Self-Fulfilling Unemployment Crises PRELIMINARY AND INCOMPLETE // NOT FOR CIRCULATION

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1 Self-Fulfilling Unemployment Crises Javier Bianchi Minneapolis Fed & University Wisconsin & NBER June 29, 25 PRELIMINARY AND INCOMPLETE // NOT FOR CIRCULATION Click for Latest Draft Abstract This paper proposes a novel theory of self-fulfilling unemployment fluctuations driven by an aggregate demand externality caused by downward wage rigidity and free capital mobility. Expectations of high unemployment, lead to low income and low aggregate demand. In turn, low aggregate demand leads to expectations of deflation and high unemployment. I show that this feedback between expectations and aggregate demand can lead to the emergence of self-fulfilling fluctuations in involuntary unemployment. Numerical simulations show that episodes of large unemployment are driven by pessimistic expectations. Conventional remedies to deal with recessions may be counterproductive. Keywords: Multiple equilibria, sunspots, unemployment, downward wage rigidity, secular stagnation JEL Classification Codes: D62, E32, E44, F32, F41 THIS IS A VERY PRELIMINARY DRAFT. I would like to thank seminar participants at the Federal Reserve Bank of Minneapolis and Society of Economic Dynamics for useful comments. Also thanks to Shiv Dixit and Jorge Mondragon for excellent research assistance. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. 1

2 The main enemy for Europe is unemployment...this is caused by a broader sentiment of lack of confidence Interview of Mario Draghi, President of the ECB, (conducted by Jean-Pierre Elkabbach (Europe 1) on Tuesday 23) 1 Introduction Fear of a prolonged period of unemployment has been at the center of the recent European recession. By itself, this lack of confidence is perceived to be causing high unemployment, and it is argued that reverting the confidence slump is crucial to bring down unemployment levels (as the quote from Draghi illustrates). Indeed, Figure 1 shows a strong negative comovement between consumer confidence and unemployment. However, if the lack of confidence is a mere symptom of high unemployment, rather than a fundamental cause of it, the only way to restore confidence might be to bring down unemployment in the first place. Is lack of confidence a symptom of high unemployment, or a fundamental cause of it? Consumer Confidence European Union Unemployment Rate Consumer Confidence Spain Unemployment Rate Index Percentage(%) Index Percentage(%) Q1 2002Q1 2004Q1 2006Q1 2008Q1 20Q1 2012Q Q1 2002Q1 2004Q1 2006Q1 2008Q1 20Q1 2012Q1 Index Consumer Confidence Greece Unemployment Rate Percentage(%) Index Consumer Confidence Portugal Unemployment Rate Percentage(%) Q1 2002Q1 2004Q1 2006Q1 2008Q1 20Q1 2012Q Q1 2002Q1 2004Q1 2006Q1 2008Q1 20Q1 2012Q1 Figure 1: Comovement between Unemployment and Consumer Confidence 2

