Confidence Crashes and Stagnation in the Eurozone

Transcription

1 Confidence Crashes and Stagnation in the Eurozone Konstantin Platonov Department of Economics University of California Los Angeles February 14, 2017 Abstract We build a model of the Eurozone crisis. We study a two-country model of a monetary union in which agents form self-fulfilling beliefs about asset prices. We show that downward revisions of beliefs about the value of assets ( animal spirits ) cause international financial contagion, stagnation in real economic activity and permanently high rates of unemployment. The economy does not have a tendency to self-recover without improvements in beliefs. We achieve these results by leaving the labor market equilibrium indeterminate. Steady state indeterminacy accounts for persistence of unemployment. Dynamic indeterminacy explains why nominal shocks have effects on real economic activity. We resolve indeterminacy by introducing a belief function as a new fundamental. Our analysis suggests that the Eurozone stagnation is not a deviation from the trend; this is a new trend. Policy aimed at recovering the Eurozone needs to trigger optimistic beliefs about the value of assets. Key words: Eurozone crisis, stagnation, confidence, beliefs, asset prices, indeterminacy JEL codes: E32, E50, F41, F44, F45 I would like to thank Roger E.A. Farmer and Aaron Tornell for their invaluable comments and support. I also thank Giovanni Nicolò, Yunfan Gu and the participants at the UCLA macro and international finance workshops. 1

2 1 Introduction The real economic activity in the Eurozone has been stagnating since 2010 when the Eurozone was hit by a debt crisis. The stagnation in the Eurozone differs from typical business cycle fluctuations. It demonstrates unemployment persisting at high rates and no recovery in real GDP. Economic models that rely on price stickiness and on the existence of the unique long-run unemployment rate fail to predict crashes like the 2010 Eurozone crisis and absence of fast recovery in real economic activity. We propose a new way of thinking about the Eurozone crisis and the recession it caused. We combine a model of a two-country monetary union with general equilibrium, labor market search and matching frictions, and asset pricing in a new way. By allowing for multiple equilibria on the labor market, we argue that beliefs about the prices of assets play a crucial role in the determination of the unemployment rate, real economic activity and international trade. With multiple equilibria, beliefs about asset prices become self-fulfilling. Sudden downward revisions of the beliefs, so called animal spirits, can trigger persistent economic recessions. In such economies, there may be no self-correction until beliefs recover. To put discipline on how equilibrium is selected, we propose the belief function, a forecasting rule, as a new fundamental. Our paper contributes to the big subject of financial crises and economic recessions. First, our model is a formalization of the crisis narrative proposed by Baldwin et al. (2015). We are sympathetic to the view that the Eurozone crisis was a selffulfilling crisis triggered by a loss of confidence in the value of assets held by the peripheral countries of the Eurozone. The peripheral countries (Greece, Ireland, Italy, Portugal, and Spain) relied on international borrowing and accumulated large debts. In 2010, investors revised their beliefs about solvency of these countries. The stock market crashes spread to the core countries, such as Austria, Belgium, France, Germany, and the Netherlands. In our model, the financial crisis is caused by self-fulfilling beliefs about the value of assets. Baccetta and van Wincoop (2016), Benhabib et al. (2016), Perri and Quadrini (2013), Martin and Rey (2006) use a similar approach. Second, we contribute to the big literature on causes and mechanisms of the Great Recession, sometimes referred to as secular stagnation (Summers 2014, Caballero et al. 2016, Eggertsson et al. 2016, Schmitt-Grohe and Uribe 2017, among many others). The standard explanation for the slow recovery of the world economy after the 2008 International Financial Crisis is the liquidity trap. Our explanation does not rely on the zero lower bound. Instead, we view the multiple equilibria on the labor market as a vehicle to capture persistence of high unemployment and the absence of automatic recovery. Third, we connect the asset prices and real economy in à la Lucas tree model, where investors animal spirits cause stock market crashes and economic recessions (Farmer 2012, Farmer 2013). Our model displays contagion, when asset price crashes transmit internationally (Benhabib et al. 2016, van Wincoop 2013, 2

