Housework and fiscal expansions∗

Stefano Gnocchi†

Daniela Hauser‡

Evi Pappa§

November 2012

Abstract

We argue that explicitly modelling a home production sector as an alternativeoption to market work is crucial for understanding the propagation of exogenouschanges in public spending to macroeconomic variables. In fact, the substitutabil-ity between market and home produced goods is an important driver of the laborsupply response to government expenditure shocks and, as a consequence, is keyto explain the magnitude of fiscal multipliers, as well as the behavior of privatemarket consumption after a fiscal expansion. We build an otherwise standardNew-Keynesian model that encompasses a home production sector and we useboth micro- and macroeconomic evidence to validate our predictions. If theelasticity of substitution between home and market goods is chosen in line withthe microeconomic estimates our model delivers impulse response functions togovernment expenditure shocks that match the VAR evidence.

JEL Codes: E24, E32, E52Keywords: Government expenditure shocks, home production

∗Evi Pappa and Stefano Gnocchi gratefully acknowledge financial support from the Spanish Min-istry of Education and Science through grant ECO2009-09847, the support of the Barcelona GSEResearch Network and of the Government of Catalonia.

†Department of Economics and Economic History, Universitat Autonoma de Barcelona andBarcelona GSE. Contact: stefano.gnocchi@uab.cat

‡Department of Economics and Economic History, Universitat Autonoma de Barcelona. Contact:daniela.hauser@uab.cat

§European University Institute, Universitat Autonoma de Barcelona and CEPR. Contact:evi.pappa@eui.eu

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1 Introduction

The recent financial crisis demanded daring initiatives in order to boost aggregateeconomic activity. Since conventional monetary policy has been limited by thezero bound, increasing political interest has turned to fiscal policy as a possibleremedy. While fiscal policy for some years has been downplayed, it faced a re-naissance with high expectations as to what it can accomplish. In many countriesthere has been a vivid debate on the need for a fiscal stimulus, its magnitude, andits composition, and several countries have undertaken fiscal stimulus packages.Calls for expansionary fiscal policy have been issued by many, including the G20summit and the EU Commission.

The renewed interest for fiscal policy begged the questions of what role gov-ernment expenditure can play in boosting aggregate demand. In the traditionalliterature on the effects of fiscal policy, the conclusions on its efficacy typicallydepend on the identification restrictions used to extract fiscal shocks from thedata1. However, Perotti (2008) and Caldara and Kamps (2008) reconcile the evi-dence and conclude that shocks to government spending generate demand effectsthat typically increase consumption and output. The estimated size of outputmultipliers varies in the (0.4, 1.5) interval, but many recent contributions2 arguethat multipliers can be even larger during recessions, reconfirming the seminalintuition by Keynes.

On the theoretical side, standard theories of business cycles have a hard timeto generate output multipliers that quantitatively match the estimates, becausethe negative wealth effect following a fiscal stimulus detains the expansion ofaggregate economic activity. As emphasized by Hall (2009), two key features areneeded for a model to deliver sizeable multipliers: a decline in price mark-ups oc-curring when production rises and a sufficiently elastic response of employment.The former mechanism couples the output expansion with a redistribution ofprofits from producers to households in the form of higher real wages that makesit particularly attractive to work and to consume when the government is spend-ing. If labor supply is sufficiently elastic, the surge in employment is strongenough to generate a large output multiplier as well as an increase in consump-tion.

In this paper, following the argument by Hall (2009), we propose a modelof housework and nominal rigidities where the substitutability between home-produced and market goods is an important driver of labor supply elasticity.Our model can account for the observed output multiplier, if the elasticity of

1Blanchard and Perotti (2002), Ramey (2011), Ramey and Shapiro (1998), Burnside, Eichenbaumand Fisher (2004), Erceg and Linde (2012), Mountford and Uhlig (2002), Canova and Pappa (2006),Pappa (2009) and Uhlig (2010) are a representative, though not exhaustive, sample.

2In particular, recent empirical work incorporates the notion that fiscal policy might have non-linear effects depending on whether: the economy is in a recession or in an expansion (Auerbach andGorodnichenko (2012)); unemployment rates are high or low (Barro and Redlick (2011)); the nominalinterest rate has reached or not the zero lower bound (Christiano, Eichenbaum and Rebelo (2011),Erceg and Linde (2010) and Canova and Pappa (2011)).

2

substitution between home and market goods is calibrated in line with the avail-able microeconomic evidence. Our emphasis on home production is motivatedby recent theoretical and empirical contributions pointing to the great deal ofsubstitutability between housework and market work. The American Time UseSurvey confirms indeed that households spend between 11 and 18 percent of theirtime endowment in home related activities, producing services that are not ex-changed on the market. Also, purchases of consumer durable goods and residen-tial investment exceed purchases of producer durable goods and non-residentialinvestment in the United Sates. Aguiar and Hurst (2005, 2007) document thatover the life-cycle people substitute market work with housework. In fact, retireesrely on home production to compensate for the fall in the value of market pur-chases typically following the exit from the labor force. In the same vein, Aguiar,Hurst and Karabarbounis (2012) document substitutability between houseworkand market work over the business cycle, by estimating that home productionabsorbs about 30 percent of foregone market work. Benhabib, Rogerson andWright (1991) and Greenwood and Hercowitz (1991) were the first to claim thathome production is an empirically significant entity and its inclusion in an oth-erwise standard business cycle model is helpful to account for macroeconomicdata. McGrattan, Rogerson and Wright (1997) first introduced housework in areal business cycle model with fiscal policy. Karabarbounis (2012) shows that amodel with home production can account for cyclical fluctuations of the laborwedge. The novelty of our paper is to show that substitutability between marketand non-market activity, coupled with a fall of price mark-ups, provides the keyfeatures advocated by Hall (2009) to reconcile the theory with the conditionalevidence on fiscal expansions.

Our findings contribute to the literature in several respects. First, we presenta channel for generating increases in private consumption and significant outputeffects after a government spending shock. In particular, we focus on how house-work affects the dynamics in an otherwise standard New-Keynesian model andwe determine the structural parameters that are crucial in matching the modelwith the empirical predictions. In line with previous theoretical contributions3,price stickiness, and some, though small, capital adjustment costs are crucial forour channel to be operative. Under flexible prices, a positive government expen-diture shock only generates, through a negative wealth effect, an increase of thelabor supply and a consequent fall in the real wage. In other words, householdsdo not work more because they find it more attractive, but simply because theywant to partially smooth the reduction in consumption that is necessary to fi-nance the increased tax burden. As a consequence, irrespective of the elasticityof substitution between home and market goods, labor supply is never elasticenough to boost market consumption and to match the observed size of the out-put multiplier. Similarly, without adjustment costs to capital, households smooththe shock by reducing investment, a fact that not only detains the increase of

3On the role of nominal rigidities and non-separability between consumption and leisure see Wood-ford (2011), Hall (2009) and Basu and Kimball (2002).

