The Paradox of Global Thrift

Transcription

1 he Paradox of Goba hrift Luca Fornaro and Federica Romei his draft: November 2017 First draft: December 2016 PRELIMINARY AND INCOMPLEE, COMMENS WELCOME Abstract his paper describes a paradox of goba thrift. Consider a word in which interest rates are ow and countries frequenty experience recessionary iquidity traps, accompanied by tightening in the access to credit and debt deeveraging. Now imagine that governments impement counterycica macroprudentia poicies, imiting debt accumuation during booms to sustain aggregate demand and empoyment during iquidity traps triggered by deeveraging episodes. We show that these poicies, whie effective when appied by singe countries, might backfire on a goba eve. he reason is that prudentia poicies by booming countries generate a rise in the goba suppy of savings or, equivaenty, a fa in goba aggregate demand. In turn, weaker goba aggregate demand exacerbates the recession in countries currenty stuck in a iquidity trap. herefore, paradoxicay, the word might very we experience a fa in empoyment and output foowing the impementation of macroprudentia poicies. JEL Codes: E32, E44, E52, F41, F42. Keywords: Liquidity traps, zero ower bound, secuar stagnation, deeveraging, capita fows, macroprudentia poicies, aggregate demand externaities, internationa cooperation. Fornaro: CREI, Universitat Pompeu Fabra, Barceona GSE and CEPR; LFornaro@crei.cat. Romei: Stockhom Schoo of Economics and CEPR; federica.romei@hhs.se. An earier version of this paper has circuated under the tite Aggregate Demand Externaities in a Goba Liquidity rap. We thank Andrea Lanteri, Dennis Novy, Michaea Schmoer and Ivan Werning for very hepfu comments, and seminar participants at CREI, Universidad de Navarra, Paris Schoo of Economics, University of Nottingham, Federa Reserve Bank of San Francisco, Bank of Spain, University of Bern and University of Oxford, and participants at the NBER IFM meeting, Aix Marseie Schoo of Economics Macroeconomic Workshop, Great Stockhom Macro Meeting, ESSIM, ADEMU conferences on Macroeconomic and Financia Imbaances and Spiovers and How much of a fisca union for the EMU?, and Cataan Economic Society Meeting, SED Meeting and Nordic Summer Symposium in Macroeconomics for usefu comments. We thank Mario Giarda for exceent research assistance. his research has received funding from the European Union s Horizon 2020 research and innovation programme under Grant Agreement No and the Barceona GSE Seed Grant.

2 1 Introduction he current state of the goba economy is characterized by exceptionay ow interest rates. In recent years, in fact, nomina rates have hit the zero ower bound in most advanced economies, incuding the US, the Euro area and Japan (Figure 1, eft pane). Interestingy, a these iquidity trap episodes have started with some turmoi on financia markets, and have been accompanied by debt deeveraging (Figure 1, right pane). he ink between deeveraging and iquidity traps has been formaized by Eggertsson and Krugman (2012) and Guerrieri and Lorenzoni (2011). ight access to credit, these authors argue, depresses aggregate demand, pushing down the natura interest rate. If the underying interest rate is ow enough, a period of debt deeveraging wi then be associated with a iquidity trap and an economic sump. Motivated by these facts, a recent iterature has suggested that, in a ow interest rate environment, governments shoud activey intervene on the financia markets by impementing countercycica macroprudentia poicies (Farhi and Werning, 2016; Korinek and Simsek, 2016). Limiting debt accumuation during a boom, the argument goes, wi sustain aggregate demand and empoyment in the event of a deeveraging episode. A benevoent government shoud then tax borrowing in periods of abundant access to credit, as a precaution against the recessionary iquidity trap that might arise foowing a negative financia shock. 1 But what happens if severa countries around the word start foowing these poicy prescriptions? In this paper we show that, as a resut, the word can fa prey of a paradox of goba thrift. Consider a word in which interest rates are ow and countries frequenty experience recessionary iquidity traps. Now imagine that governments in booming countries impement macroprudentia poicies to insure against future iquidity traps. hese poicy interventions wi generate a rise in the goba suppy of savings or, equivaenty, a fa in goba aggregate demand. In turn, weaker goba aggregate demand wi produce a drop in interest rates throughout the word, exacerbating the recession in countries currenty stuck in a iquidity trap. herefore, paradoxicay, the word might very we experience a fa in empoyment and output foowing the impementation of prudentia poicies. o formaize this insight, we deveop a tractabe framework of an imperfecty financiay integrated word, in which equiibrium interest rates are ow and monetary poicy is occasionay constrained by the zero ower bound. he mode is simpe enough so that many resuts can be derived anayticay, but sti sufficienty rich to perform a quantitative anaysis. We study a word composed of a continuum of sma open economies inhabited by infinitey ived agents. Countries are hit by uninsurabe idiosyncratic shocks. Because of this feature, there is heterogeneity in the demand and suppy of savings across countries, and foreign borrowing and ending emerge naturay. For most of the paper, we study stationary equiibria in which word output and the cross-country distribution of net foreign assets are constant. Of course, due to the idiosyncratic shocks, individua countries experience fuctuations in their foreign asset position and in economic 1 he need for government intervention arises due to an aggregate demand externaity, caused by the fact that atomistic agents do not internaize the impact of their financia decisions on aggregate spending and income. 1

