Heterogeneous household finances and the effectof fiscal policy∗

Javier Andrésa, José E. Boscáa,b, Javier Ferria,b and Cristina Fuentes-Alberoc

a University of Valenciab FEDEA

c Federal Reserve Board

February, 2016.

Abstract

This paper analyses the link between fiscal policy, heterogeneous household finances, andhouseholds’ consumption response. Our model economy is populated by six types of householdswith identical labour income, but different balance sheet composition. We show that heterogeneityin the structure of household finance is key to understanding the effects of fiscal shocks. In particular,we conclude that: (1) the marginal propensity to consume is negatively correlated with net worth;(2) the size of fiscal effects is positively correlated with wealth inequality; and (3) the welfare effectsamong heterogeneous households depend heavily on the composition of net worth.

Keywords: household finances, fiscal policy, heterogeneity.JEL Classification: E21, E62.

1. IntroductionWealth ownership in many advanced countries has always been concentrated in the handsof a small minority of the population. In fact, wealth inequality increased in the GreatModeration period in the US and other developed countries and continued to do so duringthe Great Recession. The wealth share of the U.S.’s top 3 percent (see Federal ReserveBoard Survey of Consumer Finances, 2014) rose from 44.8 percent of the country’s wealth

∗ This work was supported by Fundación Rafael del Pino; BBVA Research; and the Spanish Ministry of Eco-nomy and Competitiveness (grant ECO2014-53150-R).

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in 1989 to 51.8 percent in 2007 and 54.4 percent in 2013. In the U.S., wealth held by the top3 percent of the population is twice as much as that in the hands of the poorest 90 percent.During the Great Moderation period, this issue received little attention from economicresearchers, given that, at the same time, consumption differences across households werereduced. The financial sector was playing a key role favouring that wealthy people (bigsavers) provided loans to finance consumption of the less favoured part of the popula-tion and, thus, reducing the differences in consumption across households. As a resultconsumption inequality was reduced, although wealth inequality increased.

However, the financial turmoil in 2008 brought about an important recompositionof the balance sheets of many households. The crisis exerted a devastating effect onthe ability of households to obtain credit and also on the prices of many financial andreal assets. While the value of private sector assets’, in particular real state, plummeted,deflation increased the real value of debt. The subsequent fiscal responses in many coun-tries were thus carried out against the backdrop of economies with households charac-terised by very different assets/liabilities positions than the ones prevailing before thecrisis. For this reason, researchers and policy makers have made substantial efforts toassess to what extent fiscal multipliers are now very different from the ones estimatedbefore the crisis (see e.g. the surveys by Ramey, 2011 and Spilimbergo et. al., 2009).The most recent economic literature has gone a step further combining macroeconomicand microeconomic empirical and theoretical analysis to shed some light on the linksbetween fiscal policy, heterogeneous household finances and their consumption responsesto shocks. The main idea of this strand of the literature consists in using microeconomicdata, coming from different surveys, to match the stylised facts regarding the compositionof households finances. This type of approach will allow a better understanding of thereaction of economies to fiscal and other kinds of shocks.

In this paper, we carry out a macroeconomic analysis of these issues within theframework of a general equilibrium model populated by six types of consumers. House-holds differ in the composition of their balance sheets. These households’ categories havebeen used individually, or in different combinations, in many macroeconomic models de-veloped in the general equilibrium literature.1 Specifically, we identify standard Ricardianoptimising households (R), typical hand-to-mouth or rule-of-thumb consumers (HNH)that hold neither assets nor liabilities, wealthy HtM consumers (HH) that hold assetsbut no liabilities, borrowers with either high or low capacity to access credit backed bycollateral (BL and BH, respectively) and, finally, what we call Eggertsson-Krugman typeof consumers (EK) that do not posses collateralisable assets and borrow against their future

1 See Eggertsson and Krugman (2012), Gali, López-Salido and Vallés (2007), Iacoviello (2015), and Andrés,Boscá and Ferri (2015 and 2016).

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labour income.Identifying marginal propensities to consume using wealth changes is difficult be-

cause individuals differ in labour income, employment status, productivity, education,etc. Our theoretical model limits the scope of heterogeneity among households only totheir balance sheet position. The paper aims to isolate net worth effects of fiscal shocksand, to that end, we assume perfect insurance to unemployment. In particular, labourincome is identical across individuals in a search and matching environment. Thus, after agovernment expenditure shock, all households in the economy face the same variation intheir labour income, but idiosyncratic reactions of their net worth. This framework allowsus to look in detail at the general equilibrium mechanism underlying the consumptionreaction to specific net wealth variations of the various agents in the economy, and in turnto the aggregate consumption and output effects of fiscal policy.

The model is calibrated to match the most salient features of the U.S. economy. Weinspect the mechanism considering alternative theoretical wealth distributions and accessto credit among the population. We then give the simulated model a more solid empiricalfoundation by improving the calibration of the model with the share of these types ofhouseholds identified in the Panel Study of Income Dynamics (PSID). We identify differenttypes of consumers that are heterogenous in terms of the composition of their balancesheets and that match to some extent the features of the individuals in our theoreticalmodel.

We conclude that matching stylised facts regarding households finances is key tounderstand the reaction of economies to fiscal shocks. Our results show that changingthe composition of the population according to their financial positions has importanteffects on the aggregate marginal propensity to consume and the output multiplier. Atthe individual level, the marginal propensity to consume is negatively related with networth. Model simulations show that the size of the fiscal effect is positively correlatedwith wealth inequality. Finally, we compute the effect in our model of fiscal shocks onhousehold’s welfare, showing that welfare effects depend heavily on the composition ofnet worth.

Summing up, we conclude that households in the lowest part of the net wealthdistribution (HH, HNH and EK households in our economy) can affect importantly themagnitude of the aggregate marginal propensity to consume, the value of the fiscal multi-plier and the distributional consequences of fiscal shocks.

Section 2 presents a succinct review of the recent empirical literature on the macro-economic implications of alternative household balance sheets. Section 3 introduces themodel and its calibration. The simulation exercises are presented in Section 4. Section5 contains a description of the data set, the criteria used to identify the different house-

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holds’ categories and some additional simulation exercises based on this data. Section 6concludes.

2. Literature reviewKaplan, Violante and Weidner (2014) use survey data on household portfolios for the U.S.,Canada, Australia, the U.K., Germany, France, Italy, and Spain to document the sharesof the so called hand-to-mouth (HtM) households across countries, their demographiccharacteristics and the composition of the assets side of their balance sheets. They identifytwo types of HtM households: poor hand-to-mouth (with little or no liquid wealth andno illiquid wealth) and the wealthy hand-to-mouth (with little or no liquid wealth, butsignificant amounts of illiquid assets). Using data of the Survey of Consumer Finances forthe U.S., they conclude that about 30% of the population is HtM, from which one-thirdis poor HtM and the remainder is wealthy HtM. The authors find that both wealthy andpoor HtM households have significantly stronger responses to transitory income shocksthan non-HtM households. They show that ignoring that wealthy hand-to-mouth can useilliquid assets to buffer large negative shocks overstates the overall financial fragility ofHtM households.

In a similar vein, Angrisani, Hurd and Rohwedder (2015) use panel data spanningthe years 2001-2011 on a complete inventory of household spending and assets. Theyestimate the response of private spending to negative wealth shocks in the US due tounexpected declines in house and stock market prices. Their main finding is that themarginal propensity to consume out of an unexpected housing wealth change is sevencents per dollar, and about four cents per dollar out of financial wealth. So, they find thatconsumption was reduced in the Great Recession because of losses in housing wealth andalso, although less precisely estimated, because of financial wealth losses.

Other authors put the emphasis on the importance of the composition of the lia-bilities side of the balance sheet of households to understand the consumption responsesof individuals to income shocks. For example, Cloyne and Surico (2014) use householdexpenditure data from 1978 to 2009 of the UK’s Living Costs and Food Survey (commonlyknown as the Family Expenditure Survey) to show that households with mortgage debtexhibit large and persistent consumption responses to changes in their income. In con-trast, homeowners without a mortgage do not appear to react, independently of the timehorizon considered.

The references above look either at the assets or the liabilities side of balance sheets.But both sides of the T-account are important in shaping the effects of shocks on house-holds’ consumption and, thus, on aggregate output in the economy. Other papers havealso looked at the net worth, defined as the value of households’ asset holdings net of

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debt, trying to understand the evolution of consumption over the recent years. Jaramilloand Chailloux (2015) base their analysis on an unbalanced panel dataset for 14 advancedeconomies, from 1998 to 2012. They separate the effects on private final consumptionexpenditure of the subcomponents of disposable income (labor income, social benefits,personal income taxes and social security contributions) and of different categories of netwealth (financial assets, housing assets, and household debt), finding a significant long-term relation between consumption and the different components of income and wealth.While labor income remains the main driver of consumption, financial assets and housingassets are found to have a positive coefficient, while household debt has a negative one.Furthermore, these authors’ results suggest that the contribution to consumption from anincrease in financial or housing assets would be more than offset if financed fully throughincreases in household debt.

