Fiscal Policy in an Equilibrium Search Model :The case against Social VAT

Franois LangotGAINS-TEPP (Universit du Mans), Cepremap & PSE

Lise PatureauEQUIPPE (Universit de Lille 1) & CES

Thepthida SopraseuthGAINS-TEPP (Universit du Mans) & Cepremap

January 2011

Abstract

We assess the macroeconomic and welfare implications of the social VAT in a generalequilibrium small-open economy model with labor market frictions, energy use andgovernment expenditures in the utility function. We fully characterize the transitionpaths from the economy prior to the reform to the economy after the change in taxschedule.

We show that the tax reform can lead to an increase in employment, domesticproduction and exports, in accordance with the effects expected by the supportersof the social VAT. Overall results lead to mixed conclusions though. If positive, thequantitative effect on employment turns out to be very limited. Further, derivingthe normative implications mitigates the appropriateness of the fiscal reform. For thebenchmark calibration, the social VAT indeed reduces welfare. This suggests that,unless households put a (unplausible) high weight on government expenditures in theirutility function, the fall in consumption, due to the heavier VAT, drives the welfaredownward.

Keywords: Fiscal policy, labor market search and matching, small-open economy,dynamic general equilibrium

JEL classification: E27, E62, H21, J38

1 Introduction

This paper aims at assessing the economic rationale behind the social VAT, i.e. a decreasein the payroll tax funded by an increase in the value added tax (VAT). Since 2007 1, this ideahas been at the heart of political and economic debates in France and is again mentionedas one of the key issues for the next presidential election2. Beyond the French debate, thesocial VAT has been implemented in Denmark (in 1987) and Germany (in 2007). Economicreports (Delaveau (2007), Arthuis (2007)) are still inconclusive about the benefits of such apolicy for the Danish and German economies.

Supporters of the social VAT claim that this fiscal policy could lower labor cost, hencefavor employment while ensuring the financial sustainability of social welfare. The need for areduced labor cost would be all the more necessary as the French labor market is characterizedby rigid labor market institutions, which hampers the competitiveness of French firms thatoperate in a globalized competitive world. The social VAT could improve the ability ofFrench firms to compete with their Foreign counterparts in the conquest for global marketsby i) cutting labor cost and ii) distorting prices in favor of home produced goods. Indeed,the social VAT increases the prices of all goods sold in France (whether imported or not).However, so long as French firms accept to reduce their price as a result of lower labor costs,home-produced goods would then be sold at a reduced price, thereby favoring consumptionof domestic over foreign products. Supporters of the social VAT expect the shift in the taxschedule to result in a trade balance surplus.

In order to assess the economic relevance of these economic mechanisms, one has then toconsider the following dimensions: open-economy framework, rigid labor market, distortingtaxes on consumption and labor in a general equilibrium model. Several papers have inves-tigated the quantitative implications of the social VAT in France using macroeconometricmodels (See Besson (2007), chapter 7 for a survey), analytical long-term settings (Beauvallet

1The debate on the opportunity of introducing a social VAT started at the time of the 2007 parliamentaryelections. On June 10th 2007 on the eve of the first round of the general elections the then Minister forthe Economy, Finance and Employment, Jean-Louis Borloo, admitted that the government was consideringthe issue. Between the first and second rounds of the elections, Prime Minister Franois Fillon stated that,in line with the undertakings of Nicolas Sarkozys election campaign, we are going to open negotiationswith social partners on a social VAT. Political leaders from the Left immediately drew more attention onthe issue in order to underline how the government implemented generous tax breaks for the richest peoplewhile threatening to lower the purchasing power for the poorest with the social VAT. Fillons statements onsocial VAT are said to have led to the loss of dozens of seats for Fillons party in the 2007 elections.

2Le serpent de mer de la TVA sociale, Le Point, 18 octobre 2010. La nouvelle bote ides de JacquesAttali. Le point, 15 octobre 2010. La TVA sociale: une obsession perverse, Le Monde, 3 novembre 2010.Manuel Valls, contre les 35h et pour la TVA sociale, LExpress, 4 janvier 2011.

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& Restout (2007), Coupet & Renne (2007a)) or dynamic general equilibrium models (Laf-fargue (2000), Coupet & Renne (2007b), Gauthier (2009), Fve et al. (2010)). However, toour knowledge, none of them has taken into account the four dimensions aforementioned.This is the ambition of the paper. To that aim, we develop a small open economy settingwith distorting taxes on consumption and labor in a model with labor market frictions. La-bor market institutions are calibrated to capture the rigidity of the French labor market.In addition, government spending are assumed to provide economic benefits, through thehouseholds utility. Finally, we introduce energy use in the production function, which al-lows the firm to adjust more promptly to the shift in the tax schedule. The variable capitalutilization, in relation with energy use, allows to assess the consequences of the social VATin a more realistic setting where firms have several margins of changes in their productionfactors. Moreover, the introduction of energy allows to take into account an interesting effectin our open-economy setting. Since energy is imported, any surge in energy imports couldactually affect the trade balance, hence counteracting the positive effect on exports expectedby the social VAT proponents. In this setting, we assess the macroeconomic effects andwelfare consequences of the implementation of the social VAT, after taking into account longterm effects as well as the transitional dynamics.

There is a considerable literature on the welfare impacts of alternative tax schemes onlabor, consumption and capital (See Trabandt & Uhlig (2010) for a survey in closed economymodels and Mendoza & Tesar (2003) in open economies). Our contribution differs from theexisting papers in several dimensions. First, we focus on the social VAT, thereby exploringthe distortion on labor versus that on consumption. Indeed, the liberalization of capitalflows seems to be the spur for a convergence in capital taxation (Mendoza & Tesar (2003)),leaving only distorting taxes on labor and consumption as fiscal tools. In addition, weexplore the consequences of alternative distorting taxes in an open economy setting, using asearch model with extensive and intensive margin on labor with energy use. Our quantitativeinvestigation includes the transitional dynamics in a framework where government spendingprovides utility flows to consumers. The papers of the existing literature miss one or severaldimensions of our analysis, which is crucial in the investigation of the social VAT.

We show that the social VAT can indeed increase employment, thus domestic production.In our model, perfectly competitive firms share their reduction in labor cost with theircustomers, by lowering their price. As a result, the model predicts a fall in the relative priceof the home-produced goods, thereby generating the improved competitiveness expectedby the supporters of the social VAT. Exports indeed go up. However, the model does not

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replicate several expected positive effects of the social VAT. First, the increase in energy use,spurred by the production boom, generates a trade deficit (rather than a trade surplus) inthe first periods of the tax change. In addition, firms also suffer from the fall in the relativeprice of the domestic goods since the purchase of capital and employees earnings have to bepaid in terms of the consumption basket. Movements in relative prices then contribute todampen the output growth generated by the social VAT. Besides, allowing firms to adjustto the fiscal change through the intensive margin (hours, variable capital utilization rate)further moderates the impact of the tax reform on employment and production. For thebenchmark calibration, our model thus predicts a very modest gain in terms of employment(8300 individuals), much lower than the estimates obtained in the literature (Fve et al.(2010), Gauthier (2009) or Besson (2007)). Finally, the social VAT reduces welfare forthe benchmark calibration, which suggests that, unless households put a high weight ongovernment expenditures in their utility function, the fall in consumption, due to the heavierVAT, drives the welfare downward.