3 percent Poicy rates United States Euro area Japan percent of GDP Credit to private sector United States Euro area Japan Figure 1: Poicy rates and credit to the private non-financia sector. Note: the eft pane shows the exceptionay ow interest rates characterizing the post-2008 period. Both panes show the emergence of iquidity traps during periods of debt deeveraging by the private sector. See Appendix D for data sources. activity over time. Aside from standard productivity shocks, we consider deeveraging shocks, which tighten a country s access to credit and generate sudden stops in capita infows. he presence of uninsurabe risk against these shocks gives rise to a demand for precautionary savings. In turn, precautionary savings, couped with a imited suppy of assets arising from frictions on the credit markets, depress goba interest rates. Due to the presence of nomina rigidities, monetary poicy pays an active roe in stabiizing the economy. In fact, when a country experiences a fa in aggregate demand triggered by a negative shock, the domestic interest rate has to fa to keep the economy at fu empoyment. he zero ower bound, however, might prevent monetary poicy from fuy offsetting the impact of negative shocks on the economy. Indeed, if goba rates are sufficienty ow, the word can be stuck in a goba iquidity trap. his is a situation in which a significant fraction of the word economy experiences a iquidity trap with unempoyment. Importanty, during a goba iquidity trap not a countries need to be constrained by the zero ower bound and experience a recession. Moreover, even among those countries stuck in a iquidity trap there is asymmetry in terms of the severity of the recession. he mode thus captures situations such as the asymmetric recovery that has characterized advanced countries in the aftermath of the 2008 financia crisis (Figure 2). Interestingy, a goba iquidity trap can persist for an arbitrariy ong time, in ine with the notion of secuar stagnation described by Hansen (1939) and Summers (2016). 2 Against this background, we show that in good times governments have an incentive to subsidize private savings, or tax borrowing, as a precaution against the risk of a future iquidity trap triggered by a negative shock. his is due to the same domestic aggregate demand externaity described by Farhi and Werning (2016) and Korinek and Simsek (2016). In fact, governments perceive that private agents save too itte in times of robust economic performance, because they do not internaize the impact that their saving decisions wi have on aggregate empoyment and income in 2 Both authors refer to a state of secuar stagnation as characterized by ow goba interest rates, and by countries undergoing ong-asting iquidity traps, foowed by fragie recoveries. 2

4 index (2007=100) GDP per capita United States Euro area Japan Germany Spain Figure 2: Rea gross domestic product per capita. Note: the figure highights the reativey fast recoveries from the 2009 recession experienced by the US and Japan, and the sow recovery in the Euro area. he figure aso shows the heterogeneity between fast-recovering core Euro area countries, captured by Germany, and the stagnation experienced by periphera Euro area countries, captured by Spain. See Appendix D for data sources. the event of a future iquidity trap. Hence, governments in countries operating at fu empoyment impement poicies to increase savings and current account surpuses beyond what private agents woud choose in a aissez faire equiibrium. he key insight of the paper is that these poicy interventions might trigger a paradox of goba thrift, which is essentiay an internationa, and poicy-induced, version of Keynes paradox of thrift (Keynes, 1933). By stimuating savings and current account surpuses, governments in countries undergoing a period of robust economic performance increase the goba suppy of savings, depressing aggregate demand around the word. Centra bank in countries stuck in a iquidity trap, however, cannot respond to the drop in goba demand by owering their poicy rate. As a consequence, the impementation of prudentia poicies by booming countries aggravates the recession in countries experiencing a iquidity trap. Hence, prudentia poicy interventions might end up, paradoxicay, exacerbating the goba iquidity trap rather than mitigating it. A crucia aspect of the paradox of goba thrift is that it arises because nationa governments do not internaize the impact of their actions on the rest of the word. In particuar, when panning their prudentia poicies governments in booming countries do not take into account the negative effects that these poicies might have on countries currenty stuck in a iquidity trap. Our anaysis thus suggests that, during a goba iquidity trap, internationa cooperation is needed in the design of effective macroprudentia poicies. Reated iterature. his paper is reated to three iteratures. First, the paper contributes to the emerging iterature on secuar stagnation in open economies (Cabaero et a., 2015; Eggertsson et a., 2016). As in this iterature, we study a word trapped in a goba iquidity trap. his is a persistent, or even permanent, state of affairs in which goba rates are extraordinariy ow and countries are frequenty constrained by the zero ower bound. Both Cabaero et a. (2015) and Eggertsson et a. (2016) study two-country overapping generations modes, in which interest rates are ow because of a goba shortage of safe assets. Instead, we study economies inhabited by 3

5 infinitey ived agents, in ine with most iterature on monetary economics. Moreover, a distinctive feature of our framework is that the shortage of safe assets driving down goba rates emerges from countries demand for precautionary savings against idiosyncratic risk. Finay, whie both Cabaero et a. (2015) and Eggertsson et a. (2016) present insightfu discussions about the internationa spiovers arising in a goba iquidity trap, we are, to the best of our knowedge, the first to derive the optima cooperative and uncooperative financia poicies in a secuar stagnating word, as we as to quantify the gains from internationa cooperation. he paper is aso reated to the iterature on deeveraging and iquidity traps. As aready discussed, Eggertsson and Krugman (2012) and Guerrieri and Lorenzoni (2011) show that in cosed economies deeveraging generates a drop in aggregate demand that can give rise to a recessionary iquidity trap. Buiding on these positive contributions, Farhi and Werning (2016) and Korinek and Simsek (2016) derive the optima financia market interventions in cosed or sma open economies at risk of a iquidity trap foowing a deeveraging shock. 3 Benigno and Romei (2014) and Fornaro (2012) study deeveraging and iquidity traps in open economies. Both works consider ony temporary iquidity traps driven by a one-time goba deeveraging shock, and do not focus on optima financia poicy. We contribute to this iterature by showing that, aside from domestic aggregate demand externaities, a goba iquidity trap is characterized by internationa aggregate demand externaities, which require internationa cooperation to be corrected. hird, our paper is reated to the vast iterature on internationa poicy cooperation. instance, Obstfed and Rogoff (2002) and Benigno and Benigno (2003, 2006) study internationa monetary poicy cooperation in modes with nomina rigidities. In these frameworks, the gains from cooperation arise because individua countries have an incentive to manipuate their terms of trade at the expenses of the rest of the word. Simiary, Acharya and Bengui (2016) show that terms of trade externaities create gains from internationa poicy cooperation during a temporary iquidity trap. In our framework, terms of trade are constant and independent of government poicy, and hence terms of trade externaities are absent. hus, our resuts show that aggregate demand externaities can, on their own, create gains from internationa poicy cooperation during a goba iquidity trap. Sergeyev (2016) studies optima monetary and financia poicy in a monetary union, and shows that gains from internationa cooperation arise because individua countries do not internaize the impact of iquidity creation by the domestic banking sector on the rest of the word. His anaysis, however, abstracts from the zero ower bound, which is the source of gains from cooperation in our framework. he rest of the paper is composed by five sections. Section 2 presents a simpe baseine framework of an imperfecty financiay integrated word with nomina rigidities. Section 3 shows how, in absence of financia market interventions, the word can fa in a goba iquidity trap. In Section 4, we introduce macroprudentia poicies and describe the paradox of goba thrift. Section 5 provides a quantitative anaysis based on an extended version of the mode. Section 6 concudes. 3 Farhi and Werning (2012a,b, 2014) and Schmitt-Grohé and Uribe (2015) study optima financia market interventions when the constraint on monetary poicy is due to fixed exchange rates. For 4

