Slides for Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Open Economy Macroeconomics M. Uribe and S. Schmitt-Groh´ e Columbia University December 6, 2016

1

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Introduction

• develop a theoretical framework with nominal rigidities that result in inefficient adjustment to aggregate disturbances • framework can be used in an intuitive manner to demonstrate how nominal rigidities amplify the business cycle in open economies • but framework can also be used to derive quantitative prediction useful for policy evaluation

2

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Some Motivation: Emerging Europe and the Global Crisis of 2008 Take a look at the next slide. • The inception of the Euro in 1999, was followed by massive capital inflows into the region, possibly driven by expectations of quick convergence of peripheral and core Europe. • Large current account deficits and large increases in nominal hourly wages, with declining rates of unemployment between 2000 and 2008. • With the Global crisis, capital inflows dried up abruptly. The region suffered a severe sudden stop (sharp reductions in current account deficits). • In spite of the collapse in aggregate demand and the lack of a devaluation, nominal hourly wages remained as high as at the peak of the boom. • Massive unemployment affected all countries in the region. 3

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Figure 9.1 Boom-Bust Cycle in Peripheral Europe: 2000-2011 Current Account / GDP

Labor Cost Index, Nominal

−2

110

−4

100

Unemployment Rate 14 13

Percent

−6 −8 −10

90

11 Percent

Index, 2008 = 100

12

80

10 9

70

8 −12 −14

60

2002 2004 2006 2008 2010 Date

50

7 2002 2004 2006 2008 2010 Date

6

2002 2004 2006 2008 2010 Date

Data Source: Eurostat. Labor Cost Index, Nominal, is the nominal hourly wage rate in manufacturing, construction and services (including the public sector, but for Spain.) Data represents arithmetic mean of Bulgaria, Cyprus, Estonia, Greece, Ireland, Lithuania, Latvia, Portugal, Spain, Slovenia, and Slovakia.

4

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

This suggests the following narrative: Countries in the periphery of the European Union, such as Ireland, Portugal, Greece, and a number of small eastern European countries adopted a fixed exchange rate regime by joining the Euroarea. Most of these countries experienced an initial transition into the Euro characterized by low inflation, low interest rates, and economic expansion. However, history has shown time and again that fixed exchange rate arrangements are easy to adopt but difficult to maintain. (Example: Argentina’s 1991 convertibility plan.) The Achilles’ heel of currency pegs is that they hinder the efficient adjustment of the economy to negative external shocks, such as drops in the terms of trade or hikes in the interest-rate. Such shocks produce a contraction in aggregate demand that requires a decrease in the relative price of nontradables, that is, a real depreciation of the domestic currency, in order to bring about an expenditure switch away from tradables and toward nontradables. In turn, the required real depreciation may come about via a nominal devaluation of the domestic currency or via a fall in nominal prices or both. The currency peg rules out a devaluation. Thus, the only way the necessary real depreciation can occur is through a decline in the nominal price of nontradables. However, when nominal wages are downwardly rigid, producers of nontradables are reluctant to lower prices, for doing so might render their enterprises no longer profitable. As a result, the necessary real depreciation takes place too slowly, causing recession and unemployment along the way. This narrative goes back at least to Keynes (1925) who argued that Britain’s 1925 decision to return to the gold standard at the 1913 parity despite the significant increase in the aggregate price level that took place during World War I would force deflation in nominal wages with deleterious consequences for unemployment and economic activity. Similarly, Friedman’s (1953) seminal essay points at downward nominal wage rigidity as the central argument against fixed exchange rates. 5

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

To formalize this narrative we build an open economy model with • downward nominal wage rigidity • a traded and a nontraded sector • involuntary unemployment To produce quantitative predictions • Estimate the key parameters of the model (with particular attention on the parameter governing downward wage rigidity) and estimate the driving forces. • Characterize response to large negative external shock under a peg and show that the model can explain the observed sudden stop. • Characterize optimal exchange rate policy. • Quantify the costs of currency pegs in terms of unemployment and welfare. The material is based on Schmitt-Groh´ e and Uribe (JPE, 2016). 6

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Section 9.1 An Open Economy Model with Involuntary Unemployment due to Downward Nominal Wage Rigidity

7

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Downward Nominal Wage Rigidity (DNWR)

Wt ≥ γ Wt−1 Wt = nominal wage rate in period t γ = degree of downward wage rigidity. γ = 0 ⇒ fully flexible wages. Think of γ as being around 1. The empirical evidence presented later in this chapter suggests γ = 0.99 at quarterly frequency.

