Unemployment (Fears), Precautionary Savings, and Aggregate Demand

Transcription

1 Unemployment (Fears), Precautionary Savings, and Aggregate Demand Wouter J. Den Haan (LSE & CEPR), Pontus Rendahl (University of Cambridge & CEPR), and Markus Riegler (LSE) June 28, 2013

2 Overview 1 Model interaction between goods and labor market precautionary savings could end up in productive investment 2 Algorithm: XPA laws of motion for aggregate variables are obtained by explicit aggregation of individual policy functions correct firm value when firm owners are heterogeneous and markets are incomplete 3 Model properties fear of unemployment exacerbates (dampens) downturn when nominal wages are (are not) sticky

3 Model: Key ingredients 1 Search frictions in labor market 2 Heterogeneous agents and incomplete markets 3 (Some) nominal wage stickiness

4 Individual agent unemployed and employed agents unemployed search for work employed get nominal wage W t exogenous job loss probability, ρ x agents can invest in money, M i,t firm ownership (equity), q i,t

5 First-order conditions C i,t + J t q i,t + M i,t = e i,t W t + (1 e i,t ) U t + q i,t 1 (D t + (1 ρ x ) J t ) + M i,t 1 q i,t 0 C i,t = P t c i,t D t = P t d t J t = P t j t

6 First-order conditions c ν i,t [ ] Pt = βe t c ν P i,t+1 t+1 ( ) ζ1 Mi,t + ζ 0 P t J t P t = βe t [ (ci,t+1 c i,t ) v ( Dt+1 + (1 ρ P x ) J ) ] t+1 t+1 P t+1

7 Job/Firm creation Standard free-entry condition: P t ψ = π f,t J t π f,t = φ o ( v t 1 n t 1 ) φ1 1 n t = (1 ρ x ) n t 1 + φ o v φ 1 t (1 n t 1 ) 1 φ 1

8 Existing firm D t = P t z t W t

9 Wage setting W t = ω 0 z ω 1 t P ω 2 t ω 1 = 0, ω 2 = 1 : sticky real wages ω 1 > 0, ω 2 = 0 : sticky nominal wages

10 Equilibrium demand for money = (constant) money supply demand for firm ownership = number of firms

11 Algorithm 1 Correctly dealing with firm value 2 XPA explicit aggregation to get aggregate variables right surprisingly few state variables

12 Firm value J t P t? = Et [ ( Dt+1 MRS i,t+1 + (1 ρ P x ) J )] t+1 t+1 P t+1 Which MRS i,t+1 to use?

13 Firm value Literature: J t P t? = Et [ ( Dt+1 MRS i,t+1 + (1 ρ P x ) J )] t+1 t+1 P t+1 representative agent: MRS t+1 = (c t+1 /c t ) ν heterogeneous agents: Krusell, Mukoyama, Sahin (2010): two assets and two outcomes for aggregate state = use prices of the two Arrow-Debreu securities dinky "solution": assume risk neutral firm manager, which is inconsistent with risk averse firm owners This paper: Get J( ) by imposing equilibrium

14 Solving for firm value J t = J (s t ) solve for J (s t ) by imposing equilibrium i q i,t di = n t LHS: demand for firm ownership from individual problem RHS: supply of firm ownership comes from free-entry condition

15 Idea behind XPA Suppose individual policy rules are linear in individual state variables: = aggregation trivial, namely k i,t = α 0 (s t ) + α 1 (s t ) k i,t 1 K t = α 0 (s t ) + α 1 (s t ) K t 1

16 Idea behind XPA Suppose individual policy rules are quadratic: = aggregation gives k i,t = α 0 (s t ) + α 1 (s t ) k i,t 1 + α 2 (s t ) k 2 i,t 1 K t = α 0 (s t ) + α 1 (s t ) K t 1 + α 2 (s t ) K t 1 (2) K t 1 (2) = ki,t 1 2 di i = we need a law of motion for K t (2) = i k2 i,t di

17 Idea behind XPA Approach #1: use k 2 i,t = (α 0 (s t ) + α 1 (s t ) k i,t 1 + α 2 (s t ) k 2 i,t 1 ) 2 K t (2) = ki,t 2 di = i ii,t ( α 0 (s t ) + α 1 (s t ) k i,t 1 + α 2 (s t ) k 2 i,t 1) 2 di = K t (3) and K t (4) become state variables, etc.