The paper is organized as follows. Section 2 presents the building blocks of our model.Section 3 provides references for the calibration and steady state computation. We assessthe macroeconomic and welfare effects of the social VAT in Section 4. Section 5 concludes.

2 Distorting taxes in a search model with intensive andextensive margins

In this section we propose a theoretical framework allowing to explain simultaneously thedynamics of employment and hours worked per employee. We also need a theory to explainthe impact of the labor market institutions such as the bargaining power and the unemploy-ment benefits. The natural candidate is then the matching model la Pissarides (1990),where both employment and hours are endogenous.

2.1 The equilibrium matching model

We present in this section a dynamic general equilibrium model where labor adjustments aredetermined by a search process and a wage bargaining process. In this respect, the model isclose to the one analyzed by Andolfatto (1996) and Chron & Langot (2004). The model isenriched to account for open-economy aspects.

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2.1.1 Labor market flows

Employment is predetermined at each time and changes only gradually as workers separatefrom jobs, at the exogenous rate s, or unemployed agents find jobs, at the hiring rate Mt.Let Nt and Vt, respectively be the number of workers and the total number of new jobs madeavailable by firms, then employment evolves according to:

Nt+1 = (1 s)Nt +Mt

withMt the number of hirings per period, determined by a constant returns to scale matchingfunction (Pissarides (1990)):

Mt = Vt

[e(1Nt)1

], 0 < < 1

The parameter measures the bargaining power of firms in the Nash negotiation processand e the constant search effort. > 0 is a scale parameter measuring the efficiency of thematching function.

2.1.2 Households

The economy is populated by a large number of identical households whose measure isnormalized to one. Each household consists of a continuum of infinitely-lived agents.

The households consumption choice can be decomposed into 3 steps. First, the represen-tative household decides on the intertemporal arbitrage between consumption and savings.Second, total current consumption is allocated between oil and non-oil goods depending ontheir relative price. Increases in the relative price of oil trigger a substitution of non-oil goodsfor oil, with the elasticity of substitution o between oil and non-oil (say, manufacturing)goods determining the strength of this substitution effect. Third, the consumption of non-oilgoods is spread over domestic production and imports depending on relative import prices.

In what follows, we first describe the intertemporal consumption choices, before deter-mining the intratemporal consumption allocation across goods.

The intertemporal program The consumption smoothing choice interacts with the labormarket behavior. Each period, an agent can engage in only one of three activities: working,searching for a job or enjoying leisure. Employed agents (N) work h hours, while unemployed(1N) expend their time searching a job. Unemployed agents are randomly matched with job

5

vacancies. Individual idiosyncratic risks faced by each agent in his job match are smoothedby using employment lotteries. Hence, the representative households preferences are:

t=0

t[NtU(Cnt , 1 ht) + (1Nt)U(Cut , 1 e) + G log(G)] (1)

where 0 < < 1 is the discount factor. The time period is normalized to 1. Cnt and Cutstand for the consumption of employed and unemployed agents, while ht denote workedhours. The contemporaneous utility function is assumed to be increasing and concave inboth arguments. As in Christiano & Eichenbaum (1988), Bec (1994) and Christiano et al.(2009), we introduce government spending in the utility function, thereby taking into accountthe households preference for public goods. In addition, we introduce separability betweenconsumption and leisure L:

U(Czt , Lzt ) = lnC

zt +

zt U zt z = n, u.

with

nt = (1 ht)1l

1 l l > 0 > 0and

ut = u(1 e)1l

1 lwith leisure time linked to worked hours through:

Lt + ht = 1

the time period being normalized to 1.A households labor supply evolves as follows:

Nt+1 = (1 s)Nt + t(1Nt) (2)

where t Mt/(1Nt) is the rate at which unemployed agents find jobs.Each household chooses {Cnt , Cut , Bt+1} to maximize (1) subject to the labor supply

constraint (2) and to the budget constraint

Pt(1 + ct ) [NtC

nt + (1Nt)Cut ] + PtBt+1

PHt(1 wt )Ntwtht + (1Nt)PHt(1 wt )bt + PtBt(1 + iFt ) + Tt + pit (3)

The real wage w and the unemployment benefit b are assumed to be paid in terms of goodslocally produced. c is the consumption tax rate and w the labor income tax rate (concerning

6

either employed or unemployed agents). T is a lump-sum transfer from the government andpi are lump-sum dividends remitted by firms.

The households resources are also made of international financial assets. We retain theassumption of incomplete financial markets. Each period, a risk-free interest rate bond isissued (in terms of the consumption bundle); when bought in period t, it yields a rate ofreturn iFt in t+1. The periods resources are used for consumption expenditures and demandfor international assets (Bt+1).

The introduction of incomplete asset markets alters the property of stationarity of themodel, since temporary shocks have permanent effects on macroeconomic variables. Follow-ing Kollmann (2002), we assume that the interest rate at which the household can borrowor lend foreign assets iFt , equals the exogenous world interest rate it plus a spread, that is adecreasing function of the countrys net foreign asset position:

1 + iFt = 1 + it b

Btnx

b > 0 (4)

where nx is the steady-state value of exports. b captures the degree of capital mobility,with a lower b representing higher capital mobility.

The dynamic problem of a typical household can be written as follows

W(Ht ) = maxCnt ,C

ut ,Bt+1

{NtU(C

nt , ht) + (1Nt)U(Cut ) + EtW(Ht+1)

}(5)

subject to (2) and (3) and given some initial conditions (N0, K0).Ht = {Nt,t, wt, ht, bt, pit, iFt , Lt} is the vector of variables taken as given by households.

Let t be the shadow price of the budget constraint. Then, the first order conditions withrespect to consumption and international bonds are respectively,

1

Cnt=

1

Cut= (1 + ct )tPt (6)

Et[(1 + iFt+1)t+1Pt+1] = Ptt (7)

As indicated by Equation (6), under the separability assumption, optimal householdsdecision rules imply that:

Cnt = Cut =

1

(1 + ct )Ptt

The intratemporal program We now turn to the determination of the optimal intratem-poral allocation between oil and non-oil goods (Cot and Cct respectively), and between do-mestic and foreign varieties in the non-oil basket of goods (CHt and CFt respectively). The

7

consumption bundle is written as

Ct =

[

1oo (C

ot )

o1o + (1 o)

1o (Cct )

o1o

] oo1

where non-oil goods consists of Home and Foreign goods:

Cct =

[

1C

1

Ht + (1 )1 C

1

Ft

] 1

with o > 1 ( > 1 respectively) refers to the elasticity of substitution between oil andnon-oil goods (Home and Foreign goods respectively). The consumption bundle implies aconsumer price index:

Pt =[o (P

et )

1o + (1 o)P 1oZt] 11o

with P et the energy price and PZt the core price index (the price index of manufacturedgoods) whose expression is given by:

PZt =[ (PHt)

1 + (1 )P 1F t] 11

with PHt and PFt the prices of the domestic and foreign (manufactured) goods respectively.The intratemporal consumption choices are such that:

Cot = o

[P etPt

]oCt (8)

Cct = (1 o)[PZtPt

]oCt (9)

and

CHt =

[PHtPZt

]Cct

CFt = (1 )[PFtPZt

]Cct

For now, prices are expressed in a currency playing the role of unit of account. Withoutloss of generality, we assume that this currency vehicle is the same across countries, so thatthe nominal exchange rate is equal to 1. This implies that:

PFt = Pt

P t denotes the foreign CPI that prevails in the rest of the world.

