When Fiscal Consolidation Meets Private Deleveraging Javier Andrés
Óscar Arce
Carlos Thomas
University of Valencia
Banco de España
Banco de Españay
January 10, 2018
Abstract We analyze the interaction between …scal consolidation and private-sector deleveraging in a model of a small open economy inside a monetary union. Long-term collateralized private debt plays a critical role in shaping …scal multipliers at di¤erent horizons. By bu¤ering the short-run fall in debtors’spending capacity, it reduces the short-run multipliers of large and/or fast consolidations. However, such aggressive consolidations increase the length and depth of private deleveraging, causing higher output losses over the medium-run. In terms of present-value multipliers and welfare, this latter e¤ect dominates, so Andrés:
[email protected]. Arce:
[email protected]. Thomas:
[email protected] Disclaimer: The views expressed herein are those of the authors and not necessarily those of Banco de España or the Eurosystem. We thank Michal Andrle, Roel Beetsma, Vítor Gaspar, Tim Kehoe, Massimiliano Pisani, Pedro Teles, Enrique Quilis, and participants in the ADEMU Workshop "Rethinking Fiscal Policy", ADEMU Workshop "Fiscal Risk and Public Sector Balance Sheets", ECB conference on “Fiscal policy during and after the crisis”, the Banco de EspañaBarcelona GSE conference "Fiscal Sustainability: XXI Century", II Workshop Anaeco at Universidad de Valencia, Simposio de la Asociación Española de Economía 2016, and seminar participants at IMF, Banco de España and AIReF for their helpful comments and suggestions. Javier Andrés acknowledges the …nancial support by the Spanish Ministry of Economy and Competitiveness (grant ECO2014-53150-R) and Generalitat Valenciana (Conselleria d’Educació, Investigació, Cultura i Esports, grant GVPROMETEO2016-097). y
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that larger and faster consolidations are relatively costlier than smaller/more gradual ones. Keywords: …scal consolidations, long term private debt, …nancial shock. JEL codes: E44, E60, E62
1
Introduction
Since the beginning of the recent crisis, public debt as a percentage of GDP has increased by more than 20 percentage points on average in the OECD countries, up to levels hardly ever seen before in peacetime. For instance, in the euro area, ratios of general government debt over GDP at the end of 2016 were at least 1.5 times higher than in 2007 in most countries, and more than twice as high in some of them. Absent in‡ation, and with the prospect of moderate growth in the coming years, considerable budgetary adjustments are called for to reduce public debt-to-GDP ratios towards more sustainable levels. This raises a number of questions about the macroeconomic impact of …scal consolidations and the strategy to conduct these processes. Issues like the appropriate pace of …scal consolidations, or whether these should be based on spending cuts or tax hikes, have been thoroughly discussed in the literature. In the aftermath of the …nancial crisis, these questions acquire a new dimension since the e¤ectiveness and costs of …scal retrenchments are likely to be a¤ected by the lack of room of manoeuvre of conventional monetary policy at the zero lower bound (ZLB) and by the legacy of high private debt. The relevance of the ZLB for …scal policy has been extensively studied in recent years.1 By contrast, the literature has largely ignored the bidirectional links between public and private debt-consolidation processes, despite the central role that such mutual interaction has occupied in policy discussions (see e.g. Draghi, 2014; and IMF, 2016). Placing private and public debt consolidation under the same umbrella helps understand better the e¤ect of alternative …scal consolidation strategies and the determinants of the length, depth and costs of private deleveraging. In this paper we develop a framework to analyze 1
See e.g. Eggertsson (2010), Christiano, Eichenbaum and Rebelo (2011), Woodford (2011) and Erceg and Lindé (2013, 2014).
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this interaction. Inspired by the current macro…nancial landscape faced by a number of countries in the euro area that are embarked in ambitious …scal consolidations, we build a general equilibrium model of a small open economy that belongs to a monetary union. The lack of an independent monetary policy produces e¤ects similar to those of a binding ZLB, but of a more structural nature. In the model, private debt is nominal and longterm, and borrowers face collateral constraints. The combination of long-term debt and collateral restrictions gives rise to an asymmetric double debt regime. When the value of collateral is su¢ ciently high relative to outstanding debt, i.e. when ‘excess collateral’is positive, borrowers obtain new credit ‡ows provided they do not exceed such excess collateral. In the opposite case, when collateral is low relative to debt, credit ‡ows freeze and outstanding debt is reduced at the pre-set contractual amortization rate, thus pushing the economy into a slow deleveraging path. Only su¢ ciently large negative shocks (such as e.g. an intense credit crunch or a large …scal contraction) drive the economy into this last regime. As time passes and legacy debts are progressively paid back, the value of collateral recovers su¢ ciently relative to outstanding debt so as to sustain new credit ‡ows, thus bringing the deleveraging process to its end. In this way, the length and depth of private deleveraging are endogenously determined in the model. In this context, we analyze how the size, speed and composition of …scal consolidations a¤ect the economy, with particular attention to how consolidations interact with private deleveraging. Our main results can be summarized as follows. First, the size of …scal consolidation, de…ned as the targeted reduction in the long-run government debt-to-GDP ratio, has di¤erent e¤ects on …scal sacri…ce ratios (i.e. output losses per unit of reduction in that target) at di¤erent horizons. Compared with small consolidations, large …scal consolidations imply lower …scal sacri…ce ratios in the short run but higher ones in the medium/long run. Consider …rst the short-run implications. When the …scal contraction is small enough so that new credit ‡ows (i.e. excess collateral) remain positive, constrained agents have to reduce their spending along with the fall in such credit ‡ows, in a nearly proportional manner. If the …scal contraction is large enough, however, borrowers’excess collateral vanishes as does the 3
‡ow of new loans. But since borrowers cannot be forced to reduce their outstanding debt faster than required by the contractual amortizations, their net debt ‡ows and hence their spending capacity no longer fall proportionally to the size of the …scal shock. Thus, by breaking the link between debt dynamics and collateral values while in a deleveraging phase, long-term debt contracts cushion the short-run impact of negative …scal shocks on borrowers’spending capacity. We label this mechanism as the ‘bu¤ering e¤ect’. On the other hand, larger consolidations imply higher relative output losses over the medium run, by depressing further the value of debtor’s collateral and thus increasing the duration and depth of private deleveraging; we call this the ‘duration e¤ect’.2 When computing present-value output multipliers or welfare losses (rescaled by consolidation size) so as to resolve this intertemporal trade-o¤, we …nd that the duration e¤ect dominates, i.e. larger consolidations are relatively costlier than smaller ones. Second, as regards the speed of a …scal consolidation (for a given size thereof), we …nd that front-loaded consolidations aimed at lowering the government debt-to-GDP ratio faster entail higher present-value output multipliers and welfare losses than more gradual adjustments. As with the size of consolidation, its speed implies too an intertemporal trade-o¤, although of a di¤erent nature: front-loaded consolidations are more costly in the short-to-medium-run, but more benign in the medium-to-longrun. However, the former e¤ect ends up dominating in present-discounted terms. Key to this result is the fact that faster consolidations produce larger falls of collateral values and debt-de‡ation e¤ects which, as explained above, prolong the duration of borrowers’deleveraging phase and postpone the economic recovery. Third, and …nally, …scal adjustments based on expenditure cuts or capital income tax hikes are much more costly than those based on consumption or labor income tax hikes. In the …rst case, expenditure cuts produce relatively large contractions in activity already on impact, given the lack of an autonomous monetary policy, which in turn spills over into a sharper fall in assets prices, in‡ation and debtors’ 2
An additional channel through which …scal consolidations may endogenously prolong the private deleveraging phase is through a classic Fisherian e¤ect: by lowering in‡ation, it increases the borrowers’real debt burden which (for a given path of collateral values) delays the moment in time in which excess collateral becomes positive again.
