Engineering a Paradox of Thrift Recession. Preliminary

Transcription

1 Engineering a Paradox of Thrift Recession Zhen Huo, and José-Víctor Ríos-Rull University of Minnesota, Federal Reserve Bank of Minneapolis, CAERP, NBER The Ohio State University, October Preliminary Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 1 / 32

2 Can a recession be the result of impovireshment? 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. Solow residual Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 2 / 32

3 Solow residual: Data source: OECD MEI Return Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 3 / 32

4 What are major detonants for 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 & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 4 / 32

5 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 & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 5 / 32

6 Ingredients 1 Exporting more is feasible but hard. It takes time to reallocate the economy to export more. (Tradables and Nontradables). Closed Economy version 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 fixed 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, Ríos-Rull, and Storesletten (2011). Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 6 / 32

7 The environment: Consumers within a period Households value varieties of nontradables: [ IN ] 1 ρ ρ 0 cni di Under equal consumption of each variety c N I ρ N = [ IN ] 1 ρ ρ 0 cni 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 N, c T ), d, n ]. Households have to search for varieties, its number is a choice. I N = d Ψ d (Q g ) Ψ d (Q g ) Probability (per search unit) of finding a variety. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 7 / 32

8 The environment: Production Firms post prices before the location is filled. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 8 / 32 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.

9 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 N. Total sales of nontradables in units of the tradable good that is the numeraire p I N c N = Ψ f (Q g ) F N (k, n) p Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 9 / 32

10 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 Complete rigidity. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 10 / 32

11 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 & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 11 / 32

12 Consumers problem subject to V (S, b, n) = max c N,c T,I N,d u(c N, I ρ N, c T, d, n) + β E{V (S, b, n )} p(s)i N c N + c T + b = (1 + r)b + w(s)n + π N (S) + π T (S) BC I N = d Ψ d [Q g (S)] SC n = (1 λ) n + Φ e [Q e (S)] (1 n) EC S = G(S) RE Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 12 / 32

13 Properties of the Solution (plus representative agent) It yields 1 Demand functions c Ni (p i, S), c T (p, S). 2 Search Intensity I N (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 N, 3 No immediate possibility of working harder. A recession. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 13 / 32

14 Nontradable firms Choose prices p j and investments Ω Nj (S, k, n) = max Ψ f [Q g (S)] C(p j, S) p j p j,i,v { Ω Nj (S, k, n } ) w(s)n i vκ + E 1 + r subject to: ( p F N (k, n) C(p j j, S) = p(s) k = (1 δ)k + i ɛn 2 n = (1 λ)n + Φ f [Q e (S)]v ) ρ 1 ρ C(S) ( ) i 2 k δ k Capital and labor are predetermined, firms adapt demand by adjusting p j. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 14 / 32

15 Tradable Goods Production: DRS & adjustment costs Ω T (S, k, n) = max i,v subject to: F T (k, n) w(s)n i vκ ɛt,n 2 k = (1 δ)k + i ( ) n 2 { Ω T n 1 (S, k, n } ) n + E 1 + r ɛt,k n = (1 λ) n + Φ f [Q e (S)] v 2 ( ) i 2 k δ k These two properties will make it difficult to adjust both fast and a lot. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 15 / 32

16 Representative Nash bargaining for wages (may not suffice) w(s) = max w [ [V n (S, b, n)] ϕ NN N ΩN n (S, K N, N N ) + N ] 1 ϕ T N ΩT n (S, K T, N T ) In steady state, we have: [ ( w = ϕ χ Ψ f (Q g )pfn N 1 ρ + Qe κ ) ] + (1 χ)(fn T + Q e κ) + (1 ϕ) ς u ct Alternatively we also explore rigid wages. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 16 / 32

17 Strategy We calibrate this economy to look like a modern economy. We study recessions made up of 1% reductions in output generated by 1 A (relatively) persistent increase to the discount rate β. 2 A destruction of wealth (net foreign asset position.) Note that the effects are the opposite to those in the standard growth model. These shocks are a stand in for whatever deteriorates the financial system. Possibly a combination of the two. We then explore the properties of the recession generated. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 17 / 32