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aggregate demand, but that also depresses future labor market productivity andthe real wage. Only when both of these features are present, one can make thelabor supply elastic enough to generate an increase of market consumption byincluding in the model a home production sector. Also, the way monetary andfiscal policy interact is key. In line with the case made by Canova and Pappa(2011), Christiano et al. (2011) and Erceg and Linde (2010), if the monetaryauthority reacts too strongly to inflation, after a government expenditure shockthe real interest rate increases so as to make consumption fall. Hence, in order tomatch the VAR evidence we include an interest rate smoother in the monetarypolicy rule that allows us both to reproduce the estimated muted response of thenominal interest rate and to generate a sizeable output multiplier.

Second, and more broadly, we see our result as pointing to the importanceof modelling housework as an alternative option to market work, if one wantsto rely on business cycle models to predict the effects of policy. In fact, thesubstitutability between home and market goods interacts with nominal andreal frictions in driving households’ incentive to participate in the labor market.Since fiscal and monetary policies affect the relevance of frictions at business cyclefrequencies, models neglecting the home sector may lead to incorrect conclusionsabout the evaluation of those policies. In our particular case, model abstractingfrom housework understate the elasticity of labor supply and this fact is partiallyresponsible for the failure of baseline business cycle models to account for theVAR evidence on fiscal shocks4.

Finally, our results are relevant for the literature suggesting consumption andhours’ complementarities in the utility function as a way of generating increasesin consumption after a fiscal expansion. For instance, see Monacelli and Per-otti (2008), Hall (2009), Christiano et al. (2011) and Nakamura and Steinsson(2011). The intuition behind their mechanism is simple: if consumption andhours worked are complements, the negative wealth effect originating from theincrease in government’s absorption should result in a positive consumption re-sponse and, as a result, in a higher output multiplier. Our home productionmodel with high substitutability between market and home consumption nests areduced-form model without home production, but in which market consumptionand market work are strong complements in the utility function. Yet, explicitlymodelling housework offers the noticeable advantage of tying the importance ofthe transmission channel to the data by relying on the abundant microeconomicevidence.

Our goal is not to give a general theory of the effects of fiscal policy onmacroeconomic variables, neither to offer an exhaustive explanation of the VARevidence. Rather, we view our mechanism as complementary to the many alter-native explanations suggested by the literature: Woodford (2011) considers thatmaking consumption respond to current income, according to the old Keynesiantradition, generates sizeable demand effects and output multipliers; along this

4See Bruckner and Pappa (2010) and Campolmi and Gnocchi (2011) for a similar argument appliedto the effects of monetary and fiscal policy on unemployment.

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line, Galı, Lopez-Salido and Valles (2007) were the first to model rule-of-thumbconsumers in order to break the link between the real interest rate and privateconsumption, allowing thus the latter to react to current income. Corsetti, Meierand Muller (2009) explain a positive private consumption response with spend-ing reversals: current higher government expenditure implies permanently lowerfuture expenditure, so as to keep constant long-run government debt. In theirsetup, an increase in government spending implies higher consumption both inthe future and, through consumption smoothing, at the time of the shock. Fi-nally, Morten, Schmitt-Grohe and Uribe (2012) focus on deep habits. In thiscase, an increase in domestic aggregate demand provides an incentive for firmsto lower markups shifting the labor demand curve outwards and increasing realwages. The rise in wages induces households to substitute consumption for leisureand this substitution effect can be strong enough to offset the negative wealtheffect and result in an equilibrium increase in private consumption.

The rest of the paper is organized as follows: Section 2 presents the model andSection 3 its baseline parametrization. Section 4 describes the dynamics of themodel after a fiscal expansion, examines the sensitivity of the results to changesin key parameters and compares the model with the VAR evidence. Section 5concludes.

2 The Model

We consider an otherwise standard New-Keynesian model, where householdshave access to a technology that combines time and capital to produce non-tradable home goods. As in Benhabib et al. (1991) and McGrattan et al. (1997)5,households enjoy leisure and consumption of a composite index that aggregatesmarket and home goods according to a constant elasticity of substitution. Thecentral bank is in charge of setting the nominal interest rate. The fiscal authoritybuys market goods and finances expenditures by levying a mix of lump-sum anddistortive taxes. In what follows we define the economic environment and agents’optimality conditions. We summarize the full system of equations defining thecompetitive equilibrium in Appendix A.

2.1 Policy makers

In the economy there are infinitely many varieties of final market consumptiongoods indexed by i ∈ [0, 1]. The fiscal authority buys each market variety Gt(i)at its market price Pt(i). We define aggregate government expenditure, Gt, as acomposite index

Gt =[∫ 1

0(Gt(i))

ε−1ε di

] εε−1

(2.1)

5Differently from Greenwood and Hercowitz (1991) we allow households to substitute leisure withtime spent working either at home or on the market.

5

where ε > 1 is the constant elasticity of substitution across varieties and log(Gt)exogenously evolves according to an AR(1) process, with mean equal to someparameter log(G). We assume that the government chooses the quantities Gt(i)in order to minimize the total expenditure

∫ 10 Pt(i)Gt(i) di, given Gt. Hence, the

condition

Gt(i) =(

Pt(i)Pt

)−ε

Gt (2.2)

pins down public consumption of each variety i where

Pt =[∫ 1

0Pt(i)1−ε di

] 11−ε

(2.3)

Government expenditure is financed by a mixture of distortive taxes on house-holds’ capital and labor income as well as by lump-sum taxes. Tax rates oncapital and labor income are exogenously given and constant, while lump-sumtaxes can be used in a state-contingent way to balance the government budgetconstraint in every period. The central bank chooses the nominal interest rateby following a simple Taylor rule that targets inflation

(1 + Rt) = β−1ΠΦπt (2.4)

with Φπ > 1 and Πt ≡ (Pt/Pt−1).