3 Kodres and Pritsker 2002, Moser 2003). The approach of this paper builds heavily on Farmer (2010, 2011, 2013) and Farmer and Platonov (2016). It differs from the standard New Keynesian paradigm in two ways. First, our model exhibits steady state indeterminacy. Due to search and matching frictions on the labor market, the labor market equilibrium is indeterminate. Following Farmer (2011), we assume away Nash bargaining over wage and let the unemployment rate be determined by the aggregate demand. In our view, the secular stagnation is not a deviation from the unique steady state; this is a new steady state. Second, each steady state exhibits dynamic indeterminacy. There are many dynamic paths that lead to the same steady state. To select a particular dynamic equilibrium, we assume that prices are set one period in advance. Price stickiness is an equilibrium feature of the model. The paper is organized as follows. Section 2 presents the model. Section 3 discusses the steady state equilibria. Section 4 discusses the dynamic equilibria and shows how a shock to confidence propagates over time and internationally. Section 5 concludes. 2 The Model 2.1 Overview We build analysis of the Eurozone crisis on the interaction between two ex ante identical countries (regions), which we call Core and Periphery. They share the same currency and have access to the common loanable funds market. Each country can issue or buy bonds on this market. Time is discrete and there is no aggregate uncertainty. Each country has a unit of non-reproducible physical capital. Physical capital plays two roles. First, combined with labor, capital produces a country-specific tradable good. Second, being a physical asset, capital has a market value which we interpret as the value of a stock market. Labor is immobile across countries. We adopt labor search and matching frictions. Firms need to withdraw labor from production and devote resources to recruiting activities. Similar to the tragedy of commons, search has negative externality on other firms. Generally, there is a positive equilibrium rate of unemployment, with a unique socially optimal level of unemployment. 1 Each country is populated by a unit continuum of overlapping generations. Every consumer has an infinite horizon but faces an age-invariant probability of death. At the beginning of each period, a new cohort of consumers is born to keep the population constant. Consumers derive utility from a final nontradable consumption 1 Stabilizing macro policy should be aimed at maintaining the unemployment rate at the socially optimal rate. Fiscal interventions and characterization of the optimal policy is beyond the scope of this paper. These topics constitute our current research agenda. 3

4 good, assembled from the local and imported intermediate goods, and of real money holdings. Search and matching frictions on the labor market generate multiple equilibria, multiple steady state rates of unemployment. Instead of allowing for bargaining over wage with constant weights as a selecting mechanism, we add a new fundamental: the belief function. The belief function is a rule used by economic agents to forecast the value of capital. The belief function does not contradict the rational expectations hypothesis because beliefs are self-fulfilling: any level of confidence can be supported in a rational-expectations equilibrium. The belief function picks a particular equilibrium out of many. When consumers believe they are rich, they demand more goods (both local and imported). Firms hire more labor to satisfy the demand. National wealth rises, and beliefs fulfill themselves. Exogenous changes in the beliefs about the value of capital ( animal spirits ) generate volatility and lead to crashes of the stock market and economic recessions. We lay out the description for one country, Core. Periphery is characterized by the same equations, with variables being marked with an asterisk. 2.2 Supply Side Intermediate-Good Producing Firms. Firms combine capital and labor to produce the intermediate good. Output is used in the domestic region for production of the final good and for exporting to the other country. The production function is given by the following CES function: ) y t = (α(k t 1 ) η 1 η + (1 α) (x t ) η 1 η η 1 η, (1) with η = 1 being Cobb-Douglas. 2 Here y t is the quantity of the intermediate good produced, k t 1 is the quantity of capital rented at the beginning of period t and x t is the amount of workers engaged in production. Hiring labor is subject to search frictions: firms need to devote a fraction of labor for recruiting. 3 We denote the search efficiency as φ t. This parameter shows how many production workers a recruiting worker can hire. The search efficiency is endogenously determined at the aggregate level but taken as given by each individual firm. If there are v t recruiting workers, the firm can hire x t = φ t v t production workers. The total employment is equal to l t = x t + v t. This allows us to write the production function in terms of total employment: ( ( ) η 1 ) η η 1 η 1 η φt η y t = αkt 1 + (1 α) l t. (2) 1 + φ t 2 We depart from the Cobb-Douglas production function to avoid the problem of peculiar financial equilibria in which stock markets turn out to be perfectly correlated and hence they represent the same investment opportunity (for discussion, see Cass and Pavlova, 2004). 3 This section is borrowed from Farmer (2013). 4