18 Idea behind XPA Approach #2: approximate k 2 i,t with ki,t 2 = α 0 (s t ) + α 1 (s t ) k i,t 1 + α 2 (s t ) ki,t 1 2 which gives K t (2) = α 0 (s t ) + α 1 (s t ) K t 1 + α 2 (s t ) K t 1 (2) = set of state variables does not increase

19 Implementation Individual problem is solved accurately with a global method and piecewise linear policy functions For aggregation a linear approximation of this nonlinear policy function is used

20 State variables Individual state variables cash on hand: q t 1 (D t + (1 ρ x ) J t ) + M i,t 1 employment status Aggregate state variables aggregate productivity number of firms = equity shares

21 Precautionary savings How to get precautionary savings in a model? typically done through β this paper through unemployment

22 Typical precautionary savings story Households want to save more = demand for consumption & prices do not adjust = demand for labor, etc. Where do savings end up? typically not allowed to end up in investment because there is no physcial investment or incorrect discounting of firm profits

23 Precautionary savings in this paper We do have something like the standard channel: unemployment = demand for money = P t = real profits (because of sticky nominal wages) = firm/job creation but in this paper!!!

24 Precautionary savings in this paper We do have something like the standard channel: unemployment = demand for money = P t = real profits (because of sticky nominal wages) = firm/job creation but in this paper!!! precautionary savings could end up in productive investment since MRS i,t when precautionary savings

25 Precautionary savings and productive investment This paper: investment in firm/job creation could when precautionary savings Reasons why it could : agents less willing to hold firm equity when profits agents less willing to hold risky assets when unemployment

26 Idiosyncratic risk & investment portfolio simple example

27 Idiosyncratic risk & investment portfolio max c 1,c 2,m,a c1 ν t + βc 1 ν t+1 s.t. c 1 = y 1 m a c 2 = y 2 + m(1 + r m ) + a (1 + r a ) y 1 = E [y 2 ] = 1 r a = { with prob with prob. 1 2, E [r a ] > r m

28 Case 1 no idiosyncratic risk no idiosyncratic risk: y 2 = 1 m = and a = no savings, m + a = 0 realizations of r a chosen to get this outcome

29 Case 2 idiosyncratic risk y 2 = 1 when r a takes on high value y 2 {0, 2} Ey 2 = 1 when r a takes on low value higher spread in recession but mean not affected (for transparency) not surprisingly, m + a to 0.226

30 Case 2 idiosyncratic risk y 2 = 1 when r a takes on high value y 2 {0, 2} Ey 2 = 1 when r a takes on low value higher spread in recession but mean not affected (for transparency) not surprisingly, m + a to but m to and a to

31 Model properties 1 Model 1: no nominal wage stickyness precautionary savings dampen downturn 2 Model 2: with nominal wage stickyness precautionary savings worsen downturn

32 No nominal wage stickyness productivity = profits = firm value = unemployment = precautionary savings = demand for firm ownership may = unemployment = demand for money = P profits since nominal wages adjust

33 No nominal wage stickyness 0.02 log P UI=0.5 UI=0.7 rep agent Precautionary demand for M reduces price increase

34 No nominal wage stickyness log J 0 UI=0.5 UI=0.7 rep agent Precautionary savings has small upward effect on firm value

35 No nominal wage stickyness log N UI=0.5 UI=0.7 rep agent Precautionary savings has small upward effect on employment

36 With nominal wage stickyness productivity = profits = firm value = unemployment = precautionary savings = demand for firm ownership may = unemployment = demand for money = P = profits unemployment = downward spiral

37 With nominal wage stickyness 0.02 log P UI=0.5 UI=0.7 rep agent Precautionary demand for M strongly reduces prices

38 With nominal wage stickyness log J 0 UI=0.5 UI=0.7 rep agent Precautionary demand for M strongly reduces firm value

39 With nominal wage stickyness log N UI=0.5 UI=0.7 rep agent Precautionary demand for M strongly reduces firm value