2.2 Households

Preferences over consumption Ct and leisure lt are defined by

E0

∞∑t=0

βt

[(Ct)b(lt)1−b

]1−σ − 11− σ

(2.5)

where b ∈ (0, 1), σ ≥ 1 and Ct is an index that combines market and home goodsdenoted by Cm,t and Cn,t, respectively, according to

Ct =[α1(Cm,t)b1 + (1− α1)(Cn,t)b1

] 1b1 (2.6)

α1 ∈ [0, 1] and b1 < 1. Therefore, households can substitute market and homegoods at a constant elasticity6 (1 − b1)−1. The market good is the standardDixit-Stiglitz aggregator of the infinitely many varieties of market consumptiongoods

Cm,t =

1∫0

(Cm,t(i))ε−1

ε di

ε

ε−1

(2.7)

6Recall the following limiting cases: when b1 approaches one, Cm,t and Cn,t are perfect substitutes.They are instead perfect complements if b1 tends to minus infinity. b1 = 0 nests the Cobb-Douglasspecification.

6

and can be bought for either consumption or investment purposes. Aggregate in-vestment also combines varieties as in (2.7), at the same elasticity of substitutionε. Let investment be denoted by It. Hence, capital evolves over time accordingto

Kt+1 = (1− δ)Kt + exp{µt}It −ξ

2

(Kt+1

Kt− 1

)2

(2.8)

and it depreciates at a rate δ. We allow for positive capital adjustment costs bysetting ξ > 0 and we consider an investment specific shock µt. In each period,the existing capital stock can be rented to firms or used by the household forhome production. Let Km,t be the capital stock available to firms and Kn,t thecapital stock available for non-market activity. Hence,

Kt = Km,t + Kn,t (2.9)

Home goods are not traded. Rather, the household produces them by allocatingcapital and labor to the following technology

Cn,t =[α2(Kn,t)b2 + (1− α2) (exp{sn,t}hn,t)

b2] 1

b2 (2.10)

where hn,t stands for hours worked at home, sn,t captures exogenous technologicalprogress in the home production sector, α2 ∈ [0, 1] and b2 < 1. As an alternativeto housework, time can be rented to firms so that the following constraint musthold

lt = 1− hm,t − hn,t (2.11)

where hm,t represents hours worked in the market and the time endowment isnormalized to one. We assume that households are price-takers in all markets andthat financial markets are complete. Therefore, optimal allocation of expenditureacross varieties implies a flow budget constraint

Et {Qt,t+1Bt+1}+ Pt(Cm,t + It)≤ Bt + (1− τh)WtPthm,t + (1− τk)rtPtKm,t + δτkPtKm,t + Tt (2.12)

Pt is the minimum cost of a unit of the composite bundle Cm,t, as in (2.3),Bt+1 is a portfolio of state contingent assets and Qt,t+1 is the stochastic discountfactor for one-period ahead nominal payoffs7. rt is the real rental price of marketcapital, Wt is the real wage and the term δτkPtKm,t arises because we assume thatdepreciated market capital is tax deductible. Finally, Tt includes all lump-sumtransfers and taxes, in addition to the profits stemming from market power.

7The stochastic discount factor in period t is the price of a bond that delivers one unit of currencyif a given state of the world realizes in period t + 1, divided by the conditional probability that thestate of the world occurs given the information available in t. The nominal interest rate Rt relates tothe discount factor according to (1 + Rt) = {EtQt,t+1}−1 by a standard no-arbitrage argument.

7

Given initial values of the capital stock K0 and assets B0, and given allprices and policies, households choose state-contingent sequences of: aggregate,market and home consumption, Ct, Cm,t and Cn,t, respectively; leisure, lt, andhours worked both on the market, hm,t, and at home, hn,t; the stock of capitalrented to firms, Km,t, and the stock used in the non-market production, Kn,t;investment, It, as well as the total capital stock, Kt+1, and the amount of bondsBt+1 to carry over to the next period. The solution to the households’ problemneeds to satisfy three intra-temporal conditions

α1

1− α1

[Cm,t

Cn,t

]b1−1

=1− α2

Wt(1− τh)

[Cn,t

hn,t

]1−b2

[exp{sn,t}]b2 (2.13)

α1

1− α1

[Cm,t

Cn,t

]b1−1

=α2

(1− τk)rt + δτk

[Cn,t

Kn,t

]1−b2

(2.14)

Wt(1− τh)(1− hn,t − hm,t) =1− b

bα1C1−b1

m,t Cb1t (2.15)

Equation (2.13) drives the optimal allocation of time between the home and themarket sector. It establishes that the marginal rate of substitution between homeand market consumption has to equalize the corresponding relative price which isthe ratio between the return to housework, i.e. the marginal productivity of laborin the non-market sector, and the return to market work, i.e. the after-tax realwage. Similarly, equation (2.14) requires that the marginal rate of substitutionbetween the two consumption goods is equal to the ratio of returns to capital inthe two sector, marginal productivity of capital at home and the after-tax mar-ket rental rate of capital, taking into account that depreciation is tax deductible.Obviously, taken together, the two conditions imply that returns to labor, rel-ative to capital, are equalized across sectors which is a direct consequence ofthe fact that the household can freely re-allocate both time and capital betweenmarket and non-market activity. Equation (2.15) is the standard intra-temporaloptimality condition solving for the leisure-consumption trade-off.

In addition, two conventional Euler equations are required for the allocationto be optimal inter-temporally, one for the capital stock and one for financialassets

βEt

{λt+1

λt

exp{µt}exp{µt+1}

[1 +

ξ

Kt

(Kt+1

Kt− 1

)]−1

[1− δ + ξ

(Kt+2

Kt+1− 1

) (Kt+2

K2t+1

)+ exp{µt+1}(1− τk)rt+1 + δτk

]}= 1

(2.16)

βEt

{λt+1

λt(1 + Rt)Π−1

t+1

}= 1 (2.17)

where λ denotes the marginal utility of consumption and reads as

λt = bα1(1− hn,t − hm,t)(1−b)(1−σ)Cb1−1m,t (Ct)b(1−σ)−b1 (2.18)

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2.3 Firms

Each market good variety i is produced by a monopolistically competitive firmthat combines market capital and time according to the production function

Yt(i) =[α3(Km,t(i))b3 + (1− α3) (exp{sm,t}hm,t(i))

b3] 1

b3 (2.19)

where α3 ∈ [0, 1], b3 < 1 and sm,t represents labor augmenting technologicalprogress. Cost minimization with respect to capital and labor subject to thetechnological constraint (2.19) yields

α3RMCt

(Km,t(i)Yt(i)

)b3−1

= rt (2.20)