5 The multiplier on labor l t, φ t /(1 + φ t ), has the notion of total labor productivity. When the search efficiency φ t is high, the overall labor is productive because firms can allocate more labor to production and less labor to recruiting. We assume perfect competition on the factor markets and the market for the goods. Firms maximize the profit: P t y W t l RR t k by choosing the quantities of capital k and labor l taking the price of output P t, rental rate of capital RR t and wage W t as given. In equilibrium, k = 1. For convenience, let w t W t /P t and rr t = RR t /P t be the respective factor prices divided by the price of the local good, i.e. real factor prices. The first order conditions for the intermediate good producers can be written in the following way: At the aggregate level, there is a matching function rr t = αy 1/η t, (3) w t l t = y t αy 1/η t. (4) f ( 1 l t, v t ) = Γ ( 1 lt ) γ ( vt ) 1 γ. (5) The first argument of the matching function is the unemployment rate. The second argument of the matching function is the fraction of workers devoted to search. Parameter Γ is a scale parameter. Assuming job separations occur at an exogenous rate of χ and using the aggregated condition l t = (1 + φ t ) v t, the law of motion for aggregate employment is given by lt = (1 χ) l t 1 + Γ ( ( ) 1 l ) 1 γ γ lt t. (6) 1 + φ t As we show further, in the absence of the labor market clearing condition the employment rates are determined by the aggregate demand. Then equation (6) determines the efficiency of search φ t and employment of each separate firm. Final-Good Producing Firms. The final good c t is assembled from goods produced locally g local,t and imported g imp,t : c t = (ω 1 ν 1 ν g ν local,t + (1 ω) 1 ν 1 ν g ν imp,t ) ν ν 1, (7) Provided the prices of the local intermediate good is P t and the price of the imported intermediate good is Pt, perfect competition drives the profits to zero and generates the following demand functions: ( ) ν ( ) Pt P ν g local,t = ω c t, g imp,t = (1 ω) t c t, (8) P t P t 5

6 where the price of the final consumption good denoted P t takes the standard form of a CES price index: P t = ( ω (P t ) 1 ν + (1 ω) (Pt ) 1 ν) 1 1 ν. (9) Define p t P t /P t the relative price of the consumption good, p t P t /Pt the relative price of the consumption good abroad, and q t P t /Pt Core s terms of trade. The demand functions and the price index can be rewritten in the following way: 2.3 Demand Side g local,t = ω ( p t ) ν c t, g imp,t = (1 ω) (q t p t ) ν c t, (10) ( p t ) 1 ν = ω + (1 ω) (q t ) ν 1 (11) There is a unit continuum of consumers. Once born, they face a constant probability of death 1 λ, 0 < λ < 1. Let s index the date of birth of a consumer. The preferences are defined over the sequences of the consumption good c t (s) and real money balances m t (s). Consumers discount the future at rate β and maximize the expected discounted flow of utility: (βλ) t s u (c t (s), m t (s)). (12) t=s The intertemporal budget constraint takes the following form: λ [M t (s) + P K,t k t (s) + A t (s)] + P t c t (s) = (1 + i t 1 )A t 1 (s) + (P K,t + RR t ) k t 1 (s) + M t 1 (s) + W t l t + T t. (13) Here M t (s) is the nominal money holding at the end of period t, P K,t is the nominal price of capital and k t (s) is the amount of capital held by an individual born at s, A t (s) is the nominal value of the bonds, RR t is the nominal rental rate of capital. We assume that all employed consumers work the same number of hours l t and earn the same money wage W t. 4 The variable T t is lump-sum transfers. The presence of the multiplier λ on the choice of portfolio in the budget constraint reflects life insurance: insurance companies subsidize the purchase of financial assets with a right to inherit the assets in case of accidental bequest. This annuity scheme follows Blanchard (1985). For convenience, divide the dynamic budget constraint by the price of the local good P t. We denote p K,t P K,t /P t the real value of capital, a t (s) A t (s)/p t 4 There is perfect insurance within generations. The employed and the unemployed enjoy the same level of consumption. 6