Carroll, Slacalek and Tokuoka (2014) document the importance of matching sty-lised facts at the household level to interpret the reaction of economies to shocks. Usingdata from 15 European countries, they find that wealth inequality and differences in thedynamics of household income affect the response of economies to fiscal stimuli in aneconomically relevant way. In their sample they track down substantial heterogeneity innet wealth to income ratios both across and within countries. Countries in which house-holds tend to hold more net wealth respond less strongly to transitory income shocks,while countries with more unequal wealth distributions have a higher aggregate marginalpropensity to consume (MPC) and also a larger dispersion of MPCs across householdsand, thus, respond more strongly to shocks. Finally, Anderson, Inoue and Rossi (2015)present empirical evidence based on a narrative approach, finding that individuals whoseconsumption levels are most negatively affected by a positive government spending unex-pected shock are the wealthiest and working-age individuals, whereas consumption of thepoorest increases the most. Thus, the interesting conclusion is that positive governmentspending policy shocks tend to decrease consumption inequality.

Overall, the most important implication of this burgeoning (mostly) empirical litera-ture is that the net wealth position of households is a major determinant of their spendingdecisions, and hence that the distribution of wealth in an economy interacts with (affectsand is affected by) fiscal policy shocks in a non trivial manner. This is true not only forthe case of tax changes, whose incidence on household wealth is more direct, but alsofollowing changes in public spending, through their macroeconomic effects on both theasset and the liabilities sides of the balance sheet.

3. The modelThis section presents a stylised version of our model economy. A complete description of

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the model can be found in the Appendix 1.The economy is populated by six different types of households, being N the total

size of the working-age population. Households differ in terms of some few characte-ristics, as housing tenancy, the degree of impatience, or the ability to accessing credit.Let Ni denote the i-type household mass, with i denoting an element of the set I ={R, HNH, HH, BL, BH, EK}. The meaning of the previous acronyms is as follows: Rstands for Ricardian households; HNH are hand-to-mouth households with no access tofinancial markets and no real or financial assets; HH captures hand-to-mouth householdsthat can purchase and own houses, but, as for HNH households, total expenditures areequal to current income every period ; BL represents households that are able to borrowagainst a low proportion of the expected value of a collateralised housing asset; BH standsfor households that are able to collateralise a higher part of the next-period expectedvalue of their housing; and EK stands for households that are allowed to borrow againsttheir future labour income. Define τi = N

i

N (∑i∈I

τi = 1) as the weight of the i-type

household in the total population. For convenience, we also define different subsets ofhouseholds belonging to I. First, let ĩ be the index for the households in the subsetĨ = {HNH, HH, BL, BH, EK} referring to the different households facing a high degreeof impatientness. Second, define the subset Î = {R, BL, BH, EK} , whose elements areindexed by î, as the subset for those households that have access to financial markets.Finally, consider I = {R, HH, BL, BH} , indexed by i, as the subset of households that ownhouses.

Financially unconstrained Ricardian households (R) have been during a long timethe main character in representative agent macroeconomic models. These households aretypically savers/lenders that own assets, but do not have liabilities. In our economy, Ri-cardian consumers coexist with financially constrained individuals, who are characterisedby having a higher degree of impatience. Typical hand-to-mouth consumers (HNH) werepopularised by Galí, López-Salido and Vallés (2007) to obtain a positive response of ag-gregate consumption to a government spending shock. Contrary to Ricardian consumers,these households have no assets, but also no liabilities, so their net worth is zero. Morerecently, Kaplan, Violante and Weidner (2014) defined the wealthy hand-to-mouth house-holds as those that consume all their disposable income every period but have sizableamounts of wealth in illiquid assets (this is the role played by our HH households). BLand BH households are of the type designed by Kiyotaki and Moore (1997) and Iacoviello(2005). These individuals own both assets and liabilities and display a positive net wealthin the long run which is lower the higher the capacity to borrow. The type of householdsthat are able to borrow against their future labour income (EK) were used by Eggertssonand Krugman (2012) to illustrate the power of fiscal policy in highly leveraged economies.

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Compared to Ricardian consumers, these households are located in the other extremeregarding the composition on their net worth, as they have only liabilities but no assets.

In order to emphasize the importance of household net wealth heterogeneity on theeffects of fiscal policy, we assume that all households in the economy receive the samelabour income. In particular, we assume that all workers are equally productive anddelegate to a trade union the negotiation with firms, so that in equilibrium all of themreceive the same wage, work the same number of hours and display identical employmentrates.

3.1 Households’ problemThe optimisation problem faced by a household of type i can be expressed as,

maxcit ,b

ît ,x

it ,d

Rt ,k

Rt ,j

Rt

Et∞

∑t=0(βi)t

[ln(

cit)

+φix ln(

xit)

+nit-1φ1(1-l1t)1−η

1-η+(1-nit-1)φ2

(1-l2)1-η

1-η

](1)

subject to:

cit+jRt

(1+

φ

2

(jRt

kRt−1

))+qt

(xit-x

it−1)= -(1+rnt−1)

(bît-1

1+πt+

dRt-11+πt

)(2)

+rtkRt−1+wtnit−1l1+b

ît+d

Rt + f

Rt +trht

kRt = jRt + (1− δ)kRt−1 (3)

biti∈ Ĩ∩ Î

≤ ϕi[

miEt

(qt+1 (1+ πt+1) xit

1+ rnt

)](4)

+(1− ϕi)[

mEKEt

((1+ πt+1)wt+1nitl1t+1

1+ rnt

)]

nit = (1− σ)nit−1 + ρit(1− nit−1) (5)

Variables in this problem are normalised by the within-group working-age popula-tion (Nit). The index i in variables and parameters points to a specific financial structureof the household. Those with a ĩ superscript refers to the subset of financial constrainedconsumers, and the ones indexed by R affects only to consumers from Ricardian house-holds. Non-indexed variables and parameters are common to all households in the modeleconomy.

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The meaning of the variables implied in the utility function (1) is the following:cit, x

it,n

it−1 and (1− nit−1) represent, respectively, consumption, housing holdings, and the

beginning of period employment and unemployment rates of different households. Thetime endowment is normalised to one and, hence, l1t and l2 are an index of hours workedper employee and hours devoted to job seeking by the unemployed. While there is aprocess of bargaining over l1t, the amount of time devoted to job seeking (l2) is assumedto be exogenous and the same among workers. The discount rate parameter, βi, and thepreferences on housing, φix, can differ depending on the household class the consumerbelongs. However, the Frisch elasticity of the labour supply, related with η, and thevaluation of leisure by employed (φ1) and unemployed (φ2) workers are assumed to bethe same for all the agents.

Regarding the budget constraint (2) all consumers earn labour income wtnit−1l1t,where wt stands for hourly real wages. Latter on we will comment that under our assump-tions nit−1 = nt−1 for all i ∈ I, so that labour income is homogeneous across all householdtypes. Also, all consumers receive (pay) the same amount of lump sum transfers (taxes)from (to) the government (trht). When trht is negative it is considered a tax. Consumptionis represented by cit.

Ricardian consumers, who are more patient than the rest of agents and, thus, arecharacterised by a high value of βi, are the only lenders in the economy. Ricardians lend inreal terms −bit to the private sector (implying that bit is negative when i = R) and −dRt tothe public sector. Debt contracts are set in nominal terms and they earn an amount −(1+rnt−1)

(bRt−1

1+πt+

dRt−11+πt

)from financial asset holdings, where rnt−1 is the nominal interest rate

on loans between t− 1 and t. These patient consumers are also assumed to be the only oneswho own physical capital (kRt ) that yields rt−1k

Rt−1, where rt represents the gross return on

physical capital. Capital accumulates according to (3), where jRt stands for productiveinvestment and δ is the depreciation rate. Investment is subject to increasing marginalcosts of adjustment which are controlled by the parameter φ. Moreover, given that firmsmake extraordinary profits, we assume that lenders receive these in the form of dividendsf Rt .