(1− α3)RMCt

(hm,t(i)Yt(i)

)b3−1

[exp{sm,t}]b3 = Wt (2.21)

where RMCt is the real marginal cost which is constant across all firms i as animplication of constant returns to scale and perfect competition on the marketsof all factors of production. We follow Calvo (1983) and we assume that in anygiven period each firm resets its price Pt(i) with a constant probability (1− θ).The demand of any good i is

Yt(i) =[Pt(i)Pt

]−ε

Y dt (2.22)

where Y dt ≡ [Cm,t + It + Gt]. Maximization of profits

Et

∞∑

j=0

θjQt,t+j [Pt(i)Yt+j(i)− Pt+jRMCt+jYt+j(i)]

(2.23)

subject to constraint (2.22) yields the following first order condition for any firmi that is allowed to re-optimize in period t

Et

∞∑

j=0

θjQt,t+jYt+j(i)[P ∗tPt

− ε

ε− 1RMCt+jΠt,t+j

] = 0 (2.24)

P ∗t is the optimal price, Qt,t+j denotes the stochastic discount factor in period tfor nominal profits j periods ahead and it is such that

Qt,t+j = βjEt

{λt+j

λtΠ−1

t,t+j

}(2.25)

and Πt,t+j ≡ (Pt+j/Pt). Calvo-pricing conventionally implies the following rela-tion between inflation and the relative price charged by re-optimizing firms

9

P ∗tPt

=(

1− θΠε−1t

1− θ

) 11−ε

(2.26)

The necessary condition for profit maximization (2.24) can easily be rewritten as

P ∗tPt

=x1,t

x2,t(2.27)

where the auxiliary variables x1,t and x2,t are recursively defined by

x1,t = Y dt

ε

ε− 1RMCt + βθEt

{λt+1

λtΠε

t+1x1,t+1

}(2.28)

x2,t = Y dt + βθEt

{λt+1

λtΠε−1

t+1x2,t+1

}(2.29)

2.4 Aggregation and market clearing

After defining aggregate production Yt

Yt =

1∫0

(Yt(i))ε−1

ε di

ε

ε−1

(2.30)

the clearing of all final goods markets implies

Yt = Cm,t + It + Gt (2.31)

Define the market capital-labor ratio, kt ≡ (Km,t(i)) / (hm,t(i)). By equations(2.20) and (2.21) the ratio is constant across firms and satisfies

kt =[rt(1− α3)exp{sm,t}

Wtα3

] 1b3−1

(2.32)

Let aggregate labor demand hdm,t be

hdm,t =

∫ 1

0hm,t(i) di (2.33)

that coincides with hm,t by the clearing of the labor market. Therefore, integrat-ing equation (2.19) over all firms i yields

Yt = ∆−1t

[α3k

b3t + (1− α3)

] 1b3 hm,t (2.34)

where ∆t denotes relative price dispersion which reads as

∆t =∫ 1

0

(Pt(i)Pt

)−ε

di (2.35)

and it is a state-variable that evolves according to

10

∆t = (1− θ)(

P ∗tPt

)−ε

+ θΠεt∆t−1 (2.36)

It is well-known that log (∆t) is a second order term and can thus be neglectedwhen the model is approximated to the first order around the non-stochasticsteady state. Aggregate demand of market capital is

Kdm,t =

∫ 1

0Km,t(i) di (2.37)

It follows that the clearing of the capital rental market implies the relation

Km,t = kthm,t (2.38)

Finally, by using (2.38) into (2.34), one can obtain the aggregate productionfunction

Yt = ∆−1t

[α3K

b3m,t + (1− α3)hb3

m,t

] 1b3 (2.39)

as well as the aggregate counterparts of equations (2.20) and (2.21)

α3RMCt

(Km,t

∆tYt

)b3−1

= rt (2.40)

(1− α3)RMCt

(hm,t

∆tYt

)b3−1

[exp{sm,t}]b3 = Wt (2.41)

3 Parametrization of the model

To begin with, we restrict the elasticity of substitution in production to 1 bychoosing b2 and b3 equal to 0. We do so in order to be comparable with mostof the related literature that focuses on the case of Cobb-Douglas productionfunctions8.

We resort to data in order to calibrate as many structural parameters aswe can, so as to match the value of endogenous variables at the non-stochasticsteady state with their observable counterparts. By doing so, we determine thefollowing parameters: α1, α2, α3, G, δ and b. Ten structural parameters areleft to be determined: the discount factor β; tax rates τk and τh; the elasticityof substitution between market and home goods (1 − b1)−1; price stickiness θ;the elasticity of substitution across market good varieties, ε; the inverse of theinter-temporal elasticity of substitution, σ; capital adjustment costs ξ; the Taylorrule coefficient Φπ. These parameters can hardly be identified by matching thesteady state with the data and they are potentially crucial for the dynamicresponse of endogenous variables to shocks. Hence, we discipline the modelby using information coming from previous studies. In the next section, we

8Table 1 summarizes the values for the other parameters.

11

perform extensive sensitivity analysis with respect to all of them in order to makeclear how the parametrization affects our results. We set the discount factor βto 0.99 which implies an annual interest rate of roughly 4 percent per year.In the baseline parametrization, we restrict to the case of lump-sum taxation,as in most of the literature that investigates the ability of standard businesscycle models in replicating empirical impulse responses of market consumptionto government expenditure shocks. We choose θ = 0.75, ε = 11, σ = 2, andΦπ = 1.5, a calibration that is fairly standard in business cycle models. As faras capital adjustment costs are concerned, estimates display great variability9,ranging from ξ = 3 to ξ = 110. We restrict to a value in the middle range,ξ = 50. (1 − b1)−1 is the parameter we are mostly interested in since affectssignificantly the elasticity of labor supply to G shocks. To have a broad idea ofan empirically relevant range for (1 − b1)−1, one can refer to a variety of bothmicro- and macroeconomic studies that find estimates between 1.8 and 510. Wefix the elasticity to 4, implying b1 = 0.75. However, in most of our exercises weleave the parameter free to vary, so as to assess its importance for the sensitivityof our results.