18 First Experiment: Persistent shock to discount factor Assume β t = βe θb t the shock to the discount factor follows an AR(1) process: log θ b t = ρ b log θ b t 1 + ε t, ε t N(0, σ b ) We then pose an initial value for ε 0 to reduce output 1%. The value of ρ b is set equals to Advantage: That induces a desire to increase saving temporarily and later to increase consumption. It makes it similar to a financial shock that increases the wealth to income target of the households. Disadvantage. If taken literally, it is silly, but we will not take it literally. Financial Friction version Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 18 / 32

19 More details about the experiments Output in terms of the tradable goods is: Y = p Ψ f (Q g )F N (K N, N N ) + F T (K T, N T ) Real output, Y is in base year prices (Use steady state, p instead of current p). Two wage protocols: Nash bargaining and complete rigidity 1 Standard Nash wage bargaining: A larger shock is needed. Nontradable firms decrease employment and vacancies but tradable firms increase employment and vacancies. 2 Completely rigid wage: Employment and vacancies drop more. Tradable firms increase employment and vacancies only because the vacancy filling rate is higher. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 19 / 32

20 Functional form Preference u(c, d, n) = 1 1 σ (c ξ d)1 σ ςn c = [ ω(c N I ρ N ) η 1 η + (1 ω)c η 1 η T ] η η 1 Production function F N (k, n) = z N k θn n 1 θn, F T (k, n) = z T k θt k n θ T n Matching technology M e (U, V ) = ν e U µ V 1 µ, M g (D, T ) = ν g D α T 1 α Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 20 / 32

21 Functional form Capital adjustment cost in the nontradable goods sector φ N (i, k) = ɛn 2 ( ) i 2 k δ k Capital adjustment cost in the tradable goods sector φ T,k (i, k) = ɛt,k 2 ( ) i 2 k δ k Employment adjustment cost in the tradable goods sector φ T,n (n, n) = ( ) n 2 2 n 1 n ɛt,n Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 21 / 32

22 Calibration: Exogenously determined parameters A period is half a quarter. Remark Parameter Value Target Value Risk aversion σ 2.0 Risk aversion 2 Discount factor β Real interest rate 4% Price mark-up ρ 1.05 Literature on price mark-up 1.05 Goods matching prob ν g 0.80 Matching prob 81% Labor matching prob ν e Monthly job finding rate 45% Labor matching elast µ 0.7 Matching elasticity 0.7 Job separation prob λ 0.05 Average duration of job 2.5 year Elasticity of substitution η 0.83 Elasticity of substitution T /N 0.83 Bargaining power of worker ϕ 0.35 Middle of Shimer & HM 0.35 Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 22 / 32

23 Calibration: Endogenously determined parameters Remark Parameter Value Target Target value Search disutility ξ 0.03 Goods market tightness 1 Working disutility ς 0.89 Consumption / output 80% Production function z N 0.48 Output 1 Production function z T 0.53 Price of nontradable goods 1 Production function θ N 0.33 Labor share in nontradable 60% Production function θ T n 0.64 Labor share in tradable 60% Production function θ T k θ T k + θt n 1 Depreciation δ Capital / output 2.5 Vacancy cost κ 0.55 Employment level 93% Home bias ω 0.92 Tradable goods / output 30% Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 23 / 32

24 Calibration: Dynamic parameters Remark Parameter Value Target Capital adjustment ɛ N Decrease of i N =4Y N Capital adjustment ɛ T,k Tradable goods sector expands 5% Labor adjustment ɛ T,n ɛ T,n = ɛ T,k Goods matching elast α, η 0.42 Employment decreases 0.5% Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 24 / 32