7 real financial asset holdings, and Π t P t /P t 1 is the inflation factor. The object (1 + i t 1 )/Π t is the ex post real interest rate payed in period t on investments made in period t 1. λ [m t (s) + p K,t k t (s) + a t (s)] + p t c t (s) = 1 + i t 1 a t 1 (s) + (p K,t + rr t ) k t 1 (s) + m t 1(s) + w t l t + t t. (14) Π t Π t To write the first order condition for the household, we must assume the absence of arbitrage opportunities between domestic equity and bonds: ( u c,t it p ) K,t+1 + rr t+1 = 0. (15) p t+1 Π t+1 p K,t The no-arbitrage condition (15) states that, adjusted for the marginal utility of future consumption, the bonds must earn as much as investment in physical capital. Because there is a single loanable funds market, the no-arbitrage condition (15) implies that the ex ante real interest rates in the Core and Periphery need to be equalized as well: u c,t+1 p t+1 ( p K,t+1 + rr t+1 p K,t+1 + rr t+1 p K,t p K,t q t q t+1 ) = 0. (16) Condition (16) has the structure similar to the uncovered interest rate parity. The first term in the parentheses is the expected real return to physical capital in Core. The second term in the parentheses is the expected real return to physical capital in Core translated into the Periphery s good as the unit of account. Finally, the multiplier u c,t+1 / p t+1 translates these two terms into consumption of period t + 1. There are two standard first-order conditions, the Euler equation and the money demand respectively: βu c,t+1 (1 + i t ) = 1, (17) u c,t Π t+1 u m,t = i t 1 + i t λu c,t p t. (18) To move beyond the general first order conditions, we adopt the logarithmic utility function, u(c, m) = (1 δ) log c + δm. (19) It follows immediately that optimal expenditure on consumption is proportional to 7

8 total wealth accumulated by an individual born at s: [ ( 1 p t c t (s) = δ c (p K,t + rr t ) k t 1 (s) i t 1 a t 1 (s) + m ) ] t 1(s) + h t (s), λ Π t Π t (20) [ ( i t 1 m t (s) = δ m (p K,t + rr t ) k t 1 (s) i t 1 a t 1 (s) + m ) ] t 1(s) + h t (s), 1 + i t λ Π t Π t (21) where δ c (1 δ)(1 βλ), δ m (1 δ)(1 βλ)/λ and h t (s) is human wealth (the present value of the flow of labor income and transfers) characterized by the law of motion h t (s) = w t l t + t t + λ Π t i t h t+1 (s). (22) Aggregating the individual choice variables across all agents, we arrive at the following equations that describe the aggregate demand (taking into account that k t 1 = 1): [ p t c t = δ c p K,t + rr t i t 1 a t 1 + m ] t 1 + h t, (23) Π t Π t i t 1 + i t m t = δ m [ p K,t + rr t i t 1 a t 1 + m t 1 + h t Π t Π t ], (24) h t = w t l t + t t + λ Π t i t h t+1. (25) Note the multiplier 1/λ on wealth drops out when aggregating because life insurance companies simply redistribute wealth across agents. 2.4 Monetary Policy The Central bank controls the quantity of money in the economy Mt CB and adjusts it through direct cash transfers to households. 5 The nominal interest rate i t adjusts to clear the money market: M CB t = M t + M t, (26) or in terms of the Core s good (i.e. divided through by P t ), m CB t 5 Farmer and Nicolo (2016) focus on an interest rate rule. = m t + m t q t. (27) 8

