A Paradox of Thrift Recession Zhen Huo and Jos´ e-V´ ıctor R´ ıos-Rull University of Minnesota, Federal Reserve Bank of Minneapolis, CAERP, CEPR, NBER Banco of Portugal October 29, 2013 Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 1 / 46
Can a recession be the result of impoverishment? • In most equilibrium models impoverishment, or in general the desire to save more, induces agents to work harder: an expansion. • This project: 1 We build a quantitative model where a contraction in demand (say, because of a shock to financial intermediation or sheer impoverishment) generates a recession. We describe what does it take for such recession to occur. 2 In addition, in our model a reduction in consumption decreases measured TFP even though the technology is unchanged. This channel greatly contributes to the recession. Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 2 / 46
Solow ∗ residual: 1990-2011. Data source: OECD MEI More data Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 3 / 46
What are major detonants of crisis in small countries? 1 Productivity/endowment shocks. (Many papers, Backus, Kehoe, and Kydland (1992) RBC, Conesa and Kehoe (2011) with governments facing debt crisis.) 2 Interest rate risk. (Neumayer and Perri (2005)) . 3 Financial Shocks that affect firms Some are based on missallocation of investments (Bernanke and Gertler (1989) and others)). Others require insufficient assets within a country (Mendoza (2010)) . 4 Financial Shocks that affect households and reduce their consumption ◮ Midrigan and Philippon (2011) explore the role that less liquidity has in shaping recessions. Wage and labor rigidity generate recessions. Guerrieri and Lorenzoni (2009), Macera (2012) ◮ Mian and Sufi (2012) report that in the current US recession, employment in nontradables drops more where household balance sheet suffers more. Not so for tradables. Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 4 / 46
Our paper • We complement the view that it is household consumption that triggers a recession, but it is not liquidity difficulties and wage rigidity, (Midrigan and Philippon (2011)) , or the zero bound of the interest rate and fixed prices (Guerrieri and Lorenzoni (2009), Eggertsson and Krugman (2011)) , although fixed prices and wages surely aggravate recessions. • We build a model where the desire to save triggers a recession because it is difficult to reallocate resources from nontradables to tradables or in general from consumption to investment. • The recession is amplified by the fact that consumption affects productivity. • The recession displays the paradox of thrift. Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 5 / 46
Ingredients 1 Exporting more is feasible but hard. It takes time to reallocate the economy to export more. (Tradables and Nontradables). 2 Labor markets are not competitive. We pose Mortensen-Pissarides determination of labor market so the static Euler equation of the household does not operate directly, although it does to some extent. We also explore the role of sticky wages. These are the only really necessary ingredients. Our contribution is to pose another channel that makes the outcome easier (i.e. smaller shocks for the same outcome): 3 Reductions in Demand (i.e. consumption expenditures) induce productivity decreases. An extension of Bai, R´ ıos-Rull, and Storesletten (2011). Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 6 / 46
The environment: Consumers within a period �� I � ρ 1 ρ Households value varieties of nontradables: 0 c Ni di �� I � ρ 1 c N I ρ = ρ Under equal consumption of each variety: 0 c Ni di Households also like tradables that combine through a standard (Armington) aggregator with nontradables and dislike work and search for goods yielding u [ c ( c N I ρ , c T ) , d , n ] . Households have to search for varieties, its number is a choice . I = d Ψ d ( Q g ) Ψ d ( Q g ): Probability (per search unit) of finding a variety. Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 7 / 46
The environment: Production Two sectors that we call tradables, & nontradables, small open economy: fixed r . We include in tradables two items normally deemed to be nontradables: Housing Construction and Structures The tradable sector has a measure one of firms. There are adjustment costs to both capital and labor, and its output is used for exports, investment, and (part of) consumption. F T ( k , n , l ) may have decreasing returns. The nontradable sector consists of a measure one of firms each one producing a different variety. Each firm/variety has a measure one of locations, each location has its own production function F N ( k , n ) . Locations may or may not be filled (get a customer). They produce only for consumption. Firms post prices before the location is filled. Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 8 / 46
Search Goods markets for nontradables. • There is a large number of varieties. Agents need to search to find varieties. • Random search. There is a CRS matching function Ψ(1 , D ). Market tightness is Q g = 1 D . The probability that a shopper finds a firm-variety: Ψ d ( Q g ) = Ψ • D • The probability that a firm finds a shopper is the measure of filled locations or of consumers buying the good: Ψ f ( Q g ) = Ψ 1 = I . • Total sales of nontradables in units of the tradable good that is the numeraire. p I c N = p Ψ f ( Q g ) F N ( k , n ) . Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 9 / 46
Frictional labor market Random search with market tightness: Q e = V • 1 − N . • Total vacancies: V = V N + V T and employment: N = N N + N T . Job finding probability Φ e ( Q e ) • Vacancy filling probability Φ f ( Q e ) • • Exogenous job destruction at rate λ • Wages (we explore various mechanisms) Nash bargaining Staggered wage contract Constant labor share Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 10 / 46
State Variables. Collapses to a simple Macro Model Aggregate. S = { θ, K N , N N , K T , N T , B } . ◮ Shocks ◮ Capital in the nontradable sector ◮ Labor in the nontradable sector ◮ Capital in the tradable sector. ◮ Labor in the tradable sector. ◮ Net foreign asset position. Individual b , n . ◮ Liquid wealth (bonds against the rest of the world, b ) ◮ Fraction of the household working n . • We use the (standard) trick that all local firms are in the hands of the local agents and do not trade them. Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 11 / 46
Consumers’ problem c N , c T , I , d u ( c N I ρ , c T , d , n ) + β E { V ( S ′ , b ′ , n ′ ) } V ( S , b , n ) = max subject to p ( S ) I c N + c T + b ′ = (1 + r ) b + w ( S ) n + π N ( S ) + π T ( S ) BC I = d Ψ d [ Q g ( S )] SC n ′ = (1 − λ ) n + Φ e [ Q e ( S )] (1 − n ) EC S ′ = G ( S ) RE Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 12 / 46
Properties of the Solution (plus representative agent) • It yields 1 Demand functions c Ni ( p i , p , S ) , c T ( p , S ). 2 Search Intensity I ( p , S ). • Shocks to patience, β (a stand in for impoverishment) or directly to net foreign asset position B , induce directly 1 A reduction in consumption per variety, c N , 2 A reduction of varieties I , 3 No immediate possibility of working harder. • A recession. Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 13 / 46
Nontradable firms’ Choose prices p j and investments Ψ f [ Q g ( S )] C ( p j , S ) p j Ω Nj ( S , k , n ) = max p j , i , v � Ω Nj ( S ′ , k ′ , n ′ ) � − w ( S ) n − i − v κ + E 1 + r subject to: � p j � ρ 1 − ρ F N ( k , n ) ≥ C ( p j , S ) = C ( S ) p ( S ) k ′ = (1 − δ ) k + i − φ N ( i , k ) n ′ = (1 − λ ) n + Φ f [ Q e ( S )] v • Capital and labor are predetermined, firms adapt demand by adjusting p j . Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 14 / 46
Tradable Goods Production: DRS & adjustment costs Ω T ( S , k , n ) = max F T ( k , n ) − w ( S ) n − i − v κ i , v � Ω T ( S ′ , k ′ , n ′ ) � − φ T , n ( n , n ′ ) + E 1 + r subject to: k ′ = (1 − δ ) k + i − φ T , k ( i , k ) n ′ = (1 − λ ) n + Φ f [ Q e ( S )] v These two properties will make it difficult to adjust both fast and a lot. Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 15 / 46
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