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net worth. Through the debt-collateral channel highlighted above, a larger initial decline in debtors’net worth increases the length and depth of private deleveraging, thus amplifying the cost of reducing public debt. In the second case, higher capital taxes reduce the demand for assets and, hence, the pace of collateral accumulation which, given everything else, also increases the duration and cost of the deleveraging process. Our results shed some light on the ongoing debate about the appropriate design of …scal consolidations in terms of their size, speed and composition. Some pundits have advocated large and quick …scal adjustments as a means of bringing public debt back into a sustainable path. According to this view, even if they accentuate the depth of the recession, sharp …scal adjustments may make it shorter and eventually less painful. Other authors support milder and/or more gradual consolidations when possible, arguing that …scal multipliers are larger in recessions. Along this line of reasoning, postponing the bulk of the …scal retrenchment until the economy starts recovering would be the appropriate recipe. The presence of long term debt and collateral constraints in our model reinforces the latter policy prescription, although it turns the argument around. Smaller consolidations actually increase the output costs in the short-run (relative to the size of the consolidation), precisely when the recession is more severe, due to the above-mentioned bu¤ering e¤ect of long-term debt on private spending. Rather, what makes small consolidations more benign in relative terms over the medium run is the fact that, by favoring a faster recovery in the value of collateral, they shorten the duration of the deleveraging phase, thus bringing forward the time at which borrowers regain access to new credit. The impact of di¤erent …scal consolidation strategies on the length and depth of private deleveraging are key implications of our model. In this sense, our results uncover a novel channel that may be relevant in the design of consolidation packages, especially in the aftermath of a …nancial crisis, namely the endogenous response of private deleveraging. Overall, our analysis provides support for the adoption of ’deleveraging-friendly’ …scal consolidation strategies, insofar as they are more conducive towards an earlier reactivation of credit ‡ows and economic activity. We …nally note that in our model …scal rules always render public debt sustainable 5
and we do not consider an endogenous response of sovereign spreads. Thus, risks to sustainability or imperfect credibility of …scal policy announcements, which may constitute powerful arguments in favor of fast consolidation programs, are absent here. Short of minimizing the importance of this channel, which may be particularly relevant in situations of …scal stress, our analysis highlights a channel that is likely to be active in a context of high private debt cum deleveraging. Our paper is related to the literature assessing the e¤ects of …scal consolidations. A fair reading of this literature suggests that …scal consolidations may exert non-negligible temporary output losses but contribute to faster growth in the medium/long term (see e.g. Clinton, Kumhof, Laxton and Mursula, 2011; and Guajardo, Leigh and Pescatori, 2014). There is also a strand of empirical work that …nds that …scal consolidations might even be bene…cial in the short run under some conditions (see e.g. Alesina and Perotti,1997; and Cogan, Taylor, Wieland and Wolters, 2013). These …ndings are relevant for policy discussions about the most adequate path to achieve public debt consolidation. In some quarters it is argued that front-loaded adjustments may entail lower costs in present value terms (ECB, 2014). Other authors defend gradual consolidations, upon the hypothesis that short term …scal multipliers in the aftermath of a …nancial crisis are likely to be higher than long- term ones (Blanchard and Leigh, 2013; Corsetti, Kuester Meier and Müller, 2010; DeLong and Summers, 2012; and Fletcher and Sandri, 2015, among others). However, the transmission mechanism of …scal shocks may be di¤erent in the aftermath of the …nancial crisis. For one thing, in many jurisdictions, the capacity of monetary policy to mitigate the short run costs of …scal retrenchments is limited by the ZLB. This circumstance raises the magnitude of …scal multipliers (Christiano, Eichenbaum and Rebelo, 2011 and Woodford, 2011) which in turn crucially depend on the incidence of …scal shocks on the duration of the ZLB regime itself (Erceg and Lindé, 2014). Moreover, Eggertsson (2010) and Erceg and Lindé (2013) argue that in the ZLB the output e¤ect of spending cuts is higher than that of tax rate hikes. Also, Bi, Leeper and Leith (2013) study the conditions under which consolidations subject to uncertainty about their composition and intensity may be expansionary in the short run, and conclude that such conditions are likely to be more demanding 6
when they are based on spending cuts and the interest rate approaches the ZLB. Besides leaving central banks with little policy space, the recent …nancial crisis has left behind a landscape of heavily indebted households and …rms (see e.g. Andrés, Arce and Thomas, 2017; Buttiglione, Lane, Reichlin and Reinhart, 2014; and Justiniano, Primiceri and Tambalotti, 2015). Thus, in this context, it seems natural to incorporate private balance-sheet conditions into the analysis of …scal policies. In spite of some recent e¤orts, there have been few attempts to analyze jointly the dynamics of private and public debt. Eggertsson and Krugman (2012) show how …scal multipliers increase in the presence of private debt overhang. Batini, Melina and Villa (2016) explore the role of …scal policy in preventing an excessive accumulation of private debt and easing …nancial conditions of debt-constrained agents. Romei (2017) explores the aggregate implications of di¤erent …scal consolidation paths in a context of a closed economy without nominal rigidities, and concludes that the growth and welfare costs of consolidating depends crucially on the consumers’initial wealth position. To the best of our knowledge, the previous literature has not considered the case of endogenous duration and depth of private deleveraging, which is a key component of our model. We …nd that the presence of long term collateralized debt has a profound e¤ect on the way private spending adjusts to exogenous shocks, …scal or otherwise. Long-term debt contracts induce non-linearities in the multipliers associated to …scal retrenchments and, what is more important, establish a theoretical link between the size and timing of …scal consolidations, the length of private deleveraging and, ultimately, the combined costs of both processes. The rest of the paper is organized as follows. The model and the baseline calibration are presented in Section 2. In Section 3 we analyze the impact of alternative consolidation strategies and in Section 4 we perform a similar exercise against the backdrop of a credit crunch scenario. Section 5 concludes.
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2
Model
We present a general equilibrium model of a small open economy that belongs to a monetary union. There are three types of consumers: patient households, impatient households, and (impatient) entrepreneurs. In the class of equilibria analyzed in the following sections, the latter two agents will borrow from the former and from the rest of the monetary union by issuing long-term nominal debt. In periods in which borrowers are able to receive new credit ‡ows, they do so subject to collateral constraints. Real estate is the only collateralizable asset. We will henceforth refer to impatient and patient households as ’constrained’and ’unconstrained’households, respectively. Entrepreneurs produce an intermediate good using -commercial- real estate, equipment capital and labor as inputs, and sell it to a sector of retailers who transform it into …nal good varieties. In addition to equipment capital producers, there are construction …rms that produce real estate both for commercial and residential purposes. Finally, a …scal authority collects taxes on households and entrepreneurs, consumes, and issues non-contingent nominal debt, which is held by unconstrained households and foreigners. All markets operate under perfect competition, except those for varieties of …nal goods and labor services which are characterized by monopolistic competition. In what follows, we describe the basic elements of the model. In the notation used herein, all variables are expressed in real terms (with the consumption goods basket acting as the numeraire) unless otherwise speci…ed. Appendix A contains the whole set of equilibrium conditions.
2.1
Households
There is a representative constrained household and a representative unconstrained household, denoted respectively by superscripts c and u. The latter household is more patient, u > c . Otherwise both households have the same preferences, given by ( Z 1 x 1+' ) 1 X nt (i) di ; (1) E0 ( x )t log (cxt ) + # log (hxt ) 1+' 0 t=0 8
x = c; u, where nxt (i) are labor services of type i 2 [0; 1], hxt are housing units, 1="H
cxH;t
cxt = ! H
("H 1)="H
! H )1="H cxF;t
+ (1
("H 1)="H
"H =("H 1)
(2)
is a basket of home and foreign goods (denoted respectively by subscripts H and F ) and Z 1
cxH;t =
"p =("p 1)
cxH;t (z)("p
1)="p
(3)
dz
0
is a basket of domestic good varieties, where "p > 1. Cost minimization by each household yields the standard demand functions, cxH;t = ! H
PH;t Pt
"H
cxt ; cxF;t = (1
!H )
"H
PF;t Pt
cxt ; cxH;t (z) =
PH;t (z) PH;t
"p
cxH;t ;
(4) x = c; u, where Pt = is the consumer price index R1 (CPI), PF;t is the price of the foreign goods basket, PH;t = ( 0 PH;t (z)1 "p dz)1=(1 "p ) is the producer price index (PPI), and PH;t (z) is the price of home good variety z 2 R1 [0; 1]. Nominal consumption spending then equals 0 PH;t (z) cxH;t (z) dz + PF;t cxF;t = PH;t cxH;t + PF;t cxF;t = Pt cxt . 1 "H (! H PH;t +(1
2.1.1
1 "H 1=(1 "H ) ! H ) PF;t )
Unconstrained households
As regards intertemporal optimization, the unconstrained household maximizes (1) for x = u subject to (1 +
c u t ) ct
h u + dt + bgu t + pt ht
(1
u h ) ht 1
=
Rt
1 t
+ (1
dt
+ bgu t 1 Z 1 Wt (i) u w nt (i) di t ) Pt 0 1
Tt ;
where dt is the real value of net private debt holdings, bgu t is the real value of government debt holdings, Rt is the gross riskless nominal interest rate, h is the depreciation rate of real estate, pht is the real price of real estate, t Pt =Pt 1 is gross CPI in‡ation, Wt (i) is the nominal wage for labor services of type i, ct and w t are tax 9
rates on consumption and labor income, respectively, and Tt are lump-sum taxes. The …rst order conditions are standard (see Appendix A). 2.1.2
Constrained households
The constrained household maximizes (1) for x = c subject to (1 +
c c t ) ct
+ pht
[ht
(1
h ) ht 1 ] = bt
Rt
1
bt
1 + (1
t
w t )
Z
1
0
Wt (i) c nt (i) di Pt
Tt ;
(5) where bt is the real value of the household’s nominal debt outstanding at the end of period t. We assume that debt contracts are long term. In particular, at the beginning of time t the household repays a fraction 1 2 (0; 1) of all nominal debt outstanding, regardless of when that debt was issued. The real value of outstanding debt principal then evolves as follows, bt =
bt
1 t
+ bnew t
(1
)
bt
1 t
= bnew + t
bt
1
;
(6)
t
where bnew denotes gross new debt minus voluntary amortizations, i.e. those over t and above the contractual debt repayment (1 ) bt 1 = t .3 As in Kiyotaki and Moore (1997), borrowing is subject to collateral constraints. Following Iacoviello (2005), we assume that real estate is the only collateralizable asset and that a borrower can pledge up to an exogenous fraction mt (the loan to value –LTV– ratio) of the expected discounted value of its real estate holdings, mt Et (Rt = t+1 ) 1 pht+1 ht , which we henceforth refer to as collateral value for short. We de…ne excess collateral as the value of collateral in excess of bt 1 = t , i.e. of outstanding debt net of the current period’s contractual amortization payments. We assume that the household can only receive new credit if excess collateral is positive; when this is the case, the household can receive new credit up to the value of such excess collateral: 3 Total debt-related payments in each period are thus [(1 ) + (Rt 1 1)] bt 1 = t , i.e. the sum of amortization and interest payments. Net debt ‡ows are therefore bnew t [(1 ) + (Rt 1 1)] bt 1 = t = bt Rt 1 bt 1 = t , as written in equation (5).