3 In this paper, we argue that restoring confidence per se can be an important factor causing high unemployment. We study a small open economy model, with a tradable and a non-tradable sector and two key ingredients: downward wage rigidity and a fixed exchange rate, as in Schmitt-Grohé and Uribe (2013). The motivation for these two features is empirical. Indeed, despite the severe recession and high unemployment in Europe, nominal wages remained high and being part of a currency union ruled out a reduction of real wages via a devaluation. The main result of the paper is that the combination of these two features can generate a novel source of multiple equilibria. We show that in the model there is a good equilibrium, where households have high consumption, financed by borrowing, and the economy is at full employment or close to it. There is a bad equilibrium, however, with high unemployment. In this equilibrium, low unemployment leads to low income and low aggregate demand, which in turn generates deflation and unemployment. The mechanism that generates multiplicity is as follows. When agents expect high unemployment, this leads to low income and low aggregate demand, which in turn leads to a low price of non-tradable goods and low employment. Market clearing imply that consumption of nontradables has to be low, which lead to a decline in the demand for tradable goods as long as tradable and non-tradable goods are complements in the utility function. In turn, an equilibrium with low tradable consumption requires a low price of non-tradables as this lowers the marginal rate of substitution between tradables and non-tradables. Since wages are downward rigid, the reduction in the price of non-tradables leads to a decline in labor demand. If the demand for non-tradables goods is sufficiently elastic, the resulting decline in employment rationalizes the expectations of high unemployment in the first place. To assess the quantitative importance of this fragility problem, we calibrate our model using Spanish data. Specifically, we calibrate our model to reproduce several features of the Spanish business cycle including wage and unemployment data, and investigates how pervasive is the phenomenon by which pessimistic expectations can induce a sudden unemployment crisis. In our dynamic model, given shocks and the endogenous debt position, the economy may be in a multiple equilibria region or in a unique equilibrium region. Numerical simulations show that the economy is in the multiple equilibria region a significant amount of time. We also show in which states the economy is more vulnerable to multiple equilibria. A switch from a good to a bad equilibrium can explain a set of key stylized facts from the European crises shown in Figure 2. Model simulations along the good equilibrium can explain the phase of low unemployment, current account deficits and high confidence that characterized the period in Europe. A switch to the bad equilibrium in our model accounts for the sharp reverse in capital flows, high unemployment and low consumption. Finally, we investigate the policy implications of our model. A key element behind the multiple equilibria is that the model rationalizes government initiatives to restore confidence in the midst of an episode of high unemployment, but only when this is due to a shift in expectations. Notable, a policy that subsidizes debt and boosts aggregate demand can take the economy out of 3

4 an unemployment trap. The welfare gains of these policies are substantial reaching about 0.8 percentage points of permanent consumption and the reduction in unemployment can reach several percentage points. 16 Unemployment Rate(%) 120 Nominal Labor Cost Index Q1 2002Q1 2004Q1 2006Q1 2008Q1 20Q1 2012Q1 2014Q Q1 2002Q1 2004Q1 2006Q1 2008Q1 20Q1 2012Q1 2014Q1 2 Current Account/GDP(%) - Consumer Confidence Indicator Q1 2002Q1 2004Q1 2006Q1 2008Q1 20Q1 2012Q1 2014Q Q1 2002Q1 2004Q1 2006Q1 2008Q1 20Q1 2012Q1 2014Q1 Figure 2: Stylized Facts: Peripheral Europe. Data represents arithmetic mean of Bulgaria, Cyprus, Estonia, Greece, Ireland, Lithuania, Latvia, Portugal, Spain, Slovenia, and Slovakia. 1.1 Related Literature There is a large and growing literature on the role of self-fulfilling expectations for aggregate economic fluctuations. To the best of my knowledge, this is the first paper that shows that the combination of downward wage rigidity and open capital markets can lead to multiple equilibria. Classic papers on multiple equilibria: Diamond (1982) Benhabib and Farmer (1994), Kiyotaki (1988) Interest-rate feedback rules: Benhabib, Schmitt-Grohe, and Uribe (2001,2002), Schmitt- Grohe, and Uribe (2014), Aruoba-Cubas-Shorfeide (2014), Mertens and Ravn (2014) 4