6 2 Baseine mode In this section we present a styized mode that deivers transparenty the key message of the paper. As we wi show in Section 5, the intuitions from this simpe mode carry through to the extended framework that we use for numerica anaysis. We consider a word composed of a continuum of measure one of sma open economies indexed by i {0, 1}. Each economy can be thought of as a country. ime is discrete and indexed by t {0, 1,...}, and there is perfect foresight. 2.1 Househods Each country is popuated by a continuum of measure one of identica infinitey ived househods. he ifetime utiity of the representative househod in a generic country i is β t og(c i,t ), (1) t=0 where C i,t denotes consumption and 0 < β < 1 is the subjective discount factor. Consumption is a Cobb-Dougas aggregate of a tradabe good Ci,t and a non-tradabe good CN i,t, so that C i,t = (Ci,t )ω (Ci,t N)1 ω where 0 < ω < 1. Each househod is endowed with one unit of abor. here is no disutiity from working, and so househods suppy ineasticay their unit of abor on the abor market. However, due to the presence of nomina wage rigidities to be described beow, a househod might be abe to se ony L i,t < 1 units of abor. Hence, when L i,t = 1 the economy operates at fu empoyment, whie when L i,t < 1 there is invountary unempoyment, and the economy operates beow capacity. Househods can trade in one-period rea and nomina bonds. Rea bonds are denominated in units of the tradabe consumption good and pay the gross interest rate R t. he interest rate on rea bonds is common across countries, and R t can be interpreted as the word interest rate. Nomina bonds are denominated in units of the domestic currency and pay the gross nomina interest rate Ri,t n. Rn i,t is the interest rate controed by the centra bank, and thus can be thought of as the domestic poicy rate. Notice that, since there is no uncertainty, enriching the menu of assets avaiabe to the househods woud not change the resuts. In fact, we restrict attention to these two bonds purey to simpify the exposition. he househod budget constraint in terms of the domestic currency is P i,tc i,t + P N i,tc N i,t + P i,tb i,t+1 + B n i,t+1 = W i,t L i,t + P i,ty i,t + P i,tr t 1 B i,t + R n i,t 1B n i,t. (2) he eft-hand side of this expression represents the househod s expenditure. P i,t and P N i,t denote respectivey the price of a unit of tradabe and non-tradabe good in terms of country i currency. Hence, P i,t C i,t + P N i,t CN i,t is the tota nomina expenditure in consumption. B i,t+1 and B n i,t+1 denote respectivey the purchase of rea and nomina bonds made by the househod at time t. If B i,t+1 < 0 or Bi,t+1 n < 0 the househod is hoding a debt. 5

7 he right-hand side captures the househod s income. W i,t denotes the nomina wage, and hence W i,t L i,t is the househod s abor income. Labor is immobie across countries and so wages are country-specific. Yi,t is an endowment of tradabe goods received by the househod. Changes in Yi,t can be interpreted as movements in the quantity of tradabe goods avaiabe in the economy, or as shocks to the country s terms of trade. Pi,t R t 1B i,t and Ri,t 1 n Bn i,t represent the gross returns on investment in bonds made at time t 1. here is a imit to the amount of debt that a househod can take. In particuar, the end-ofperiod bond position has to satisfy B i,t+1 + Bn i,t+1 P i,t κ i,t, (3) where κ i,t > 0. In words, the maximum amount of debt that a househod can take is equa to κ i,t units of tradabe goods. he househod s optimization probem consists in choosing a sequence {C i,t, CN i,t, B i,t+1, B n i,t+1 } t to maximize ifetime utiity (1), subject to the budget constraint (2) and the borrowing imit (3), taking initia weath P0 R 1B i,0 + Ri, 1 n Bn i,0, a sequence for income {W i,tl i,t + Pi,t Y i,t } t, and prices {R t, Ri,t n, P i,t, P i,t N} t as given. he househod s first-order conditions can be written as ω C i,t βω = R t Ci,t+1 + µ i,t (4) ω C i,t = Rn i,t P i,t P i,t+1 βω C i,t+1 + µ i,t (5) B i,t+1 + Bn i,t+1 P i,t κ i,t with equaity if µ i,t > 0 (6) C N i,t = 1 ω ω Pi,t Pi,t N C i,t, (7) where µ i,t is the nonnegative Lagrange mutipier associated with the borrowing constraint. Equations (4) and (5) are the Euer equations for, respectivey, rea and nomina bonds. Equation (6) is the compementary sackness condition associated with the borrowing constraint. Equation (7) determines the optima aocation of consumption expenditure between tradabe and non-tradabe goods. Naturay, demand for non-tradabes is decreasing in their reative price Pi,t N/P i,t. Moreover, demand for non-tradabes is increasing in Ci,t, due to househods desire to consume a baanced basket between tradabe and non-tradabe goods. 2.2 Exchange rates, interest rates and aggregate demand Before moving on, it is usefu to iustrate the channes through which the poicy rate and the word interest rate affect demand for non-tradabe goods. Let us start by estabishing a ink between demand for non-tradabes and the exchange rate. Since the aw of one price hods for the tradabe 6