3.1 Data

We collect time series of capital, investment, market consumption, governmentexpenditure and the consumer price index (price index for personal consumptionexpenditure) from the U.S. Bureau of Economic Analysis. All the series refer tothe time period 1950:Q1-2007:Q2, excluding the financial crisis, they are availableat a quarterly frequency, with the exception of capital that is annual, and theyare all seasonally adjusted. The data have been downloaded in current dollarsand divided by the consumer price index. We obtain a measure of GDP bysumming up market consumption, investment and government expenditure. Weonly consider purchases of goods in government expenditure and we excludepurchases of non-military durable goods and structures. The series of marketconsumption includes non-durable goods and services, after subtracting the valueof services from housing and utilities that in turn we consider as a part of thenon-market sector11. We obtain total investment by adding purchases of durablegoods to the fixed investment component, both residential and non-residential,but we leave out inventories, as in Smets and Wouters (2007). Consistently, we

9For a survey see Neiss and Pappa (2002)10The preferred calibration chosen by Benhabib et al. (1991) in their seminal contribution about

home production is 5. McGrattan et al. (1997) estimate a version of the model by Benhabib et al.(1991) via maximum likelihood and find a value slightly below 2. Chang and Schorfheide (2003)estimate a home production model with Bayesian techniques and find that (1− b1)−1 is roughly 2.3.Aguiar et al. (2012) use data from the American Time Use Survey (ATUS) to establish that homeproduction absorbs about 30 percent of foregone market work hours at business cycle frequencies.Then, they show that the Benhabib et al. (1991) model is consistent with the ATUS evidence undera 2.5 elasticity. Karabarbounis (2012) shows that a value of 4 accounts for cyclical fluctuations of thelabor wedge.

11This is conventional in the home production literature. See for instanceMcGrattan et al. (1997).

12

assign fixed non-residential assets to market capital, while we consider residentialassets and the stock of durable goods as part of the home capital. Governmentexpenditure as a share of GDP amounts to 0.18, which we use to calibrate themean of the stochastic process for public spending G. The market and homecapital to output ratio, 1.29 and 1.69, are informative for choosing technologyparameters α3 and α2, respectively. Data on capital and investment pin downthe depreciation rate δ. We normalize the time endowment to 1 and we matchsteady state hours worked in the market and in the home sector with averagesobserved in the data by choosing utility parameters b and α1, respectively. Tothis purpose, we use the information contained in the American Time Use Survey(ATUS) as summarized by Aguiar et al. (2012). The ATUS provides nationallyrepresentative estimates of how Americans spend their time supplying data on awide range of non-market activities, from child-care to volunteering, for a cross-section of roughly 100000 individuals over the period 2003-2010. Respondentsare randomly selected from a subset of households that have completed theireight and final month of interviews for the Current Population Survey (CPS). Asa fraction of the weekly endowment, time allocated to market work is 0.33, timefor housework amounts to 0.19 and the rest is devoted to leisure which excludessleeping, eating and personal care time12.

3.2 Non-stochastic steady state and calibration

We find the non-stochastic steady state of the model by setting all shocks totheir unconditional mean which we normalize13 to 0 for sm, sn and µ. Then,the equilibrium conditions evaluated at the non-stochastic steady state are usedto recover the values of α1, α2, α3, G, δ and b, given the calibration targets.The steady state version of the capital accumulation equation, (2.8), determinesthe depreciation rate, δ, by using data on capital and investment. The Eulerequation on capital, (2.16), thus implies that the steady state rental rate is

r =1− βδτk − β(1− δ)

β(1− τk)(3.1)

which is pinned down by knowing β, δ and the capital income tax rate. Equations(2.26)-(2.29), together with the monetary rule (2.4), imply that the steady statevalue of the real marginal cost is

RMC =ε− 1

ε(3.2)

12As reported by Aguiar et al. (2012) in Table B1 of their online Appendix, the average respondentdevotes 31.62 hours to market work and 18.12 hours to home production per week. Our figures obtainafter subtracting from the weekly time endowment sleeping, personal care and eating, for a total of72.92 hours. Instead, if those activities are included, market work and home production time result in0.18 and 0.11, respectively. Both ways of accounting time are used in the home production literature.We choose the former in our baseline calibration, but we check that our results are robust to the latterdefinition.

13Instead, log(G) is chosen consistently with the data as we show below.

13

while Π = P ∗/P = ∆ = 1 and (1 + R) = β−1. By equation (2.40),

Km

Y=

(rε

α3(ε− 1)

) 1b3−1

(3.3)

which allows to retrieve α3 given the market capital-to-output ratio, b3 and ε,after substituting equation (3.1). Furthermore, we use the production function(2.39) to find

hm

Y=

[1

1− α3− α3

1− α3

(Km

Y

)b3] 1

b3

(3.4)

which is solely a function of known parameters. Therefore, given the target onhm, one can easily solve for Y and Km via (3.3) and (3.4), while equation (2.41)determines the real wage W

W =(1− α3)(ε− 1)

ε

(hm

Y

)b3−1

(3.5)

If Y is known, it follows from definitions (2.28) and (2.29) that

x1 = x2 = (1− βθ)Y (3.6)

Conditions (2.13) and (2.14) imply

hn

Y=

[α2W (1− τh)

(1− α2)[(1− τk)r + δτk]

] 1b2−1 Kn

Y(3.7)

and α2 must be chosen to make consistent the target on hours worked at homewith the observed home capital-to-output ratio. Once α2 has been set, also Kn

is pinned down, hence Cn can be found by using (2.10). Define g as the share ofgovernment expenditure in GDP. The resource constraint (2.31) together with(2.13) yields

α1

1− α1

[(1− g)Y − I

Cn,t

]b1−1

=1− α2

Wt(1− τh)

[Cn,t

hn,t

]1−b2

(3.8)

where all endogenous variables have been determined. As a consequence, givenb1 and b2, α1 must be chosen such that (3.8) holds. Finally, G = gY whilethe labor supply equation (2.15) recovers the value of b consistent with all ourtargets.

4 Housework, market consumption and fis-

cal multipliers

The purpose of this section is twofold. First, we document that in the modelsubstitutability between market and home consumption is an important driver

14

of the labor supply response to government expenditure shocks and, as a conse-quence, it affects the predicted magnitude of the fiscal multiplier as well as theeffect on market consumption of fiscal expansions. Finally, we compare the pre-dictions of our model with the VAR evidence on the macroeconomic consequencesof exogenous changes in public spending.