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bnew mt Et (Rt = t+1 ) 1 pht+1 ht bt 1 = t . On the contrary, when excess collateral t is negative, the borrower cannot receive new credit, although it may still choose to make early repayments: bnew 0: Putting things together, and using (6), we have t that outstanding debt is limited by the following asymmetric borrowing constraint, bt
max mt Et
bt
t+1 h p ht ; Rt t+1
1
(7)
:
t
This asymmetry gives rise to a double debt regime. When collateral values exceed bt 1 = t , debt is restricted by the former; we refer to this as the ’high collateral’ regime. When collateral values fall below bt 1 = t , the household cannot pledge su¢ cient collateral so as to tap new credit and simply pays back debt (at least) at the contractual rate: bt bt 1 = t ; we call this the ’low collateral’ or ’slow deleveraging’regime.
2.2 2.2.1
Production Entrepreneurs
A representative entrepreneur produces an intermediate product and sells it to retailP t log cet , ers at a perfectly competitive real price mct . The entrepreneur maximizes E0 1 t=0 with the consumption basket cet de…ned analogously to (2), subject to a budget constraint. Entrepreneurs, who obtain operating pro…ts from their activities, are also assumed to own the …rms in the other productive sectors of the economy. All operating pro…ts (net of capital depreciation) are taxed at rate kt ; since pro…ts accrue to entrepreneurs and these are the sole owners of productive capital in the model, we will henceforth refer to kt as the capital income tax. The entrepreneur’s budget constraint is given by (1 +
c e t ) ct
=
1
k t
qt [kt
mct yte (1
Wt e n + bet Pt t
k ) kt 1 ] +
k t
Rt t
h e h pt ht 1
1 e bt 1
+
pht het
k qt k t
1
+ 1
e h ) ht 1
(1 k t
X
s=r;h;k
11
s t;
where yte = kt k1 het 1 h (net )1 k h is output of the intermediate good, kt 1 is capital equipment with unit price qt and depreciation rate k , het 1 is commercial real estate, net is a basket of labor services, Wt is a nominal wage index, bet is the real value of entrepreneurial debt outstanding at the end of period t, and f st gs=r;h;k are real pro…ts from the retail, construction and equipment capital-producing sectors, respectively. Entrepreneurs’ maximization is also subject to an asymmetric borrowing constraint analogous to the one on constrained households, bet
max met Et
t+1 h pt+1 het ; Rt
e e bt 1
;
(8)
t
where we allow for a di¤erent LTV ratio (met ) and contractual amortization rate e (1 ) for entrepreneurs. 2.2.2
Retailers
A continuum of monopolistically competitive retailers indexed by z 2 [0; 1] purchase the intermediate input from entrepreneurs at the real price mct , and transform it one for one into …nal good varieties. Retailers’real marginal cost is thus mct . Each re"p P (z) yt ytd (PH;t (z)), where yt is aggretailer z faces a demand curve yt (z) = H;t PH;t gate demand of the consumption basket. Let et 1= [cet (1 + ct )] denote the entrepreneur’s marginal utility of real income. Assuming Calvo (1983) price-setting, a retailer that has the chance of setting its nominal price at time t chooses h PH;t (z) to maximize i P1 s et+s P r d k r ( ) (P ) (P (z)), where 1 mc e H;t p t+s yt+s (P ) t t+s t+s s=0 Pt+s t are the retailer’s period-t pro…ts, p is the probability of not adjusting the price. The …rst-order condition is standard, with all time-t price setters choosing a common optimal price P~H;t . 2.2.3
Construction and equipment capital-producing …rms
A representative construction …rm maximizes its expected discounted stream of profP t et Wt h k h h h h its, E0 1 1 n iht , subject to the production e t t , where t = pt It t=0 Pt t 0
12
technology
( "
! nht
Ith =
iht 1
h
2
2
iht iht
1 1
#)1
!
;
where nht are labor services, iht is a basket of domestic and foreign goods (ihH;t ; ihF;t ) analogous to (2), and Ith are new real estate units. A representative equipment capital producer maximizes its expected discounted P t et k k k stream of pro…ts, E0 1 1 it , subject to the e t t , where t = qt It t=0 0
technology It = it 1
k
2
2
it
it
1
1
, where it is a basket of domestic and foreign
goods (iH;t ; iF;t ) analogous to (2), and It are new equipment capital goods. 2.2.4
Unions/wage setting
Both entrepreneurs and construction …rms use the following basket of labor service varieties, Z 1 "w =("w 1) ("w 1)="w s s ; nt (i) di nt = 0
s = e; h, where "w > 1 and i denotes the same variety in both baskets. Cost minimization implies nst (i) = (Wt (i) =Wt ) "w nst for each i 2 [0; 1], where Wt R1 ( 0 Wt (i)1 "w di)1=(1 "w ) is the nominal wage index. The nominal wage bill in sector R1 s = e; h is therefore 0 Wt (i) nst (i) di = Wt nst . Total demand for each labor variety is thus nt (i)
net
(i) +
nht
(i) =
Wt (i) Wt
"w
net + nht
ndt (Wt (i)) :
Producers distribute their demand for each labor variety randomly across the household population. This implies that the share of constrained and unconstrained households in type-i labor coincides with their (equal) share in the overall population: nut (i) = nct (i). As in Erceg, Henderson and Levin (2000; EHL), nominal wages are set à la Calvo (1983). In particular, a union representing all type-i workers maximizes the utility of the households to which such workers belong. Let xt 1= [cxt (1 + ct )] denote the marginal utility of real income for each household type x = c; u. Then, 13
a union that has the chance to reset the nominal wage at time t chooses Wt (i) to maximize " # 1+' 1 d X X n (W (i)) W (i) t t t+s s x w Et ( x w) ndt+s (Wt (i)) ; t+s 1 t+s P 1+' t+s x=c;u s=0 where w is the probability of not adjusting the wage. All time-t wage-setters choose ~ t ; see the …rst-order condition in the Appendix. a common optimal wage W
2.3
International linkages
A representative exporter produces a basket of domestic consumption goods, xt , that is de…ned analogously to (3). Cost minimization implies demand curves analogous R1 to the last equation in (4), and total spending is 0 PH;t (z) xt (z) dz = PH;t xt . The exporter sells the basket in export markets under perfect competition. The zero pro…t condition implies that the market price of the export basket is PH;t . Foreign demand for the basket of domestic goods is given by xt = (PH;t =PF;t ) "F yF;t , where PF;t and yF;t are the foreign price level and aggregate demand (both exogenous) and "F is the price elasticity of exports. As mentioned before, domestic agents can lend to and borrow from foreigners and other domestic agents at the riskless nominal rate Rt . Following standard practice in the literature, in order to guarantee stationarity of the country’s net foreign asset Pt nf at , for > 0, where position, we assume that Rt is given by Rt = R exp PH;t gdpt R is the area-wide nominal interest rate (which is assumed to be constant here), and nf at and gdpt are the country’s real (CPI-de‡ated) net foreign asset position and real (PPI-de‡ated) GDP.
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2.4
Fiscal authority
Real government debt bgt evolves as follows, bgt =
Rt t
1 g bt 1
k t
"
+
mct yte
PH;t gt Pt Wt e n Pt t
P
w Wt t Pt
Tt
x=c;u
h e h pt ht 1
+
U nC t + nt
k qt k t 1
+
c t
P
s=r;h;k
U e cC t + ct + ct # s t
(9)
:
We have assumed full home bias in government consumption, such that its nominal value equals PH;t gt . A …scal rule ensures stability of government debt. In particular, we will consider rules of the form f it = f it
1
+
b
bgy t 1
bgy +
b
bgy t
bgy t 1 ;
(10)
P bg
t t where bgy is the government debt-to-quarterly GDP ratio, bgy is its long-run t PH;t gdpt target, and f i 2 fg; w ; c ; k g is the …scal instrument that is endogenized through the …scal rule. The other …scal instruments are held constant at the steady state level f i 2 fg; w ; c ; k g.
The model is completed by the market clearing conditions and a number of de…nitions, which are shown in Appendix A.
2.5
Calibration and solution method
We calibrate the model to the Spanish economy. As explained in the introduction, we are motivated by the recent experience of euro area countries, which are still embarked in a lengthy process of both …scal consolidation and private sector deleveraging, Spain being a good example thereof. The time period is a quarter. We match the model’s steady state to a number of empirical targets in 2007, the year prior to the start of the …nancial crisis. Hence, our model’s steady state should be interpreted as the economy’s initial condition for the purpose of our simulation exercises.4 4
Of course, we do not claim that the Spanish economy was at its steady-state equilibrium in 2007.
15
The discount factor of impatient agents is set to = 0:98, following Iacoviello (2005). For patient households, we choose u = 1:025 1=4 , which is consistent with y a steady state nominal interest rate of Rss = 1:0251=4 ss = R e (nf ass ) . The unionwide in‡ation is F;ss = 1, which implies H;ss = ss = 1 in a stationary equilibrium. The union’s nominal interest rate is R = 1:021=4 and we set to replicate net foreign assets over GDP in 2007, nf ayss = 79:3%. The inverse labor supply elasticity is set to ' = 4, consistently with a large body of micro evidence. The weight parameter in the consumption basket, ! H , is set to match gross exports over GDP in 2007 (26:9%). The price elasticity of exports and imports is set to "F = "H = 1 (García et al., 2009) and the scale parameter in export demand, , is chosen such that steady-state terms of trade pss are normalized to 1. The elasticities of substitution across varieties of consumption goods and labor services, "p and "w , determine the desired markups in product and labor markets, respectively. We set "p = 7, consistent with an initial price markup of "p =("p 1) = 1:17, which is consistent with the …ndings of Montero and Urtasun (2014) for Spanish …rm-level data. To calibrate wage markups we follow Galí (2011) who interprets EHL model of wage-setting in a way that delivers equilibrium unemployment (see Appendix B for details). Targeting an unemployment rate of 8:6% in 2007, we obtain an initial wage markup of "w =("w 1) = 1:43, which we achieve by setting "w = 3:31. The elasticity of entrepreneurial output with respect to capital and real estate are set to k = 0:11 and h = 0:21, which help to replicate the labor share of GDP in 2007 (61:6%) and the share of equipment capital in the total stock of productive capital.5 Following Iacoviello and Neri (2010) we set h = 0:01, whereas k is set to a standard value of 0:025. The elasticity of construction output with respect to labor, !, is chosen to match the construction share of total employment in 2007 (13:4%). We set the weight of utility from housing services, #, to replicate gross household debt over annual GDP (80:2%). The scale parameters of convex investment adjustment costs, h and k , are chosen such that the dynamics of construction and equipment capital investment in our baseline deleveraging scenario resembles their behavior 5
The value of equipment capital was estimated at 21:4 per cent of the total value of productive capital in 2007 (using data from BBVA Research).