The rest of consumers in the economy, those belonging to the subset Ĩ, are assumedto be more impatient than Ricardians and face the same discount factor, βĩ < βR. From thesubset of impatient consumers only those belonging to Î have access to credit, althoughin a restrictive way. These are households of type BL, BH, EK. Loans have differentconsideration depending on the degree of securitization. There is debt backed by collateralbut also not morgaged debt in the economy, and the possibility of access each of themdepends on the parameter ϕi. We assume that for BL, BH households ϕi = 1, whichmeans that the total amount of debt they can get is a fraction of the liquidation value

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of their housing stock. However for the EK consumers we assume that ϕi = 0 so thatthey can take loans up to a proportion of the discounted expected tomorrow’s labourincome.2 The impatient households’ intertemporal substitution is limited as representedby the corresponding Euler equation in consumption,

λi1ti∈ Ĩ∩ Î

= βiEtλĩ1t+1

(1+ rnt

1+ πt+1

)+ µit (1+ r

nt ) (6)

where µit is the shadow price associated with the constraint (4).

There is a fixed amount of real estate in the economy and the term qt(

xit − xit−1)

denotes housing investment, where qt is the real housing price.The remaining constraint faced by households concerns the law of motion for em-

ployment. Each period, jobs are destroyed at the exogenous rate σ. Likewise, new em-ployment opportunities come at the rate ρwt that represents the probability that one un-employed worker will find a job, which is taken as exogenous by individual workersbut is endogenously determined at aggregate level. Actually, ρwt can be defined as thenumber of matched workers during period t over the volume of unemployed workers atthe beginning of period t,

ρwt (1− nt−1) = χ1vχ2t [(1− nt−1) l2]

1−χ2 (7)

where vt stands for the number of active vacancies during period t, being χ1 and χ2 theparameters in the matching function.

For later use we define the marginal value of employment for a worker (λiht) as,

∂Wit∂nit−1

≡ λiht=λi1twtl1t+(

φ1(1-l1t)1−η

1-η-φ2(1-l2)1−η

1-η

)+ (1-σ-ρwt )β

iEtλiht+1 (8)

where Wi(Ωit) represents the value function of households’ maximum utility. λiht measures

the marginal contribution of a newly created job to the utility of the household. The firstterm captures the value of the cash-flow generated by the new job in t, i.e. the labourincome measured according to its utility value in terms of consumption (λi1t is the marginalutility of consumption). The second term on the right-hand side of (8) represents the netutility stemming from the newly created job. Finally, the third term represents the "capitalvalue" of an additional employed worker, given that the employment status will persist inthe future, conditional to the probability that the new job will not be lost.

2 Alternatively we could have allowed for different types of loans for all impatient households, with a propor-tion refereing to mortgaged debt and the rest being just backed by expected labor income. We find our modelingchoice easier to handle without much loss of accuracy in the exercises berlow.

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3.2 Firms’ problemFor convenience, production is organised in three different levels: (1) a wholesale sector(indexed by j) where firms use labour and capital to produce a homogenous good thatis sold in a competitive flexible price market at a price Pwt ; (2) an intermediate sectorwhose firms (indexed by j̃) operates in a monopolistically competitive fashion in whichprices are sticky. These firms buy the homogenous good and transform it, without theuse of any other input, into a firm-specific variety; (3) a competitive retail aggregator thatbuys differentiated varieties (y j̃t) from the intermediate sector at a price P̃jt and sells ahomogeneous final good (yt) at price Pt.

The competitive retail sector

The competitive retail aggregator buys differentiated goods from firms in the intermediatesector and sells a homogeneous final good yt at price Pt. Each variety y j̃t is purchased at aprice P̃jt. Profit maximisation by the retailer implies

Maxy j̃t

{Ptyt −

∫P̃jty j̃td j̃

}subject to,

yt =[∫

y(1−1/θ)j̃t

d j̃

] θθ−1

(9)

where θ > 1 is a parameter that can be expressed in terms of the elasticity of substitutionbetween intermediate goods (κ), as θ = (1+κ) /κ. The retailer’s price is given by:

Pt =[∫ 1

0

(P̃jt)1−θ

dj̃] 1

1−θ(10)

The monopolistically competitive intermediate sector

The monopolistically competitive intermediate sector comprises j̃ = 1, ... J̃ firms, each ofwhich buys the production of competitive wholesale firms at a common price Pwt and sellsa differentiated variety y j̃t at price P̃jt to the final competitive retailing sector describedabove. Variety producers stagger prices. In keeping with Calvo (1983), only some firmsset their prices optimally each period. Those firms that do not reset their prices optimallyat t adjust them according to a simple indexation rule to catch up with lagged inflation.Thus, each period a proportion ω of firms simply set P̃jt = (1+ πt−1)

ς P̃jt−1 (with ςrepresenting the degree of indexation and πt−1 the inflation rate in t− 1). The fraction of

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firms (of measure 1−ω) that set the optimal price at t seek to maximise the present valueof expected profits. Consequently, 1−ω represents the probability of adjusting prices eachperiod, where ω can be interpreted as a measure of price rigidity. The solution to choice ofthe optimal price for the representative variety producer is

P∗t =(

θ

θ-1

) Et ∑∞s=0 (βRω)s λR1t+s[

mct+s (Pt+s)θ yt+s

(s

∏s′=0

(1+πt+s′-1)ς)-θ]

Et ∑∞s=0(

βRω)s

λR1t+s

[(Pt+s)

θ-1 yt+s

(s

∏s′=0

(1+πt+s′-1)ς)1-θ] (11)

where P∗t is the price set by the representative optimizing firm at time t, and mctrepresents the real marginal cost. In accordance with the ownership structure of the eco-

nomy, future profits are discounted at the relevant rate((βR)s

λR1t+sλR1t

)of the patient house-

hold.Taking into account (10) and that θ is assumed time invariant, the corresponding

aggregate price level is given by,

Pt =[ω(

Pt−1πςt−1)1−θ

+ (1−ω) (P∗t )1−θ] 1

1−θ (12)

The competitive wholesale sector

The competitive wholesale sector consists of j = 1, ...J firms, each selling a different quan-tity of a homogeneous good at the same price Pwt to the monopolistically competitiveintermediate sector. Firms in the perfectly competitive wholesale sector carry out theactual production using labour and capital. Capital demand and vacancy posting aredecided by solving the cost minimisation problem faced by the representative competitiveproducer,

minkt ,vt

Et∞

∑t=0(βR)t

λR1t+1

λR1t(rt−1kt−1 + wtnt−1l1t + κvvt) (13)

subject to the production function

yt = Ak1−αt−1 (nt−1l1t)α (14)

and the law of motion for employment

nt = (1− σ)nt−1 + ρft vt (15)

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From the firms’ point of view, labour is homogeneous regardless of the type of householdthat provides it and ρ ft is the probability that a vacancy will be filled in any given periodt. The probability of filling a vacant post ρ ft is exogenous from the perspective of the firm.However, as far as the overall economy is concerned, this probability is endogenouslydetermined according to the following Cobb-Douglas matching function:

ρft vt = χ1v

χ2t [(1− nt−1) l2]

1−χ2 (16)

The solution to the optimisation program above generates the following first-orderconditions for private capital and the number of vacancies

rt = (1− α)mct+1yt+1

kt(17)

κv

ρft

= βlEtλl1t+1

λl1t

∂Vt+1∂nt

(18)

Expression (18) reflects that firms choose the number of vacancies in such a way that themarginal recruiting cost per vacancy, κv, is equal to the expected present value of opening

the vacancy βREtλR1t+1

λR1tρ

ft

∂Vt+1∂nt+1

, where ∂Vt∂nt represents the next period marginal value of an

additional job that is defined as

λ f t ≡∂Vt

∂nt−1= αmct

ytnt−1

− wtl1t + (1− σ)βlEtλl1t+1

λl1t

∂V ft+1∂nt

(19)

where the marginal contribution of a new job to profits equals the marginal product net ofthe wage rate, plus the capital value of the new job in t, corrected for the probability thatthe job will continue in the future.

3.3 Trade in the labour market: the labour contractWe assume, as in Boscá et al. (2011), that although households’ types may differ in theirreservation wages, they delegate wage and hour bargaining to a trade union. This tradeunion maximises the aggregate marginal value of employment for workers and distributesemployment according to their shares in the working-age population. Thus, all workersreceive the same wage, work the same number of hours and have the same unemploymentrates.