5 Secular stagnation: Eggerston and Mehrota (2014), Benigno and Fornaro (2015) Other related papers: Heathcote and Perri (2014), Kaplan and Menzio (2014), Farmer (2013, 2014), Chamley (2014), Benhabib and Wang (2013) RELATIONSHIP TO BE DESCRIBED The paper is organized as follows. Section 2 presents the model. Section 3 presents a simple two period example to illustrate the self-fulfilling unemployment crises. Section 4 presents the quantitative analysis (incomplete). 2 A Two-Period Model of Self-Fulfilling Unemployment We start the analysis with a two-period example to illustrate the source of multiplicity. consider a small open economy with a tradable and a non-tradable sector, a fixed exchange rate regime and downward wage rigidity, which builds on Schmitt-Grohé and Uribe (2013). There are two time periods t = 1, 2 and there is no uncertainty. We assume that the law of one price holds for tradable goods Pt T = Pt T E t and that the price of foreign tradable Pt T is constant and equal to one. An important assumption that we make is that E t = 1, which corresponds to a fixed exchange rate policy or equivalently an economy that belongs to a currency union. These assumptions together imply that the price of tradables is fixed P T t = 1 in domestic currency. We 2.1 Households The economy is populated by a continuum of identical households of measure one with preferences given by: u(c T 1, c N 1 ) + βu(c T 2, c N 2 ) (1) where c T t, c N t denote tradable and non-tradable consumption at period t. In period 1, households receive an endowment of tradables y T 1, supply labor n and collect profits π from firms. Because households do not value leisure, they supply all available hours h. Because of downward wage rigidity, however, the effective number of hours supplied could be lower than their available time, leading to involuntary unemployment. Households trade a bond denominated in units of tradables that pay an interest rate r. Accordingly, their budget constraint in period 1 is c T 1 + c N 1 p N 1 + b 1 R = yt 1 + wn + π 1 (2) where prices are expressed in units of tradables or equivalently in foreign currency, given the law of one price and the fixed exchange rate. 5

6 In period 2, households collect savings, an endowment of non-tradables and consume: c N 2 p N 2 + c T 2 = p N 2 y N 2 b 1 (3) Accordingly, the household problem consists of max c T 1,cN 1,cT 2,cN 2 u(c T 1, c N 1 ) + βu(c T 2, c N 2 ) subject to the lifetime budget constraint c T 1 + c N 1 p N 1 + cn 2 p N 2 + c T 2 R = y T 1 + wn + π 1 + yn 2 R The optimality conditions equate the intratemporal marginal rate of substitution to the relative price of non-tradables u N (c T, c N ) u T (c T, c N ) = pn (4) where u j = u(c). for j = T, N, and the marginal utility of tradable consumption in period 1 to c j the marginal utility of saving u T (c T 1, c N 1 ) = βru T (c T 2, c N 2 ) (5) Critical for the emergence of self-fulfilling unemployment fluctuations is the dependence of the marginal utility of non-tradables on tradable consumption, as we will show below. 2.2 Firm Firms in the non-tradable sector have a production function y N = zh α, with α < 1,. Taking as given prices and wages, firms solve the following problem: max p N t h α wh h Firms first order condition is: p N αh α 1 = w (6) which in turn determines a labor demand equation: h(w) = ( αzp N 1 w ) 1 1 α. Critical for the emergence of self-fulfilling unemployment fluctuations is the increasing relationship between p N and labor demand. 6

7 2.3 Downward wage rigidity There is a lower bound on equilibrium wages so that W W. This constraint captures the fact that wages are downward sticky due to unions, minimum wage regulations or because of the reluctance of employers on reducing wages. This constraint produces involuntary unemployment whenever the wage that would clear the labor market is lower than the minimum wage. That is, (W W )(h 1) = 0 (7) Given a fixed exchange rate regime, this imply: w w (8) Following Schmitt-Grohé and Uribe (2013), closure of labor markets require (w w)(h h) = 0 (9) Unemployment (h < h) require a binding wage constraint (w = w), whereas a market wage that is higher than the minimum (w > w), imply full employment h = h. In the current draft, I focus on the case where h is arbitrarily large. 2.4 Market Clearing and Competitive Equilibrium Non-tradable goods market must clear c N t = y N t () and the labor demand by firms must be equal to the number of hours that households work h = n (11) A competitive equilibrium is a set of prices and allocations { } p N 1, p N 2, w, n, h, c T 1, c N 1, c T 2, c N 2 such that: 1. HH max. utility c T 1 + c N 1 p N 1 + cn 2 p N 2 + c T 2 R u N (c T t, c N t ) u T (c T t, c N t ) = pn t = y T 1 + wn + π 1 + yn 2 R u T (c T 1, c N 1 ) = βru T (c T 2, c N 2 ) 2. Firms maximize profits h(w) = ( αzp N 1 w ) 1 1 α 7