25 Results: I. Shock to patience, households increase savings We look for shocks to β, that follows an AR(1) with.95 persistence that induces an increased desire to save and that generates a 1% output drop in various economies: 1 Baseline economy: wages determined via Nash bargaining and relatively flexible tradable sector (tradable sector expands by 5%). 2 Baseline economy with high adjustment cost in tradable sector: Figures Wages determined via Nash bargaining and very rigid tradable sector. (tradable sector expands by 1%). 3 Baseline economy with fixed wage rate: Figures same dynamic parameters as the baseline economy but with fixed wage rate. 4 Baseline economy without goods market frictions: Figures same dynamic parameters as the baseline economy but without shopping. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 25 / 32

26 Other features: Size of the Shocks Huo Output & Ríos-Rull in RBC(UMN, is the Mpls initialfed, increase CAERP) of output Engineering a one-good a Paradox small open of Thrift economy Recession business cycle October model. 9, OSU, Econ 26 / 32 Percentage increase Model economy β N Solow C Recover time Output in RBC Baseline year Baseline+Fixed wage year 3.23 Baseline+high adj year Baseline, no shopping year Compare with financial shock Does Shopping Matter? Yes Figures Without the contribution of shopping to productivity, the required size of the shock to generate a 1% drop in output is much larger. This is the main contribution of the paper. *Recover time is measured by the duration of employment below the trend.

27 Properties of Shocks to β A recession can be triggered by a desired to save which generates (temporarily) the paradox of thrift. After consumers cut their consumption: Output, consumption, investment and employment decrease. Prices for nontradables and wage rate (if set by bargarning) decrease. Technology is unchanged, but measured Solow residual decreases. It becomes more difficult for the nontradable firms to find a shopper. Tradable sector with decreasing returns to scale expands. The extent of the recessions depend on the rigidity of prices and the flexibility of factor reallocation. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 27 / 32

28 Results II: Impoverishment, Permanent Consumption Drop We look for wealth destruction shocks that induce 1% output drops in economies with shopping (demand increases productivity) and a labor matching model a la Mortensen-Pissarides. The economies are 1 Baseline economy 2 Baseline economy with high adjustment cost in tradable sector Figures 3 Baseline economy with fixed wage rate Figures 4 Baseline economy without goods market frictions Figures Model economy Wealth N Solow C Baseline Baseline+Fixed wage Baseline+high adj Baseline, no shopping Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 28 / 32

29 Properties of Shocks to wealth B A permanent output and consumption drop can be triggered by a loss of wealth. Mild permanent reduction in employment There is a permanent deterioration of relative prices. Technology is unchanged, but measured Solow residual decreases. It becomes more difficult for the nontradable firms to find a shopper. The extent of the recessions depend on the rigidity of prices and the flexibility of factor reallocation. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 29 / 32

30 Version of the Model with Financial Frictions Financial Friction version Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 30 / 32

31 Conclusions and Summary 1 We have developed a theory of how a desire to save generates a recession and via the paradox of thrift, a temporal reduction of wealth. 2 We have found that recessions can be the result of a desire to increase savings due to some financial mishap. The crucial ingredients are: Limited drop in interest rates. The more rigid the economy (prices, wages, sector reallocation), the worse the recessions. The shopping structure allow the shocks to be smaller than more standard models with similar ingredients (small open economy, rigid wages, Mortensen-Pissarides). All these are important departures from the standard model with productivity shocks (either new keynesian or neoclassical). Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 31 / 32

32 References Backus, D. K., P. J. Kehoe, and F. Kydland International Business Cycles. Journal of Political Economy 100 (4): Bai, Yan, José-Víctor Ríos-Rull, and Kjetil Storesletten Demand Shocks as Productivity Shocks. Working Paper, Federal Reserve Bank of Minneapolis. Bernanke, B. and M. Gertler Agency Costs, Net Worth and Business Fluctuations. American Economic Review 79 (1): Conesa, J.C. and T.J. Kehoe Gambling for Redemption and Self-Fulfilling Debt Crises. Manuscript, University of Minnesota. Eggertsson, G. and P. Krugman Debt, deleveraging, and the liquidity trap: a Fisher-Minsky-Koo approach. Federal Reserve Bank of New York, unpublished manuscript, February. Guerrieri, Veronica and Guido Lorenzoni Liquidity and Trading Dynamics. Econometrica 77 (6): Mendoza, E.G Sudden stops, financial crises, and leverage. The American Economic Review 100 (5): Mian, A. and A. Sufi What Explains High Unemployment? The Aggregate Demand Channel. Unpublished Manuscript, Booth School of Business. Midrigan, V. and T. Philippon Household Leverage and the Recession. NYU Working Paper No. FIN Neumayer, P.A. and Fabrizio Perri Business Cycles in Emerging Economies: The Role of Interest Rates. Journal of Monetary Economics 52 (2):345. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 32 / 32