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2.1.3 Firms

There are many identical firms in the economy. Each firm chooses a number Vt of jobvacancies, produces goods and pays wages and capital services. The unit cost of maintainingan open vacancy is . Each firm has access to a Cobb-Douglas production technology toproduce output:

Yt = At (utKt) (Ntht)

1, 0 < < 1 (10)

At represents the global productivity of factors in the economy. The production functionsatisfies standard properties, constant return to scale and a unitary elasticity of substitutionbetween labor and capital. ut is an index of the utilization rate of capital. For a given capitalstock Kt, ut determines the flow of capital services utKt. Capital evolves according to:

Kt+1 = (1 (ut))Kt + It

Following Finn (1995, 2000), the depreciation of capital depends on how intensively itis used in production. With (ut) > 0 and (ut) > 0, a higher utilization causes fasterdepreciation of capital (at an increasing rate). As suggested by Finn (1995, 2000),

(ut) =j1ut with j1 > 0 and > 1

In addition, an increase in the utilization rate requires more energy per unit of capital:

etKt

= g (ut)

with g (ut) > 0 and g (ut) > 0. Finn (1995, 2000) motivates the convexity by considera-tions of diminishing marginal energy efficiency. We follow Finns (1995, 2000) specification:

g (ut) =j2gugt with j2 > 0 and g > 1

Investment is a CES aggregator with the same elasticities of substitution as the con-sumption basket. In addition, investment is subject to quadratic adjustment costs that arespecified as in Ireland (2001):

ACKt =K2

(Kt+1 Kt)2Kt

Job vacancies are matched at rate t = Mt/Vt. Hence, a firms labor employment evolvesas:

Nt+1 = (1 s)Nt + tVt (11)

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Each firm chooses {Vt, Nt+1, Kt+1, It, et, ut|t 0} to maximize the discounted value ofthe dividend flow:

W(Ft ) = maxVt,Nt+1,Kt+1,It,et

pit + Et

[t+1tW(Ft+1)

](12)

with pit = PHtYt PtIt P et et PtVt PHt(1 + ft )wtNthtPtACKtS (PHtYt PHtwtNtht (ut)KtPt) (13)

ft stands for the payroll tax paid by firms and S the corporate tax. pit can be rewrittenas:

pit =(1 S)PHtYt PtIt PtACKt P et et PtVtPHt(1 + ft S)wtNtht + S(ut)PtKt

The firms objective is to maximize its profit (Equation (12)) given the technology pro-duction function (10) and subject to the following constraints:

Nt+1 = (1 s)Nt + tVt (14)Kt+1 = (1 (ut))Kt + It (15)etKt

= g(ut) (16)

with Ft = {Nt, Kt,t, wt, ht} and initial conditions N0, K0 are considered as given bythe firm. Let qNt, qKt and qet denote the Lagrange multipliers associated with equations(14), (15) and (16) respectively.Denoting Tobins QKt as:

QKt = 1 + KKt+1 Kt

Kt= 1 + K

It (ut)KtKt

The first-order conditions of the firms problem can be written as:

QKt = Et

(t+1Pt+1tPt

) (1 S) PHt+1Pt+1 Yt+1Kt+1 +QKt+1 (ut+1) (1 S) P et+1et+1Pt+1Kt+1

+ K2

(It+1(ut+1)Kt+1

Kt+1

)2

(1 S) PHt

Pt

Ytut

= Kt

[P etPtg(ut) + (1 S)(ut)

]

t= Et

[(t+1Pt+1tPt

)( (1 S) PHt+1

Pt+1

Yt+1Nt+1

PHt+1Pt+1

(1 + ft+1 S)wt+1ht+1+

t+1(1 s)

)]

10

Given the functional forms retained, the relevant equations characterizing the firmsproblem are given by the following set of equations:

Kt+1 =

(1 j1

ut

)Kt + It

etKt

=j2gugt

Nt+1 = (1 s)Nt + tVtYt = At(utKt)

(Ntht)1(

1 S) PHtPt

Ytut

= Kt

[(1 S) j1u1t + P etPt j2ug1t

]QKt = 1 + K

It j1 utKtKt

and

t= Et

[Pt+1t+1Ptt

{ (1 S) PHt+1

Pt+1(1 ) Yt+1

Nt+1

(1 + ft+1 S)PHt+1Pt+1 wt+1ht+1 + (1 s) t+1

}](17)

QKt = Et

Pt+1t+1Ptt

(1 S) PHt+1

Pt+1 Yt+1Kt+1 P et+1

Pt+1

et+1Kt+1

+QKt+1

j1ut+1

(1 S)+ K

2

(It+1 j1 ut+1Kt+1

Kt+1

)2 (18)

2.1.4 Nash bargaining

Wages and hours are determined via generalized Nash bargaining between individual workersand their firms:

maxwt,ht

St = (tVFt )(VHt )1 (19)

with St the total surplus of a match, VFt = W(Ft )

Ntthe marginal value of a match for a firm

and VHt = W(Ft )

Ntthe marginal value for a match for a worker. denotes the firms share of

a jobs value.

The solution to this problem are hours and wage contracts. With an efficient bargainingover wages and hours, the optimal choice of hours worked by employee is closed to thewalrasian case. However, the wage contract takes into account the dynamic behavior oftaxes and the unemployment benefits. Details on the computation of the Nash bargainingis available in Appendix A.

The negotiated amount of worked hours per worker is given by:

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(1 S) PHt

Pt(1 ) Yt

Ntht= nt

(1 ht)ltPt

with tax wedge nt defined as:

nt 1 + ft S

1 wtLet us define labor market tightness t is the ratio of vacancies to unemployed workers Vt1Nt .Given the expressions for t Mt/(1 Nt) and t Mt/Vt, one can show that they arerelated to the labor market tightness as follows:

t =tt

The equilibrium value for the wage bill can be expressed as a weighted average of theworkers outside option and the bargained surplus :

(1 + ft S

) PHtPt

wtht = nt

[(1 wt )

PHtPt

bt nt utPt

]

Outside option

(20)

+ (1 )[(1 S)PHt

Pt(1 ) Yt

Nt+ SCt

]

Bargained Surplus

where SCt denotes search costs:

SCt =

{1 s

t

(1 Et

[ntnt+1

])+

Vt1NtEt

[ntnt+1

]}The wage bill can be rewritten as:

(1 + ft S

)wtht = (1 )BSt + nt

[(1 wt ) bt

nt utPt

]with BSt the bargaining surplus defined as

BSt =(1 S) PHt

Pt(1 ) Yt

Nt+ SCt

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2.1.5 Government and trade balance

Government Each period the government runs a balanced budget, such as:

Tt = ct PtCt + PHt(

ft +

wt )wthtNt (1Nt)PHt(1 wt )bt Gt

+S (PHtYt PHtwtNtht (ut)KtPt)

Trade balance The demand for the home good equals:

Yt = DHt +DHt

where DHt and DHt are the demand functions for the Home good coming from the domesticand foreign countries respectively. Domestic demand for the home manufactured good em-anates from households and firms for motives due to consumption, investment, costs on jobposting, according to:

DHt =

[PHtPZt

]Zct

The basket of non-oil goods Zct and oil are given by:3

Zct = (1 o)[PZtPt

]Dt

Zot = o

[P etPt

]Dt

with the private aggregate demand Dt defined as follows:

Dt = Ct + It + Vt +K2

(Kt+1 Kt)2Kt

Foreign demand for home good is specified as follows:

DHt = (1 )[PHtP Zt

]Zt

where Zt is an exogenous term scaling overall foreign demand.

We assume that the share of energy in the basket of goods in the foreign country isnegligible, so that P Zt = P t with P t the foreign consumption price index.

The current account then evolves as:

Bt+1 (1 + iFt )Bt =PHtPt

Yt [Dt +Gt] Pet

Ptet

The general equilibrium model is solved using Dynare. All equations are reported inAppendix B.

3This is obtained by extending Equation (9) to demand for investment and job posting motives.

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3 Calibration

Calibration of structural parameters is made on a quarterly basis using French data whenavailable, if not European data. Table 1 summarized the calibration.

is set to 0.36. The discount factor is set to 0.99, which corresponds to a real annualinterest rate equal to 4%, as commonly retained in the literature (Christoffel et al. (2006),among others). We follow Finn (2000) for the calibration of parameters j1, scaling thecapital depreciation function, as well as for j2 and g that intervene in the energy efficiencyfunction. We calibrate the steady-state value of the ratio peE/Y as in Finn (2000). Theparameter scaling the adjustment costs on capital K is based on Patureau (2007) andclose to Kollmann (2001). The weight of domestic goods in the non-oil basket of goods and the weight of oil in the consumption bundle o come from Jacquinot et al. (2008)based on Euro area data. We also follow their estimates of and o that correspond to theelasticity of substitution between domestic and foreign (non-oil) goods and to the elasticityof substitution between oil and non-oil goods respectively.

We calibrate N corresponding to an unemployment rate of 9%, as observed in Franceover the period 1995 2008. The steady-sate value for worked hours is set to h = 1/3, whilethe fraction of time spend searching e is set equal to 1/6 as in Chron & Langot (2004)or Hairault (2002). Calibration of l is based on estimated of the labor-supply elasticityh given the steady-state relation l = 1hh h. The literature does not reach some clear-cutconsensus regarding the value of h. Most microeconomic studies estimates this elasticity tobe small, close to 0 and not higher than 0.5. We follow Trigari (2004) and Christoffel et al.(2006) in calibrating l in order to have h = 0.1. We calibrate the firms bargaining powerin the Nash bargaining and the weight of vacant jobs in the matching function based onLangots (1996) estimates on French data. The probability of finding a job is set so as toreproduce the mean duration of unemployment of 14.25 months observed in France over theperiod 1995-2008, using OECD data. Combined with our calibration for N , this implies asteady state value of the job destruction rate s = 0.0209. We follow Den Haan & Watson(2000) to calibrate the probability of filling a vacant job . We calibrate the cost of jobposting by setting V/Y = 0.01 as in Hairault (2002). This calibration lies within the rangeof values used in the literature (0.005 in Chron & Langot (2004) or 0.05 in Krause & Lubik(2007)). We set the steady-state ratio of net foreign asset position to GDP bsy B/Yequal to 0.0066 based on the AWM database on the Euro zone. We set the parameter Bas in Kollmann (2002). The unemployment benefit ratio rr b/w is set to 0.562 based on

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OECD data for France over the 1995-2008 period. Calibration for the corporate tax rateS is based on the AWM database for the period 1980-2006. Finally, benchmark values for c and f stem from labor market institution database by Nickell (2006). The calibrationfor w is based on Trabandt & Uhlig (2010), whose value is consistent with other paperson distorting taxes on labor (Fve et al. (2010), Prescott (2004), Mendoza (2001)). Finally,the government expenditure to GDP ratio (G/Y = 0.24) reflects the French annual averagebased on OECD Main Economic Indicators over the 1995-2008 period. The parameter thatscales the weight of government expenditures in the utility function G is crucial in ourquantitative analysis. We adopt a benchmark value of G = 13 but a sensitivity analysis isperformed in Section 4.2.

Table 1: Calibration of structural parameters

Parameter Value Parameter Value 0.99 N 0.91 0.36 h 0.33j1 0.04 0.3j2 0.01 0.65 1.3 0.2105g 1.53 e 1/6peE/Y 0.043 V/Y 0.01K 7 0.7 0.64 bsy 0.0066o 0.21 B 0.0019 1.5 l 20o 0.21 rr 0.562 c 0.22 f 0.27 s 0.0656 w 0.456

G/Y 0.24

The computation of the steady state is reported in Appendix C.

4 Social VAT

Table 2 reports tax revenues in the 2008 data versus in the model. Using Eurostat Fiscaldata and figures from the Plan de Loi de Finance 2008, we report tax revenues collected in

15

Table 2: Tax revenues in the benchmark calibration

Data Data ModelTax revenues Mil. euros % %Value added type taxes (a) cC 136838 0.20 0.22Taxes on income +Employees social contributions (a,b) 281558 0.41 0.47Employers actual social contributions (a,c) 214001 0.31 0.28Corporate Tax (d,e) 48803.6 0.07 0.04Total 681200.6 1 1(a) Source : Eurostat 2008(b) In terms of the models notations, equal to w pHP wNh(c) In terms of the models notations, equal to f pHP wNh(d) In terms of the models notations, equal to S

(pHP Y pHP wNh (u)K

)(e) Source : PLF 2008

France from value added taxes, payroll taxes, taxes on employees labor (income tax andsocial contribution) and corporate tax. The share of each source of tax revenue is matched bythe model. Notice that, in the model, as well as in the data, taxes on employment constitutea major source of tax revenues, thereby suggesting that the social VAT, by lowering thepayroll tax, could actually reduce tax revenues, unless the fall in the tax rate is compensatedby an increase in the tax base (wNh). As expected, our discussion of the social VAT relatesto Laffer curve effects.

In this section, we evaluate the consequences of the so-called TVA sociale fiscal reform,where payroll taxes are reduced in the attempt of boosting employment whereas indirecttaxation is raised to offset the consequences of the tax break on government budget. In afirst step, we evaluate the consequences of a given reduction in payroll taxes on aggregatedynamics and welfare. In a second step, we carry out a sensitivity analysis to the magnitudeof the payroll tax reduction in terms of welfare. This drives us to make some normativerecommendations with regards to the appropriateness of the TVA sociale reform.