8 3. Market clearing y N t = c N t, n = h 4. Labor market conditions w w, (w w)(h h) = 0, h h 2.5 Solution of the Model We will show that the equilibrium can be solved in a block-recursive way by reducing the equilibrium to a system of 2 2 equations and two unknowns (h, c T ). To do this, combine the static equilibrium conditions (4),(6), () to obtain a Price Schedule u N (c T 1, zh α ) u T (c T 1, zhα ) = wh1 α z that equates the price implied by households first order condition to the price implied by the firm first order condition. In addition, substituting market clearing conditions () for t = 1, 2, and using budget constraints (2) and (3) and plugging in (5), we obtain a Savings Schedule (12) u T (c T 1, zh α ) = βru T ((y T c T )R, y2 N ) (13) }{{} c T 2 A competitive equilibrium in this economy is given by (h, c T ) so that (12) and (13) are satisfied. As we will show below, under some fairly general conditions to be analyzed, these two schedules intersect more than once leading to multiple equilibria, as shown in Figure 3. The pricing schedule is upward sloping if tradable and non-tradable goods are normal. A higher tradable consumption imply a higher relative price of non-tradables to satisfy the household first order condition, and a higher relative price of non-tradables require higher employment to satisfy the firm first-order condition. An upward sloping Savings Schedule indicates that a higher level of tradable consumption requires a higher level of employment to yield allocations consistent with the Euler equation and market clearing. The key assumption that guarantees this positive relationship is u NT > 0. That is, a higher level of tradable consumption implies that there is a higher marginal value from consuming non-tradables, which in turn requires a higher level of employment to fulfill the higher demand of non-tradable goods. If u T N = 0, the borrowing schedule would be a vertical line, whereas u T N < 0 would imply a decreasing saving schedule. Whether the two upward sloping curves intersect more than once leading to multiple equilibria depends on the extent to which the demand for non-tradable consumption respond to income, i.e., on the income elasticity of non-tradable goods. Considering non-homothetic preferences are therefore crucial for multiplicity results. 1 As an example, we consider preferences given by: 2 u(c) = c1 σ 1 σ, c = [ω(c T ) η T + (1 ω)(c N ) η N ] 1/η, 1 There is a large literature in trade, development that establishes that non-homotheticity is important to reconcile several stylized facts. Specifically, the literature on structural change emphasize the need of high income elasticity of services to reconcile sectoral growth over time as well as cross-sectional facts. 2 This simple form of non-homotheticity allows us to reduce the system to a single non-linear equation. 8

9 where η T > η N to deliver an income elasticity of non-tradables goods higher than one. Household optimality conditions are: and p N = η N ω(c T ) η T +1 η T (1 ω)(c N ) η N +1 (14) c σ 1 η 1 ω(c T 1 ) ηt 1 = βrc σ 1 η 2 ω(c T 2 ) ηt 1 Observe that (12) can be solved for an explicit employment ĥ( ) as a function of tradable consumption: ( αηn ω(c T 1 ) η T +1 h = z η N ηt (1 ω)w ) 1/(ηN α+1) (15) and substituting this into (13) u T (c T 1, zh α ) = βru T ((y T c T 1 )R, y N 2 ) yields a single non-linear equation characterizing the equilibrium. Let us denote F as F (c T 1 ) = u T (c T 1, zh α ) = βru T ((y T c T 1 )R, y N 2 ) The appendix characterizes necessary and sufficient conditions for multiplicity. Key for the existence of multiplicity is that the slope of F changes sign within the range of possible values of equilibrium consumption c T 1 (0, y T ). Observe that: F (c T 1 ) = u T T + u T N zαĥ (c T ) α 1 +βr 2 u T T ( ( y T c T ) 1 R, y N }{{} 2 ) AggDemExt Two key elements are the cross partial derivative u T N and ĥ (c T ), which we label aggregate demand externality. As for the first term, u T N = 0 imply together with second-order conditions that F is strictly negative leading to a unique equilibrium, as discussed above. If u T N > 0 and the aggregate demand externality is sufficiently strong, this could lead to multiple c T 1 that satisfy F (c T 1 ) = 0. The mechanics behind multiple equilibria are as follows. Starting from the high employment/high consumption equilibrium, consider another equilibrium with low employment/low consumption equilibrium. When agents expect high unemployment, this leads to low income and low aggregate demand, which in turn leads to a low price of non-tradable goods and low employment in the non-tradable sector. Market clearing imply that consumption of non-tradables has to be low, which lead to a decline in the demand for tradable goods as long as U T N > 0 and a decline in the price of non-tradable goods for the marginal rate of substitution between tradables and non-tradables to be equal to the price. Since wages are downward rigid, this leads to a decline in labor demand, which rationalizes the expectations of high unemployment in the first place. To ensure that the low employment/low consumption is effectively equilibrium, the demand effects low income resulting from low employment has to more than offset the reduction in the price of non-tradables so that the demand for non-tradable goods fall in equilibrium. This occurs when the income elasticity of non-tradables goods is sufficiently larger than one. The two key elements of the environment that are key to generate multiplicity are downward wage rigidity and open capital markets. With flexible wages, the level of employment is determined by the supply h = h. With a closed capital account c T = y T, and as a result the level of employment is determined by (2.5). 9