33 A Theory of Household Financial Distress and Savings I Imagine that the household has to use financial services to provide insurance to its non-working members. The total net transfer of resources to non-working members is subject to a financial cost ψ per unit transferred. There are shocks to ψ. Assuming the working and non-working members must exert the same shopping effort, but the level of consumption could be different for the two groups. Nontradable firms catter some of its locations for the employed and some for the unemploeyed. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 33 / 32

34 The household problem V (S, b, n) = max n u ( c cn 0 N 1 I N ρ, ct 1, d, 1) + (1 n)u ( cn 0 I N ρ, ct 0, d, 0),c0 T,c1 N ct 1,I N,d + β E {V (S, b, n )} subject to (1 n)[p(s)i N cn 0 + c1 T ] + b + FC(1 n)+ n[p(s)i N cn 1 + c1 T ] = (1 + r)b + w(s)n + π N(S) + π T (S) I N = d Ψ d [Q g (S)] n = (1 λ) n + Φ e [Q e (S)] (1 n) S = G(S) FC = ψ ( ct 0 + p(s)c0 N I N [π(s) + (1 + r)b] ) BC SC EC RE FC Back to Experiments Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 34 / 32

35 Mapping from the shock to ψ to the shock to β Euler conditions of the household { } u c 1 = (1 + r)e β[1 + ψ (1 n )]u T ct 1 { u c 0 = (1 + r)e β[1 + ψ (1 n )] 1 + ψ } T 1 + ψ u ct 0 The effect of a shock to the financial cost is similar to a shock to β: β = nβ[1 + ψ (1 n )] + (1 n)β[1 + ψ (1 n )] 1 + ψ 1 + ψ Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 35 / 32

36 Results 1 Baseline economy 2 Baseline economy with high adjustment cost in tradable sector Figures 3 Baseline economy with fixed wage rate Figures Model economy β N Solow C (1 n)fc/y Baseline Baseline+Fixed wage Baseline+high adj Compare with β shock Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 36 / 32

37 A Theory of Household Financial Distress and Savings II Imagine that the household has to use financial services to provide insurance to its non working members. The total net transfer of resources to non-working members is sublect to a financial cost ψ per unit transferred. There are shocks to ψ. In this world there will be specialization: there is enough of a competitive search structure to differentiate goods by markets. Consequently, the unemployed household members will buy cheaper and harder-to-find non-tradable goods. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 37 / 32

38 The implied household problem in a two class worldcolumbusus, V (S, b, n) = ( max n u c 1 N I 1 ρ cn 0 N, c 1 T, d 1, 1 ) + (1 n)u ( cn 0 I0 Nρ, c 0 T, d 0, 0 ),c0 T,I0 N,d0 cn 1,c1 T,I1 N,d1 + β E {V (S, b, n )} subject to (1 n)[p 0 (S)I 0 NcN 0 + c1 T ] + b + FC(1 n)+ n[p 1 (S)I 1 NcN 1 + c1 T ] = (1 + r)b + w(s)n + π N(S) + π T (S) I N = d Ψ d [Q g (S)] n = (1 λ) n + Φ e [Q e (S)] (1 n) S = G(S) FC = ψ ( ct 0 + p0 (S)cN 0 I0 N [π(s) + (1 + r)b] ) BC SC EC SV FC Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 38 / 32