4.1 Consequences of the social VAT

In accordance with the Besson (2007) report, we evaluate the consequences of a 2-pointreduction in payroll taxes f (i.e., from the benchmark value of 0.27 to 0.25) that is ac-companied by an appropriate increase in indirect taxes c so as to balance the governmentsbudget constraint. We assume that the reform is simultaneously announced and set in place

16

(in period 1).Lets be more specific about the reform exercise considered here. Unlike Fve et al. (2010)

or Mendoza & Tesar (1998), we consider as a starting point of the tax reform a decrease inthe payroll taxes paid by firms f .4 Besides, as contemplated in the Besson (2007) report,the reduction in payroll taxes is associated with an increase in the indirect tax rate c. Thequestion is then, how to balance the governments budget? There is no unique answer inthe related literature. For instance, Mendoza & Tesar (1998) consider that the governmentadjusts her debt or transfers so as to balance her intertemporal budget constraint. Fveet al. (2010) assume that, given a change in VAT, the payroll tax adjusts each period, alongthe transition path, in order to balance the government budget, after taking into accountthe higher VAT and the endogenous macroeconomic response to the modified tax scheme.

We follow here another route in order to mimic the situation faced by the French gov-ernment: for a given reduction in payroll taxes f , denoted f , we deduce the subsequentincrease in c (denoted c) so as to balance the budget ex ante (i.e., considering tax basesin period 0, set to their initial steady state values given the benchmark calibration). The exante endogenous increase in the indirect tax rate is then given by the following equation:

c = f w0N0h0C0

(21)

with C0, N0, h0, w0 denoting the initial steady-state values of consumption, employment,worked hours and wage. In accordance with the spirit of the reform contemplated by theFrench government, we determine the required increase in indirect taxes needed to compen-sate for the reduction in payroll taxes so as to maintain the budget constant, in an ex anteperspective.

However, the fiscal reform implies changes in the equilibrium values of various macroeco-nomic variables, which in turn affects the tax bases, hence the governments budget constraintalong the transition path. When taking into account these general equilibrium effects, wemaintain the assumption that the governments budget constraint is balanced every period;potential surplus or losses induced by changes in tax rates are offset through adjustmentsin public spending (G) and transfers (T ), the share between public spending and transfersbeing maintained constant throughout the transition path. In doing so, we have in mindthat the arbitrage between public spending G on the one hand, and transfers and lump-sumtaxes T on the other hand is a long-term choice, that cannot be adjusted over the business

4These authors consider things the other way round.

17

cycle. More precisely, for the benchmark calibration, the share of fiscal revenues that goes totransfers amounts to 0.55, 0.45 being affected to public spending as revealed in the (ex-ante)steady-state. As a result, the budget surplus (if positive) coming from the tax reform isinjected in public spending (for 45%) and transfers (for 55%), so that the budget constraintis balanced each period along the transition dynamics.

We first evaluate the consequences of the fiscal reform with regards to the dynamicsof macroeconomic variables. The convergence to the new steady state is achieved in 500periods. However, the figures will show the aggregate dynamics for the first 100 periods.Figure 1 reports the paths of all tax rates c, f and w. In period 1, payroll taxes f arereduced from 27% to 25%, while indirect taxes c are raised from 22% to 24%. The changein VAT is deduced from Equation (21). The employees labor tax w is kept constant.

Figure 1: Tax reform: changes in tax rates

0 20 40 60 80 1000.215

0.22

0.225

0.23

0.235

0.24

0.245c

0 20 40 60 80 100-1

-0.5

0

0.5

1

1.5w

0 20 40 60 80 1000.245

0.25

0.255

0.26

0.265

0.27

0.275f

Figures 2, 3, 4 and 5 present the dynamics of aggregate variables following the tax reform.As indicated in Figure 2, consumption falls as a consequence of the rise in the indirect taxrate c. The potential negative wealth effect is however offset through the bargaining processon the labor market. As shown in Figures 2 and 4, both worked hours and the real wage

18

increase with the tax reform. So as to compensate the purchasing power loss implied bythe tax reform, households indeed accept to bargain an increase in worked hours h as longit is accompanied by an increase in the real wage w. The magnitude of the wage increasemore than compensates that of indirect taxes, so that the purchasing power of the real wageincreases, which contributes to induce a positive wealth effect of the tax reform, as shown bythe reduction in in Figure 3. The positive wealth effect is also attributable to the rise inlump-sum transfers. The increase in public spending (Figure 3) indeed indicates that the taxreform induces a budget surplus along the transition path, which is partly (at 55%) assignedto households as lump-sum transfers. Furthermore, as some portion of these surpluses isused to increase public goods, the losses in private consumption may (at least partially) beoffset in the utility function. The magnitude of this effect on welfare notably depends onthe parameter G scaling the weight of public spending in the utility function. We thereforepay a particular attention to this parameter value when conduction our welfare analysis ofthe desired pattern of the tax reform (Section 4.2).

From the firms side, the reduction in payroll taxes f entices them to increase totalemployment. On impact, the employment level N being predetermined, this is achievedthrough an increase in worked hours h. In parallel, firms start opening vacant jobs, so asto adjust at the extensive margin through the employment level the periods after the fiscalshock. As reported in Figure 2, the employment level monotonically increases with thetax reform. In that respect, our results indicate that the tax reform reaches its assignedobjective, i.e. the reduction in unemployment.

Without endogenous capital utilization, the rise in worked hours is the only way to adjustproduction on impact, the capital and employment stocks being fixed. The variable capitalutilization rate provides firms with another adjustment margin. Figure 3 thus reports anincrease in the utilization rate ut. Firms are all the more enticed to use physical capital moreintensively as the marginal productivity of capital increases with the rise in worked hoursand in employment. This also induces firms to invest more in physical capital, consistentlywith the dynamics of investment reported in Figure 2. The rise in both the capital utilizationrate and worked hours account for the immediate increase in production reported in Figure2. In subsequent periods onwards, the gradual increases in the employment level (Figure 2)and the capital stock (Figure 3) contribute to further raise output, which thus monotonicallyincreases until reaching its new (higher) steady-state level. As more physical capital is used,more energy is required (Figure 3).

In a perfect competing goods market, the reduction in payroll taxes generates a reduction

19

Figure 2: Tax reform: Effects on macroeconomic variables (1)

0 20 40 60 80 1001

1.0005

1.001Y

0 20 40 60 80 1000.556

0.558

0.56C

0 20 40 60 80 1000.1252

0.1253

0.1254

0.1255I

0 20 40 60 80 1000.9096

0.9098

0.91N

0 20 40 60 80 100

0.3334

0.3335

0.3336h

0 20 40 60 80 1005.006

5.008

5.01K / Y

in the domestic good price Ph. With a small open economy setting, the foreign price isexogenous in the consumption price index P. As a result, P declines with the reduction inPh, but less than proportionally. The relative price of domestic goods Ph/P then falls withthe fiscal reform, whereas that of foreign goods P /P rises, as shown in Figure 4.

