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) January 27, 2014

2 Overview Heterogeneous agents: influence of precautionary savings on employment role of nominal wage rigidity correctly discounting profits

3 Overview 1 Model interaction between goods and labor market precautionary savings could end up in productive investment 2 Model properties fear of unemployment dampens downturn when nominal wages are not sticky exacerbates downturn when nominal wages are sticky

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

5 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

6 Individual agent Budget constraint: max t β t [u (c i,t ) + v ( Mi,t P t )] P t 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

7 First-order conditions Money: c ν i,t Equity, if q i,t > 0: J t P t = βe t [ ] Pt = βe t c ν P i,t+1 t+1 [ (ci,t+1 c i,t ( ) ζ1 Mi,t + ζ 0 P t ) ν ( Dt+1 + (1 ρ P x ) J ) ] t+1 t+1 P t+1

8 Policy functions q employed q unemployed m employed m unemployed cash on hand

9 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

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

11 Wage setting W t = ω 0 z ω 1 t P ω 2 t ω 1 < 1 : sticky real wages ω 2 < 1 : sticky nominal wages

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

13 Algorithm Correctly dealing with 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?

14 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 = β (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

15 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

16 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

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

18 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 physical investment or incorrect discounting of firm profits

19 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!!!

20 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

21 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

22 Model properties 1 Model 1: no nominal wage stickiness W t = ω 0 z 0.3 t P t precautionary savings dampen downturn 2 Model 2: with nominal wage stickiness W t = ω 0 z 0.3 t P 0.85 t precautionary savings worsen downturn

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

24 No nominal wage stickiness heterogeneous agents representative agent 0.01 z log difference from SS time Productivity z

25 No nominal wage stickiness 0.05 heterogeneous agents representative agent P log difference from SS time Precautionary demand for M makes price procyclical!

26 No nominal wage stickiness heterogeneous agents representative agent 0.2 real price of equity 0.15 log difference from SS time Precautionary savings has small upward effect on firm value for low z

27 No nominal wage stickiness heterogeneous agents representative agent 0.02 N absolute difference from SS time Precautionary savings has small upward effect on employment for low z

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

29 With nominal wage stickiness 0.05 heterogeneous agents representative agent P log difference from SS time Precautionary demand for M makes price procyclical!

30 With nominal wage stickiness heterogeneous agents representative agent 0.2 real price of equity 0.15 log difference from SS time Firm value strongly reduced in a downturn

31 With nominal wage stickiness heterogeneous agents representative agent 0.02 N absolute difference from SS time Employment strongly reduced in a downturn

32 Role of nominal wage stickiness Change from boom to recession for representative agent (red) vs heterogeneous agents (blue) P 0 x real wage ω 2 real price of equity ω ω 2 N ω 2