16
Table 1: Baseline calibration Parameter Value Preferences u
' # "p "w !H "H "F
0.994 0.98 4 0.35 7 3.31 0.65 1 1 0.83
Description
unconstrained household discount factor constrained household discount factor (inverse) labor supply elasticity weight on housing utility elasticity of subst. across consumption varieties elasticity of substitution across labor varieties weight home goods in consumption basket elasticity of imports wrt terms of trade elasticity of exports wrt terms of trade scale parameter export demand
Technology
0.21 0.11 k ! 0.50 0.01 h 0.025 k 12.0 h 9.9 k Price/wage setting 0.67 p 0.75 w Debt constraints m 0.85 me 0.69 0.98 e 0.97 h
elasticity output wrt real estate elasticity output wrt equipment elasticity construction wrt labor depreciation real estate depreciation equipment investment adjustment costs construction investment adjustment costs equipment fraction of non-adjusting prices fraction of non-adjusting wages household LTV ratio entrepreneur LTV ratio amortization rate household debt amortization rate entrepreneurial debt
Fiscal policy c w k
g bgy =4 bgy bgy
0.08 0.16 0.18 0.57 0.80 0.035 0.387
initial tax rate on consumption initial tax rate on labor income initial tax rate on capital income initial government spending long-run target for gov’t debt-to-annual GDP response coe¢ cient in …scal rule response coe¢ cient in …scal rule
17
during the crisis.6 The Calvo parameters are set to p = 2=3 and w = 3=4, such that prices and wages are adjusted every 3 and 4 quarters on average, respectively. This is consistent with survey evidence for the Spanish economy (see e.g. Druant et al., 2009). Regarding the debt contract we set m = 0:85 for the household’s initial loanto-value ratio, consistently with Spanish evidence on pre-crisis LTV ratios for new mortgages,7 while the entrepreneurial initial loan-to-value ratio, me = 0:69, is chosen to match the ratio of gross non-…nancial corporate debt to annual GDP (125:4% e in 2007). We calibrate the contractual amortization rates, 1 and 1 , to replicate the average age of the stock of outstanding mortgage debt prior to the e crisis: 1 = 0:02 and 1 = 0:03 per quarter.8 As explained above, all …scal instruments other than the one in the …scal rule (equation 10) are held constant at some initial values f s gs=c;w;k and g. We calibrate the initial tax rates f s gs=c;w;k as in Stähler and Thomas (2012), who calculate precrisis average implicit tax rates for di¤erent taxes. We set g such that g=gdpss equals the government spending share of GDP in 2007 (18:3%). In the …scal rule, we set the long-run target for the government debt-to-(quarterly) GDP ratio to bgy = 0:80 4, consistently with levels reached in Spain only a few years after the start of the crisis and with our focus on scenarios that involve a relatively large reduction (20 percentage points in our baseline exercise) in government debt ratios towards the EU Treaty target (60% of GDP). The response coe¢ cients in the rule, b and b , are calibrated to make the dynamic change in current de…cit roughly comparable across consolidation scenarios based on the di¤erent …scal instruments. Table 1 summarizes 6
The accumulated fall in construction and equipment capital investment 8 quarters after the …nancial shock replicate their accumulated fall 8 quarters after their peak in 2007:Q4 (24:5 per cent and 28 per cent respectively). 7 See e.g. Masier and Villanueva (2011, Table A1), and Akin et al. (2014, Table A.1). 8 Under our debt contracts (with a constant fraction of outstanding debt amortized each period), e the average age of the debt stock converges in the steady state to = (1 ) and e = (1 ) for households and entrepreneurs, respectively. According to calculations by Banco de España, based on data from the Land Registry o¢ ce and large …nancial institutions, the average age of outstanding mortgage debt prior to the crisis was close to 12:5 years for households and 8 years for non…nancial corporations and entrepreneurs. This yields = 12:5 4=(12:5 4 + 1) = 0:98 and e = 8 4=(8 4 + 1) = 0:97.
18
the calibration. Solution algorithm. We assume perfect foresight in all our simulations. We solve for the fully nonlinear equilibrium path, using a variant of the Newton-Raphson algorithm developed by La¤argue (1990), Boucekkine (1995) and Juillard (1996) (LBJ). Our assumption of long-run debt contracts gives rise to two debt regimes for households and entrepreneurs, as shown in equations (7) and (8) respectively. We have therefore modi…ed the LBJ algorithm to allow for endogenous change of debt regime. In all our simulations we consider one-time, unanticipated shocks. Provided the shocks (…scal of …nancial) are large enough for borrowers to endogenously enter the slow deleveraging regime, they do so on impact. The dates at which entrepreneurs and (constrained) households exit the latter regime, which we denote by T and T , respectively, are solved as equilibrium objects together with the paths of the endogenous variables.
3
E¤ects of a …scal consolidation
We …rst look at the isolated e¤ects of …scal consolidations, abstracting from any other disturbances. This allows us to illustrate some channels of transmission that will play a critical role in the full analysis of …scal consolidations in a private debt overhang presented later. The consolidations we study consist of reductions in the long-run target for the government debt to (annual) GDP ratio, i.e. bgy =4 in the the …scal rule (equation 10), from its initial value (80 per cent). We will refer to the numerical reduction in such target as the size of the …scal consolidation. A key outcome variable will be the dynamic …scal sacri…ce ratio, de…ned as the percentage GDP loss at each time t for each percentage point of reduction in the long-run debt/GDP ratio: gdpt = bgy (Erceg and Lindé, 2013). To further clear the desk, we focus for now on consolidations via government spending, i.e. we set f i = g in the …scal rule (equation 10).9 Figure 1 depicts the …scal sacri…ce ratios associated to two di¤erent consolidation 9
The results using alternative …scal instruments are qualitatively similar and are available on request.
19
sizes: a ’small’one of 1 percentage point (red continuous lines), and a ’large’one of 20 percentage points (dashed blue lines). The exercise in the left plot is simulated under the standard assumption of one-period private debt ( = e = 0), such that debt stocks are always constrained by collateral values; in the right plot, we simulate our benchmark model featuring long-term household and entrepreneurial debt. The comparison of both models is useful to clarify the type of non-linearities that arise here in the presence of long-term debt, due to the resulting asymmetric borrowing constraints (equations 7 and 8) and the resulting potential for debt-regime changes. Indeed, unlike in models with one-period debt, in our model the response to shocks need not be symmetric (as it may depend on the sign of the shocks) nor proportional to the shock size. In both cases, the (endogenous) contraction in government spending lowers GDP in a persistent manner. To a large extent, this persistence re‡ects the gradual adjustment prescribed by the …scal rule itself, but also a protracted e¤ect of the …scal shock on collateral values and hence on borrowers’net worth. Beyond this similarity, the dynamic path of output varies substantially depending on the maturity of debt. In the case of one-period debt (left plot of Figure 1), sacri…ce ratios are largely invariant to the size of the consolidation; i.e. that model is basically linear with respect to consolidation size. On the contrary, when private debts are long-term (right plot), the relative output response depends substantially on the size of the consolidation program. A small …scal adjustment has a stronger short-run relative e¤ect than a large one, but this pattern is reversed in the medium term, when the larger adjustment produces higher relative output losses.
20
Figure 1. Dynamic sacri…ce ratios (…scal consolidation only)
What is the reason for this intertemporal trade-o¤ in the sacri…ce ratios of di¤erently sized consolidations? In our model, long-run debt contracts imply that borrowers’debt repayments are bounded by the contractual amortizations.10 This dampens the impact on their spending capacity of shocks that reduce collateral values below outstanding debt. To see this, consider the real net debt ‡ows of indebted households, bt Rt t 1 bt 1 , which together with disposable labor income determines their spending capacity (equation 5).11 If the …scal adjustment is su¢ ciently small, then so is the fall in collateral values and excess collateral remains positive, i.e. Rt =mtt+1 pht+1 ht > bt t1 . This allows borrowers to tap new credit up to the limit dictated by such excess collateral; equivalently, debt equals the collateral value: bt = Rt =mtt+1 pht+1 ht . In this case, net debt ‡ows evolve according to bt
Rt
1 t
bt
1
=
mt ph ht Rt = t+1 t+1
Rt
1
bt 1 :
t
Along this path, the fall in collateral values Rt =mtt+1 pht+1 ht triggered by the …scal contraction reduces net debt ‡ows one for one. This adds to the standard debtde‡ation channel that raises the real value of the debt burden, Rt t 1 bt 1 . The resulting contraction in net debt ‡ows reduces debtors’spending capacity. 10
Indeed, due to their relative impatience, borrowers never choose to make voluntary debt repayments, i.e. in equilibrium constraints (7) and (8) are always binding. As a result, gross new credit is either positive and equal to excess collateral, or zero (when excess collateral is negative). 11 The argument applies analogously to entrepreneurs.