8 good we have that 4 Pi,t = S i,t Pt, (8) ( ) where Pt 1 exp 0 og P j,t dj is the average word price of tradabes, whie S i,t is the effective nomina exchange rate of country i, defined so that an increase in S i,t corresponds to a nomina depreciation. Equations (7) and (8) jointy impy that, keeping Pi,t N and P t constant, a nomina exchange rate depreciation increases demand for the non-tradabe good. Intuitivey, when the exchange rate depreciates the reative price of non-tradabes fas, inducing househods to switch expenditure away from tradabe goods and toward non-tradabe goods. We now reate the exchange rate to the poicy and the word interest rates. Combining (4) and (5) gives a no arbitrage condition between rea and nomina bonds R n i,t = R t P i,t+1 Pi,t. (9) his is a standard uncovered interest parity condition, equating the nomina interest rate to the rea interest rate mutipied by expected infation. Since rea bonds are denominated in units of the tradabe good, the reevant infation rate is tradabe price infation. Combining this expression with (8) gives Ri,t n S i,t+1 Pt+1 = R t. S i,t aking everything ese as given, this expression impies that a drop in R n i,t produces a rise in S i,t. In words, a fa in the poicy rate eads to a nomina depreciation, which induces househods to switch expenditure out of tradabe goods and toward non-tradabes. hrough this channe, a cut in the poicy rate boosts demand for non-tradabe goods. Conversey, a fa in the word interest rate R t generates a nomina exchange rate appreciation which, due to its expenditure switching effect, depresses demand for non-tradabes. o capture these effects more compacty, it is usefu to combine (7) and (9) into a singe aggregate demand (AD) equation P t C N i,t = R tπ i,t+1 R n i,t Ci,t Ci,t+1 Ci,t+1, N (AD) where π i,t Pi,t N/P i,t 1 N. his expression is essentiay an open-economy version of the New- Keynesian aggregate demand bock. As in the standard cosed-economy New-Keynesian mode, demand for non-tradabe consumption is decreasing in the rea interest rate R n i,t /π i,t+1 and increasing in future non-tradabe consumption Ci,t+1 N. In addition, changes in the consumption of tradabe goods act as demand shifters. As aready expained, a higher current consumption of trad- 4 o derive this expression, consider that by the aw of one price it must be that Pi,t = S j i,t P j,t. for any i and j, where S j i,t is defined as the nomina exchange rate between country i s and j s currencies, that is the units of country i s currency needed ( to buy one unit of country j s currency. aking ogs and integrating across j gives Pi,t = S i,tpt, ) ( 1 ) where S i,t exp og 0 Sj i,t dj and Pt 1 exp og P 0 j,tdj. 7

9 abe goods increases the current demand for non-tradabes. Instead, a higher future consumption of tradabes induces househods to postpone their non-tradabe consumption, thus depressing current demand for non-tradabe goods. Finay, due to the expenditure switching effect just discussed, a ower word interest rate is associated with ower demand for non-tradabe consumption. 2.3 Firms and nomina rigidities Non-traded output Yi,t N is produced by a arge number of competitive firms. Labor is the ony factor of production, and the production function is Yi,t N = L i,t. Profits are given by Pi,t NY i,t N W i,tl i,t, and the zero profit condition impies that in equiibrium Pi,t N = W i,t. We introduce nomina rigidities by assuming that nomina wages are subject to the downward rigidity constraint W i,t γw i,t 1, where γ > 0. his formuation captures in a simpe way the presence of frictions to the downward adjustment of nomina wages, which might prevent the abor market from cearing. In fact, equiibrium on the abor market is captured by the condition L i,t 1, W i,t γw i,t 1 with compementary sackness. (10) his condition impies that unempoyment arises ony if the constraint on wage adjustment binds Monetary poicy We describe monetary poicy in terms of targeting rues. In particuar, in our baseine mode we consider centra banks that target infation of the domesticay produced good. More formay, the objective of the centra bank is to set π i,t = π. hroughout the paper we focus on the case π > γ, so that when the infation target is attained the economy operates at fu empoyment (π i,t = π L i,t = 1). Hence, monetary poicy faces no confict between stabiizing infation and attaining fu empoyment, thus mimicking the divine coincidence typica of the baseine New Keynesian mode (Banchard and Gaí, 2007). 6 he centra bank runs monetary poicy by setting the nomina interest rate Ri,t n, subject to the 5 his form of wage rigidity gives rise to a non-inear wage Phiips curve. For vaues of wage infation ower than γ the reationship between wage infation and empoyment is vertica. Instead, in presence of unempoyment the wage Phiips curve becomes horizonta. It woud be easy to aow for an upward-soped wage Phiips curve. For instance, one coud assume that W i,t γ(l i,t)w i,t 1, where γ ( ) 0, to capture a setting in which wages are more downwardy fexibe the ower empoyment. For simpicity, in our baseine mode we focus on the specia case γ ( ) = 0, but our resuts readiy extend to the more genera case γ ( ) 0. 6 Since ony the non-tradabe good is produced, we are in practice assuming that the centra bank foows a poicy of producer price infation targeting. his is a common assumption in the open economy monetary iterature. Another option is to consider a centra bank that targets consumer price infation. We have experimented with this possibiity, and found that the resuts are robust to this aternative monetary poicy target. he anaysis is avaiabe upon request. 8