Following standard practice, the Nash bargaining process maximises the weighted

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product of the parties’ surpluses from employment.

maxwt,l1t

(∑i∈I

τiλihtλi1t

)λw (λ f t

)1−λw= max

wt,l1t(λht)

λw(

λ f t

)1−λw(20)

where λw ∈ [0, 1] reflects workers’ bargaining power. The term λht represents the averageworker’s surplus, whereas the term λ f t is the firm’s surplus. More specifically, λ

iht/λ

i1t de-

note the earning premium (in terms of consumption) of employment over unemploymentfor a type-i household, respectively. Solving the Nash maximisation problem we get theoptimal real wage and hours worked

wtl1t = λw[

mctαyt

nt−1+

κvvt(1− nt−1)

]+(1− λw)

[(φ2(1− l2)1−η

1− η − φ1(1− l1t)1−η

1− η

)∑i∈I

τi

λi1t

]

+(1− λw)(1− σ− ρwt ) ∑ĩ∈ Ĩ

τiEtλĩht+1

λĩ1t+1

(βR

λR1t+1

λR1t− βĩ λ

ĩ1t+1

λĩ1t

)(21)

mctαyt

nt−1l1t= φ1(1− l1t)−η ∑

i∈I

τi

λi1t(22)

3.4 Policy instruments and resources constraintWe assume the existence of a central bank that follows a Taylor’s rule,

1+ rnt =(1+ rnt−1

)rR ((1+ πt)1+rπ (yty)ry

(1+ rn))1−rR

(23)

where y and rn are steady-state levels of output and interest rate, respectively. The para-meter rR captures the extent of interest rate inertia, and rπ and ry represent the weightsgiven to inflation and output objectives.

Revenues and expenditures are made consistent by means of the government in-tertemporal budget constraint:

bpt = gt + trht +(1+ rnt−1)

1+ πtbpt−1 (24)

In order to make the debt to GDP ratio stationary, the following fiscal policy reactionfunction is imposed:

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trht = trht−1 − ψ1

[bt

gdpt−(

bgdp

)]− ψ2

[bt

gdpt− bt−1

gdpt−1

](25)

where ψ1 > 0 captures the speed of adjustment from the current ratio towards the desired

target(

bgdp

). The value of ψ2 > 0 is chosen to ensure a smooth adjustment of current debt

towards its steady-state level.Finally, the aggregate resource constraint guarantees that the sum of demand com-

ponents plus the cost of posting vacancies be equal to aggregate output,

yt = Atk1−αt−1 (nt−1l1t)α = ct + jt

(1+

φ

2

(jt

kt−1

))+ gt + κvvt (26)

3.5 CalibrationThe calibration strategy for our benchmark model consists in using standard values inthe literature for some parameters and matching some relevant data moments for the USeconomy. In Table 1 we present the values of those parameters that allow us to identifythe six different types of households that populate our benchmark economy. Thus, firstwe define the shares of the households’ categories in the total population, assuming thatRicardian households represent 50 percent of the population (τR = 0.5) and the otherfive type of individuals amount each to 10 percent of it (τHNH = τHH = τBL = τBH =τEK = 0.1). The subjective intertemporal discount rate of patient households is βR =0.99, while all other five types are more impatient, presenting a discount factor of 0.95(see Iacoviello, 2005). All individuals that own houses in our economy share the samepreferences parameter on housing, φix = 0.12. This value, as well as the the total stockof housing, X, depend on the value we assign to the ratio of assets of patient households(b

R) to total output (y) in the steady state, that we set following also Iacoviello (2005) such

that the total stock of housing over yearly output is 140 percent. Finally, ϕi is set to onefor BL and BH households, indicating that these individuals take credit using housing ascollateral, and to zero for EK individuals, indicating that they borrow against their futurelabour income. Loan-to-value ratios are set to 0.735 (for BL households) and 0.985 (for BHand EK individuals), values that are slightly lower and higher than those in Iacoviello andNeri (2010).

The remaining set of parameters is shown in Table 2. We take very standard valuesfor the Cobb-Douglas parameter α = 0.7 and the depreciation rate of physical capitalδ = 0.025. The elasticity of matching to vacant posts χ2 = 0.5 comes from Monacelliet al (2010), whereas the exogenous transition rate from employment to unemployment,

15

Table 1. Parameterization of householsType τi β φix ϕ

i mi

R 0.5 0.99 0.12 −− −−HNH 0.1 0.95 0 −− −−HH 0.1 0.95 0.12 −− −−BL 0.1 0.95 0.12 1 0.735BH 0.1 0.95 0.12 1 0.985EK 0.1 0.95 0 0 0.985

σ = 0.15, is taken from Andolfatto (1996) and Cheron and Langot (2004). These authorsalso provide some average steady-state values, such as the probability of a vacant positionbecoming a productive job, which is assumed to be ρ f = 0.9, the fraction of time spentworking, l1 = 1/3, and the fraction of time households spend searching l2 = 1/6. Thelong-run employment ratio is computed to be n = 0.75 as in Choi and Rios-Rull (2008).Furthermore, we assume that equilibrium unemployment is socially-efficient (see Hosios,1990) and, as such, λw = 0.5 is equal to 1− χ2. For the intertemporal labour elasticity ofsubstitution, we consider η = 2 implying that average individual labour supply elasticity(

η−1(

1/l1 − 1))

is equal to 1, the same as in Andolfatto (1996). The adjustment costsparameter for productive investment φ = 5.5, is taken from QUEST II, which considers thesame function as ours for capital installation costs. Parameters affecting the New PhillipsCurve are also standard in the literature. We set a value of θ = 6 for the elasticity offinal goods implying a steady state markup of θθ−1 = 1.2. Hence, the steady state valuefor the marginal cost is obtained as mc = θ−1θ . The probability of not changing prices,ω, is set to 0.75, meaning that prices change every four quarters on average, whereas wetake an intermediate value, ς = 0.4, for inflation indexation. Regarding Taylor’s rule, theparameters rR = 0.73 and rπ = 0.27 are taken from Iacoviello (2005). We choose a value of0, for the parameter measuring the interest rate reaction to output ry.

We normalise both steady-state output (y) and real housing prices (q) to one. Steady-state government expenditure g/y, is set to 17 per cent of output, matching US data. Weobtain the long-run value for vacancies from (19) v = σn/ρ f . Then, we calibrate the ratioof recruiting expenditures to output (κvv/y) to represent 0.5 percentage points of output,as in Cheron and Langot (2004) or Choi and Rios-Rull (2008), and very close to the value of0.44 implied by the calibration of Monacelli et al. (2010). From this ratio we obtain a valueof κv = 0.04 and using the steady-state version of the equation (18), we can solve for thevalue of wages (w). The steady-state value of matching flows in the economy equals theflow of jobs that are lost (σn) and we use the equality (σn = χ1v

χ2 [(1− n) l2]1−χ2 ) to solvefor the scale parameter of the matching function χ1 = 1.56.

The long-run value of total factor productivity, A = 1.50, is calibrated from the

16

Table 2. Parameter valuesPreferences:Labour elasticity, η 2Leisure preference (empl.), φ1 1.59 Leisure preference (unempl.), φ2 1.04Technology:Labour share in production, α 0.7 Depreciation rate of capital, δ 0.025Elasticity of final goods, θ 6 Entry fixed cost, κ f 0.167Frictions:Probability of not changing prices, ω 0.75 Investment adjustment costs, φ 5.5Inflation indexation, ς 0.4Labour market:Matching elasticity, χ2 0.5 Transition rate, σ 0.15Workers’ bargaining power, λw 0.5 Cost of vacancy posting, κv 0.04Scale parameter matching, χ1 1.56Policy:Fiscal reaction parameter, ψ1 0.01 Fiscal reaction parameter, ψ2 0.2Interest rate smoothing, rR 0.73 Interest rate reaction, rπ 0.27Interest rate reaction, ry 0

production function to obtain the steady-state value of Tobin’s q ratio, λl2

λl1. The return

on capital (r) comes from the first-order conditions and the steady-state value for capitalstock (k) from (17). Capital stock, together with the depreciation rate and the adjustmentcost parameter, allows us to calculate the value of gross investment for the steady stateand, using the aggregate constraint, the level of consumption c. The steady-state valueof the nominal interest rate rn, is related to the intertemporal discount rate of Ricardianhouseholds through the steady-state version of the first-order condition for consumption.The value for the lump-sum transfers in the steady state is such that from the governmentbudget constraint the resulting debt-to-output ratio is 93 per cent on annual terms. Inorder to compute κ f , we use the following equality between the source of income andaggregate spending

c+ j(

1+ δφ

2

)+ gt = nwl + rk+ κ f

where κ f =(

1− τb)

dR.Steady-state levels of the marginal utilities of consumption of the different types

of consumers, λR1 , λ

HNH1 , λ

HH1 , λ

BL1 , λ

BH1 , and λ

EK1 come from their respective first-order

conditions. As regards leisure preference parameters in the household utility function,φ1 = 1.59 is calculated from the steady-state version of expression (22). A system of sevenequations implying the steady state of expressions (8) for the six categories of individualsand (21) is solved for φ2, λ

Rh , λ

HNHh , λ

HHh , λ

BLh , λ

BHh , and λ

EKh . The resulting value for φ2 is

17

1.04. Therefore the calibrated values for φ1 and φ2 imply that the value attributed to leisureby an employed worker is well above that attributed by an unemployed worker.