Adjustments in relative prices therefore favor domestic goods at the expense of the for-eign ones. In accordance with the projections of the Besson (2007) report, the social VATimproves the competitiveness of domestic firms, which boosts domestic exports as displayedin Figure 5 (through the dynamics of DH). However, notably due to the significant increasein energy consumption, total imports increase as well. As shown in Figure 5, the price com-petitiveness effect on exports is not large enough to overcome the rise in imports, hence thetrade balance deteriorates for some period after the tax reform. Yet, as the consumption ofenergy gradually vanishes over time (Figure 3), imports slightly decrease while exports go

20

Figure 3: Tax reform: Effects on macroeconomic variables (2)

0 20 40 60 80 1001.44

1.46

1.48

0 20 40 60 80 1000.24

0.242

0.244G

0 20 40 60 80 1000.066

0.066

0.066Energy

0 20 40 60 80 1000.025

0.025

0.025 (u)

0 20 40 60 80 1000.9888

0.989

0.9892Utilization rate

0 20 40 60 80 1005.008

5.01

5.012K

on increasing: at some point, trade balance becomes positive, thereby displaying a J-curveprofile along the transition path.

From an open-economy perspective, our results support the view that the tax reform maybenefit the trade balance through a positive price competitiveness effect in favor of domesticgoods. Indeed, in our model, firms accept to lower their price, thereby sharing the benefitsof the cut in labor costs with their customers. In addition, we also show that this effect willoccur with a delay, as the rise in imports notably tied to energy requirement, outweighsthe boosts in domestic exports in the immediate periods after the tax reform. Furthermore,if positive on exports, the price competitiveness effect may also have adverse effects onthe firms behavior. The reduction in the relative price of domestic goods (PH/P ) indeedreduces the firms profit opportunity, which in turn may limit the magnitude of the increasein their production factors use, and notably employment, as firms have to pay workers and

21

Figure 4: Tax reform: Effects on macroeconomic variables (3)

0 20 40 60 80 1000.9998

0.9998

0.9999

0.9999

1Ph/P

0 20 40 60 80 1001

1.0001

1.0002

1.0003

P*/P

0 20 40 60 80 1000.9995

0.9996

0.9997

0.9998

0.9999

1Ph / P*

0 20 40 60 80 100

1.88

1.89

1.9

1.91

w

investment in terms of composite goods. This relative price effect is specific to the openeconomy setting. Our open-economy framework therefore sheds light on an uncovered aspectof the social VAT reform, that mitigates its ability to raise employment.

The social VAT leads to a 0.065% increase in GDP for a fall in payroll tax from 27%to 25%. For a similar tax cut, Fve et al. (2010) would find a 0.089% GDP growth. Inaddition, the model predicts that lowering the payroll tax would induce a 0.031% increase inemployment (8300 individuals), which lies below the predicted increase of 20500 individualsin Fve et al. (2010), for a similar tax cut. Our model therefore invites to revisit Fve et al.(2010)s estimates because we take into account the small open economy setting and allowfor adjustments at the intensive margin. Indeed, movement in relative prices tend to dampenthe output growth generated by the social VAT. Besides, firms can adjust to the fiscal changethrough the intensive margin (hours, variable capital utilization rate), which moderates the

22

Figure 5: Tax reform: Effects on macroeconomic variables (4)

0 20 40 60 80 1000.2656

0.2657

0.2657

0.2657

0.2657

0.2657

0.2658

0.2658Df

0 20 40 60 80 1000.3316

0.3317

0.3317

0.3318

0.3318Total imports

0 20 40 60 80 1000.5277

0.5278

0.5279

0.528

0.5281

0.5282Dh*

0 20 40 60 80 1000.196

0.1961

0.1961

0.1962

0.1962

0.1963

0.1963Trade balance

impact of the tax reform on the employment stock. As a result, our models predictions interms en employment growth lies below the estimates in the literature (Fve et al. (2010),Gauthier (2009) and macroeconometric models, see Besson (2007), where a 2-point cut inpayroll tax would be associated with an employment growth of 22 000 to 47 000 individuals.Taking into account that firms in an open world have several margins for changing theirproduction factors, leads to much more mitigated effects of social VAT on the employmentlevel.

Figure 6 reports the consequences of the tax reform on the instantaneous welfare, byreporting the welfare level implied by the tax reform and the counterfactual welfare levelthat would have been obtained without the fiscal reform (respectively denoted Wt and W0in Figure 6), as defined by Equations (22) and (23).

23

Wt = lnCt +N

(1 ht )1l

1 l + (1Nt )

u + G log(Gt ) (22)

W0 = lnC0 +N0

(1 h0)1l1 l + (1N

0)u + +G log(G0) (23)

Figure 6: Tax reform: Effects on welfare

0 10 20 30 40 50 60 70 80 90 100-1.0963

-1.0962

-1.0961

-1.096

-1.0959

-1.0958

-1.0957

-1.0956

-1.0955

WtW0

As reported in Figure 6, the tax reform reduces welfare. The final effect on welfaremay be decomposed in two opposite effects. On the one hand, the reduction in consumptioninduced by the rise in indirect taxation, reduces utility. On the other hand, given that publicgoods yields utility, the increase in public spending coming from the budget surplus of thereform, raises utility. The final effect on welfare depends on which effect dominates.5 For ourbenchmark calibration, the dominant effect is the negative impact on private consumption,leading to a reduction in welfare throughout the transition path. This reasoning makes clearthat the final effect on welfare will crucially depend on the calibration of G, that scales theweight of public goods in the utility function. This leads us to conduct a sensitivity analysisto this parameter in the welfare analysis that follows.

5For all calibration values, consumption and government expenditures explain a large fraction of theevolution of welfare. The terms related to labor and leisure quantitatively play a minor role in our welfareanalysis.

24

4.2 Social VAT, or not?

Our previous results indicate that the tax reform contemplated by the Besson (2007) report,that consists in a 2-point reduction in payroll taxes, is not appropriate as it is welfare-decreasing. How should the reform be conducted then? We investigate this question in thissection, by evaluating the welfare implications of a large range of values for the payroll taxes f (accompanied by adequate changes in the indirect tax rate as given by Equation (21)).

To evaluate the welfare gain (or loss) of a given reform, and compare the various scenariosin this respect to determine the best one, we rely on the approach developed by Lucas (1987)and used for similar purposes by Fve et al. (2010). We calculate the welfare gain associatedwith a given tax reform, by comparing two economies both starting from the initial steady-state (before the tax change). The first economy is not hit by the fiscal reform and remainsad vitam at its initial steady state. The second economy is hit by the fiscal shock, with thedynamic effects described above. Let denote {Ct , Nt , ht , Gt}t=0 the paths of consumption,employment, worked hours and public spending in the second economy, and

W [{Ct , Nt , ht , Gt}t=0] =t=0

t[lnCt +N

t

(1 ht )1l1 l + (1N

t )

u + G log(Gt )

]the associated actualized welfare. Let us also define:

W [{(1 + )Ct, Nt, ht, Gt}t=0] =t=0

t[ln((1 + )C0

)+N0

(1 h0)1l1 l + (1N

0)u + G log(G0)

]the actualized welfare in the economy that permanently remains in the initial regime andwhose consumption level is each period multiplied by the compensation 1+. We determinethe welfare gain (or loss) of the reform by the compensation level that verifies the followingequation:

W [{(1 + )Ct, Nt, ht, Gt}t=0] = W [{Ct , Nt , ht , Gt}t=0]Thus, captures the compensation that should be given to agents for them to accept to

stay in the economy that does not benefit from the fiscal reform.