21
By contrast, if the size of the …scal consolidation is large enough to drive excess collateral below zero, then gross new credit bnew collapses to zero and, for as long t as this deleveraging regime lasts, net debt ‡ows simply equal (minus) the sum of interest and amortization payments, bt
Rt
1
bt
1
=
(Rt
t
1
1) + (1
)
bt 1 :
t
Therefore, in this regime net debt ‡ows are not directly a¤ected by changes in collateral values. Fiscal consolidations a¤ect net debt ‡ows only through the standard debt de‡ation channel.12 The previous mechanism, by which long-term debt contracts protect borrowers’ spending capacity from the e¤ect of large falls in collateral values and hence in net worth, may be interpreted as a ’bu¤ering e¤ect’ of long-run debt. Figure 2 illustrates this decoupling between net worth and spending by displaying the impact multipliers (impact response rescaled by consolidation size) of constrained households’ consumption and net worth.13 Notice …rst that the net worth response is basically proportional to the consolidation size, re‡ecting a roughly linear e¤ect of the latter size on the fall in collateral values. The same is not true for consumption. For instance, a 1 pp consolidation reduces consumption on impact by almost 0.7 per cent, quite close to the impact fall in net worth (0.8 per cent); for consolidations larger than 10 pp, however, the impact consumption multiplier drops to values in the range 0.1-0.2 per cent. This re‡ects the fact that, with small consolidations, borrowers never enter the slow deleveraging regime or do so only very brie‡y, whereas for larger consolidations they spend longer periods in the slow deleveraging regime, where their consumption becomes largely isolated from the fall in collateral values and net worth.14 This nonlinear e¤ect of consolidation size on constrained agents’ 12
Notice that the Fisherian debt de‡ation channel, which hinges here on the size of the sum of net interest and the amortization rate, (Rt 1 1) + (1 ), is weaker under multi-period loans (1 < 1) than under the standard one-period loan assumption (1 = 1). 13 The picture for entrepreneurs is very similar and is available upon request. 14 For the 5 pp consolidation, only (constrained) households enter the slow deleveraging regime and remain there only for 1 quarter. See Figure 4 below for further information on the duration of the deleveraging phases for di¤erent consolidation sizes.
22
consumption multipliers carries over to GDP (blue lines), thus producing milder relative contractions on impact following larger consolidations. Figure 2. Impact multipliers (…scal consolidation only)
However, the impact response of GDP only provides a small piece of information about the total output loss caused by a …scal consolidation. While the short-term sacri…ce ratio of larger consolidations is moderated by the bu¤ering e¤ect of long-term debt, larger consolidations also cause a larger contraction of asset prices and collateral values. For a su¢ ciently large consolidation, indebted consumers are pushed into the regime with negative excess collateral and slow deleveraging, in which new credit vanishes. This entails a potentially prolonged period of spending moderation, until the relative levels of debt and collateral are restored and new credit becomes accessible again. Figure 3 illustrates this phenomenon, comparing the evolution of household debt and collateral values under two consolidations of sizes 20 and 40 pp, respectively.15 Before the …scal shock (t = 0), the economy rests in the steady state of the baseline 15
Again, the picture is very similar for entrepreneurs and is also available upon request.
23
regime, where debt levels equal pledgeable collateral values.16 In both cases, excess collateral becomes negative on impact and constrained households enter the slow deleveraging regime, in which they receive no new credit and simply amortize their outstanding debt at the contractual rate. This deleveraging lasts until collateral values catch up with outstanding debt, i.e. until excess collateral becomes positive again, at which point households regain access to new credit. This gives way to a “releveraging” process, along which the evolution of the stock of debt becomes linked to that of collateral values. The di¤erence between both scenarios is the length of the deleveraging phase, which is almost two years longer under the larger (40 pp) consolidation. Two channels are responsible for prolonging the deleveraging. First, a larger consolidation depresses collateral values more, as shown by the dashed lines in the …gure, and therefore ceteris paribus they take longer to catch up with outstanding debt. Second, a larger consolidation also reduces in‡ation by more and hence raises the real value of the debt burden. Both e¤ects combine to produce the observed delay in the end of deleveraging. A longer deleveraging in turn prolongs the period of spending restraint by borrowers, thus making the aggregate recession longer-lasting and deeper. 16
Indeed, the fact that constrained households and entrepreneurs are both more impatient than unconstrained households, < u , guarantees that the collateral constraint binds for both agents in the steady state.
24
Figure 3. Collateral values and debt dynamics (…scal consolidation only)
Figure 4 takes a closer look at how consolidation size a¤ects the end-of-deleveraging periods for entrepreneurs (T ) and households (T ). As mentioned above, a 1 pp consolidation is small enough that neither group enters the deleveraging regime, whereas for a 5 pp consolidation only households do so and only for T 1 = 1 quarter. As consolidations become larger in size, the length of borrowers’deleveraging phase becomes longer and longer, re‡ecting larger falls in collateral values and stronger debt de‡ation e¤ects. Larger consolidations thus postpone the reactivation of credit and hence the recovery in borrowers’spending. This ’duration e¤ect’explains why severe consolidations produce higher medium-term relative output losses, as shown in Figure 1.
25
Figure 4. End-of-deleveraging dates (T ; T ), …scal consolidation only
3.1
Welfare and present-value multipliers
So far, we have seen that larger consolidations entail smaller relative output losses in the short run but larger ones in the medium run. In light of this intertemporal trade-o¤, it is useful to summarize the overall e¤ects of alternative consolidations at di¤erent horizons. A …rst natural statistic is social welfare, given by E0
1 hX X t=0
x=c;u
(
x t
) U (cxt ; hxt ; fnxt g) +
t
i log cet ;
where U is the period utility function of households as introduced in equation (1). We compute the welfare loss of a …scal consolidation as the percentage change in permanent consumption of all agents that is required to compensate for the e¤ects of the consolidation.
26
Table 2. Welfare losses and present-value multipliers (…scal consolidation only) Size (pp) Welfare loss (rescaled by size) PV GDP multiplier [T ; T ]
1
5
20
40
0.016 0.066
0.017 0.067
0.020 0.070
0.024 0.076
[ ; 2]
[3; 8]
[6; 15]
[ ;
]
Welfare losses as % of permanent consumption
Table 2 shows that the welfare loss, rescaled by the consolidation size, increases monotonically with such size. This reveals that the duration e¤ect dominates the bu¤ering e¤ect. That is, even though long-term debt protects borrowers’short-run spending capacity in the face of large consolidations, the latter prolong borrowers’ deleveraging phase and delay the economic recovery, and it is through this last e¤ect that welfare losses increase more than proportionally with the consolidation size. The same pattern is observed when we compute the present-value GDP multiplier, P P de…ned as Tt=1 ( u )t 1 gdpt = Tt=1 ( u )t 1 bgy , i.e. the present-discounted value of the GDP change over the T periods following the …scal shock divided by the present-discounted value of the …scal shock.17 Again, the present-value multiplier increases more than proportionally as we increase the consolidation size, re‡ecting the additional (relative) output costs in the medium term of larger consolidations.
4
Fiscal consolidations in an environment of private deleveraging
In this section we use our framework to analyze the e¤ects of di¤erent …scal consolidation strategies against the backdrop of a private deleveraging process that is already unfolding as a consequence of a negative …nancial shock. In mind we have the recent experience of a number of European countries where the main motivation for consolidating public …nances was the worsening of their macro…nancial landscape 17
We set the horizon of the present-value multiplier to T = 80. Results for longer horizons are qualitatively similar.
27
that followed from the crisis initiated in 2008. In this sense, although we do not model the consolidation decision, we analyze its macroeconomic e¤ects in a more realistic environment in which, contrary to the previous section, the trigger of private deleveraging is not primarily the result of the …scal retrenchment itself. In this richer context, that combines …scal policy shocks and …nancial shocks, we …rst analyze the relative cost of large versus small consolidation programs. Second, we study the cost of gradual versus front-loaded consolidation programs (of a given size). And, …nally, we compare the e¤ects of alternative instruments (government spending vs di¤erent taxes) used to adjust the government debt ratio towards its target.18
4.1
A baseline scenario of private deleveraging
We start by constructing the baseline private deleveraging scenario, absent any …scal consolidation. In order to re‡ect the …nancial origin of recent global crisis, we shock our model economy with an unexpected, gradual and permanent drop in the LTV ratios of both households and entrepreneurs. We assume an autoregressive process for e x the LTV ratios, xt = (1 ) x + x xt 1 , x = m; me , where we set m = m = 0:75. We then simulate an unanticipated fall in the long-run LTV ratios (m; me ) of 5 percentage points from their baseline values in Table 1, a conservative choice in the light of recent experience in Spain.19 Figure 5 depicts the response of the main variables to the deleveraging shock. The latter is large enough to push the economy into the deleveraging regime already on impact. Total consumption declines as a result of the deleveraging process, and then it experiences successive recoveries when, …rst, entrepreneurs and, then, households regain access to new loans. The shock has also a negative impact on total investment, driven by lower expenditure in both real estate and equipment capital. 18
In the …rst two exercises we focus just on consolidations based on adjustments in government spending (gt ). The results for consolidations based on capital income taxes ( k ) and consumption taxes ( c ) are qualitatively similar. See Appendix C for details on the analysis of the e¤ects of the size of consolidations based on k and c . 19 Data from the Spanish Land Registry o¢ ce shows that average LTV ratios for new mortgages declined by 7:7 percentage points in the 6 years between 2007:Q3 and 2013:Q3.
28
Figure 5. Baseline deleveraging scenario (no …scal consolidation)
The de‡ationary process caused by the …nancial shock leads to a temporary depreciation of the terms of trade, which fosters gross exports. Moreover, imports fall due to the combined e¤ect of the terms-of-trade depreciation and the severe contraction in domestic demand. Both e¤ects give rise to a substantial improvement in net exports during the deleveraging period. The positive contribution of the external sector, however, is not su¢ cient to avoid a protracted recession that lasts two years. As shown in Andrés, Arce and Thomas (2017), the presence of long-run debt allows a related model to replicate reasonably well the dynamics of private debt observed during historical deleveraging episodes, and to clearly outperform a model version with one-period debt (as typically assumed in standard models) in that respect.