4. Simulation results

4.1 The distribution of net wealth across householdsTable 3 presents steady state levels of consumption, labour income and net wealth (andits distribution between assets and liabilities) across all six household categories in oureconomy. The model assumptions on the labour market warrant the same labour incomeacross all household types (second column of Table 3) so that, as Table 3 shows, there is avery unequal steady state distribution of net wealth but a more egalitarian distribution ofconsumption.

Ricardian consumers own the bulk of assets and most net wealth in the economy,with a ratio of net worth over labour income close to sixty. This is not surprising, as inour model these households are the only ones that save, provide credit funds and own allproductive capital. But net wealth is also very different among those household types thatare subject to some kind of borrowing constraint, depending on the composition of theirbalance sheets. In particular, and focusing on assets and liabilities holdings, we covera wide range of combinations that range from households with assets and no liabilities(our R households or Ricardian consumers) to the Eggerstsson and Krugman householdstype with liabilities and no assets (our EK households), through consumers with neitherassets nor liabilities (our HH or RoT households), or those households that hold assetsand liabilities in different proportions depending on their easiness of access to credit (ourBL and BH or the Iacoviello type households). Also, although our HH consumers sharewith Ricardians a positive net worth, given that both do not hold liabilities, they differin their inability to smooth consumption over time, so that they exhaust all their incomeevery period. Thus, although the wealthy-hand-to-mouth individuals of Kaplan et al.(2014), hold presumably much more total wealth than our HH households, the fact thatthey chose to save most of that wealth in highly illiquid assets, clearly differentiates theirpattern of consumption with respect to Ricardian consumers.

Overall, the picture that arises from Table 3 with respect to the distribution of networth and labour income, summarised in the last column of the table (representing theratio of net wealth over labour income), is in line with empirical estimates by Carrollet al. (2014). These authors use data from the European Household Finance and Con-sumption Survey to show substantial heterogeneity in wealth-to-permanent income ratios,both across and within countries. Regarding the steady state levels of consumption across

18

Table 3. Steady state consumption, labour income and net wealthCons Lab income Net wealth Assets Liabilities Ratio

(1) (2) (3) (4) (5) (3)/(2)R 0.760 0.578 33.104 33.104 0 57.3HNH 0.557 0.578 0 0 0 0HH 0.557 0.578 1.344 1.344 0 2.3BL 0.534 0.578 0.829 3.128 2.299 1.4BH 0.501 0.578 0.085 5.702 5.616 0.15EK 0.551 0.578 -0.569 0 0.569 -0.98

agents, presented in column 1 of the table, not surprisingly Ricardian consumers displaythe highest levels of per capita consumption across households, since they hold most assetsin the economy and have no liabilities.

Both types of hand-to-mouth consumers are the ones who achieve the highest con-sumption levels among the restricted household types in our setting. This is so, becausein the steady state they consume all their labour income and, given that they do not haveliabilities on their balance sheets, they do not need to make any interest rate payments(notice also that in the steady state there is no housing investment, so HH consumers donot spend on housing). Finally, among the household types that participate in the creditmarket per capita consumption levels are inversely related with the amount of liabilitiesthey hold. Thus, EK consumers consume more than borrowers with a low capacity toget credit, and these more than the ones with easy access to loans. In the steady stateindebted households have to distribute their incomes between consumption and debtinterest payments. So, given equal labour incomes, heavily indebted households will reachlower consumption levels.

4.2 Consumption dynamicsIn this subsection, we analyze the role played by household balance-sheet heterogeneityin shaping the short-run response of consumption to a transitory government spendingshock. Figure (1) shows the impulse response functions of output and consumption forthe benchmark parameterization. Upon impact, the response of output to a 1% increaseis government spending is larger than 1%. Therefore, the output multiplier is largerthan 1. The government spending shock generates a crowding-in effect in consumption.This aggregate response of consumption, however, hides a very heterogeneous reaction ofconsumption and net wealth for the different households. The extreme cases are: (i) theconsumption by EK households increases by about 4% upon impact and (ii) the consump-tion by Ricardian households declines upon impact.

Figure (2) shows the response of consumption (with respect to its steady state),labor income, and net worth for each type of household. Consumption is a function

19

2 4 6 8-1

0

1

2

3

4

5Consumption

BL

BH

RH

RNH

EK

O

2 4 6 8-15

-10

-5

0

5Net Wealth

BL

BH

RH

EK

O

2 4 6 8-0.5

0

0.5

1

1.5Output and Consumption

C

Y

Figure 1: Impulse-response to a 1 percent GDP increase in government spending (relative variation)

of labour income and net worth. As the movement of labour income is the same allacross households, the response of net wealth becomes central to understand differentconsumption multipliers.

Ricardian households are affected by the deterioration in their net worth causedby the fall of the price of real state and productive capital. The fact that debt contractsare set in nominal terms reinforces the negative wealth effect as the real value of debt(

bît−11+πt

+dRt−1

1+πt

)is eroded as a consequence of the rise in current inflation πt. Although

labour income increases after the shock, the fall in the value of the large amount of wealthheld by Ricardians consumers dominates, causing a downward adjustment in their spen-ding.

Turning now to the other households categories, their total spending capacity de-pends on current labour income, net wealth and the new credit flow. From (2), totalspending capacity can be rewritten as:

cit + qtxit = b

it︸︷︷︸

new credit flow

+ qtxit−1 − (1+ rnt−1)bit−1

1+ πt︸ ︷︷ ︸net financial wealth

+ wtl1tnt−1︸ ︷︷ ︸++ trhtcurrent labour income

(27)

Net wealth also falls for households BL and BH due basically to the downward movementof the price of housing qt, the only asset available for them. However, this effect is partiallycompensated by a debt deflation induced by the rise in inflation, which affects negatively

the termbit−1

1+πt. The effect on net financial wealth is negative but less pronounced for

20

2 4 6 8-10

-8

-6

-4

-2

0

2

Periods

R

ConsumptionIncomeNet Wealth

2 4 6 8-1

-0.5

0

0.5

1

1.5

2BL

2 4 6 8-1

-0.5

0

0.5

1

1.5

2BH

2 4 6 8-1

-0.5

0

0.5

1

1.5

2HH

2 4 6 8-0.5

0

0.5

1

1.5

2HNH

2 4 6 8-0.5

0

0.5

1

1.5

2

2.5EK

Figure 2: Response of consumption by household type to a 1 percent GDP increasein government spending (per capita absolute variation)

lowly leveraged borrowers. Actually, although BL households are less leveraged than BHhouseholds (bBLt−1 < b

BLt−1), so that the Fisher effect has less punch on real debt for them,

they also demand less housing (xBLt−1 < xBHt−1), implying that the fall in qt has a weaker

effect on lowly indebted households. Considering just the response of labour income andnet financial wealth, we would expect a more muted response of consumption for BHthan for BL households. However, Figure (2) shows the oppositve. The explanation forthis result relies in the new credit flow term, bit, that responds very differently for indebtedconsumers. The fiscal shock increases the expected value of the collateral (Etqt+1xbt ) andreduces the real interest rate in t, (1+r

nt )

1+πet+1, which according to (4) facilitates the access to

credit. This effect is stronger for BH household since they have a higher loan-to-valueratio mb.

For EK households, the term qtxit−1 is absent from the spending restriction. Thus,they do not suffer the drop in the value of assets, but still they take advantage of theerosion of their real outstanding debt which makes net wealth to jump initially. Also,they can easily call for more credit because the increase in the expected tomorrow’s labourincome. As a consequence, these households are the ones with a stronger response ofconsumption on impact.

21

Households HH and HNH do not have access to credit, so they cannot accumulate

debt so the terms bit andbit−1

1+πtdo not appear as consumption drivers in the equation

above. A typical hand-to-mouth consumer, as it has been considered in the literature,does not possess assets, so for HNH households terms qtxHNHt and qtx

HNHt−1 disappear

and consumption replicates the evolution of current income, which stimulate a sizableresponse in the first period. Wealthy hand-to-mouth households (HH) suffer the decline inthe value of their assets with no compensation by the other side of their balance sheet and,hence, their consumption response is the lowest one among the financially constrainedhouseholds.