A positive value of means that some positive compensation has to be given to agentsthat are not affected by the reform, in order to obtain a welfare level identical to thosewho benefit from it: the tax reform is thus welfare-increasing.

25

Symmetrically, a negative value for indicates that some amount of money should bepaid by agents that do not benefit from the reform, in order for them to have the samewelfare as those who benefit from it. In that case, the tax reform is welfare-decreasing.

We evaluate the welfare gains (or losses) of the tax reform, measured by , for variousvalues of changes in payroll taxes f . Results are reported in Figure 7. From the benchmarkcalibration of the payroll tax ( f = 0.27), as we move to the left, the social VAT is imple-mented (fall in labor cost funded by additional VAT). Theses cases are referred to as TVAsociale. The anti-TVA sociale case means increasing the payroll tax (from 27% upward)while decreasing the VAT.

In addition, as highlighted in our previous discussions, the parameter G plays a key rolein determining the welfare effects of a given reform. We then carry out the analysis for threealternative values of this parameter, G = 0 (public goods do not provide utility), G = 1/3(our benchmark calibration) and G = 1/2.

Figure 7: TVA sociale or anti-TVA sociale?

0.15 0.2 0.25 0.3 0.35-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

f

Com

pensa

tion

0.27 current tax rate0.27 current tax rate

G = 0

G = 1/3

G = 1/2

anti - TVA socialeTVA sociale

When G = 0, the social VAT is always welfare decreasing ( < 0 and all the morenegative as the change in the payroll tax is more negative). The fall in consumption, dueto the increase in VAT, is the dominant source of the decline in welfare. As a result, the"anti-TVA sociale" scenario is welfare improving.

26

With G = 1/2, the social VAT always pushes welfare upward. The fall in consumptionis compensated by the expansion in the provision of public goods, which is highly valued byhouseholds.

For the benchmark calibration, G = 1/3, both effects play a key role in determiningwelfare. For large declines in the payroll tax (meaning a steeper increase in VAT), the fall inconsumption dominates: the change in the tax schedule is welfare worsening. It is also thecase for large increases in the payroll tax (in the anti-TVA sociale scenario, on the far rightof figure 7). Indeed, with a high distorting tax on employment, labor demand falls leadingto a depleted economy, with lower output and government expenditures. Figure 7 suggeststhat, for the benchmark calibration, there is a Laffer curve on welfare whose highest pointlies on the right of the benchmark calibration. This means that we could improve welfareby lowering the VAT and increasing the payroll tax (from 27% to 30%). The subsequentconsumption boom could improve welfare in spite of the fall in government expenditure.

5 Conclusion

We assess the macroeconomic and welfare implications of the social VAT, meaning a decreasein the payroll tax funded by a higher VAT in a general equilibrium setting. This investigationis performed in a small-open economy model with labor market frictions, energy use, andgovernment expenditures in the utility function with a complete characterization of thetransition paths from the economy prior to the reform to the economy after the change intax schedule.

We show that the social VAT can indeed increase employment, thus domestic production.In our model, firms share their reduction in labor cost with their customers, by lowering theirprice. As a result, the model predicts a fall in the relative price of the home-produced goods,thereby generating the improved competitiveness expected by the supporters of the socialVAT. Exports indeed go up. However, the model does not replicate several expected positiveeffects of the social VAT. First, the increase in energy use, spurred by the production boom,generates a trade deficit (rather than a trade surplus) in the first periods of the tax change.In addition, movements in relative prices and the possibility for firms to adjust the intensivemargin (through hours and capital utilization) moderate the impact of the tax reform on theemployment stock. As a result, our model predicts a very limited increase in the employmentlevel with social VAT, far below the estimates in the literature.

Finally, the social VAT reduces welfare for the benchmark calibration, which suggests

27

that, unless households put a high weight on government expenditures in their utility func-tion, the fall in consumption, due to the heavier VAT, drives the welfare downward.

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30

A Nash bargaining

Let us recall that, under the separability assumption, optimal households decision rulesimply:

Cnt = Cut = Ct =

1

(1 + ct )tPt

Denoting :Unt = ln(Ct) +

nt

andUut = ln(Ct) +

u

it comes that:Uut = U

nt + (

u nt )From the households intertemporal program, one gets:

VHt = nt u + PHtt(1 wt ) [wtht bt] + (1 st) Et[W(Ht+1)Nt+1

](24)

In parallel from the firms program, we obtain:

VFt = (1 S)PHtF2tht PHtwtht(

1 + ft S)

+ (1 s) Et[t+1t

W(Ft+1)Nt+1

](25)

where F2tht is the output for a person that works ht hours.

Maximizing the surplus of a match (Equation (19)) with respect to wt, taking into accountthe marginal values of a match for a worker and a firm respectively (Equations (24) and (25)):

VHt =1

1 wt1 + ft S

(tVFt

)(26)

that gives:

tVHt = (1 )

1 wt1 + ft S

VFt (27)

From Equation (19), we obtain the following first order condition on worked hours ht:

VFt

(VFtht

)+

1 VHt

(VHtht

)= 0 (28)

31

that becomes:t

(1 wt

1 + ft S)(

VFtht

)+

(VHtht

)= 0 (29)

with

VFtht

=(1 S)PHtF2t PHtwt(1 + ft S) (30)

VHtht

= tPHtwt (1 wt ) (1 ht)l (31)

Replacing (30) and (31) into (29) and dividing by Ptt delivers the following expressionfor the negotiated amount of worked hours:(

1 wt1 + ft S

)(1 S) PHt

Pt(1 ) Yt

Ntht= (1 ht)l

tPt(32)

In order to characterize the wage dynamics, let us go back to equation (27), with VHt andVFt given by Equations (24) and (25) respectively.

Let us first compute the term on the left hand side of equation (27). We obtain that:

tVHt =

t

nt u + PHtt(1 wt ) [wtht bt]+ (1 st) Et

[1

1wt+11+ft+1S

t+1VFt+1] (33)

Let us now compute the term on the right hand side of equation (27) using equation (25):

(1 )(

1 wt1 + ft S

)VFt = (1 )

(1 wt

1 + ft S) (1 S)PHtF2tht PHtwtht (1 + ft S)

+ (1 s) Et[t+1tVFt+1

] (34)

Replacing (33) and (34) into (27) and dividing by (1 wt ) finally delivers the followingexpression for the wage equation:

PHtwtht =

[PHtbt

nt u

(1 wt )t

]+ (1 ) (1

S)

1 + ft SPHtF2tht

+(1 )

1 + ft S(1 s) Et

[t+1tVFt+1

] 1

(1 wt )(1 st) Et

[1 wt+1

1 + ft+1 St+1tVFt+1

](35)

32

Note that the wage equation is not affected by wealth effects on the labor supply.