9 2.5 Beliefs Economic agents form self-fulfilling beliefs about the future real value of capital. In general form, the beliefs can be represented by the belief functions defined by the following equations 6 : p K,t+1 = Θ t, (28) p K,t+1 = Θ t. (29) Under perfect foresight, the left-hand sides of (28) and (29) are the exact future values of the two stock markets. As of period t, however, the future values p K,t+1 and p K,t+1 should be treated as rational expectations of the underlying variables. Unanticipated exogenous changes in p K,t+1 and p K,t+1 represent shifts in the moods of investors which we call the animal spirits. 2.6 Definition of the Equilibrium A competitive perfect-foresight equilibrium in the monetary union is a sequence of GDP series of labor, quantities of intermediate goods { l t, lt, g local,t, g imp,t, glocal,t, g imp,t, y t, yt }, labor productivities {φ t, φ t }, a sequence of the relative prices and inflation factors { p t, p t, Π t, Π t, q t, rr t, rrt, w t, wt, p K,t, p K,t }, a sequence of consumption, human wealth, real money holdings and financial interest-bearing assets {c t, c t, h t, h t, m t, m t, a t, a t }, and a sequence of the monetary policy variables {i t, m CB t } such that, given sequence of the nominal stock of market {Mt CB } and a sequence of beliefs {Θ t, Θ t }, the following conditions hold: 1. First order conditions for the intermediate good producing firms (3) and (4) hold, along with their equivalents for Periphery 2. Labor l t and l t and labor prodctivities φ t and φ t satisfiy the law of motion (6) and its equivalent for Periphery 3. Intermediate goods g local,t, g imp,t, g local,t, and g imp,t satisfy the demand functions (10) and their equivalents for Periphery 4. The intermediate goods markets clear: y t = g local,t + g imp,t, (30) y t = g local,t + g imp,t. (31) 5. Zero-profit condition (11) and its equivalent for Periphery hold 6. Demand functions for consumption (23) and real money balances (24) hold, along with their equivalents for Periphery 6 For an extensive discussion of belief functions, see Farmer (2016b) 9

10 7. Human wealth h t and h t satisfy the law of motion (25) and its equivalent for Periphery 8. Balance of payments holds: 9. Money market and monetary policy satisfy (27) a t 1 + i t 1 Π t a t 1 = y t p t c t (32) 10. The no-arbitrage conditions (15) and (16) and their equivalents for Periphery hold 11. Loanable funds market clears: a t + a t q t = 0 (33) 12. Values of capital p K,t and p K,t satisfy the belief functions (28) and (29) 13. Necessary transversality conditions hold. We do not state them here These equilibrium conditions are standard with one exception. The innovation of the paper is the introduction of the belief functions that govern the values of capital. 3 Steady State Equilibria By giving up Nash bargaining over wage with constant bargaining powers, we leave the labor market equilibrium indeterminate. However, once we introduce the belief function and once we allow beliefs about asset prices to determine the aggregate demand, the equilibrium becomes unique. Our model is isomorphic to a model with Nash bargaining where the bargaining weights are dependent on the aggregate demand. The steady state in our model has two distinctive features. First, beliefs about the value of assets are self-fulfilling. If economic agents believe prices of assets must be high, the economy will be in equilibrium with high output and consumption, low unemployment, and high values of capital. Second, any unemployment rate can be sustained at the steady state. We call this property the steady-state indeterminacy. 7 For given beliefs, there is a unique unemployment rate. Since a range of beliefs can be sustained at the steady state, there is a continuum of steady states indexed by the beliefs about the value of capital. An immediate implication of the steady state 7 Farmer (2016a) discusses the evolution of the models with determinate and indeterminate steady states. 10