10 zero ower bound constraint R n i,t 1.7 monetary poicy (MP) rue 8 Monetary poicy can then be captured by the foowing Ri,t n 1 if Yi,t N = = 1, π i,t = π = 1 if Yi,t N < 1, π i,t = γ, where we have used (10) and the equiibrium reationships W i,t (MP) equation captures the fact that unempoyment (Yi,t N constrained by the zero ower bound (Ri,t n = 1). (MP) = Pi,t N and L i,t = Yi,t N. he < 1) arises ony if the centra bank is 2.5 Market cearing and definition of competitive equiibrium Since househods inside a country are identica, we can interpret equiibrium quantities as either househod or country specific. For instance, the end-of-period net foreign asset position of country i is equa to the end-of-period hodings of bonds of the representative househod, NF A i,t = B i,t+1 + Bi,t+1 n /P i,t. hroughout, we focus on equiibria in which nomina bonds are in zero net suppy, so that B n i,t = 0, (11) for a i and t. his impies that the net foreign asset position of a country is exacty equa to its investment in rea bonds, i.e. NF A i,t = B i,t+1. Market cearing for the non-tradabe consumption good requires that in every country consumption is equa to production Instead, market cearing for the tradabe consumption good requires C N i,t = i,t. (12) C i,t = Y i,t + R t 1 B i,t B i,t+1. (13) his expression can be rearranged to obtain the aw of motion for the stock of net foreign assets owned by country i, i.e. the current account NF A i,t NF A i,t 1 = CA i,t = Y i,t C i,t + B i,t (R t 1 1). As usua, the current account is given by the sum of net exports, Yi,t C i,t, and net interest 7 We provide in appendix C some possibe microfoundations for this constraint. In practice, the ower bound on the nomina interest rate is ikey to be sighty negative. In this paper, with a sight abuse of anguage, we wi refer the the ower bound on R n i,t as the zero ower bound. It shoud be cear, though, that conceptuay it makes no difference between a sma positive or a sma negative ower bound. 8 One coud think of the centra bank as setting R n i,t according to the rue ( ( Ri,t n = max R i,t n πi,t ) ) φπ, 1, π where R n i,t is the vaue of R n i,t consistent with π i,t = π. In the baseine mode we focus on the imit φ π. his means that the infation target can be missed ony if the zero ower bound constraint binds. 9

11 payments on the stock of net foreign assets owned by the country at the start of the period, B i,t (R t 1 1). Finay, in every period the word consumption of the tradabe good has to be equa to word production, 1 0 C i,t di = 1 0 Y i,t di. his equiibrium condition impies that bonds are in zero net suppy at the word eve 1 We are now ready to define a competitive equiibrium. 0 B i,t+1 di = 0. (14) Definition 1 Competitive equiibrium. A competitive equiibrium is a path of rea aocations {C i,t, CN i,t, i,t, B i,t+1, B n i,t+1, µ i,t} i,t, infation rates {π i,t } i,t, poicy rates {R n i,t } i,t and word interest rate {R t } t, satisfying (4), (6), (11), (12), (13), (14), (AD) and (MP ) given a path of endowments {Y i,t } i,t, a path for the borrowing imits {κ i,t } i,t, and initia conditions {B i,0 } i. 2.6 Some usefu simpifying assumptions We now make some simpifying assumptions that aow us to sove anayticay the baseine mode. We wi reax these assumptions in Section 5, where we perform a numerica anaysis. We want to consider a word in which the goba suppy of saving instruments is imited, and in which borrowing constraints are tight. he simpest way to formaize this idea is to focus on the imit κ i,t = κ 0 for a i and t, so that househods cannot take any (significant amount of) debt. his corresponds to a zero iquidity economy, in the spirit of Werning (2015). Later on, in Section 5, we wi reax this assumption and aow househods to take some debt. We aso focus on a specific process for the tradabe endowment. We consider a case in which there are two possibe reaizations of the tradabe endowment: high (Yh ) and ow (Y ) with Y < Yh. We assume that haf of the countries receives Y h in even periods and Y in odd periods. Symmetricay, the other haf receives Y during even periods and Yh during odd periods. From now on, we wi say that a country with Yi,t = Y h is in the high state, whie a country with Yi,t = Y is in the ow state. his endowment process captures in a tractabe way an environment in which countries are hit by asymmetric shocks. Finay, we are interested in studying stationary equiibria in which the word interest rate and the net foreign asset distribution are constant. As we wi see, this requires that the initia bond position satisfies B i,0 0 for every country i, which we assume throughout our anaysis of the baseine mode. Moreover, we focus on equiibria in which a the countries with the same endowment shock behave symmetricay. Hence, with a sight abuse of notation, we wi sometime omit the i subscripts, and denote with a h () subscript variabes pertaining to countries in the high (ow) state. 10

12 3 Equiibrium under financia aissez faire Before introducing governments interventions on the financia markets, we characterize the equiibrium under financia aissez faire. his wi serve as a benchmark against which to contrast the equiibrium with financia poicy. We start by soving for the behavior of a singe sma open economy, taking the word interest rate as given. We then turn to the goba equiibrium, in which the word interest rate is endogenousy determined. 3.1 Sma open economy o streamine the exposition, we impose some restrictions on the word interest rate. We wi ater show that these restrictions emerge naturay in genera equiibrium. Assumption 1 he word interest rate is constant (R t = R for a t) and satisfies βr < 1. Soving for the path of tradabe consumption is straightforward. From period 0 on, the economy enters a stationary equiibrium in which househods purchase B h,t+1 = B h 0 bonds in the high state, whie the borrowing constraint binds in the ow state, so that B,t+1 = B = 0. 9 he Euer equation (4) in the high state then impies 1 C h βr 1 C, (15) where we have removed the time subscripts to simpify the notation. Combining this expression with the resource constraint (13) and using B = 0 gives the optima demand for bonds in the high state { β B h = max 1 + β From this expression it is then easy to sove for C and C h using (Y h Y ) }, 0, (16) βr C h = Y h B h (17) C = Y + RB h. (18) Notice that, since βr < 1 and Yh > Y, the competitive equiibrium is such that Ch > C. Hence, fuctuations in the endowment transate into fuctuations in the consumption of tradabe goods. We now turn to the market for non-tradabe goods. Equiibrium on this market is reached at the intersection of the (AD) and (MP) equations, which we rewrite here for convenience i,t = Rπ i,t+1 R n i,t C i,t C i,t+1 i,t+1. (AD) 9 o be precise, we shoud write B h κ 0 and B = κ 0. o streamine the exposition, however, we sighty abuse the notation and describe the case κ = 0. 11