4.1 Inspecting the mechanism

Under our calibration, market consumption increases after a positive govern-ment expenditure shock. This result stands in contrast with the predictions of abaseline business cycle model with nominal rigidities. Figure 1 makes clear thecontribution of home production by comparing impulse response functions acrosstwo alternative parameterizations. We label as “GHP” the responses obtainedunder the calibration reported in Table 1, while “Baseline” refers to a counter-factual world where hours worked and capital in the home sector are set to zero.In both cases, we consider an exogenous increase in government expenditure thatis normalized to one percentage point of steady state GDP and we analyze itsimpact on market consumption, hours worked on the market, real wages, GDPand investment. We assume14 that the shock follows an AR(1) process withpersistence ρg = 0.8. The responses of consumption and investment have beenexpressed as shares of GDP, while for GDP and real wages we present percentagedeviations from the steady state15. As a consequence, the impact of the shockon GDP can be conventionally interpreted as the fiscal multiplier and directlycompared to the corresponding VAR evidence. We maintain this normalizationin the rest of the paper. It is evident that the “GHP” model implies bigger fiscalmultipliers, as compared to the baseline, and it predicts a positive rather thannegative consumption response. This is because the substitutability between thetwo goods induces a higher elasticity of labor supply to exogenous changes inpublic spending. The intuition of the result is straightforward. The householdneeds to pay for the shock out of her wealth in the form of higher current orfuture taxes, so that a temporary fiscal expansion has a negative wealth effect.Therefore, it is optimal to reduce investment on the one hand and to work moreon the other hand, so as to spread the tax burden between lower savings andlarger labor income. Also, in a model with nominal rigidities a positive gov-ernment expenditure shock induces substitution of leisure and housework withmarket work for an additional reason. The fiscal expansion stimulates aggregatedemand, reduces price mark-ups and consequently raises the real wage, makingit relatively more attractive to work in the market sector. The wealth and theaggregate demand effects reinforce each other in boosting employment, but theypush the real wage in opposite directions and the final outcome is ultimately

14Monacelli and Perotti (2008, 2010) show that ρg = 0.8, implying that roughly fifty percent of theshock dies out in about four quarters, is in line with the VAR evidence. We further discuss such valuebelow when we compare our model with an identified government expenditure shock.

15To this purpose, we multiply the log response of consumption and investment by their steadystate shares in GDP. Everything is multiplied by 100 so that the scale is already in percentage points.

15

a quantitative question. In a model without home production market hoursworked increase and generate a positive fiscal multiplier on output which is notlarge enough to allow for an increase of market consumption: the additional laborincome is indeed only used to finance the tax burden. However, when the house-hold has the possibility of reallocating time from housework to market activity,the incentive to do so clearly depends on the elasticity of substitution betweenhome and market goods and one would expect a stronger response of hours whenb1 grows larger16. Figure 2 confirms that this is indeed the case. In fact, if wereduce the elasticity of substitution from 4 to 1 and keep all the remaining pa-rameters at the values displayed in Table 1, the response of hours is dampenedenough to make market consumption fall, as in the baseline business cycle model.Not surprisingly, also the fiscal multiplier is smaller. Hence, we conclude thatneglecting the substitutability between housework and market work downplaysthe actual elasticity of labor supply to fiscal shocks and, as a consequence, theirimpact on production and market consumption.

Nominal rigidities are key in shaping the relationship between the elasticityof substitution b1 and the elasticity of labor supply to G shocks, as it becomesclear from Figure 3, where the elasticity of substitution is kept constant andequal to its baseline value, while price stickiness varies from 0 to 0.75. If nominalrigidities are low enough, our transmission channel does not seem to be operative.This fact can be easily explained by the behavior of the real wage. When pricesbecome more flexible, a fiscal expansion affects price mark-ups to a lesser extent.As a result, the outward shift of the labor supply curve due to the negative wealtheffect becomes more and more important, relatively to the fall in mark-ups, andthe real wage does not increase much or it even falls. It follows that a highelasticity of substitution between home and market goods cannot reinforce theincrease in market hours worked: the household does not find it more attractive towork on the market, rather it works the amount needed to pay the tax burden andoptimally smooth the shock over time. To conclude, the elasticity of substitutionbetween home and market goods is relevant if households work more on themarket after the shock not simply because they have to, but because they findit more attractive than home producing.

4.2 Robustness

We now discuss the robustness of our results. In fact, the model parametrizationmay hide some forces that can under- or overstate the quantitative importance ofsubstitutability between market and home goods. We postpone to the next sec-tion an extended discussion emphasizing that a proper modelling of the interac-tion between monetary and fiscal policy is crucial to obtain sensible predictions17.Two structural parameters are naturally expected to be relevant: the cost of ad-

16Recall that higher values of b1 imply a higher elasticity of substitution and when b1 = 0 preferencesare Cobb-Douglas.

17For an illustration of the empirical importance of monetary accommodation after fiscal shocks seefor instance Canova and Pappa (2011).

16

justment of the capital stock, ξ, and the inverse of the inter-temporal elasticity ofsubstitution, σ. Intuitively, the former discourages households from smoothingthe fiscal shock by reducing savings and investment. The latter, as emphasizedby Basu and Kimball (2002), also acts through the inter-temporal margin and itaffects the complementarity between hours worked and consumption. In partic-ular, a smaller inter-temporal elasticity of substitution, i.e. a higher σ, magnifiesthe relevance of our channel. We finally show that our results are robust to theinclusion of distortive tax rates on capital and labor income. In all of the follow-ing exercises we maintain parameters to the calibrated values displayed in Table1, unless otherwise specified.

In Figure 4, we plot the impulse response function of market consumptionfor different values of ξ that we decrease from 50 to the lower bound of theempirically relevant range, 3. This exercise shows that capital adjustment costsare important for the elasticity of labor supply to government expenditure shocks.However, under our baseline parametrization, market consumption increases forall the values of the adjustment cost that are above the lower bound typicallyused in the literature.

As far as σ is concerned, its quantitative relevance is assessed in Figure 5. Theleft hand panel displays the impulse response of market consumption for differentvalues of σ, while the right hand panel shows the corresponding plots for themodel without a home production sector. It is evident that the inter-temporalelasticity of substitution is a key parameter, even though an elasticity in linewith the microeconomic evidence cannot generate a rise in market consumptionif a home production sector is not included in the model.

Figure 6 makes sure that the inclusion of distortive tax rates on capital andlabor income does not undermine our results. In particular, the figure plots theimpulse response of market consumption and GDP when capital and labor aretaxed at rates equal to 0.57 and 0.23, respectively. The values have been chosenin line with the estimates by McGrattan et al. (1997).