11 indeterminacy is that there is no tendency for the economy to self-correct in response to shocks. Because of the complexity of the model, it is impossible to obtain the closed-form solution for the steady state. We use the numerical solutions and demonstrate the comparative statics graphically. We adopt the parameter values provided in Table 1 and plot the steady states on Fig. 1. Table 1: Parameter Values Parameter Interpretation Value α Coefficient on capital in the production function 0.33 β Time discount factor 0.99 λ Probability of surviving 0.99 δ Coefficient on money in utility 0.01 ω Home bias in consumption 0.75 η Elasticity of substitution between capital and labor 0.50 ν Elasticity of substitution between domestic and foreign goods 1.50 (µ, 1 µ) Distribution of cash transfers (0.50, 0.50) χ Job separation rate 0.50 Γ Scale parameter on matching function 1.38 To plot the steady state diagrams on Figure 1, we begin at a symmetric steady state where the unemployment rate in both economies is equal to 10%. Then we keep the real value of capital in Periphery p K constant and vary the value of capital in Core p K to trace, how the steady state equilibria change. The panels on Fig. 1 show the percentage deviations of the variables from the original symmetric steady state. For the nominal interest rate and the unemployment rate, we show the exact percentage values. The solid lines are for Core and the dashed lines are for Periphery. Panel (a) displays output in Core and Periphery. Output in Core is increasing in the value of capital in Core. There is negligible positive effect of value of capital in Core on output in Periphery too. As value of capital and therefore wealth rise, larger aggregate demand raises output and reduces the unemployment rate, depicted on panel (b). Panels (c) and (d) show the positive effect of the value of capital in Core on consumption and real money holdings in Core and Periphery. Due to international trade, consumption in Periphery is more responsive to cross-country increases in the value of capital than output. Real money holdings increase because money holdings are complementary to consumption; households prefer to hold more money when they consume more. Panel (e) displays the nominal interest rate. As consumption in Core and Periphery increase, so does the demand for money. Provided the Central bank keeps the nominal supply of money constant, the money market will clear at a higher interest rate. Panel (f) shows the amounts of bonds held by Core and Periphery. Negative bond holdings mean debt. As the value of capital increases in Core, Core has less 11

12 Figure 1: Steady state comparative statics: the role of beliefs in the determination of equilibrium 12

13 financial wealth. Core accumulates debt because Periphery prefers to buy Core s bonds. This is a consequence of the common loanable funds market. When the value of capital in Core rises, the rate of return to capital in Core increases., which attracts capital inflows. Arbitrage drives the interest rate up till the point when the returns to capital in both countries and on bonds are equalized. Panels (g) and (h) display Core s terms of trade (the price of export divided by the price of import) and net exports for Core and Periphery. They show that Core s terms of trade decrease and net exports increase as the value of capital in Core increases. The deterioration of the terms of trade is caused by expanding of Core s production, which leads to increase in net export from Core to Periphery. Finally, keeping beliefs constant, money is neutral. The quantity of money chosen by the Central bank determines only the scale of nominal prices but leaves the real economic activity unaffected. This section presented the comparative steady state statics. It shows that an economy with optimistic beliefs has higher output with consumption and lower unemployment rate. This section also shows that, keeping beliefs constant and the current value of capital equal to the expected value, there are limited international spillover effects of confidence in Core on the real economic activity in Periphery. In addition, when beliefs are equal to the realized value and are kept constant, monetary shocks are neutral. Monetary shocks scale all nominal prices up by the same factor and leave real variables unaffected. The next section studies the transition between the steady states. 4 Dynamic Equilibria and Confidence Crashes This section considers the dynamic equilibrium of our model. It describes how the economy moves between the steady states presented in the section above. We loglinearize the model around a steady state and study its properties. We preserve the calibration values from Table 1. Beliefs determine not only the steady state, but also the dynamic path of the economy that leads to the steady state. To highlight the role of beliefs, we consider two sets of beliefs functions. The first set of beliefs is called the exogenous beliefs: p K,t+1 = Θ, p K,t+1 = Θ, (34) under which economic agents believe the real future value of capital will be equal to a known constant. The other set of beliefs is called the endogenous beliefs: p K,t+1 = p K,t, p K,t+1 = p K,t. (35) Under the endogenous beliefs, the economic agents believe the real future value of capital will be equal to its current value, but this value is determined endogenously. 13

