Business Failure and Labour Market Fluctuations Seong-Hoon Kim* Seongman Moon** *Centre for Dynamic Macroeconomic Analysis, St Andrews, UK **Korea Institute for International Economic Policy, Seoul, Korea Korea Institute of Finance 11 September 2014
MPL = w Circular Flow Y MRS = w C
MPL MRS General Equilibrium Y C
Model (a prototype RBC) A t f n (k t 1, n t ) y t = A t f (k t 1, n t ) U n(c t,n t) U c(c t,n t) c t + {k t (1 δ)k t 1 }
Data A t f n (k t 1, n t ) y t = A t f (k t 1, n t ) U n(c t,n t) U c(c t,n t) c t + {k t (1 δ)k t 1 }
cyclical behaviour Data Define wedge = MRS MPL = Un(ct,nt)/Uc(ct,nt) A tf n(k t 1,n t) = φ (1 α) n 1/γ t y t/n t /c 1 t with y t = A t k α t 1 n1 α t and U(c t, n t ) = ln c t φ n1+1/γ t. 1+1/γ In data, wedge or ln(wedge) are procyclical.
Why? exogenous randomness? Benhabib et al. (1991) Hall (1997) Holland and Scott (1998) search-and-matching frictions? Andolfatto (1996) departure from a competitive equilibrium? Cole and Ohanian (2002) Comin and Gertler (2003) Gali et al. (2007) departure from other simplifying assumptions? Chang and Kim (2007)
Proposed answer business failure (bankruptcy risk) firm s optimal labour demand: household s optimal labour supply: MPL Pr (business success) = w MRS = w in equilibrium, MPL Pr (business success) = MRS or MPL {1 Pr (business failure)} = MRS
Proposed answer business failure (bankruptcy risk) firm s optimal labour demand: household s optimal labour supply: MPL Pr (business success) = w MRS = w in equilibrium or Pr (business success) = MRS MPL = wedge 1 Pr (business failure) = MRS MPL = wedge
Key mechanism MPL {1 Pr (business failure)} = MRS In data (in our theory) 1. Labour market wedge moves procyclically. (due to countercylical bankruptcy rate) 2. Employment is volatile as much as output. (due to responsiveness of N-demand, wealth effect, substitution effect on N-supply) 3. Employment and labour productivity are nearly uncorrelated. (because of underlying reasons in 2)
Giants Greenwald and Stiglitz (1987) risk-adjusted MPL Farmer (1985) interest rate shocks and labour demand
Model Firms standard role - own capital k t 1, hire labour n t, and produce y t = A tf (k t 1, n t) - make investment i t and accumulate k t = (1 δ)k t 1 + i t - earn d t = A tf (k t 1, n t) w tn t {k t (1 δ)k t 1} modifications (1) debt financing: - have period liability R t 1b t 1 and borrow b t (2) tax benefit: - borrow b t at the effective rate Rt τ = 1 + (1 τ)r t (3) idiosyncratic shock: - see sales revenue A tx tf (k t 1, n t), x t [x, x] (4) bankruptcy law (Chapter 11): - equity holders have limited responsibility: Pay back up to sales revenue for very low realization of x t. Possibly, managers are sacked by equity holders or replaced by court. Firms continue business without costly liquidation of capital.