We conclude this section by showing that under a plausible parametrizationthe model is not able to generate a positive response of market consumptioneither when the home production sector is not included or when one abstractsfrom nominal price rigidities. To this purpose, we consider 50000 draws of pa-rameters from uniform distributions defined over an empirically relevant range.In particular, we consider the following parameters with their respective bounds:θ ∈ [0, 0.8], ξ ∈ [0, 25], ρg ∈ [0, 0.99], Φπ ∈ [1.1, 1.5], ε ∈ [6, 11], G ∈ [0.05, 0.25],and b1 ∈ [0.3, 0.8]. The 50000 draws generate a distribution of impulse responsefunctions of market consumption to government expenditure shocks. Figure 7plots the median, the 75-th and the 25-th quantiles of such distribution. The lefthand panel reports the case without home production but with nominal rigidi-ties, while the right hand panel shows the case of home production under flexibleprices.

17

4.3 Comparison with the VAR evidence

The VAR evidence seems to agree that fiscal expansions stimulate demand andincrease aggregate consumption. See for instance Caldara and Kamps (2008)and Perotti (2008). Various theories accounting for the VAR estimates havebeen proposed in the literature. Our main argument is not meant to be anexhaustive alternative explanation, rather it is intended to point out that thesubstitutability between market and home consumption has important effects onthe labor supply elasticity that are relevant for fiscal expansions. Still, we believeit is interesting to see to what extent our channel alone is consistent with theconditional evidence. To this purpose, we identify fiscal shocks by resorting tothe restriction proposed by Blanchard and Perotti (2002) and we quantify theirimpact on market consumption, GDP and the nominal interest rate in the data.Then, we compare the empirical responses with the predictions of our model.We are interested in the behavior of the nominal interest rate, because, as weanticipated above, modelling the interaction between monetary and fiscal policyis crucial.

In addition to the data described above, we collect the quarterly and season-ally adjusted time series of tax revenues net of transfers from the U.S. Bureauof Economic Analysis and the three month treasury bill rate from the FederalReserve Bank of St. Louis database. The reduced form model contains a con-stant and a trend and the following variables in this particular order: The log ofreal per capita tax revenues, the log of real per capita government consumptionexpenditures, the log of real GDP per capita, the log of real private consumptionexpenditures and the rate on T-bills. The lag length of our VAR model is basedon information criteria and set equal to two. The ordering of the variables inthe VAR implies that government spending does not react contemporaneouslyto changes in output and private consumption, nor to changes in the monetarypolicy instrument18. Figure 8 presents the responses of endogenous variables toa shock in government spending normalized to one percent of GDP. After theshock, both output and consumption increase significantly and tax revenues re-act positively with a lag. The nominal interest rate does not react significantlyon impact, it increases two periods after the shock and falls thereafter and sig-nificantly so approximately six quarters after the initial impact.

In order to compare the model to the data, we perform the following exercise.First, we choose a monetary policy rule that qualitatively matches the responseof the nominal interest rate to an expansionary fiscal shock. Then, we look for theelasticity of substitution between home and market goods such that the modeldelivers an impact response of market consumption that is consistent with thedata. Finally, we make sure that the needed value of b1 agrees with previousestimates and, in particular, with microeconomic data.

A simple Taylor rule as the one assumed in (2.4) implies that the central bank

18We have used alternative sign restrictions to identify the government spending shock as a shockthat moves positively output, deficits and government spending. Results are very similar and we donot present them here for economy of space.

18

tightens the monetary stance by raising the nominal interest rate, after an expan-sionary fiscal shock. However, even though the monetary policy maker wants toaggressively react to inflation unconditionally, she may prefer to accommodate anexogenous government expenditure shock and avoid increasing the interest rateright when the fiscal policy maker is expanding. This intuition seems to be con-sistent with our estimated response of the nominal interest. A simple monetaryrule augmented with an interest rate smoother that keeps a long-run inflation re-sponse of 1.5 as in (2.4) qualitatively replicates the conditional evidence. Hence,we consider the following rule

(1 + Rt) = (1 + Rt−1)ρm

{β−1ΠΦπ

t

}1−ρm

(4.1)

We maintain Φπ as in Table 1 and we choose19 ρm = 0.82. Also, we set ρg = 0.85to match the persistence of the identified government expenditure shock. Finally,we choose b1 = 0.8. Figure 8 shows that our mechanism is able to reproduce theconditional evidence on the response of market of consumption and it generatesa fiscal multiplier higher than 1, that is however somewhat over-predicted. Sinceb1 = 0.8 is admittedly on the upper bound of available estimates, we repeatthe comparison in Figure 9 by imposing a more conservative parametrizationand setting b1 = 0.6. In this case, we can explain about half of the response ofconsumption and we match exactly the impact response of GDP. The model failsto replicate the persistence of both consumption and output.

5 Conclusions

We build an otherwise standard New-Keynesian model that encompasses a homeproduction sector and we show that, for plausible calibrations of the elasticityof substitution between home and market goods, after a fiscal expansion mar-ket consumption increases. In addition, we can match the predicted size of theoutput multipliers with the empirical estimates. The presence of nominal rigidi-ties and the possibility of substituting housework with market work makes itmore attractive to work on the market and to consume market goods when thegovernment is spending. The higher elasticity of labor supply to governmentexpenditure shocks explains the improved ability of the model to match the con-ditional evidence, as compared to the baseline business cycle model.

19See Smets and Wouters (2007), Justiniano, Primiceri and Tambalotti (2010) and Justiniano,Primiceri and Tambalotti (2011).

19

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20

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21

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22

A Equilibrium Definition

The equilibrium of the model is a set of state contingent plans for variables Ct,Cm,t, Cn,t, Km,t, Kn,t, Kt, hm,t, hn,t, It, λt, Yt, Πt, ∆t,

P ∗tPt

, x1,t, x2,t, RMCt, Rt,Wt and rt that satisfy the following system of equation

Ct =[α1(Cm,t)b1 + (1− α1)(Cn,t)b1

] 1b1 (A.1)

Cn,t =[α2(Kn,t)b2 + (1− α2) (exp{sn,t}hn,t)

b2] 1

b2 (A.2)

Kt = Km,t + Kn,t (A.3)

exp{µt}It = Kt+1 − (1− δ)Kt +ξ

2

(Kt+1

Kt− 1

)2

(A.4)

α1

1− α1

[Cm,t

Cn,t

]b1−1

=1− α2

Wt(1− τh)

[Cn,t

hn,t

]1−b2

[exp{sn,t}]b2 (A.5)

α1

1− α1

[Cm,t

Cn,t

]b1−1

=α2

(1− τk)rt + δτk

[Cn,t

Kn,t

]1−b2

(A.6)

