Li. Consumption taxes and precautionary savings. Economics Letters,

119(3):238–242, June 2013.

A. Anagnostopoulos, E. Carceles-Poveda, and D. Lin. Dividend and capital gains taxation under

incomplete markets. Journal of Monetary Economics, 59(7):599–611, Extended version 2012.

J. Berkovec and D. Fullerton. A general equilibrium model of housing, taxes, and portfolio choice.

Journal of Political Economy, 100(2):390–429, April 1992.

T. Bewley. Stationary monetary equilibrium with a continuum of independently fluctuating con-

sumers. In Contributions to Mathematical Economics in Honor of Gerard Debreu, Hildenbrand

and Mas-Colell ed., 1986.

c. D. Carroll, R. E. Hall, and S. P. Zeldes. The buffer-stock theory of saving: Some macroeconomic

evidence. Brookings Papers on Economic Activity, 1992(2):61–156, 1992.

M. Chambers, C. Garriga, and D. E. Schlagenhauf. The tax treatment of homeowners and landlords

and the progressivity of income taxation. Federal Reserve Bank of St. Louis: Working Paper

Series, December 2007.

J. F. Cocco. Portfolio choice in the presence of housing. The Review of Financial Studies, 18(2):

535–567, Summer 2005.

22

W. J. Coleman II. Welfare and optimum dynamic taxation of consumption and income. Journal

of Public Economics, 76:1–39, 2000.

J. C. Conesa, S. Kitao, and D. Krueger. Taxing capital? not a bad idea after all! American

Economic Review, 99(1):25–48, March 2009.

I. Correia. Consumption taxes and redistribution. American Economic Review, 100(4):1673–94,

September 2010.

A. Diaz, J. Pijoan-Mas, and J.-V. Rios-Rull. Precautionary savings and wealth distribution under

habit formation preferences. Journal of Monetary Economics, 50(6):1257–1291, 2003.

D. Domeij and J. Heathcote. On the distributional effects of reducing capital taxes. International

Economic Review, 45(2):523–554, May 2004.

J. Dvila, J. H. Hong, P. Krusell, and J.-V. Ros-Rull. Constrained efficiency in the neoclassical

growth model with uninsurable idiosyncratic shocks. Econometrica, 80(6):2431–2467, November

2012.

J. Fernandez-Villaverde and D. Krueger. Consumption and saving over the life cycle how important

are consumer durables. Macroeconomic Dynamics, 15(05), November 2011.

M. Gervais. Housing taxation and capital accumulation. Journal of Monetary Economics, 49:

1461–1489, 2002.

M. Gouveia and R. P. Strauss. Effective federal individual income tax functions: An exploratory

empirical analysis. National Tax Journal, 47(2):317–39, June 1994.

R. Hall and A. Rabushka. A Flat Tax Reform. Hoover Institution Press, 1995.

M. Huggett. The risk-free rate in heterogeneous-agent incomplete-insurance economies. Journal of

Economic Dynamics and Control, 17:953–969, 1993.

K. L. Judd. The welfare cost of factor taxation in a perfect-foresight model. Journal of Political

Economy, 95(4):675–709, August 1987.

M. J. Luengo-Prado. Durables, nondurables, down payments and consumption excesses. Journal

of Monetary Economics, 53:1509–1539, 2006.

N. G. Mankiw. Hall’s consumption hypothesis and durable goods. Journal of Monetary Economics,

10:417–425, 1982.

L. S. Seidman. Conversion to a consumption tax: The transition in a life-cycle growth model.

Journal of Political Economy, 92:247–67, April 1984.

23

G. Ventura. Flat tax reform: A quantitative exploration. Journal of Economic Dynamics and

Control, 23:1425–1458, 1999.

F. Yang. Consumption over the life cycle: How different is housing? Review of Economic Dynamics,

12:423–443, 2009.

A Data and Regression

B Computation Algorithm

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