Model - are liable up to Firms { Rt 1b τ t 1 A tx tf (k t 1, n t) for x t x t for x t < x t where x t is such that A t x tf (k t 1, n t) = R τ t 1b t 1, defining an implicit function x(n t, k t 1, b t 1; A t) = Rτ t 1 b t 1 A t f (k t 1,n t ) - earn d t = A tx tf (k t 1, n t) w { tn t {k t (1 δ)k t 1} Rt 1b τ t 1 for x t x t +b t µb t A tx tf (k t 1, n t) for x t < x t - maximize max {nt,k t,b t } E 0 t=0 m0,tdt
Model - are liable up to Firms { Rt 1b τ t 1 A tx tf (k t 1, n t) for x t x t for x t < x t where x t is such that A t x tf (k t 1, n t) = R τ t 1b t 1, defining an implicit function x(n t, k t 1, b t 1; A t) = Rτ t 1 b t 1 A t f (k t 1,n t ) - earn d t = A tx tf (k t 1, n t) w { tn t {k t (1 δ)k t 1} Rt 1b τ t 1 for x t x t +b t µb t A tx tf (k t 1, n t) for x t < x t - maximize max {nt,k t,b t } E 0 t=0 m0,tdt
Model Firms FOCs { n t : w t = A tf n(k t 1, n t) 1 } x t 0 }{{} xtdg(xt) MPL k t : δ = E tm t,t+1 A t+1f k (k t, n t+1) }{{} MPK b t : 1 = µ + E tm t,t+1rt τ {1 G( x t+1)} }{{} Effective loan rate { 1 x t+1 0 x t+1dg(x t+1) }
Model Households - aim to [ ] max {ct,n t,l t,s t } E 0 t=0 βt ln c t φ n1+1/γ t 1+1/γ subject to c t + T t + l t + (s t s t 1) p t = w tn t + Rt 1l f t 1 + s t 1d t + dt b - consume c t, pay lump-sum tax T t, and supply labour n t - lend l t to banks at the riskfree rate Rt f = 1 + rt f - trade a market portfolio of shares s t at index p t - earn w tn t, receive Rt 1l f t 1, dividends s t 1d t and dt b
Model Households FOCs (c t, n t) : φ n1/γ t ct 1 }{{} MRS (c,n) [ c 1 t+1 (c t, l t) : βe t = w t R f ct 1 t ] } {{ } MRS (c0,c1) = 1, (c t, s t) : βe t [ c 1 t+1 ct 1 { } ] d t+1 + p t+1 = 1 p t } {{ } MRS (c0,c1) ( by forward substitution: p t = E c 1 ) t j=1 βj t+j ct 1 d t+j }{{} m t,t+j
Model Banks - transform l t to b t (i.e., financial intermediaries) - earn dt b = x t (1 + r t 1) b t 1dG(x t) + x t {Atxtf (kt 1, nt)} dg(xt) + lt 0 Rt 1l f t 1 b t - maximize max {lt,b t } E 0 t=0 m0,tdb t FOCs l t : 1 = E tm t,t+1r f t b t : 1 = E tm t,t+1 (1 + r t) {1 G( x t+1)}
Model Calibration (model parameters) α 0.36 capital income share β 0.99 discount factor γ 1.5 Frish elasticity δ 0.025 capital depreciation rate φ 10 labour utility parameter τ 25% tax rate µ 0.5% loan arrangement fee portion x 1.7 upper bound of idiosyncratic shock x 0.3 lower bound of idiosyncratic shock ρ 0.7 persistence of aggregate technology shock
Model Calibration (steady states) A 1 aggregate technology n 0.225 labour G( x) 4.6% probability of bankruptcy b/y 36% short-term debt to GDP ratio r f 1.01% riskfree rate r 1.42% loan rate
Results (IRF) 1.2 1 output consumption employment 1.2 1 output labour productivity employment 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0.2 0.2 0.4 0 5 10 15 20 0.4 0 5 10 15 20
Results (IRF) 1 0.8 employment wedge 50 bankruptcy rate interest rate spread 0.5 0.6 0 0 0.4 0.2 0 50 0.5 0.2 0.4 0 5 10 15 20 100 0 5 10 15 20 1
Results (Fitness) US data Model σ c/σ y 0.77 0.85 σ i /σ y 2.84 3.19 σ n/σ y 0.91 0.86 σ y/n /σ y 0.51 0.51 Corr(y, c) 0.77 0.17 Corr(y, i) 0.78 0.86 Corr(y, n) 0.86 0.86 Corr(y, y/n) 0.42 0.51 Corr(n, y/n) -0.10-0.01
Conclusions Having business failure into the otherwise standard RBC helps, without further extra market frictions, to reconcile three key labour market puzzles at once: - procyclical labour market wedge - high volatility of employment - low correlation between worked hours and labour productivity
Remarks The presence of business failure forms a crucial part of labour market fluctuations, while connecting all three markets (goods, labour, financial). And to the very extent, it should be a crucial part of business cycle study.