10 3 2.5 Fiscal Stimuls Saving Schedule Employment 2 Bad Eq. Fiscal Stimulus 1.5 Price Schedule Good Eq. Fiscal Stimulus Tradable Consumption 3 Policy Implications Figure 3: Multiple Equilibria We study here the implications of our model for economic policy. It is important to observe that equilibria with high employment deliver higher welfare than equilibria with low employment. 3 One way to rule out the bad equilibrium is by providing a large subsidy on borrowing when the economy is in the bad equilibrium. To see this, consider the borrowing schedule with a subsidy τ on borrowing. u T (c T 1, zh α ) = βr(1 τ)u T ((y T c T 1 )R, y N 2 ) By setting τ large enough, the government can ensure that the desired level of tradable consumption is the one associated with the good equilibrium. 4 Consider next a devaluation that lowers the nominal wage in units of tradables. Since the wage rigidity applies to nominal wages, i.e., W/E t W, and increase in the exchange rate mitigates downward wage rigidity, as it well understood. What is subtle, however, is that a devaluation that does not go far enough, can actually make matters worse. To see, this consider the effects of a devaluation in the block recursive system given by the Price and Savings schedules. Notice that the price schedule is shifted up with the reduction in the real wage, whereas the saving schedule remains unaffected. As illustrated in the left panel of Figure 4, the level of unemployment in the bad equilibrium is reduced whereas the level of unemployment in the good equilibrium is increased. Equivalently, consider a fiscal devaluation along the lines of Farhi et al. (2014) and Schmitt-Grohé and Uribe (2013). In this case, firms solve max h p N (1 + s N )zh 1 α wh(1 s h ) where s h is a payroll subsidy and s N is a subsidy on non-tradable goods. 5 The results are the same as with the nominal devaluation. Fiscal devaluation reduces nominal wages and leads to different effects on unemployment depending on the equilibrium in which the economy is. 3 A formal proof works through revealed preference: households with income of the good equilibrium can afford the consumption bundle of the bad equilibrium. 4 Schmitt-Grohé and Uribe (2013) and Farhi and Werning (2012) study the role for taxes/subsidies on borrowing for aggregate demand management, but do not study multiplicity. ( ) 1 5 αzp N 1 α 1 Let s = (1 + s N )/(1 s h ), the labor demand condition becomes h(w) = w(1 s)..