If all taxes are constant, the equation above becomes:

PHtwtht =

[PHtbt

nt u

(1 w)t

]+

(1 )1 + ft S

[(1 S)PHtF2tht + tEt

[t+1tVFt+1

]]From the firms decision problem, we also have that:

Et

[t+1tVFt+1

]=Pt

t(36)

The previous equation thus becomes:

PHtwtht =

[PHtbt

nt u

(1 w)t

]+

(1 )1 + ft S

[(1 S)PHtF2tht + tPt

t

]Labor market tightness t is defined as the ratio of vacancies to unemployed workers

Vt1Nt . Given the expressions for t Mt/(1Nt) and t Mt/Vt, one can show that theyare related to the labor market tightness as follows:

t =tt

The equilibrium value for the real wage thus becomes:

PHtPt

wtht =

[PHtPt

bt nt u

(1 w)t

]+

(1 )1 + ft S

[(1 S)PHt

PtF2tht + t

](37)

This equation is consistent with the literatures findings (see Chron & Langot (2004),among others) and has a similar economic interpretation.

Coming back to equation (35), in the general case with time-varying taxes, dividing byPt, it becomes:

33

PHtPt

wtht =

[PHtPt

bt nt u

(1 wt )tPt

](38)

+ (1 ) (1 S)

1 + ft SPHtPt

F2tht

+(1 )

1 + ft S(1 s) Et

[t+1PttVFt+1

] 1

(1 wt )(1 st) Et

[1 wt+1

1 + ft+1 St+1PttVFt+1

]

Total labor cost can then be decomposed in two terms:

(1 + ft S

) PHtPt

wtht =

(1 + ft S

)(1 wt )

[(1 wt )

PHtPt

bt nt utPt

]

Outside option

(39)

+ (1 )[(1 S)PHt

Pt(1 ) Yt

Nt+ SCt

]

Bargained Surplus

that is, Equation (20) where, using Et[t+1tVFt+1

]1Pt

= t, search costs SCt are defined as:

SCt =

Vt

1NtEt

[(1+ft S

1+ft+1S

)(1wt+11wt

)]+1s

t

(1 Et

[(1+ft S

1+ft+1S

)(1wt+11wt

)])

Recall that t Mt/(1Nt) and t Mt/Vt so that tt = Vt1Nt

B Equations

Let us define t = tPt. Note also that only relative prices matter. The set of relevantequations is given by:

1. t = t

2. QKt = 1 + K It(ut)KtKt

3. t = V 1t

[e(1Nt)]1

34

4. Yt = At (utKt) (Ntht)

1

5. 1Ct

= (1 + c,t)t

6. SCt = {

1st

(1 Et

[ntnt+1

])+ Vt

1NtEt[ntnt+1

]}7. BSt = (1 S)PHtPt (1 ) YtNt + SCt

8. nt = (1h)1l

1l

9. (1 S)PHtPt

(1 ) YtNtht

= nt(1ht)

t

10.(

1 + ft S)PHtPtwtht =

nt

[(1 wt ) bt

nt ut

]+ (1 )BSt

11. Mt = V t[e(1Nt)1

]12. Yt = DHt +DHt

13. DHt = [PHtPZt

]Zct

14. DHt = (1 )[PHtP Zt

]Zt

15. Zct = (1 o)[PZtPt

]Dt

16. Zot = o[P etPt

]Dt

17. Dt = Ct + It + Vt + K2(Kt+1Kt)2

Kt+Gt

18.(1 S) PHt

PtYtut

= Kt

[(1 S) j1u1t + P etPt j2ug1t ]

19. PZtPt

=

[(PHtPt

)1+ (1 )

(PFtPt

)1] 1120. 1 =

[o

(P etPt

)1o+ (1 o)

(PZtPt

)1o] 11o21. et

Kt= j2

gugt

22. (ut) = j1 ut

23. 1 + iFt = 1 + it b Btnx35

24. Kt+1 = (1 (ut))Kt + It

25. Nt+1 = (1 s)Nt +Mt

26. Bt+1 (1 + iFt )Bt = PHtPt Yt Dt P etPtet

27. t = Et[(

t+1t

)((1 S)PHt+1

Pt+1(1 ) Yt+1

Nt+1+ t+1 (1 s) (1 + ft+1 S)wt+1ht+1

)]

28. QKt = Et

(t+1t

)(1 S) PHt+1

Pt+1 Yt+1Kt+1 P et+1

Pt+1

et+1Kt+1

+QKt+1 (ut+1)(1 S)+ K

2

(It+1(ut+1)Kt+1

Kt+1

)2

29. 1 = Et[(

t+1t

)((1 + it+1) b Bt+1nx

)]30. nt =

1+ft S1wt

31. Gt = share

( ctCt +

PHtPt

( ft + wt )wthtNt (1Nt)PHtPt (1 wt )bt

+S

(PHtPtYt PHtPt wtNtht (ut)Kt

) )

C Steady state

As detailed in Section 3, we calibrate the parameters j1, j2, , g so as to match the averagevalue of capital utilization around u = 0.82 (United States), the depreciation rate = (u) =0.025 observed in the data, and the average energy share in output, pee/Y = 0.043 in theUS economy. Under the assumption that in steady-state, all prices are equal to one, thiscorresponds to the ratio e/Y . To determine the steady-state equilibrium values, we startfrom the first-order condition on capital accumulation (in steady-state):

1

=(1 S) pH Y

K pe e

K+ 1 (1 S)

which after some manipulations, gives the steady-state capital-to-output ratio ksy KY:

ksy =

(1 S) esy

1 1 + (1 S)

with esY peeY

the calibrated share of energy in output.We then have to solve a system of three equations, for three variables to determine: , g

and u (assuming values for j1 and j2). The system is made of the first-order condition on u,

36

the definition of (u), with calibrated and the definition of g(u). In steady state and usingour previous results, it can be written as:

ksy= +

g

(1 S)esy

ksy

=j1u

e

K=

j2gug

esyksy

=j2gug

Solving this system yields the steady-state values of u, and g. Leduc & Sill (2004) use asimilar reasoning but so as to match the ratio e/K, i.e. the ratio of oil usage to the capitalstock, equal to e/K = 0.005 in US data. Our method of calibration leads to a value for E/Kconsistent with this value.

From this, we can derive the steady-state values for K, I and e, recalling that Y = 1:

K = ksy Y

I = K

e =j2gugK

If Foreign asset holding is not zero at the steady state, bsy is calibrated, and we get:

B = bsy Y

37

We then obtain the following steady-state values:

iF =1

1

E =j2gug = esyY

D = iF bsy Y + Y EZc = (1 o)DZo = oD

DH = Zc

DH = Y DHY = DH +D

H Z =

1

1 (Y DH)Oc = Zo + En

i = iF + bB

nx

with nx the steady-state value of exports, equal to DH in our notations. With the ratioV sY V

Ycalibrated, the rest of steady state values are such that:

V =s

N

= V sYY

VC = D I V =

1

(1 c)C

38