4.3 Marginal propensities to consumeFrom expression (27), we can obtain the different sources for the marginal propensity toconsume out of labour income (MPC) as,

∆cit∆labit

= 1+∆bit

∆labit+

∆nwit∆labit

−∆(qtxit

)∆labit

(28)

where nwt is the term qtxit−1− (1+ rnt−1)bit−1

1+πtrepresenting the financial net wealth and labit

is the current income. From expression (28), we conclude that the change in consumptionin response to the change in current income induced by the shock will be 1 for a householdwith no access to fresh credit, no net worth and no houses (our HNH households). How-ever, for the other categories of households the marginal propensity to consume dependson the induced effect that the change in labour income produces on new debt, net wealthand housing investment. Table 4 quantifies the importance of the sources behind the MPCfor each type of household.

A first conclusion from Table 4 is the large heterogeneity across households in theconsumption expenditure response to the increase in labour income induced by the shock.We have ordered households according to their initial wealth, so that comparing the firstand the last column we see a clear negative relationship between the marginal propensityto consume, out of current labour income, and the wealth of the household. Householdswith less wealth respond more strongly to an increase in (government spending induced)income, a result which is consistent with some recent empirical linking wealth and con-sumption (Carroll et al., 2014; Kaplan et al., 2014; Angrisani et al, 2015). The centralcolumns actually corroborate that balance sheets are pivotal in the distinct reaction ofhousehold consumption, an idea that has already been documented empirically by Parkeret al, 2013; Agarwal and Qian, 2014; Acconcia et al., 2015; Sahm et al., 2015; Surico andTrezzi, 2015.

22

Table 4. Sources of the marginal propensities to consume out of current income

∆cit∆labit

∆nwit∆labit

∆bit∆labit

∆(qtxit)∆labit

NW − SSR -0.1471 -2.2722 -1.2680 -3.5491 33.104HH 0.0540 -0.2867 – 0.6593 1.344BL 0.0892 -0.3756 1.4106 1.9458 0.829BH 0.3336 -0.5039 5.8540 6.0165 0.085HNH 1.0000 – – – 0EK 1.1556 0.0722 0.0837 – -0.569

In our model, the negative response of Ricardian households’ consumption is mostlydriven by the drop in net worth, whereas the intense fall in housing investment preventsconsumption spending to go down by more. On the other extreme the net worth multiplierto labour income is not large for EK consumers, but in this case its effect on consumptionis reinforced by the additional credit that the increase in expected income makes available.Fresh credit is the main driver explaining the differences between BL and BH consumers’spending decisions. Also, a comparison between the two categories of hand-to-mouthhouseholds (RoTs, HNH, and wealthy hand-to-mouth, HH) makes clear the two channelspulling down the MPC of HH households: declining wealth and, more importantly, diver-sion of spending towards additional housing.

4.4 Fiscal multipliers

The distinctive reaction of household consumption induced by the government spendinggenerates a clear correlation pattern linking the composition of the population and theaggregate output multiplier. In Table 5, we calculate the output and consumption im-pact multiplier to a fiscal shock under different scenarios regarding the distribution ofhouseholds among the six types considered. In the first row we assume an economypopulated entirely by a representative Ricardian consumer. The government spending in-crease triggers the standard crowding out effect in consumption and an output multiplierlower than one. In the following rows we keep the share of Ricardian in a 50 percent anddistribute the remaining 50 percent equally among the different types of non Ricardianconsumers in a sequential way. For example, the second row population is split on equalproportions between Ricardian and HH households, whilst in the last row the differentclass of non Ricardian households represent each a 10 percent of the total population. Theparticular sequence we have chosen for this exercise implies a continuos change in thesize of the multiplier as we are adding new households categories to the economy. Thisexercise offers a rough indicator of what we miss in terms of the effect of fiscal policy bynot providing enough detail on the households’ side. Overall, the output multiplier to agovernment spending shock augments by more than 50 percent if we compare the result

23

Table 5. Fiscal multipliers∆yt∆gt

∆ct∆gt

R 0.805 -0.205R+HH 0.851 -0.147R+HH+BL 0.874 -0.099R+HH+BL+BH 0.978 0.044R+HH+BL+BH+RNH 1.078 0.166R+HH+BL+BH+RNH+EK 1.224 0.344

of a representative Ricardian household economy to that from an economy with a sensibledistribution of a wide variety of household categories.

4.5 Wealth inequality and the fiscal multiplierWe can also derive from our model some implications regarding the relationship betweenwealth inequality and the fiscal multiplier. This relates to the work of Carroll et al. (2014)who postulate a positive association between wealth inequality and the aggregate MPC.We explore this issue in Figure (3) plotting the impact output multiplier against a Ginicoefficient representing different scenarios about the distribution of households’ categoriesin total population. In particular, we start by representing the Gini coefficient and theaggregate output multiplier corresponding to the benchmark calibration (the Bench pointin the figure) and proceed as follows: we increase τHH for HH households from 0.1 to0.2 and reduce correspondingly τR for the Ricardians from 0.5 to 0.4, and then computefor this new distribution the Gini coefficient and the output multiplier (point HH in theFigure (3)). We repeat the same exercise for the rest of households in our model.

The results establish a clear association between the output multiplier and wealthdispersion. Fiscal policy in a more unequal economy would display larger effects in termsof output, as the positive slope in regression line indicates. This relationship is no morethan the reflection of the heterogeneity in the MPC that we have explained in Table 4.

4.6 Welfare effectsThe heterogeneity in our model allows us to compare the effect of a government spen-ding change on the consumption response across households categories. But households’utility also depends on their real state holdings. To assess the distributional consequencesof the policy in a more global way we compute its effect on household’s welfare. Wedefine welfare Vi as the discounted sum of a household i period utility, conditional onthe economy being at the steady state in period 0 (common to all the experiments) and

24

Figure 3: Simulated fical multiplier for different distributions of wealth

remaining constant throughout

Vi =∞

∑t=0(βi)t

ln(cit)+ φix ln(xit)+ nt−1φ1 (1−l1t)1−η1−η+(1− nt−1)φ2

(1−l2)1−η1−η

,

where i is the index referring to household’s type. Now, we define Vi,s as the welfare of ahousehold of type i under a shock, conditional on the state of the economy in period t = 0and taking into account the reaction of the variables before returning again to their initialsteady state

Vi,s =∞

∑t=0(βi)t

ln(ci,st )+ φix ln(xi,st )+ nst−1φ1 (1−ls1t)1−η1−η+(1− nst−1)φ2

(1−l2)1−η1−η

, (29)

where ci,st , xi,st , n

st−1 and l

s1t denote consumption, housing, employment rate and hours per

worker, respectively, under a fiscal shock. We calculate the welfare cost ∆i associated witha fiscal measure as the fraction of steady state consumption that a household would be

25

Figure 4: Welfare effects by household category

willing to give up in order to be as well off after the fiscal shock. That is,

Vi,s =∞

∑t=0(βi)t

ln [cit (1− ∆i)]+ φix ln(xit)+ nt−1φ1 (1−l1t)1−η1−η+(1− nt−1)φ2

(1−l2)1−η1−η

. (30)Thus, from (29) and (30):

∆i = 1− exp{(

Vi,s −Vi) (

1− βi)} (31)

where a negative value for ∆ implies a welfare gain.Figure (4) shows that the effect in terms of welfare derived from the increase in

government spending in our model is actually very heterogeneous among households.There is a drop in aggregate welfare that affects basically Ricardians and borrowers withhouse tenure (much more to BH households than to BL households). Wealthy and poorhand-to-mouth (HH and HNH households) and Eggertsson-Krugman type households,on the contrary, improve slightly as a consequence of the measure. The main messagearising from this result is that, besides targeting a short run effect on output, standardfiscal policy, even under the assumption that it does not affect preferences, can also beseen as generating a non negligible distributional response. The way in which householdspecific welfare is affected depends very much on her position in the financial market,which determines to a great extent their balance sheets. It is also important to qualify the

26

effects of fiscal consolidations given that our results suggest that they can benefit the mostthe wealthiest part of the population.

5. Looking at the dataGiven the relative role played by household heterogeneity in quantifying fiscal effects,we turn to micro data in oder to estimate the fraction of U.S. households belonging toeach of the categories we establish in our theoretical model. The PSID contains detailedinformation on income, consumption, and wealth at the household level starting fromthe 1999 wave. The survey is conducted in a biannual basis. Our sample has 55, 105observations over the pooled years 1999− 2013. Following Kaplan, Violante and Weidner(2014), we classify households in terms of their wealth. Let lnwit be the net wealth ofhousehold i defined as the value of checking accounts, saving accounts, money marketfunds, certificates of deposits, savings bonds, Treasury Bills, other IRAs; the value ofprivate annuities or IRAs; the value of other investment in trusts or estates, bond funds,life insurance policies, special collections; the net value of farm or business assets; the netvalue of real estate other than main home; the net value of vehicles; and the value of debtsother than mortgages. Therefore, our measure of wealth abstracts from real estate assetsconsidered as the main home and mortgage debt. Let incit be the income of household idefined as salaries and other compensation plus private and government transfers.