14 The endogenous beliefs imply that there is no predicted trend in the value of capital. A stochastic equivalent of the endogenous beliefs would be the random walk. In both cases, the left-hand sides of (34) and (35) should be regarded as expectations of the corresponding future real values of capital made in period t. The log-linearized system can be written in a state space representation: Γ 0 X t = Γ 1 X t 1, (36) where X t is the vector of log deviations of the endogenous variables from the steady state, and matrices Γ 0 and Γ 1 govern the dynamics of the system. Under the calibration from Table 1, we find that our model has three degrees of dynamic indeterminacy. This means that there are many dynamic equilibria, and all of them converge to the same steady state. We need to specify three initial conditions to pin down a particular dynamic equilibrium. 8 We assume that producer prices and terms of trade are predetermined and set one period in advance, so that they cannot respond to shocks instantly. 9 This price rigidity links our paper with New Keynesian models that rely on price stickiness. However, in our model price stickiness arises in equilibrium as one of possible equilibria. This is not artificial price barriers that make prices sticky; this is the belief that prices are slow to respond. We illustrate the dynamic properties of the model by studying the impact of a confidence shock (a downward revision of beliefs in Periphery) and of a monetary shock. Also, we define contagion as response of the asset prices in one region to a shock to confidence in the other country. We show that even when beliefs are exogenous, our model displays contagion and a crisis in one country causes stagflation in the whole monetary union. Exogenous Beliefs. In this part, we adopt the belief functions given by (34). in period 0, The economy is at a symmetric steady state with Θ = Θ. In period 1, the belief about Periphery s future value of capital, Θ, goes down by 1% and remains 1% lower for ever after. We keep Core s belief Θ and the nominal supply of money unchanged. Figure 2 displays the dynamic response of the economy to this shock. Vertical axes measure the percentage deviations of the variables from the original steady state values. On Figure 2, Panel (a) shows the exogenously determined path for beliefs. Core s beliefs do not respond by assumption. Panel (b) shows the dynamics of the realized value of capital. Panel (c) shows that pessimistic beliefs in Periphery reduce output in period 1, at the moment of the shock. Since Periphery s consumers believe their wealth will go down, they reduce consumption immediately (see Panel (d)). At the same time, Core s consumers expect smaller demand from Periphery and reduce 8 When a system is dynamically determinate, there is only one initial point that leads the economy to the steady state. 9 This assumption implies that all four prices, two producer prices and two consumer price indices, are predetermined. Farmer (2000) and Farmer and Platonov (2016) use the same way to resolve dynamic indeterminacy. 14