4.2
The size of the …scal adjustment
We discuss now the output e¤ects of the size of the consolidation program. Figure 6 depicts the …scal sacri…ce ratio associated to spending-based consolidations of two 29
di¤erent sizes: 1 pp (red continuous line) and 20 pp (blue dashed line). Since now there are two shocks (…nancial and …scal) taking place simultaneously, in what follows we calculate the GDP e¤ect of a …scal consolidation ( gdpft c ) as the di¤erence between (a) the GDP path in the scenario with both …nancial and …scal shocks and (b) that in the baseline scenario with the …nancial shock only. The dynamic sacri…ce ratio is then given by gdpft c = bgy . Figure 6. Dynamic sacri…ce ratios under private deleveraging
Notice …rst that the main results from the analysis of isolated …scal consolidations in Section 4 are preserved in the presence of a separate …nancial shock: larger consolidations imply smaller sacri…ce ratios in the short run, but larger ones over the medium run. Both the bu¤ering e¤ect and the duration e¤ect, already analyzed in Section 4, show up in this context too. Compared with the sacri…ce ratio in the …scal-shock-only case (Figure 1), the former e¤ect seems to be weaker now, whereas the duration e¤ect remains strong. The latter e¤ect is analyzed more closely in Figure 7, which displays the same objects as Figure 3 but for the present case in which the deleveraging shock accompanies the …scal consolidation.
30
To illustrate how consolidations size a¤ects the duration of deleveraging, we compare two …scal consolidations of 1 pp (red lines) and 20 pp (blue lines) respectively.20 The larger consolidation prolongs the length of the deleveraging phase for both entrepreneurs and households, through the same two channels discussed in Section 4. First, larger consolidations depress collateral values more. Second, they raise the real debt burden more, through a stronger debt de‡ation e¤ect. Both channels delay the moment in time in which collateral values catch up with outstanding debt, i.e. in which excess collateral becomes positive again, thus delaying the end of borrowers’ deleveraging phase. Since borrowers’spending experiences a surge in the period in which they regain access to new credit, larger consolidations have a longer-lasting and deeper contractionary e¤ect on GDP, as seen in Figure 6 above.21 20 While the blue lines in Figure 7 show the adjustment of collateral values and debt stocks in the case of a small (1 pp) …scal consolidation, they are very similar to the corresponding objects in the baseline scenario with deleveraging shock only (and no …scal consolidation) represented in Figure 5 above. 21 Figure 7 also helps understand the spikes in the dynamic sacri…ce ratio associated to the larger consolidation in Figure 6. The latter …gure shows di¤ erences in the GDP path with respect to the baseline scenario with deleveraging shock but no …scal consolidation. By delaying the end of deleveraging and hence the surge in borrower spending, the larger consolidation produces downward spikes in the GDP path with respect to the no-consolidation scenario. These spikes do not show up in the case of a 1 pp consolidation, since the latter is small enough to leave the length of deleveraging una¤ected.
31
Figure 7. Collateral and debt under private deleveraging and …scal consolidation
As in the no-…nancial-shock case analyzed in the previous section, we may resolve the apparent intertemporal trade-o¤ observed in Figure 6 by computing welfare losses (relative to the consolidation size) and present-value output multipliers.22 The results are shown in Table 3. Once again, the duration e¤ect that delays the exit from deleveraging for private-sector borrowers outweighs the short-run bu¤ering e¤ect, such that both welfare losses and discounted future output losses increase more than proportionally with the consolidation size. Table 3. Welfare losses and present-value multipliers under private deleveraging Consolidation size (pp)
1
20
Welfare loss (rescaled by size) Present-value GDP multiplier
0.024 0.034
0.026 0.040
[T ; T ]
[8; 15]
[11; 19]
Welfare losses as % of permanent consumption 22
In this case, welfare and output e¤ects are computed relative to the baseline (no-consolidation) scenario.
32
4.3
Gradualism vs front-loading
Another dimension of …scal consolidations that has been much discussed in policy circles is the appropriate pace of debt (or de…cit) adjustment. So far we have kept constant the speed of …scal consolidation as captured by the coe¢ cients in the …scal rule, and focused on di¤erences across consolidation sizes. In this section we …x the consolidation size at 20 percentage points and consider di¤erent values of the response coe¢ cient ( b ) to debt deviations from target (bgy bgy ). In this way we t 1 analyze two types of …scal adjustments: front-loaded consolidations (high b ) and gradual consolidations (low b ).23 A key question is to what extent the speed of adjustment a¤ects the response of GDP and interacts with the duration of private-sector deleveraging (T ; T ).24 As can be seen in Figure 8, a higher degree of gradualism reduces the short-tomedium-run costs of the …scal consolidation, but raises the medium-to-long-run costs. To resolve this trade-o¤, we compute again welfare losses.25 As shown in Table 4, front-loaded consolidations imply larger welfare losses than more gradual ones. The reason, once again, is the endogenous e¤ect of the …scal consolidation on private deleveraging dynamics. Front-loaded consolidations entail larger losses in collateral values and debt de‡ation e¤ects in the short to medium run. This postpones the end of deleveraging for (constrained) households and entrepreneurs, as shown in 23
In particular, we set b to 0.08 (front-loaded scenario) and 0.02 (gradual scenario). The baseline value is still given by the one in Table 1. 24 In our analysis, we abstract from the existence of credit spreads on government debt, and hence from the possible e¤ect of di¤erent consolidation scenarios on such spreads. In particular, it may be argued that gradualism in …scal consolidation may be less benign in a situation in which such gradualism may impact adversely on sovereign spreads vis-à-vis a more front-loaded strategy. We consider however that this omission is unlikely to matter signi…cantly for the purpose at hand, for two reasons. First, we restrict our attention to scenarios in which the government credibly commits to reducing its debt ratio. It is thus di¢ cult to see that more gradualism could have adverse e¤ects on spreads in this context. Second, we have in mind a setup in which spreads are low and stable, as is currently the case in basically all euro zone economies. Again, in this context, it is unlikely that spreads should react di¤erently to more gradual versus front-loaded consolidation strategies. Bi (2012) shows that the spread may be ‡at for high values of the debt to GDP ratio and that it only increases, rapidly once the perceived probability of default rises signi…cantly above zero. 25 Since the consolidation size is …xed in this subsection (at 20 pp), there is no need to rescale welfare losses by such size here. Table 4 therefore shows actual welfare losses, i.e. without rescaling.
33
the last column of the table, and hence delays the economy recovery. Thus, frontloaded consolidations prolong the associated short/medium-run GDP losses beyond what would be dictated by the sheer timing of the …scal adjustment. Through this endogenous, non-linear e¤ect on debt deleveraging, the intertemporal trade-o¤ in the dynamic e¤ects of front-loaded vs gradual consolidations is tilted in favor of the latter. The importance of this channel is further con…rmed by the fact that the degree of front-loading raises welfare losses more strongly for borrowers (constrained households and entrepreneurs).26 Figure 8. Output costs of consolidation: the e¤ect of gradualism
26
Similar results are obtained if gradualism concerns the smoothing parameter ized speci…cation that allows for a time-varying debt ratio target (bgy t ), bgy t =
gy bgy bt 1
+ (1
These results are also available upon request.
34
bgy ) b
gy
:
bgy
in a general-
Table 4. Welfare losses from …scal consolidation under private deleveraging Scenario Front-loaded Baseline Gradual
Aggregate Unconst. HHs Const. HHs Entrepreneurs [T ; T ] 0.83 0.55 0.42
0.25 0.09 0.06
1.90 1.18 0.91
1.66 1.37 1.08
[12; 22] [11; 19] [10; 18]
Note: welfare losses in % of permanent consumption
These results o¤er a new perspective on the desired pace of …scal adjustments. Some authors defend a more gradual pace of consolidation, arguing that gradualism helps to avoid large …scal shocks in the short run, i.e. at the time when the …scal multiplier is presumably larger, specially in a context with high levels of private debt and lack of room for maneuver on the side of monetary policy. In our model of private debt deleveraging, the rationale for gradual consolidations is di¤erent. Front-loaded consolidations entail larger …scal adjustments in the early years of the consolidation program, i.e. while private borrowers are still reducing their debt stocks. This means that the adjustment thus hits harder at a time when borrowers’ spending capacity is actually protected from large falls in collateral values that come along with a sharper contraction in economic activity. However, larger falls in collateral values (and stronger debt de‡ation e¤ects) also prolong the deleveraging phase, thus producing a longer-lasting and deeper recession. It is this last e¤ect the one that turns out to dominate and, hence, determine the welfare impact of alternative consolidation paces.