13 R n R n AD h M P AD h M P R n h R n h AD AD AD h R n h R n 1 R n 1 AD 1 1 Figure 3: Aggregate demand and empoyment. Left pane: equiibrium on market for non-tradabes. Right pane: high R (soid ines) vs. ow R (dashed ines). Ri,t n 1 if Yi,t N = = 1, π i,t = π = 1 if Yi,t N < 1, π i,t = γ, (MP) where we have used the equiibrium condition Ci,t N = Y i,t N. Let us start by taking a partia equiibrium approach, i.e. by deriving the equiibrium hoding future variabes constant. Figure 3 shows the AD and MP curves in the Ri,t n Y i,t N space. he AD curve captures the negative reationship between aggregate demand and the poicy rate, whie the L-shape of the MP curve captures the aggressive response of the centra bank to unempoyment. In the eft pane, we have drawn two AD curves. he AD h curve refers to demand in the high state, whie AD captures demand in the ow state. he diagram shows that changes in tradabe consumption act as demand shifters, so that aggregate demand is ower in the ow state compared to the high state. Hence, when the economy transitions from the high to the ow state the centra bank decreases the poicy rate to sustain aggregate demand. he right pane of the figure shows how the equiibrium is affected by changes in the word interest rate R. he soid ines capture a word in which R is high. In this case, aggregate demand is sufficienty strong for the economy to operate at fu empoyment in both states. Instead, the dashed ines refer to a ow R word. In this case, in the ow state aggregate demand is so weak that monetary poicy is constrained by the zero ower bound and the economy experiences unempoyment. It turns out that the insights of the partia equiibrium anaysis extend to the genera equiibrium. We summarize these resuts in the foowing proposition. Assumption 2 he parameter γ and the word interest rate R are such that Rγ > 1. Proposition 1 Sma open economy under financia aissez faire. here exists a threshod R, such that if R R then Yh N = Y N = 1, otherwise Yh N = 1 and Y N = R π max ( βr, Y /Yh ) < 1. R soves R π max ( βr, Y /Yh ) = 1. Proof. See Appendix B.1. 12

14 Proposition 1 states that there exists a threshod R for the word interest rate, such that if R R the economy aways operates at fu empoyment. Instead, if R < R aggregate demand in the high state is strong enough to guarantee fu empoyment, whie in the ow state aggregate demand is sufficienty weak so that monetary poicy is constrained by the zero ower bound and unempoyment arises. he roe of assumption 2 is to guarantee that demand in the high state is aways strong enough so that Yh N = 1. Whie in principe one coud imagine a case in which iquidity traps have infinite duration, here we restrict attention to the, more traditiona, case in which iquidity traps are temporary. 3.2 Goba equiibrium We now sove for the goba equiibrium. In a goba equiibrium the word bond market has to cear, so that (14) hods. Bonds are suppied by countries in the ow state. hese countries are against the borrowing constraint, and hence the suppy of bonds is B = Demand for bonds comes from countries in the high state and is given by B h. In genera equiibrium it must then be that B h = B = 0. Hence, the equiibrium aocation of tradabe consumption corresponds to the financia autarky one, impying that C h = Y h and C = Y. he equiibrium word interest rate must be such that countries in the high state do not want to borrow or save. 11 he vaue of the equiibrium word interest rate can then be found by substituting C h = Y h and C = Y in (15) hoding with equaity R = Y βyh R f, (19) where the superscript f stands for financia aissez faire. Expression (19) reates the word interest rate to the fundamentas of the economy. Naturay, a higher discount factor β eads to a higher demand for bonds by saving countries, and thus to a ower word interest rate. Moreover, the word interest rate is decreasing in Yh /Y, because a higher distance between the two reaizations of the endowment increases the desire to save to smooth consumption for countries in the high state. Notice that the equiibrium interest rate satisfies βr < 1, consistent with assumption 1. We coect these resuts in the foowing emma. Lemma 1 Goba equiibrium under financia aissez faire. In a goba equiibrium C h,t = Yh, C,t = Y. Under financia aissez faire the equiibrium word interest rate is R t = Y /(βyh ) R f < 1/β for a t. Depending on fundamentas, R f might be greater or smaer than R, the threshod word interest rate beow which the zero ower bound binds for countries in the ow state. 12 We think 10 o be precise, since κ 0, the suppy of bonds is positive, abeit infinitesimay sma. We write, with a sight abuse of notation, B = 0 to streamine the exposition. 11 In fact, if the borrowing constraint were to bind in the high state, a the countries in the word woud want to borrow (abeit an infinitesimay sma amount) preventing equiibrium from being reached. 12 Precisey, R f < R if π < β(yh /Y ) 2, otherwise R f R. 13