11 Fiscal Stimuls Employment 2 Bad Eq. Fiscal Dev 1.5 Good Eq. Fiscal Dev Employment 2 Bad Eq. Fiscal Stimulus 1.5 Good Eq. Fiscal Stimulus Tradable Consumption Tradable Consumption Figure 4: Devaluation (left panel) and Fiscal Stimulus (right panel) The policy we study next is traditional fiscal policy. The government spends g N and finances it through lump sum taxes. By modifying the market clearing condition to y N = c N + g N, this leads to the following changes in the price and saving schedules. η N ω(c T ) η T +1 η T (1 ω)(zh α g N ) η N +1 = w t αzh α 1 u T (c T 1, zh α g N ) = βru T ((y T c T 1 )R, y N 2 ) The right panel of Figure 4 shows the effects of this policy. Notice that compared to the devaluation, the policy works relatively better when the economy is in the good equilibrium. 4 Infinite Horizon Model We extend our analysis to a fully dynamic model, along the lines of Schmitt-Grohé and Uribe (2013). Households Preferences are given by E 0 t=0 ( c β t 1 σ ) t 1 1 σ c = [ω(c T ) η T + (1 ω)(c N ) η N ] 1/η, In each period t, households receive an endowment of tradable goods y T t, collect profits and labor income w t n t. Households also trade a zero-coupon non-state contingent bond denominated in units of tradables. b t+1 R t + c T t + p N t c N t = b t + y T t + π + w t n t, Firms Every period firms solve π N = max h pn zh α t wh t 11

12 and satisfy the following first-order condition αp N t z t h α 1 t Downward Wage Rigidity - We assume that there is a stochastic process for minimum wages W t so that that equilibrium wages need to satisfy 6 W t W t Using w t = W t /E t and that E t is fixed, we have that the nominal wage rigidity is translated into a real wage rigidity condition: As in the two-period model, we impose the condition w t w t = w t (w t w t )(h t 1) = Recursive Equilibrium The fundamental aggregate states of the economy are the level of bonds, and the interest rate shock, productivity shocks and minimum wage shock. In addition, we consider an exogenous sunspot variable ζ t, which determines which equilibrium is selected. The variable ζ is independently and uniformly distributed on the interval [0, 1]. If ζ < ζ, the equilibrium selected is the bad one. 7 We start the definition of the equilibrium in recursive form by setting up the recursive problem of households. We denote by X = {B, s} the aggregate state where s collects all the exogenous states s = {R, w, y T, ζ}. We follow the convention of denoting current variables without subscript and denoting next period variables with the prime superscript the exogenous states. Let Γ( ) the forecast function of aggregate bond holdings, i.e., B = Γ(X). The problem of a representative household can then be written as: V (X) = subject to max u(c(c T, c N )) + βe s sv (b, B, X ) (16) b,c T,c N b R + pn (X)c N + c T = y T + b(1 + r) + w(x)n(x) + π(x) B = Γ(X) In this problem prices w(x), p N (X), employment n(x) and profits π(x)are taken as given by the representative agent. The solution to the household problem yields decision rules for individual bond holdings ˆb(X), tradable consumption ĉ T (X) and nontradable consumption ĉ N (X). The household optimization problem induces a mapping from the perceived law of motion for aggregate bond holdings to an actual law of motion, given by the representative agent s choice ˆb(B, X). In a rational expectations equilibrium, as defined below, these two laws of motion must coincide. Definition. (Decentralized Recursive Competitive Equilibrium) Given a process for s = {R, w, y T, ζ}, a recursive competitive equilibrium for our SOE is defined by pricing functions 6 In work in progress, we consider Schmitt-Grohé and Uribe (2013) specification where W t ΓW t 1 so that the minimum wage is related to t 1 wage. 7 For now, we consider only the equilibrium with the possible lowest and highest unemployment, and ignore the intermediate ones. 12