Table 6. Identification criterion for PSID dataHousehold Wealth Homeowner High LTV Low LTV No Mortgage

R lnwit ≥ 0.5 ∗ incit ? ? ? ?BH lnwit ≤ 0 X X x xBL lnwit ≤ 0 X x X xEK lnwit ≤ 0 x x x xHH 0 < lnwit < 0.5 ∗ incit X x x X

HNH 0 < lnwit < 0.5 ∗ incit x x x xNOTES: incit stands for wealth and lnw

it for income.

Our identification strategy is described in Table 6. Ricardian households are thosewhose average liquid wealth balances are positive and equal to or more than half of theirincome. Following Kaplan, Violante and Weidner (2014), half of the earnings per pay-period is due to the assumption that resources are consumed at a constant rate. Wedo not impose any additional constraint to identify Ricardian households, that is, theymay or may not be homeowners and they may or may not have a mortgage. Hand-to-mouth consumers, both poor and wealthy, are assumed to have positive wealth balances

27

Table 7. Sample Weights (in %) in PSID1999 2001 2003 2005 2007 2009 2011 2013

R 50 50 49 48 48 43 42 41BH 5 6 7 7 7 8 7 7BL 3 3 3 3 3 3 3 3EK 17 17 17 18 19 23 24 24HH 5 4 5 4 4 3 4 4

HNH 20 20 19 19 20 20 20 21Total obs 5,836 6,134 6,504 6,677 7,037 7,342 7,661 7,914

but these are less than half their earnings. Wealthy hand-to-mouth households, HH,are homeowners, therefore they hold illiquid wealth, but do not have mortgage debtoutstanding. Poor hand-to-mouth households, HNH, are restricted to not be homeownersnor having mortgage debt outstanding. The remaining three categories of households,borrowers with high loan-to-value (LTV hereafter) ratio, BH, borrowers with low LTVratio, BL, and Eggerston-Krugman households, EK, are assumed to hold negative liquidwealth balances. While EK households do not hold real estate nor mortgage debt, BHand BL households are homeowners and have mortgage debt outstanding. We classify ahousehold as BH if her LTV ratio is equal to or larger than the average LTV in the sampleperiod.

We report the sample weights for each type of households in Table 7. Overall, thedistribution of household types is fairly stable with a notable exception: over time, thefraction of Ricardian households in the U.S. economy has declined from 50% in 1999 to41% in 2013, with the proportion of EK households increasing in parallel from 17% to24%. We feed the model with the estimated weights from the PSID data and compute thefiscal multiplier. Table 8 reports the evolution of the multiplier. In the years prior to theGreat Recession, the fiscal multiplier remains fairly stable. The fiscal multiplier increasessignificantly whenever the relative weight of Ricardian households and EK householdschanges. The response of consumption by EK households to a fiscal shock was the largestin our baseline calibration, while the response of Ricardian households was negative.Therefore, it is not surprising that the size of the fiscal multiplier increases when the shareof Ricardians drops or the share of EK households increases. Overall, between 2005 and2013 the multiplier grows more than 30 per cent.

6. Concluding remarksWe have introduced an otherwise standard New Keynesian DSGE augmented to allowfor some degree of heterogeneity in the population. More specifically we focus on thepresence of individuals with different connections with the financial market, that generateheterogeneity in their balance sheet composition. To facilitate the theoretical analysis of

28

Table 8. The evolution of the fiscal multipliers1999 2001 2003 2005 2007 2009 2011 2013

∆yt∆gt 1.69 1.71 1.70 1.79 1.85 2.22 2.26 2.37∆ct∆gt 0.90 0.93 0.92 1.03 1.11 1.57 1.61 1.75

the effect of wealth on consumption, we abstract from differences in labor income. Thecategories of households that we consider match some of the most popular ones in theliterature along with some others that have attracted much attention recently: Ricardians,rule-of-thumbers, mortgagors with high or low capacity of borrowing, hand-to-moutherswith illiquid wealth (real state) but no liabilities, and Eggertsson-Krugman consumers,who can borrow but have not real state to collateralize their debt that has to be guaranteedwith expected future income.

We have studied several issues related to the economy’s response to fiscal shocksunder different assumptions concerning the structure of individual balance sheets in theeconomy. Then we have taken a closer look at the some of the most salient features ofthis structure for the US economy, using the Panel Study of Income Dynamics (PSID). Weconclude that while the distribution of households is fairly stable for most of the types,the share of Ricardians significantly declines during the Great Recession and its aftermathwhile the share of Eggertsson-Krugman consumers increases. Given that the consumptionresponse to a fiscal shock by Eggertsson-Krugman consumers is the largest, our estimatessuggest that the fiscal multiplier grows more than 30% between 2005 and 2013.

We show that matching stylised facts regarding households finances is key to un-derstand the reaction of economies to fiscal shocks. There are a number of relevant con-clusions that can be drawn from our analysis. First, the marginal propensity to consumeis negatively related with the net worth. Second, the size of the fiscal effect is positivelycorrelated with ex ante wealth inequality. Third, changing the composition of the popu-lation importantly affects the aggregate marginal propensity to consume and the outputmultiplier. Fourth, fiscal shocks have non negligible distributional effects that are reflectednot only in size but also in the sign of welfare changes for different segments of thepopulation.

29

ReferencesAcconcia A., G. Corsetti and S. Simonelli (2015): "The Consumption Response to Liquidity-Enhancing

Transfers: Evidence from Italian Quakes", CSEF Working Paper No. 396.

Agarwal S. and W. Qian (2014): "Consumption and Debt Response to Unanticipated Income Shocks:Evidence from a Natural Experiment in Singapore", American Economic Review, 104(12), 4205-4230.

Angrisani, M., Hurd M.D. and S. Rohwedder (2015): "The Effect of Housing and Stock Wealth Losseson Spending in the Great Recession", RAND Working Paper WR-1101.

Anderson, E., Inoue A., and B. Rossi (2015): "Heterogeneous Consumers and Fiscal Policy Shocks",Mimeo.

Andolfatto, D. (1996): "Business Cycles and Labor-Market Search", American Economic Review, 86 (1),112–132.

Andrés, J., Boscá, J. E. and J. Ferri (2015): "Household Leverage and Fiscal Multipliers", Economica,82, 1048-1081.

Andrés, J., Boscá, J. E. and J. Ferri (2016): "Instruments, rules, and household debt: the effects offiscal policy", Oxford Economic Papers, doi: 10.1093/oep/gpv088.

Boscá, J.E., Doménech, R. and J. Ferri (2011): "Search, Nash Bargaining and Rule-of-Thumb Con-sumers", European Economic Review, 55, 927-942.

Calvo, G. (1983): "Staggered Pricing in a Utility Maximizing Framework", Journal of Monetary Eco-nomics, 12, 383-96.

Carroll, C. D., Slacalek, J. and K. Tokuoka (2014): "The Distribution of Wealth and the MPC: Im-plications of New European Data", American Economic Review: Papers & Proceedings, 104(5),107-111.

Chéron, A. and F. Langot (2004): "Labor Market Search and Real Business Cycles: Reconciling NashBargaining with the Real Wage Dynamics", Review of Economic Dynamics, 7, 476-493.

Choi, S. and J. V. Rios-Rull (2009): "Understanding the Dynamics of Labor Share: The Role of Non-competitive Factor Prices", Annales d’Economie et de Statistique, 95/96, 251-277.

Cloyne, J. and P. Surico (2014): "Household Debt and the Dynamic Effects of Income Tax Changes",Bank of England Working Paper No. 491, Bank of England, London.

Eggertsson, G. B. and P. Krugman (2012): "Debt, Deleveraging, and the Liquidity-Trap: A Fisher,Minsky, Koo Approach", Quarterly Journal of Economics, 127, 1469–1513.

Galí, J., Lopez-Salido, J. D. and J. Vallés (2007): "Understanding the Effects of Government Spendingon Consumption", Journal of the European Economic Association, 5(1), 227-270.

Hosios, A. J. (1990): “On the Efficiency of Matching and related Models of Search Unemployment”.Review of Economic Studies, 57, 279-98.

Iacoviello, M. (2005): "House Prices, Borrowing Constraints, and Monetary Policy in the BusinessCycle", American Economic Review, 95, 739-764.