15 of the case R f < R as capturing a word trapped in a goba iquidity trap. In such a word, goba aggregate demand is weak and countries hit by negative shocks experience iquidity traps with unempoyment. Interestingy, this state of affair can persist for an arbitrariy ong period of time, as ong as goba forces impy that R f < R. In this sense, the mode captures in a simpe way the saient features of a word undergoing a period of secuar stagnation, in which interest rates are ow and iquidity traps frequent (Summers, 2016). 4 Macroprudentia poicies and the paradox of goba thrift Since there is no disutiity from working, unempoyment in our mode is inefficient. Hence, governments have an incentive to impement poicies that imit the incidence of iquidity traps on empoyment. For instance, a arge iterature has emphasized how raising expected infation can mitigate the inefficiencies due to the zero ower bound. However, a robust concusion of this iterature is that, in presence of infation costs, circumventing the zero ower bound by raising infation expectations is not an option when the centra bank acks commitment (Eggertsson and Woodford, 2003). In this paper we take a different route and consider the roe of financia poicies, broady defined as poicies that affect the country s saving and borrowing decisions, in stabiizing aggregate demand and empoyment. In particuar, we wi endow governments with the power to choose directy the country s net foreign asset position and the path of tradabe consumption, as ong as these do not vioate the resource constraint (13) and the borrowing imit (3). Definition 2 Equiibrium with financia poicy. An equiibrium with financia poicy is a path of rea aocations {C i,t, CN i,t, i,t, B i,t+1, B n i,t+1, µ i,t} i,t, infation rates {π i,t } i,t, poicy rates {R n i,t } i,t and word interest rate {R t } t, satisfying (3), (11), (12), (13), (14), (AD) and (MP ) given a path of endowments {Y i,t } i,t, a path for the borrowing imits {κ i,t } i,t, and initia conditions {B i,0 } i. An equiibrium with financia poicy has to satisfy a the conditions of a competitive equiibrium, except for the Euer equation (4). Hence, even in presence of financia poicy the market for non-tradabe goods cears competitivey, so that the (AD) and (MP) equations have to hod. 13 We wi ater discuss which instruments governments need to impement the aocation under financia market interventions as part of a competitive equiibrium. 4.1 Sma open economy Let us start by considering a singe sma open economy. o understand why a government might choose to intervene on the financia markets to stabiize empoyment, consider that, combining 13 Notice that to derive that (AD) equation we have used the no arbitrage condition between rea and nomina bonds. Hence, we are assuming that in an equiibrium with financia poicy househods decide how to aocate their savings between the two bonds. his assumption captures a word with high degree of capita mobiity, in which it is difficut for governments to discriminate between domestic and foreign assets. 14

16 R n M P AD h R n h AD 1 AD 1 Figure 4: Response to increase in B h. Soid ines refer to ow B h, dashed ines refer to high B h. (AD) and (MP ), output in the ow state under financia aissez faire can be written as = min ( R πc /C h, 1), (20) where we have used the fact that Proposition 1 impies Yh N = 1, π h = π. Now consider a case in which the zero ower bounds binds, so Y N < 1 and output in the ow state is demand determined. Imagine that the government impements a poicy that eads to an increase in househods savings whie the economy is booming, so that B h increases. On the one hand, higher savings in the high state depress C h. On the other hand, househods now enter the ow state with higher weath and, since they are borrowing constrained, increase spending so that C rises. he net resut is that C /C h increases, boosting demand for non-tradabes in the ow state. In turn, since the centra bank is constrained by the zero ower bound, higher demand for non-tradabes eads to higher output and empoyment. Graphicay, as iustrated by Figure 4, an increase in B h makes the AD curve shift right to AD, and generates a rise in Y N. 14 Notice that atomistic househods, which take aggregate demand and empoyment as given, do not internaize the impact of tradabe consumption decisions on production of non-tradabe goods. As we wi see, the presence of this domestic aggregate demand externaity might ead governments to impement financia poicies to infuence private agents saving and borrowing decisions. How does a government optimay intervene on the financia markets? We address this question by taking the perspective of a domestic government, or panner, that designs financia poicy to maximize domestic househods wefare. Importanty, since each country is infinitesimay sma, the domestic government takes the word interest rate R as given, and does not internaize the impact of its actions on the rest of the word. Because of this, we refer to the domestic panning aocation as the non-cooperative financia poicy. As it turns out, the panning aocation might differ depending on whether the government operates under commitment or discretion. Rather than considering both cases, throughout the paper we restrict attention to a government that acks commitment, and hence takes future variabes as 14 One can show that in our baseine mode, as ong as < 1, changes in C /C h do not ater aggregate demand in the high state, and hence the AD h curve does not move after the increase in B h. 15

17 given. We do this for two reasons. First, the existing iterature has shown that if the government operates under commitment monetary poicy aone can mitigate substantiay the inefficiencies due to the zero ower bound. his suggests that aternative poicies, such as financia market interventions, are most usefu when the government operates under discretion. Second, the panning probem under discretion highights transparenty the macroprudentia roe of financia poicy in stabiizing the economy. Formay, we define the period t probem of the domestic panner in a generic country i as max C i,t, i,t,b i,t+1 t=0 β t ( ω og Ci,t + (1 ω) og Yi,t N ) (21) subject to C i,t = Y i,t B i,t+1 + RB i,t (22) i,t RP(B i,t+1, Y i,t+1) B i,t+1 κ i,t (23) i,t 1 (24) C i,t C (B i,t+1, Y i,t+1 )(B i,t+1, Y i,t+1). (25) he resource constraints are captured by (22) and (24). (23) impies that the government is subject to the same borrowing constraint imposed by the markets on individua househods. 15 Instead, constraint (25), which is obtained by combining the (AD) and (MP) equations, encapsuates the requirement that consumption of non-tradabe goods is constrained by private sector s demand. he functions P(B i,t+1, Yi,t+1 ), C (B i,t+1, Yi,t+1 ) and (B i,t+1, Yi,t+1 ) determine respectivey infation, consumption of tradabe goods and production of non tradabe goods in period t + 1 as a function of the country s stock of net foreign assets (B i,t+1 ) and the endowment of tradabes (Yi,t+1 ) at the beginning of next period. Since the current panner cannot make credibe commitments about its future actions, these variabes are not into its direct contro. However, the current panner can sti infuence these quantities through its choice of net foreign assets. In what foows, we focus on equiibria in which these functions are differentiabe, and in which C B, (B i,t+1, Y i,t+1 ) 0. he first order conditions are λ i,t = ω C i,t + ῡ i,t i,t C i,t (26) 1 ω i,t = ν i,t + ῡ i,t (27) 15 o write this constraint we have used the equiibrium condition B n i,t+1 = 0. It is straightforward to show that aowing the government to set B n i,t+1 optimay woud not change any of the resuts. 16