4.4
Alternative …scal instruments
Finally, we analyze how the e¤ects of a …scal consolidation of a given size (20 pp) change depending on the used …scal instruments: government spending (gt ), consumption tax ( ct ), and capital income tax ( kt ).27 As can be seen in Figure 9, 27
The coe¢ cients of the rules have been chosen so that adjustment in di¤erent instruments lead to equal responses of the public de…cit at time t = 1. The e¤ects of consolidations based on labor income taxes ( w t ) are relatively similar to those of a consumption tax-based consolidation, and we
35
di¤erent instruments give rise to distinct patterns in the dynamic output e¤ects of the …scal consolidation, out of which several features stand out.28 First, consolidations implemented through adjustments in taxes induce more moderate output losses in the short run than those based on government spending cuts. The reason is twofold. On the one hand, government spending cuts are more de‡ationary than consumption (or labor income) tax hikes, because the latter tend to raise …rms’ marginal costs ceteris paribus. In a context such as ours in which monetary policy does not accommodate the de‡ationary impact of …scal adjustments, government spending shocks produce a larger increase in real interest rates, as already emphasized in the literature (see e.g. Eggertsson, 2010, and Erceg and Lindé, 2013). On the other hand, and di¤erently from previous literature, a spending-based consolidation depresses collateral values (both though higher real interest rates and lower economic activity) more than a tax-based one does which, together with stronger debt de‡ation e¤ects, delays by more the end of deleveraging and prolongs the contractionary e¤ects of the consolidation. Indeed, we …nd that the spending-based consolidation lengthens the deleveraging phase (vis-à-vis the baseline no-consolidation scenario) by 4 and 3 quarters for entrepreneurs and constrained households respectively, whereas the consumption-tax-based one does so by 1 quarter for the former only. thus omit them for brevity. 28 As discussed in the context of Figure 6, in Figure 9, the spikes in the GDP e¤ects re‡ect …scally-induced changes in the end-of-deleveraging dates T and T (and hence in the dates at which the associated surges in entrepreneurs’and households’spending take place) relative to the baseline no-consolidation scenario.
36
Figure 9. Dynamic sacri…ce ratios across …scal instruments
Second, while the short-run e¤ect on output is similar for consolidations based on capital income and consumption taxes, consolidation through capital taxes becomes much more costly over time, as its negative e¤ect on debtors’net worth and collateral accumulation gathers momentum. Indeed, the instrument that exerts the most distinctive impact on the dynamics of GDP is k . This re‡ects the fact that the adjustment in capital income taxes prolongs considerably entrepreneurs’deleveraging (by 4 quarters relative to the baseline scenario) while leaving the duration of households’deleveraging una¤ected. Thus, the e¤ect of capital income tax hikes on investment and collateral accumulation is stronger than that on consumption, which explains a more gradual but eventually stronger contractionary e¤ect on GDP as compared with the impact of ct and gt . While hikes in capital income taxes have mild short-run e¤ects on consumption and output (similar to those of consumption tax increases), by inhibiting the accumulation of collateralizable capital assets (and keeping their market value low), they lead to longer and deeper entrepreneurial deleveraging and hence to higher medium-to-long-run output losses.
37
5
Concluding remarks
Motivated by the recent experience of a number of countries in the euro area, we have analyzed the e¤ects of …scal consolidations in an economy inside a monetary union where households and …rms are embarked in a lengthy debt-reduction process. We have focused on the macroeconomic impact of the size, speed, and composition of consolidation programs, with particular attention to how the latter a¤ect the endogenous dynamics of private debt deleveraging. To this end, we have developed a model that sheds light on several largely unexplored channels of mutual feedback between private and public debt reduction processes. Our analysis shows that larger consolidation programs produce smaller …scal multipliers in the very short-run but larger ones in the medium-run. Long-term private secured (mortgaged) debt plays a critical role in these results. Contrary to the canonical assumption of one-period debt, allowing for more realistic maturity pro…les for private loans limits the speed of deleveraging, at the cost of making it lengthier. In this way, long-term debt provides some cushioning for borrowers’ spending after a negative shock. This cushioning e¤ect is more important, in relative terms, for large …scal consolidations, thus giving rise to a negative relation between the size of the consolidation and its associated (relative) short-run output cost. On the ‡ip side, larger consolidations depress by more the value of collateral. As a result, it takes longer for collateral values to recover su¢ ciently relative to outstanding debt, and hence for borrowers to regain access to new credit. Thus, larger consolidations prolong the duration of deleveraging and make the recession longer and deeper. Through a similar channel, front-loaded (faster) consolidation programs delay as well the reactivation of credit and the economic recovery, although they allow smaller …scal adjustments and lower costs later on. In terms of welfare costs (relative to the consolidation size) or present-value output multipliers, the above intertemporal trade-o¤s are resolved in favor of smaller and more gradual consolidations. Finally, the previous e¤ect on the duration of the recession, along with the lack of monetary policy accommodation, entails higher costs from spending-based or capital tax-based consolidations compared to consumption tax-based ones. 38
In short, the endogenous e¤ect on the duration and depth of private debt deleveraging turns out to be a powerful transmission mechanism of …scal consolidations in a context of private debt overhang, one that has been largely neglected in the previous literature. Overall, our results suggest that, in such a context, smaller and/or gradual consolidations tend to be more deleveraging-friendly and, as a result, more conducive towards an earlier reactivation of credit ‡ows and economic activity. In interpreting these results, it is worth recalling that we have analyzed a model economy where the …scal authority can credibility commit to alternative consolidation paths, all of which render public debt sustainable. Hence, we do not consider an endogenous response of sovereign spreads. In some real-life contexts, as it could have been the case in a number of euro area countries during the turbulences in the sovereign debt markets in 2010-2012, this last channel can constitute a powerful argument in favor of fast consolidation programs. In this sense, our benchmark economy can be best understood as one where any potential obstacles limiting the credibility of the government to pursue a given …scal strategy have already been dispelled. Alternatively, one might interpret our exercises as featuring changes in the degree of …scal gradualism of a magnitude not large enough so as to trigger a reassessment of the credibility of the …scal strategy by the holders of government debt.
39
References [1] Alesina, A. and R. Perotti (1997): “Fiscal Adjustments in OECD Countries: Composition and Macroeconomic E¤ects". International Monetary Fund Sta¤ Papers, 44(2), 210-248. [2] Andrés, J., O. Arce and C. Thomas (2017): "Structural reforms in a debt overhang", Journal of Monetary Economics, 88, 15–34. [3] Batini, N., G. Melina and S. Villa (2016): "Fiscal Bu¤ers, Private Debt, and Stagnation: The Good, the Bad and the Ugly", International Monetary Fund, Working Paper No. 16/104. [4] Bi, H., (2012): “Sovereign default risk premia, …scal limits, and …scal policy,” European Economic Review, 56, 389–410. [5] Bi, H., E. Leeper.and C. Leith (2013): “Uncertain Fiscal Consolidations,” The Economic Journal 123(566): F31–F63. [6] Blanchard, O. and D. Leigh (2013): "Fiscal consolidation: At what speed?", VoxEu [7] Boucekkine, R., 1995. An Alternative Methodology for Solving Nonlinear Forward-Looking Models. Journal of Economic Dynamics and Control, 19(4), 711-734. [8] Buttiglione, L., P. R. Lane, L. Reichlin and V. Reinhart (2014). “Deleveraging? What Deleveraging?” ICMB, CEPR, Geneva Reports on the World Economy no. 16. [9] Calvo, G., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, 12(3), 383-398. [10] Christiano, L., Eichenbaum, M. and S. Rebelo (2011) "When is the Government Spending Multiplier Large?", Journal of Political Economy, 119, 78-121. 40
[11] Clinton, K., M. Kumhof, D. Laxton, S. Mursula (2011): "De…cit Reduction: Short-term Pain for Long-term Gain", European Economic Review, 55 (2011), 118–139. [12] Cogan, J. F., Taylor, J. B., Wieland, W. and M. H. Wolters (2013): "Fiscal Consolidation Strategy", Journal of Economic Dynamics and Control, 37, 404– 421. [13] Corsetti, G.,Kuester, K., Meier, A. and G. J. Müller (2010): "Debt Consolidation and Fiscal Stabilization of Deep Recessions", American Economic Review, 100(2), 41-45. [14] DeLong, J. Bradford, and Lawrence H. Summers (2012): Fiscal Policy in a Depressed, Brookings Papers on Economic Activity, 233–297. [15] Draghi, M. (2014). "A consistent strategy for a sustained recovery", Lecture at Sciences Po, Paris, 25 March 2014. [16] Druant, M., Fabiani, S., Kézdi, G., Lamo, A., Martins, F., Sabbatini, R., 2009. How are …rms’wages and prices linked: survey evidence in Europe. ECB working paper (1084).. [17] ECB (2014): "Fiscal Multipliers and the Timing of Consolidation", ECB Monthly Bulletin, April, European Central Bank, Frankfurt. [18] Eggertsson, G., (2010): "What …scal policy is e¤ective at zero interest rates? NBER Macroeconomics Annual, 25,59–112. [19] Eggertsson, G. B. and P. Krugman, 2012. "Debt, Deleveraging, and the Liquidity Trap: A Fisher-Minsky-Koo Approach," Quarterly Journal of Economics, 127(3), 1469-1513. [20] Erceg, C. J., D. W. Henderson and A. Levin, (2000): "Optimal monetary policy with staggered wage and price contracts," Journal of Monetary Economics, 46(2), 281-313. 41
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43
Appendix A. Equilibrium conditions Let p~t P~H;t =PH;t , pH;t Equilibrium conditions:
PH;t =Pt , wt
~ t =Wt , W
Wt =Pt , w~t
wt
Wt =Wt 1 .