8

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Traded and Nontraded Goods Traded goods, stochastic endowment: ytT Nontraded goods, ytN , produced with labor, ht: ytN = F (ht) The nominal prices of tradables and nontradables: PtT and PtN . PtN The relative price of nontradables: pt = T Pt

Nominal exchange rate: Et , domestic currency price of one unit of foreign currency (Et ↑ depreciation of domestic currency). Depreciation rate: t = Et /Et−1 . Law of one price holds for tradables: PtT = Et Pt∗. Assume that Pt∗ = 1, so that PtT = Et 9

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

The Nontraded Sector Profits: Φt = PtN F (ht) − Wtht Firms maximize profits taking as given PtN and Wt Optimality Condition: PtN F 0(ht) = Wt Divide by PtT = Et and rearrange pt =

Wt/Et F 0(ht)

Interpret as a supply schedule for nontradables.

10

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Figure 9.3 The Supply Of Nontradables

pt = price, p

Wt/Et F 0(F −1(ytN )) W 1 /E0 F 0 (F −1 (y N ))

W 0 /E0 F 0 (F −1 (y N ))

• A decrease in nominal wage from W1 to W0 < W1 shifts the supply schedule down. • A devaluation Et ↑ (not shown) shifts the supply schedule in the same manner as a nominal wage cut.

quantity, yN

11

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Households max

N {cT t ,ct , dt+1}

E0

∞ X

β t U (ct )

t=0

subject to dt+1 T T N N + W h + E y + P c + E d = P + Φt PtT cT t t t t t t t t t t 1+r ht ≤ ¯ h

t

N ct = A(cT t , ct )

• First constraint: dt = one-period debt chosen in t, due in t + 1. Debt is denominated in units of traded goods → full liability dollarization. Original Sin: In emerging countries almost 100% issued in foreign currency (Eichengreen, Hausmann, and Panizza, 2005). • Second constraint: Workers supply ¯ h hours inelastically, but may not be able to sell them all. They take ht ≤ ¯ h as given. • Third constraint: Consumption is a composite of traded and nontraded goods. A(., .) increasing, concave, and HD1 12

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Optimality Conditions associated with the Household Problem

dt+1 T T N N T T Pt ct + Pt ct + Et dt = Pt yt + Wtht + Et + Φt 1 + rt ht ≤ ¯ h N) A2(cT , c t t = pt N) A1(cT , c t t N ))A (cT , cN ) λt = U 0(A(cT , c 1 t t t t

λt = β(1 + rt)Et λt+1

13

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

The Demand For Nontradables Look again at the optimality condition N A2(cT t , ct ) = p . t N) A1(cT , c t t

If A(cT , cN ) is concave and HD1, then given cT t , the left-hand side is decreasing in cN t . This means that, all other things equal, an increase in pt reduces the desired demand for nontradables, giving rise to the downward sloping demand schedule shown in the next slide. Note that cT t acts as a shifter of the demand schedule for nontradables: given pt , an increase in cT t is associated with an equiproportional desired increase in cN t . Of course, this shifter is endogenously determined.

14

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Figure 9.2 The Demand For Nontradables A2(cT , cN ) t t pt = N A1(cT t , ct ) A 2 (c T1 , c N )

price, p

A 1 (c T1 , c N )

• here we treat cT t as a shifter of the demand schedule. T T • A increase in cT t from c0 to c1 > cT 0 , shifts the demand schedule up and to the right.

A 2 (c T0 , c N ) A 1 (c T0 , c N )

quantity, cN

15

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Closing of the Labor Market Impose the following slackness condition: (¯ h − ht) Wt − γWt−1 = 0


According to this expression, if in any period t there is involuntary unemployment (ht < ¯ h), then in that period the lower bound on nominal wages must be binding. Also, in any period t in which the lower bound on wages is not binding, the labor market must feature full employment. Let hst denote labor supply. Here it is constant, hst = ¯ h. Let hdt denote labor demand. It is implicitly given by pt F 0(hdt) = Wt/Et . Let ht denote the equilibrium level of labor, which is determined as the minimum between labor supply and labor demand, that is, ht = min hst, hdt 



That is, labor is either supply or demand determined (as opposed to always demand determined.) 16

Market clearing in the Nontraded Sector N cN t = yt = F (ht)

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

A competitive equilibrium is a set of stochastic processes {cT t , h t , wt , dt+1 , pt, λt}∞ t=0 satisfying dt+1 T T ct + dt = yt +

1 + rt T λt = U 0(A(cT t , F (ht)))A1(ct , F (ht))

λt = β Et λt+1 1 + rt A2(cT , F (ht )) t pt = A1(cT t , F (ht )) wt pt = F 0(ht) wt−1 wt ≥ γ t h!t ≤ ¯ h wt−1 ¯ (h − ht) wt − γ = 0 t

(1) (2) (3) (4) (5) (6) (7) (8)

given an exchange rate policy {t }∞ t=0, initial conditions w−1 and d0, and exogenous stochastic processes {rt, ytT }∞ t=0 . 17

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Section 9.2: Currency Pegs

Et = E0 ;

∀t ≥ 0.