39 Nontradable firms problem in a two class world Ω Nj (S, k, n) = subject to: max {p jl,k l,n l,x l } 1 l=0 v,i 1 l=0 x l Ψ f [Q gl (S)] C(p jl, S) p jl { Ω N (S, k, n } ) w(s)n i vκ + E 1 + r ( ) p F N (k l, n l ) C(p jl jl ρ 1 ρ, S) = C l (S), l = 1, 2 p(s) k = (1 δ)k + i ɛn 2, ( i k δ ) 2 k, n = (1 λ)n + Φ f [Q e (S)]v, x 0 k 0 + x 1 k 1 = k, x 0 n 0 + x 1 n 1 = n, x 0 + x 1 = 1. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 39 / 32

40 Search frictions in a two class world Now market tightness in both types of non-tradable goods will be different because firms allocate different fractions of its plants or locations differently: Q g0 = X 0 N D 0, Q g1 = X 1 (1 N)D 1. Clearly, the price will be lower and the tightness higher in the market that caters to the unemployed. Ψ f (Q g1 )p 1 = Ψ f (Q g0 )p 0 The prices for nontradable goods p i make sure: c 1 N = c0 N Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 40 / 32

41 Results 1 Baseline economy 2 Baseline economy with high adjustment cost in tradable sector Figures 3 Baseline economy with fixed wage rate Figures Model economy β N Solow C (1 n)fc/y Baseline Baseline+Fixed wage Baseline+high adj Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 41 / 32

42 A Theory of Household Financial Distress and Savings III Consider a version of this economy with heterogenous agents and idyosyncratic risks. Let the agents borrow up to the natural borrowing limit b. Let the interest rate for borrowing have a premium over the world interest rate r b = r + ε with ε being an AR(1). We are now exploring the relation between the size of a shock β and a shock to r b. How big do they have to be to generate the same expenditure drop? Return Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 42 / 32

43 Two-sector closed economy Consider a version with a consumption goods sector and an investment goods sector in a closed economy. The consumption goods sector faces search frictions as before. The investment goods sector has DRS and is difficult to expand quickly. The households trade stocks instead of bonds. The experiment is a shock to β. Return Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 43 / 32

44 Household problem subject to: V (S, b, n) = max c,i,d u(ciρ, d, n) + β E { V (S, b, n ) θ } p(s)ci + p b (S)b = b[p b (S) + π C (S) + π I (S)] + w(s)n I = Ψ d [Q g (S)] d n = (1 λ)n + Φ e [Q e (S)](1 n) S = G(S) BC SC EC SV. The stochastic discount factor is Θ = uc p(s)i Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 44 / 32

45 Consumption firm s problem Ω Cj (S, k, n) = max Ψ f [Q g (S)] C(p j, S) p j p j,i,v subject to: w(s)n i vκ + E ( p F C (k, n) C(p j j, S) = p(s) k = (1 δ)k + i ɛc 2 n = (1 λ)n + Φ f [Q e (S)]v } {β Θ Θ ΩCj (S, k, n ) ) ρ 1 ρ C(S) ( ) i 2 k δ k Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 45 / 32

46 Investment firm s problem Ω I (S, k, n) = max i,v subject to: F I (k, n) w(s)n i vκ ɛi,n 2 k = (1 δ)k + i ( ) n 2 } n 1 n + E {β Θ Θ ΩI (S, k, n ) ɛi,k n = (1 λ) n + Φ f [Q e (S)] v 2 ( ) i 2 k δ k Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 46 / 32

47 Properties of shock to β A recession is triggered by a desired to save. Figures After consumers cut their consumption: Output, consumption and employment decrease. Prices for consumption goods and wage rate (if set by bargarning) decrease. Technology is unchanged, but measured Solow residual decreases. Investment increases due to a lower real interest rate. Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 47 / 32

48 Ideas are useful to study International Business Cycles Data: for US and EU15 Quantities Data Standard IRBC Shopping model cor z shocks cor θ shocks A. Variance relative to output (US) Consumption Investment Employment Net exports B. International comovement Output Consumption Investment Employment C. Co-movement within a country NX/output, Output Real Exchange Rate, ch/cf Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 48 / 32