Unconstrained household budget constraint and …rst-order conditions (dt , hut ), (1 +
gu c u h t ) ct +dt +bt +pt
hut
u h ) ht 1
(1 u t
u t
u h t pt
=
=
u
Rt
Et
dt
1
u t+1
+ bgu t 1 +(1
u w t ) wt nt
(11)
;
(12)
u t+1 ;
(13)
c u t ) ct
(1 + Et
1 t
t+1
# + hut
Rt
1
u
=
=
h h ) pt+1 :
(1
(14)
Constrained household budget constraint, debt constraints, and …rst-order conditions (bt , ht ), (1 +
c c t ) ct
+ pht [ht
(1
h ) ht 1 ]
c h t pt
where and #t
t
Rt t+1
=
bt
t+1 h p ht ; Rt t+1
max mt Et c t
= Et
1
1
w c t ) wt nt
+ (1
t
bt
c t
Rt
= bt
c t+1
# + Et hct
=
+ t 1#t c t+1
1 (1 + 0
+
c c t ) ct
is the Lagrange multiplier on bt mt Et Rt+1 pht+1 ht bt 1 = t . t 44
1
(16)
t
(17)
; Et
t 1#t <0
h h ) pt+1
(1
bt
t+1
1 t
1#t+1 <0 ;
(18)
t+1 h p ; Rt t+1
(19)
t+1
+ t 1#t 0 mt Et bt
Tt ; (15)
, 1( ) is the indicator function
Tt ;
Entrepreneur budget constraint, technology, debt constraints, and …rst-order conditions (bet , het , net , kt ), (1+ ct ) cet =
k t
1-
Wt e n + bet Pt t
mct yte
qt [kt
(1
k ) kt 1 ]
t
1 e bt 1
h e h pt ht 1
k t
+
Rt
+
pht het k qt k t 1
(1- h ) het
1
X
k t
+ 1
(20) s t;
s=r;h;k
yte = kt k1 het bet
max met Et e t
e t
e h t pt
= Et
Rt t+1
k t+1
1
= Et
e t+1
+
mct+1
=
e
Et
k t+1
1
1 c e t ) ct
(1 +
e e t 1#t 0
mct+1
h
1
k
e k yt+1 =kt + 1= et+1
(23) e
Et
e t+1 t+1
k t+1 h
+
h
1
1
(net ) k
e
e bt
where et is the Lagrange multiplier on bet e e bt 1 = t .
(22)
t
;
h
het
(21)
;
e e bt 1
e e t 1#t <0
+
k ) kt 1
h
k
t+1 h p he ; Rt t+1 t
e e h yt+1 =ht + 1= et+1
wt = mct (1 e t qt
=
(net )1
h
1
1 t
+
and #et
pht+1
h
(24)
1#et+1 <0 ;
k
k t+1 k
+ et met Et ; qt+1
met Et
;
t+1
Rt
t+1
ph 1#e 0 ; Rt t+1 t (25) (26) (27)
pht+1 het
Retailers’optimal price decision, and aggregate pro…ts,
Et
1 X s=0
(
s
p)
e t+s
k t+s
1 e t
2
6 p~t 6 s 4Q
pH;t+s
H;t+j
"p "p
j=1
r t
= yt (pH;t
45
mct
t) ;
30 Q s
1"p
7 B j=1 H;t+j C B C yt+s = 0; mct+s 7 5@ A 1 p~t (28) (29)
Dynamics of PPI in‡ation and price dispersion, 1 "p
1 = (1
) p~t
(1
) p~t
t
"p
"p 1 H;t ;
+
"p H;t
+
(30) (31)
t 1:
Construction …rm output, …rst order conditions (nht , iht ), and pro…ts, Ith =
wt =
1 =
! nht
pht
e t+1 e t
+
pht !
(1
1 1
!)
! nht
( "
iht 1
! 1 nht
iht
k t+1 h pt+1 k t
iht =iht
1
1 1
h
1
iht
2
2
1 1
!
h
1 iht+1
2 h
1
wt nht
2
(32)
;
#)1
!
(1-!)
= pht Ith
#)1 2
iht
2 diht
h
! nht+1
h t
for diht
iht
1
iht
2
( "
2
iht
h
diht
!
(33)
;
2
diht
h
2 diht+1
iht iht
(34) 1
!
iht ;
h
diht+1 (35)
1.
Equipment capital producers output, …rst order condition (it ), and pro…ts, "
k
It = it 1
1 = qt 1
k
2
2
(dit )
k
(dit )
2 it
it k t
for dit
it =it
1
+ 1
= qt It
1.
46
2
it it
1 1
e t+1 e t
1 1
it ;
#
(36)
;
k t+1 q k t+1 t
k
(dit+1 )
i2t+1 ; (37) i2t (38)
iht+1 iht
2
;
Optimal wage decision, 1 XX
(
6 16 w) 4 Q s s
x
x=c;u s=0
with
c
2
w t+s
w~t wt+s 1= xt+s
"w
w;t+j
'
nxt+s "w 1
1
0
B w~t B s @Q
w;t+j
j=1
j=1
C C A
s "w ' 3 0 Q
7 B j=1 w;t+j C 7B C 5@ A w~t (39)
= .
Dynamics of wage in‡ation and wage dispersion, 1 = (1 w;n t
~t1 "w w) w
+
"w 1 w wt ;
"w
+
"w w wt
= (1
~t w) w
(40)
w;n t 1:
(41)
Fiscal authority’s budget constraint and …scal rule, bgt =
Rt t
1 g bt 1
k t
"
+
PH;t gt Pt Wt e n Pt t
mct yte
f it = f it with f i 2 fg;
w
;
c
;
k
1
+
P
w Wt t Pt
Tt
x=c;u
h e h pt ht 1
+
U nC t + nt
k qt k t 1
+
c t
P
s=r;h;k
b
bgy t 1
bgy +
b
bgy t
bgy t 1 ;
U e cC t + ct + ct # s t
;
(42)
(43)
g.
Aggregate employment, Ntc = nct
w;n t ;
(44)
Ntu = nut
w;n t ;
(45)
Nt = Ntc + Ntu ;
(46)
Export demand, xt = (pt )
47
"F
yF;t :
1"w
(47)
nxt+s =0;
Intermediate good market clearing, yt
t
= kt k1 het
h
1
(net )1
h
k
(48)
;
Labor market clearing and distribution across households, nct + nut = net + nht ;
(49)
nct = nut ; Consumption goods basket market clearing, yt = ccH;t + cuH;t + ceH;t + iH;t + ihH;t + xt + gt
(50)
Real estate market clearing, ht + hut + het = Ith + (1
h)
ht
1
+ hut
1
+ het
1
:
(51)
Equipment capital market clearing, kt = (1
k ) kt 1
+ It :
(52)
;
(53)
:
(54)
Real wages, wt = wt
wt 1 t
Terms of trade, pt = pt
H;t 1
F;t
Relative demand for domestic goods, ccH;t = ! H pH;t"H cct ;
(55)
cuH;t = ! H pH;t"H cut ;
(56)
48
ceH;t = ! H pH;t"H cet ;
(57)
iH;t = ! H pH;t"H it ;
(58)
ihH;t = ! H pH;t"H iht ;
(59)
Relative domestic producer prices, H;t
pH;t = pH;t
1
(60)
;
t
CPI in‡ation, 1 "H t
=
! H pt
1 "H 1
1 "H
! H pt
1
+1
!H
1 "H H;t
+
1 ! H pt
!H 1 "H
1
+1
!H
;
(61)
Real (PPI-de‡ated) GDP, gdpt = yt +
1 pH;t
(qt It
it ) +
1 pH;t
pht Ith
iht ;
(62)
Gross nominal interest rate, (dt + bgu bt bet t ) pH;t gdpt
Rt = R exp
bgt
(63)
B. Equilibrium unemployment Following Galí (2011), we assume that each representative household consists of a unit squared of individuals indexed by (i; j) 2 [0; 1] [0; 1], where i represents the variety of labor service provided by the individual and j indexes her disutility from working, given by j ' . Let nxt (i) denote the number of variety-i workers in household x = c; u employed at time t. Total household disutility from working is given by Z
0
1
Z
nx t (i)
'
j djdi =
0
Z
0
49
1
nxt (i)1+' di; 1+'
for x = c; u. Given the type-speci…c wage Wt (i), the number of type-i workers that each household would like to send to work is given by arg max x nt (i)
(
nxt (i)1+' 1+'
x Wt (i) x nt (i) t Pt
)
x t
=
1='
Wt (i) Pt
ltx (i) ;
1=cxt . Unemployment in the market for type-i labor is for x = c; u, where xt just the number of workers willing to work at the going wage minus e¤ective labor P P x x demand: ut (i) x=c;u lt (i) x=c;u nt (i) :Let ltx
Z
x t
1
ltx
(i) di =
0
Ntx
Z
Wt Pt
1='
Z
0
1
nxt
1
(i) di =
nxt
0
Z
1
0
Wt (i) Wt
Wt (i) Wt
1='
di =
x t
Wt Pt
1='
w;l t ;
"w
di = nxt
w;n t ;
denote total household-speci…c labor supply and labor demand, respectively, for x = R1 R1 1=' w;n c; u, where w;l (W (i) =W ) di and (Wt (i) =Wt ) "w di are indexes t t t t 0 0 of wage dispersion. Then aggregate unemployment is ut
Z
1
ut (i) di = lt
Nt :
0
P P x x where lt x=c;u Nt are aggregate labor supply and labor x=c;u lt and Nt ut =lt . demand, respectively. Finally, the unemployment rate is urate t
5.1
C. The size of the …scal adjustment:
k
and
c
based
consolidations. Figure C1 and C2 display the GDP e¤ects of …scal consolidations based on capital income and consumption taxes respectively. In the …gure we appreciate a similar pattern in the comparison across di¤erent consolidation sizes: a large consolidation produces (slightly) smaller short-run costs, but persistently higher costs in the medium run. 50
Figure C1
Figure C2
The economics of these responses is similar to that following an adjustment in government spending. As to the di¤erences between both tax-based consolidations, they re‡ect their distinct e¤ect on T and T . The small downward spike observed in the case of the consumption tax-based consolidation re‡ect the fact that T is just slightly delayed relative to the no-consolidation scenario. When consolidations are implemented via adjustments in capital income taxes, we observe a signi…cant downward spike associated to the larger consolidation (20 pp). This is due to the fact that the relevant e¤ect of this tax rate, as far as the deleveraging period is concerned, operates mainly via T , which is delayed by 4 quarters. Thus, as discussed above, it is through lower capital accumulation by entrepreneurs that consolidations based on capital income tax hikes produce persistent output losses.
51