18 λ i,t = βr λ i,t+1 + µ i,t + ῡ i,t i,t [ YB,N (B i,t+1, Y i,t+1 ) (B i,t+1, Y i,t+1 ) + P B(B i,t+1, Y i,t+1 ) P(B i,t+1, Y i,t+1 ) C B, (B i,t+1, Y C (B i,t+1, Y i,t+1 ) i,t+1 ) ] (28) B i,t+1 κ i,t with equaity if µ i,t > 0 (29) i,t 1 with equaity if ν i,t > 0 (30) i,t Rπ t+1 C i,t C i,t+1 i,t+1 with equaity if ῡ i,t > 0, (31) where λ i,t, µ i,t, ν i,t, ῡ i,t denote respectivey the nonnegative Lagrange mutipiers on constraints (22), (23), (24) and (25). In addition, P B (B i,t+1, Yi,t+1 ), Y B,N(B i,t+1, Yi,t+1 ) and C B,t(B i,t+1, Yi,t+1 ) are the partia derivatives of P(B i,t+1, Yi,t+1 ), (B i,t+1, Yi,t+1 ) and C (B i,t+1, Yi,t+1 ), respectivey, with respect to B t+1. o understand why the panner aocation can differ from the competitive equiibrium, it is usefu to combine (26) and (28) to obtain 1 C i,t ( ω + ῡi,t Yi,t N ) βr = + ῡ i,t i,t C i,t+1 ( ω + ῡi,t+1 i,t+1) + µi,t [ YB,N (B i,t+1, Y i,t+1 ) (B i,t+1, Y i,t+1 ) + P B(B i,t+1, Y i,t+1 ) P(B i,t+1, Y i,t+1 ) C B, (B i,t+1, Y C (B i,t+1, Y i,t+1 ) i,t+1 ) ]. (32) his is the panner s Euer equation. Comparing this expression with the househods Euer equation (4), it is easy to see that the margina benefit from a rise in Ci,t perceived by the panner differs from househods whenever ῡ i,t > 0 in any period t, that is when the zero ower bound constraint binds. his happens because, contrary to atomistic househods, the government internaizes the aggregate demand externaities that financia decisions have on the domestic economy. For instance, consider a case in which the borrowing constraint does not bind µ i,t = 0, the economy operates at fu empoyment in the present ῡ i,t = 0, but the zero ower bound binds next period ῡ i,t+1 > 0. In this case, savings are higher in the panning aocation compared to the financia aissez faire equiibrium. he panner, in fact, internaizes that increasing savings in the present eads to higher aggregate demand and output next period. he next proposition characterizes the non-cooperative financia poicy in a sma open economy as a function of the word interest rate. Proposition 2 Sma open economy aocation under non-cooperative financia poicy. Consider stationary soutions to the non-cooperative panning probem. Define R = ωy /(βyh ) and R (ω/( πβ)) 1/2. he panning aocation is such that Yh N = 1, B = 0 and 17

19 B h = 0, Y N = R πy B h = β ω+β (Yh ωy βr < 1 if R < R ), = R 2 πβ/ω < 1 if R R < R /Y h B h = Y h R πy 1+R 2 π, = 1 if R R < R { ) } B h = max β 1+β (Yh Y βr, 0, = 1 if R R. (33) Moreover, µ h > 0 if R < R or R R < Y /(Y h β), otherwise µ h = 0. Proof. See Appendix B.2. Coroary 3 Consider a sma open economy facing the word interest rate R. If R < R < R both Y N and B h are higher under the non-cooperative financia poicy than under financia aissez faire, otherwise the two aocations coincide. Coroary 3 provides two resuts. First, if R R, so that the zero ower bound never binds, the panner chooses the same path for tradabe consumption and bonds that househods woud choose in absence of financia reguation. his resut highights the fact that in our simpe mode there is no incentive for the domestic government to intervene on the financia markets if monetary poicy is not constrained by the zero ower bound. Second, when the zero ower bound binds in the ow state (R < R ), the government intervenes on the financia markets to stabiize output. hese interventions have a macroprudentia favor. In fact, the government boosts savings in the high state, when the economy is booming, to mitigate the recession occurring when the economy transitions to the ow state. 16 In our financiay integrated word, moreover, domestic financia poicies have a natura counterpart in terms of internationa capita fows. current account. Indeed, higher domestic savings manifest themseves in an improvement in the Hence, the government financia poicy can be interpreted as improving the current account during booms, so that the economy enters the iquidity trap with a higher stock of externa weath. Before moving on, it is usefu to spend some words on the instruments that a government needs to decentraize the panning aocation. One possibiity is to give to the government the power to impose a borrowing imit tighter than the market one, so that (3) is repaced by B i,t+1 + Bn i,t+1 P i,t { } min κ i,t, κ g i,t, where κ g i,t is the borrowing imit set by the government. By setting κg h,t < κ i,t appropriatey, the government can repicate the panning aocation as part of a competitive equiibrium. Aternativey, the panning aocation coud aso be decentraized by means of a subsidy on savings/tax on borrowing. he government woud then increase the subsidy in the high state, to foster househods savings. We refer the reader to Farhi and Werning (2016) and Korinek and Simsek (2016) 16 More precisey, macroprudentia poicies are most often defined as poicies that reduce debt during booms. As we show in Section 5, this is exacty what happens in our fu mode. 18