49 β shock Return Real output Solow residual Employment Investment Output of nontradable Output of tradable Baseline economy Baseline economy with high adj cost Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 49 / 32

50 β shock Return Number of varieties Price for nontradable Real wage Wealth Consumption Net export/output ratio Baseline economy Baseline economy with high adj cost Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 50 / 32

51 β shock Return Real output Solow residual Employment Investment Output of nontradable Output of tradable Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 51 / 32

52 β shock Return Number of varieties Price for nontradable Real wage Wealth Consumption Net export/output ratio Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 52 / 32

53 β shock Return Real output Solow residual Employment Investment Output of nontradable Output of tradable Baseline economy Baseline economy without shopping Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 53 / 32

54 β shock Return Number of varieties Price for nontradable Real wage Wealth Consumption Net export/output ratio Baseline economy Baseline economy without shopping Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 54 / 32

55 Wealth shock Return Real output Solow residual Employment Investment Output of nontradable Output of tradable Baseline economy Baseline economy with high adj cost Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 55 / 32

56 Wealth shock Return Number of varieties Price for nontradable Real wage Wealth Consumption Net export/output ratio Baseline economy Baseline economy with high adj cost Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 56 / 32

57 Wealth shock Return Real output Solow residual Employment Investment Output of nontradable Output of tradable Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 57 / 32

58 Wealth shock Return Number of varieties Price for nontradable Real wage Wealth Consumption Net export/output ratio Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 58 / 32

59 Wealth shock Return Real output Solow residual Employment Investment Output of nontradable Output of tradable Baseline economy Baseline economy without shopping Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 59 / 32

60 Wealth shock Return Number of varieties Price for nontradable Real wage Wealth Consumption Net export/output ratio Baseline economy Baseline economy without shopping Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 60 / 32

61 Financial shock I Return Real output Solow residual Employment Investment Output of nontradable Output of tradable Baseline economy Baseline economy with high adj cost Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 61 / 32

62 Financial shock I Return Number of varieties Price for nontradable Real Wage Wealth Consumption Net export/output ratio Baseline economy Baseline economy with high adj cost Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 62 / 32

63 Financial shock I Return Consumption of employed Consumption of unemployed Financial cost-output ratio Vacancy of nontradable Vacancy of tradable Wage Baseline economy Baseline economy with high adj cost Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 63 / 32

64 Financial shock I Return Real output Solow residual Employment Investment Output of nontradable Output of tradable Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 64 / 32

65 Financial shock I Return Number of varieties Price for nontradable Real Wage Wealth Consumption Net export/output ratio Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 65 / 32

66 Financial shock I Return Consumption of employed Consumption of unemployed Financial cost-output ratio Vacancy of nontradable Vacancy of tradable Wage Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 66 / 32

67 Financial shock II Return Real output Solow residual Employment Investment Output of nontradable Output of tradable Baseline economy Baseline economy with high adj cost Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 67 / 32

68 Financial shock II Return Capacity of firms for employed Capacity of firms for unemployed Wage Wealth Consumption Net export/output ratio Baseline economy Baseline economy with high adj cost Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 68 / 32

69 Financial shock II Return Consumption of employed Consumption of unemployed Vacancy of nontradable Vacancy of tradable Price for employed Price for unemployed Baseline economy Baseline economy with high adj cost Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 69 / 32

70 Financial shock II Return Real output Solow residual Employment Investment Output of nontradable Output of tradable Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 70 / 32

71 Financial shock II Return Capacity of firms for employed Capacity of firms for unemployed Wage Wealth Consumption Net export/output ratio Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 71 / 32

72 Financial shock II Return Consumption of employed Consumption of unemployed Vacancy of nontradable Vacancy of tradable Price for employed Price for unemployed Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 72 / 32

73 Closed economy Return Real output Solow residual Employment Investment Consumption Output of investment firm Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 73 / 32

74 Closed economy Return Number of varieties Price for consumption Wage Labor market tightness Vacancy of consumption firms Vacancy of investment firms Baseline economy Baseline economy with fixed wage Huo & Ríos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 74 / 32