Iacoviello, M. and S. Neri (2010): "Housing Market Spillovers: Evidence from an Estimated DSGEModel", American Economic Journal: Macroeconomics, 2, 125-64.

Jaramillo, L. and A. Chailloux (2015): "It’s Not All Fiscal: Effects of Income, Fiscal Policy, and Wealth

30

on Private Consumption", IMF Working Paper WP/15/112.

Kaplan, G., Violante, G. L. and J. Weidner (2014): "The Wealthy Hand-to-Mouth", Brookings Papers onEconomic Activity, Spring, 77-138.

Kiyotaki, N. and J. Moore (1997): "Credit Cycles", Journal of Political Economy, 105, 211-248.

Monacelli, T., Perotti, R. and A. Trigari (2010): "Unemployment Fiscal Multipliers", Journal of Mone-tary Economics, 57, 531-553.

Parker, J. A., Souleles, N. S., Johnson, D. S. and R. McClelland (2013): "Consumer Spending and theEconomic Stimulus Payments of 2008", American Economic Review, 103(6), 2530-2553.

Ramey, V. A. (2011): "Can government purchases stimulate the economy?", Journal of Economic Lite-rature, 49(3), 673-685.

Sahm, C. R., Shapiro, M. D. and J. Slemrod (2015): "Balance-sheet households and fiscal stimulus:lessons from the payroll tax cut and its expiration", NBER Working Paper 21220.

Spilimbergo, A., Symansky, S. and M. Shindler (2009): "Fiscal Multipliers", IMF Staff Position Note,SPN/09/11.

Surico, P. and R. Trezzi (2015): "Consumer Spending and Property Taxes", Finance and EconomicsDiscussion Series 2015-057. Washington: Board of Governors of the Federal Reserve System.

31

Appendix 1: The complete model

A.1 Households’ problems equations

First order conditions:

λi1t =1cit

i = {R, HNH, HH, BL, BH, EK} (1.1)

λR2tλR1t

= βREtλR1t+1

λR1t

{rt+1 + δ+

φ

2jR2t+1kR2t

+λR2t+1

λR1t+1(1− δ)

}(1.2)

λR2t = λR1t

[1+ φ

(jRt

kRt−1

)](1.3)

λR1t = βREtλR1t+1

{1+ rnt

1+ πt+1

}(1.4)

λi1t = βiEtλi1t+1

(1+ rnt

1+ πt+1

)+ µit (1+ r

nt ) i = {BL, BH, EK} (1.5)

λR1tqt =φRxxRt+ βREtqt+1λR1t+1 (1.6)

λi1tqt =φixxit+ µitm

iEtqt+1(1+ πt+1) + βiEtqt+1λi1t+1 i = {BL, BH} (1.7)

λHH1t qt =φHHxxHHt

+ βHHEtqt+1λHH1t+1 (1.8)

λiht = λi1twtl1t +

(φ1(1− l1t)1−η

1− η − φ2(1− l2)1−η

1− η

)(1.9)

+(1− σ− ρwt )βiEtλiht+1 i = {R, HNH, HH, BL, BH, EK}

32

Constraints:

cit+ qt(

xit − xit−1)= −(1+ rnt−1)

(bit−1

1+ πt

)+wtnit−1l1+ b

it+ trht i = {BL, BH, EK}

(1.10)

cHNHt = wtnHNHt−1 l1 + trht (1.11)

cHHt + qt(

xHHt − xHHt−1)= wtnHHt−1 l1 + trht (1.12)

bit ≤ miEt

(qt+1 (1+ πt+1) xit

1+ rnt

)i = {BL, BH} (1.13)

bEKt ≤[

mEKEt

((1+ πt+1)wt+1nEKt l1t+1

1+ rnt

)](1.14)

kRt = jRt + (1− δ)kRt−1 (1.15)

nit = (1− σ)nit−1 + ρwt (1− nit−1) (1.16)= (1− σ)nit−1 + χ1v

χ2t [(1− nt−1) l2]

1−χ2 i = {R, HNH, HH, BL, BH, EK}

A.2 Aggregation

ct = τRcRt + τHNHcHNHt + τ

HHcHHt + τBLcBLt + τ

BHcBHt + τEKcEKt (1.17)

nt = τRnRt + τHNHnHNHt + τ

HHnHHt + τBLnBLt + τ

BHnBHt + τEKnEKt (1.18)

τBLbBLt + τBHbBHt + τ

EKbEKt + τRbRt = 0 (1.19)

33

τHHxHHt + τBLxBLt + τ

BHxBHt + τRxRt = X (1.20)

kt = τRkRt (1.21)

jt = τR jRt (1.22)

dt = −τRdRt (1.23)

A.3 Firms

πt = γf Etπt+1 + $m̂ct + γbπt−1 (1.24)

mct = mc(1+ m̂ct) (1.25)

rt = (1− α)mctyt

kt−1(1.26)

yt = Ak1−αt−1 (nt−1l1t)α (1.27)

λ f t = αmctyt

nt−1− wtl1t + (1− σ)βREt

λR1t+1

λR1tλ f t+1 (1.28)

κvvt = ρft vtβ

REtλR1t+1

λR1tλ f t+1

= χ1vχ2t [(1− nt−1) l2]

1−χ2 βREtλR1t+1

λR1tλ f t+1 (1.29)

34

ρft =

χ1vχ2t [(1− nt−1) l2]

1−χ2

vt(1.30)

A.4 Bargaining in the labour market

wtl1t = λw(

αmctyt

nt−1+

κvvt(1− nt−1)

)+(1− λw)

[(τR

λR1t+

τHNH

λHNH1t+

τHH

λHH1t+

τBL

λBL1t+

τBH

λBH1t+

τEK

λEK1t

)(φ2(1− l2)1−η

1− η − φ1(1− l1t)1−η

1− η

)]

+(1− λw)(1− σ− ρwt )τHNHEtλHNHht+1

λHNH1t+1

(βR

λR1t+1

λR1t− βHNH λ

HNH1t+1

λHNH1t

)

+(1− λw)(1− σ− ρwt )τHHEtλHHht+1

λHH1t+1

(βR

λR1t+1

λR1t− βHH λ

HH1t+1

λHH1t

)

+(1− λw)(1− σ− ρwt )τBLEtλBLht+1

λBL1t+1

(βR

λR1t+1

λR1t− βBL λ

BL1t+1

λBL1t

)

+(1− λw)(1− σ− ρwt )τBHEtλBHht+1

λBH1t+1

(βR

λR1t+1

λR1t− βBH λ

BH1t+1

λBH1t

)

+(1− λw)(1− σ− ρwt )τEKEtλEKht+1

λEK1t+1

(βR

λR1t+1

λR1t− βEK λ

EK1t+1

λEK1t

)(1.31)

αmctyt

nt−1l1,t=

[τR

λR1t+

τHNH

λHNH1t+

τHH

λHH1t+

τBL

λBL1t+

τBH

λBH1t+

τEK

λEK1t

]φ1(1− l1t)−η (1.31)

ρwt =χ1v

χ2t [(1− nt−1) l2]

1−χ2

(1− nt−1)

A.5 Policy instruments and resources constraint

yt = ct + jt

(1+

φ

2

(jt

kt−1

))+ gt + κvvt (1.32)

35

1+ rnt =(1+ rnt−1

)rR ((1+ πt)1+rπ (yty)ry

(1+ rn))1−rR

(1.33)

dt = gt + trht +(1+ rnt−1)

1+ πtdt−1 (1.34)

trht = trht−1 − ψ1

[btyt−(

by

)]− ψ2

[btyt− bt−1

yt−1

](1.35)

36

Appendix 2: Income and wealth in the PSID

INCOME

Income of a household contains the following categories:

• Salary• Dividends• Rent payments received• Worker comp• Trust fund income• Financial support from relatives• Financial support from non-relatives• Child Support Recieved• Alimony Recieved• Supplemental security income, temp assistance for needy families (state program),

Other welfare

• Pensions/annuity• Lump Sum Payments∗ Inheritances, itemized deductions

• Financial Support given to others

WEALTH

Variable Wealth1 in the PSID includes

• Net value of farm or business assets• Value of checking accounts, saving accounts, money market funds, certificates of de-

posit, savings bonds, Treasury Bills, other IRAS.

• Value of debts other than mortgages (credit cards, student loans, medical or legal bills,personal loans).

• Net value of real estate other than main home.• Value of shares of stock in publicly held corps, mutual funds or investment trusts.• Net value of vehicle or other assets ’on wheels’.• Value of other investment in trusts or estates, bond funds,