13 } p N (X), w N (X), profits π(x) a perceived law of motion Γ(X) and decision rules {ˆb(b, X), ĉ T (b, X), ĉ N (b, X), h(b, X), n(b, X) with associated value function V (b, X) such that the following conditions hold: 1. Household optimization: {ˆb(b, X), ĉ N (b, X), ĉ N (b, X), V (b, X)} solve the recursive optimization problem of the household. 2. Firm optimization h(x) satisfy p N (X)αzh(X) α 1 = w(x) 3. Rational expectation condition: the perceived law of motion is consistent with the actual law of motion: Γ(X) = ˆb(B, X). 4. Markets clearing in non-tradable goods: y N = ĉ N (b, X) and the resource constraint for tradable goods holds ˆb(B, X) + ĉ T (b, X) = y T + B(1 + r). 5. Labor market conditions: n = h In addition, there is a condition w(x) w (w(x) w)(h(x) 1) = 0 h(x) 1 5 Quantitative Analysis TO BE COMPLETED 6 Conclusions, References Bengino, G. and Fornaro, L. (2015). Twin Traps in a Keynesian Growth Model. LSE Working Paper. Benhabib, J. and Farmer, R. E. (1999). Indeterminacy and sunspots in macroeconomics. Handbook of macroeconomics, vol. 1, Benhabib, J., Schmitt-Grohé, S., and Uribe, M. (2001). The perils of Taylor rules. Journal of Economic Theory, vol. 96, no. 1, Benhabib, J., Schmitt-Grohé, S., and Uribe, M. (2002). Avoiding liquidity traps. Journal of Political Economy, vol. 1, no. 3, Benhabib, J. and Wang, P. (2013). Financial constraints, endogenous markups, and self-fulfilling equilibria. Journal of Monetary Economics, vol. 60, no. 7, Eggertsson, G. B. and Krugman, P. (2012). Debt, deleveraging, and the liquidity trap: A fisher-minsky-koo approach*. The Quarterly Journal of Economics, vol. 127, no. 3,

14 Eggertsson, G. B. and Mehrotra, N. R. (2014). A model of secular stagnation. Technical report, National Bureau of Economic Research. Eggertsson, G. B. et al. (2003). Zero bound on interest rates and optimal monetary policy. Brookings Papers on Economic Activity, vol. 2003, no. 1, Farhi, E., Gopinath, G., and Itskhoki, O. (2014). Fiscal devaluations. The Review of Economic Studies, vol. 81, no. 2, Farhi, E. and Werning, I. (2012). Dealing with the trilemma: Optimal capital controls with fixed exchange rates. NBER Working Paper. Farmer, R. E. (2012). The evolution of endogenous business cycles. Cambridge Univ Press. Farmer, R. E. (2013). Animal Spirits, Financial Crises and Persistent Unemployment*. The Economic Journal, vol. 123, no. 568, Hall, R. E. (2005). Employment fluctuations with equilibrium wage stickiness. American economic review, pages Hansen, A. H. (1939). Economic progress and declining population growth. The American Economic Review, pages Heathcote, J. and Perri, F. (2014). Wealth and volatility. Mimeo, Minneapolis Fed. Kaplan, G. and Weidner, J. (2014). The Wealthy Hand-to-Mouth. Brookings Papers on Economic Activity. Kocherlakota, N. (2009). Bursting bubbles: Consequences and cures. Schmitt-Grohé, S. and Uribe, M. (2011). Pegs and pain. Schmitt-Grohé, S. and Uribe, M. (2013). Downward nominal wage rigidity, currency pegs, and involuntary unemployment. Unpublished manuscript, Columbia University. Shimer, R. (2012). Wage rigidities and jobless recoveries. Journal of Monetary Economics, vol. 59, S65 S77. 14

15 15 NUMERICAL ILLUSTRATIONS

16 Bonds Good Eq. Bad Eq Price of Non-Tradables Good Eq. Bad Eq Unemployment Good Eq. Bad Eq Figure 5: Policy Functions Saving, Price of non-tradables and Unemployment for current bond choices good vs. bad equilibrium. Policies conditioned on average shocks for TFP, interest rate and a high minimum wage.

17 Frequency Unemployment 90 Figure 6: Distribution of Unemployment Frequency Unemployment Figure 7: Distribution of Unemployment conditional on high minimum wage 12 Frequency Unemployment Figure 8: Distribution of Unemployment conditional on bad equilibrium 17