15 Figure 2: Exogenous beliefs: Response of the economy to a 1% crash in Periphery s beliefs. 15

16 their consumption (to a smaller extent), which lowers Core s output on Panel (c). In period 1, since all prices are predetermined, the real money balances holdings depicted on Panel (e) remain unchanged. The nominal interest rate goes down a little in period 1 to reflect the decrease in the money demand. In period 2, when all prices become fully flexible, terms of trade from Panel (g) go down by 0.6% to reflect the decrease in the aggregate demand from Periphery. This makes Periphery s goods relatively cheaper. Core keeps positive net export with Periphery (see Panel (j)). Value of capital in Periphery (Panel (b)) remains permanently lower due to the self-fulfilling nature of beliefs. Consumption and output in Periphery level off below the pre-crisis value. This implies that Periphery will have a permanently higher rate of unemployment than before. Core s consumption and output remain below the original level too, but the decrease is smaller than in Periphery. Endogenous Beliefs. Now we assume endogenous beliefs, described by (35). We perform the same exercise. In period 0 the economy is at the steady state. In period 1, beliefs in Periphery, given by p K,2, decrease by 1%. However, the subsequent dynamics of beliefs both in Core and Periphery is governed by the belief function (35). Figure 3 shows the dynamic path of the economy. The immediate response of the economy is identical to the case when beliefs are exogenous. However, now in period 1, the decline of the asset prices in Core becomes supported by self-fulfilling beliefs, and the decline becomes permanent. This leads to a greater drop in output and consumption both in Core and Periphery. The two dynamic experiments presented above illustrate our logic of the stagnation in the Eurozone. Core s asset prices respond to a shock to confidence in Periphery. The channel for contagion is international trade. There are mutual benefits from trade. When consumers in Periphery become pessimistic about the value of their assets, production and consumption in Periphery fall. For consumers in Core, Periphery s goods become relatively more expensive, so they reduce import. The wealth effect makes them reduce consumption and hence production in Core. The decline of output in Core is smaller than in Periphery for two reasons. First, there is substitution effect: both economies switch to the Core goods agains the Periphery goods. Second, the two countries share the same currency and prefer to hold money proportional to consumption. As consumption falls in Periphery, Core holds more currency than Periphery, which prevents big drops in Core s output. Monetary Expansion and Endogenous Beliefs. Here we show the effects of a 1% permanent unanticipated increase in the nominal supply of money under endogenous beliefs. In period 0 the economy is at the steady state and in period 1 there is an unexpected permanent increase in the quantity of money. For simplicity, the newly printed money is evenly distributed as cash transfers across the two countries. Figure 4 shows the symmetric response of the economy. Panel (a) and Panel (b) show the dynamics of the value of capital and of the belief about it. Because prices are predetermined in period 1, the nominal shock increases real value of wealth (Panel (a) and Panel (b)), output and consumption 16

17 Figure 3: Endogenous beliefs: Response of the economy to a 1% crash in Periphery s beliefs. 17

18 Figure 4: Endogenous beliefs: Response of the economy to a 1% increase in the quantity of money. 18

19 (Panel (c) and Panel (d)). However, since households believe the current value will prevail and there is no shocks thereafter, the economy remains with permanently higher output and permanently lower unemployment rate. Terms of trade (Panel (g)), financial wealth (Panel (i)) and net export (Panel (j)) do not change because both countries respond to the monetary shock symmetrically. Inflation rates (Panel (h)) do not increase because all the monetary shock has been absorbed by the real variables, real value of capital and output. Increases in output in Core and Periphery reinforce each other, resulting in an increase in GDP by more than 1%. Panel (f) shows that the interest rate rises a little because the real money demand increases more than the real supply of money. An important feature of monetary policy in our model is that it does not rely on the interest rate channel. Instead, it operates through the wealth channel. Due to price stickiness, nominal increase in the quantity of money adds to the real total wealth and drives consumption and output up. 5 Conclusion We have proposed a two-country model of a monetary union which describes the crisis in the Eurozone. By combining search and matching frictions on the labor market, abandoning the Nash bargaining over wage, and allowing for self-fulfilling beliefs about asset prices, we build a model that is consistent with the stylized facts about the Eurozone crisis and stagnation. First, the trigger of the crisis is a negative shock to confidence, to the beliefs about the value of assets in the periphery. Second, our model demonstrates financial contagion. Pessimism about the value of assets in the periphery spreads over to the core countries, causing an economic collapse all over the monetary union. Third, in our model, confidence crashes have permanent effects: high unemployment and low output can persist indefinitely long, without tendency to self-recover. Finally, in our model the economy can return to the precrisis level if the Central bank could step in as a lender of last resort and increase the money supply. Our results rely on two distinctive features of our approach. First, the model displays steady state indeterminacy caused by multiple equilibria on the labor market. This breaks the assumption that the unemployment rate returns to its unique long-run rate. Second, the model displays dynamic indeterminacy. We focus the analysis on a dynamic equilibrium with predetermined prices. Nominal shocks have impact on real economic activity and asset prices. Self-fulfilling beliefs propel the shocks over time. We view this model as a rich environment for policy analysis. The future work will add fiscal policy and study the optimal stabilizing policy. 19

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