Wt(1− τh)(1− hn,t − hm,t) =1− b

bα1C1−b1

m,t Cb1t (A.7)

βEt

{λt+1

λt

exp{µt}exp{µt+1}

[1 +

ξ

Kt

(Kt+1

Kt− 1

)]−1

[1− δ + ξ

(Kt+2

Kt+1− 1

) (Kt+2

K2t+1

)+ exp{µt+1}(1− τk)rt+1 + δτk

]}= 1

(A.8)

βEt

{λt+1

λt(1 + Rt)Π−1

t+1

}= 1 (A.9)

λt = bα1(1− hn,t − hm,t)(1−b)(1−σ)Cb1−1m,t (Ct)b(1−σ)−b1 (A.10)

P ∗tPt

=(

1− θΠε−1t

1− θ

) 11−ε

(A.11)

P ∗tPt

=x1,t

x2,t(A.12)

x1,t = Ytε

ε− 1RMCt + βθEt

{λt+1

λtΠε

t+1x1,t+1

}(A.13)

23

x2,t = Yt + βθEt

{λt+1

λtΠε−1

t+1x2,t+1

}(A.14)

Yt = Cm,t + It + Gt (A.15)

Yt = ∆−1t

[α3K

b3m,t + (1− α3)hb3

m,t

] 1b3 (A.16)

α3RMCt

(Km,t

∆tYt

)b3−1

= rt (A.17)

(1− α3)RMCt

(hm,t

∆tYt

)b3−1

[exp{sm,t}]b3 = Wt (A.18)

∆t = (1− θ)(

P ∗tPt

)−ε

+ θΠεt∆t−1 (A.19)

(1 + Rt) = β−1ΠΦπt (A.20)

for all t, for given tax rates and government expenditure. To close the equi-librium definition we furthermore need a specification for monetary policy andthe respective law of motion for market- and home productivity and governmentexpenditures.

24

0 10 20−0.2

0

0.2

0.4

0.6

Consumption

0 10 200

0.5

1

1.5

GDP

0 10 200

0.5

1

1.5

Market Hours0 10 20

0

0.1

0.2

0.3

0.4

Wages

0 10 20−0.025

−0.02

−0.015

−0.01

−0.005

0

Investment0 10 20

0

0.2

0.4

0.6

0.8

1

Govt. Exp.

GHPBaseline

Figure 1: Impulse responses for the model calibrated as in Table 1, labelled as GHP,and impulse responses of the model without home sector, labelled as Baseline.

25

0 5 10 15 20−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25bb

1=0

bb1=0.5

bb1=0.6

bb1=0.75

Figure 2: Impulse responses of market consumption to a G shock for different values ofthe elasticity of substitution between home and market goods. All the other parametersare calibrated as in Table 1.

26

0 5 10 15 20−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3θ=0θ=0.5θ=0.66θ=0.75

Figure 3: Impulse responses of market consumption to a G shock for different valuesof price stickiness. All the other parameters are calibrated as in Table 1.

27

0 5 10 15 200

0.05

0.1

0.15

0.2

0.25ξ=3ξ=10ξ=20ξ=50

Figure 4: Impulse responses of market consumption to a G shock for different valuesof capital adjustment costs. All the other parameters are calibrated as in Table 1.

28

0 5 10 15 20−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7σ=1σ=1.5σ=2σ=2.5σ=4

0 5 10 15 20−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1σ=1σ=1.5σ=2σ=2.5σ=4

Figure 5: Impulse responses of market consumption to a G shock for different valuesof the elasticity of inter-temporal substitution. All the other parameters are calibratedas in Table 1. The left and the right panel show the model with and without homesector, respectively.

29

0 10 20−0.2

−0.1

0

0.1

0.2

Consumption

0 10 200

0.5

1

1.5

GDP

0 10 200

0.5

1

1.5

Market Hours0 10 20

−0.1

0

0.1

0.2

0.3

Wages

0 10 20−0.06

−0.04

−0.02

0

0.02

Investment0 10 20

0

0.2

0.4

0.6

0.8

1

Govt. Exp.

GHPBaseline

Figure 6: Impulse responses for the case of distortive taxation. All the other parametersare calibrated as in Table 1. The impulse responses of the model without home sectorare labelled as Baseline.

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1 2 3 4 5−0.25

−0.2

−0.15

−0.1

−0.05

0

1 2 3 4 5−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

Figure 7: 75th, 50-th and 25-th quantiles of the distribution of impulse responses ofmarket consumption to a G shock for 50000 draws uniform distributions of the followingparameters, with their respective bounds: θ ∈ [0, 0.8], ξ ∈ [0, 25], ρg ∈ [0, 0.99], Φπ ∈[1.1, 1.5], ε ∈ [6, 11], G ∈ [0.05, 0.25], and b1 ∈ [0.3, 0.8]. All the other parameters arechosen as in Table 1. The left hand panel reports the case without home production butwith nominal rigidities, while the right hand panel shows the case of home productionunder flexible prices.

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0 5 10 150

0.5

1

Govt. Exp.

datamodelconfidence bands

0 5 10 150

1

2

GDP

0 5 10 15−1

0

1

Consumption0 5 10 15

−0.2

0

0.2

Interest rate

Figure 8: Empirical and theoretical impulse responses after an identified governmentexpenditure shock, b1 = 0.8.

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0 5 10 150

0.5

1

Govt. Exp.

datamodelconfidence bands

0 5 10 150

1

2

GDP

0 5 10 15−1

0

1

Consumption0 5 10 15

−0.2

0

0.2

Interest rate

Figure 9: Empirical and theoretical impulse responses after an identified governmentexpenditure shock, b1 = 0.6.

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Parameter Mnemonic ValueDiscount Factor β 0.99Risk Aversion σ 2Preference parameter α1 0.5438Preference parameter b 0.5089Technology parameter α2 0.1034Technology parameter α3 0.0485Inverse elasticity of substitution home-market goods 1− b1 0.25Inverse elasticity of substitution capital-labor at home 1− b2 1Inverse elasticity of substitution capital-labor on the market 1− b3 1Elasticity of substitution among final goods varieties ε 11Capital adjustment costs ξ 50Price stickiness θ 0.75Inflation reaction coefficient φ 1.5Depreciation rate of capital δ 0.0241Labor income tax rate τh 0Capital Income tax rate τk 0Steady state government expenditure G 0.0602

Table 1: Baseline calibration

34