That is, the (gross) devaluation rate is unity

t = 1 Use the graphical apparatus just developed to show that a boombust cycle leads to –nominal wage growth and real appreciation during the boom phase – involuntary unemployment and insufficient real depreciation during the bust phase For the moment we treat a boom-bust cycle as a rise in cT followed by a fall in cT 18

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Figure 9.4 Currency Pegs, Downward Nominal Wage Rigidity and Unemployment (here assume that γ = 1) A 2 (c T1 , F (h)) A 1 (c T1 , F (h)) p

W 1 /E0 F 0 (h)

A 2 (c T0 , F (h)) pboom

pbust

C

A 1 (c T0 , F (h))

W 0 /E0 F 0 (h)

D

=

W 1 /E1 F 0 (h)

B A

p0

hbust

¯ h

T cT < c 1 0 negative external shock h possibly caused by rt ↑ 19

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

The boom bust cycle, observations on figure 9.4. The initial situation is point A. There is full employment, h = ¯ h. Now a boom starts. We capture this by an increase in cT (perhaps because r falls). Given nominal wages the economy moves to point B. But at point B, there is excess demand for labor. Thus nominal wages will rise. By how much? Until the excess demand for labor has diappeard. That will be at point C. Thus the boom leads to an increase in nominal wages (W ↑) and a real appreciation (p ↑). The economy continues to operate at full employment. Next the boom is over and the bust comes. We capture this by assuming that cT falls back to its original level, cT0 . This shifts the demand for nontradables back to its original position. The new intersection between supply and demand is at point D. At D, labor supply exceeds labor demand. However, because nominal wages are downwardly rigid and the nominal exchange rate is fixed, the supply schedule does not shift, (here we assume γ = 1). Thus the economy is stuck at point D. At point D there is involuntary unemployment (¯ h − hbust ) and there is insufficient real depreciation, ie, p falls to decline enough to bring about full employment.

20

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Section 9.2.2 Volatility and Average Unemployment The model predicts that aggregate volatility increases the mean level of unemployment. This prediction gives rise to large welfare benefits of stabilization policy. — This prediction is not due to the assumption of downward nominal wage rigidity, but due to the assumption that employment is determined by the minimum of labor demand and labor supply. (Note: key difference with Calvo-style sticky wage models in which employment is always demand determined.) — Downward nominal wage rigidity amplifies the connection between aggregate volatility and mean unemployment. 21

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

To see this consider the following example: N T N U (A(cT t , ct )) = ln ct + ln ct

dt = 0 (no access to international financial markets) T ⇒ cT t = yt .

ytT =

(

1 + σ prob 1 2 1 1 − σ prob 2

E(ytT ) = 1 and var(ytT ) = σ 2. F (ht) = hα t ¯ h=1 Et = E¯ (currency peg) 22

W−1/E = α The equilibrium conditions associated with this economy are cT t =p t cN t αpt (ht )α−1 = Wt/E T cT t = yt α cN t = ht

Wt = αE Step 1: Find labor demand: hdt = αytT /(Wt/E) Step 2: Find equilibrium labor as ht = min{¯ h, hdt}

Case 1: Assume bi-directional nominal wage rigidity. Wt = αE Then, ht =

(

1−σ 1

if if

ytT = 1 − σ ytT = 1 + σ

Let ut ≡ ¯ h − ht denote the unemployment rate. It follows that the equilibrium distribution of ut is given by σ with probability 1 2 . ut = 0 with probability 1 2 The unconditional mean of the unemployment rate is then given by σ E(ut ) = . 2 Average level of unemployment increases linearly with the volatility of tradable endowment, in spite of the fact that wage rigidity is symmetric! (

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

Case 2: assume ‘only’ downward nominal wage rigidity, Wt ≥ Wt−1 Then, Wt = α(1 + σ) > α and ht =

(

1−σ 1+σ

1

if if

ytT = 1 − σ ytT = 1 + σ

E(ut) = σ/(1 + σ) > σ/2 (recall that σ must be less than 1). Thus uni-directional wage rigidity strengthens the link between mean unemployment and volatility.

23

Uribe & Schmitt-Groh´ e

Chapter 9: Nominal Rigidity, Exchange Rates, And Unemployment

An Analytical Example

Adjustment To A Temporary Interest Rate Fall: Here is an example that shows that under a currency peg and downward nominal wage rigidity, a good shock, in this case a fall in the country interest rate rt, can be the prelude to very bad things to happen later. Consider the following environment: N N T U (A(cT t , ct )) = ln ct + ln ct

F (ht) = hα t ¯ h = 1;

ytT = y T > 0; rt =

γ = 1; (

d0 = 0;

w−1 = αy T

r t>0 r