New Business Start-ups and the Business Cycle

New Business Start-ups and the Business Cycle Ali Moghaddasi Kelishomi (Joint with Melvyn Coles, University of Essex) The 22nd Annual Conference on Monetary and Exchange Rate Policies Banking Supervision and Prudential Policies May 27, 2012

Motivation Introduction This paper extends the search and matching literature by incorporating a model of business start-ups. Mortensen and Pissarides (1994) has been the leading framework for analyzing the evolution of unemployment over the business cycle. This paper shows how replacing the free entry of vacancies assumption with Diamond entry and with a time-to-build constraint not only yields the required volatility in unemployment, vacancy dynamics, it also generates the right degree of persistence (autocorrelation of variables over time) and the Beveridge curve (negative covariance between unemployment and vacancies).

Motivation Table of contents 1 Motivation 2 Evidence on New Business Start-ups 3 The model The start-up process Timeline Equilibrium Dynamics 4 Simulation Model Calibration Impulse Responses Volatilities Relationship with adjustment cost models 5 Conclusion

Evidence on New Business Start-ups Evidence on New Business Start-ups new start-up firms (defined as firms aged less than one year) are important for the U.S. economy as: net job creation by startups is large (around 3 million new jobs created each year) and is relatively inelastic over the cycle, while net job creation by existing firms is typically negative and recessions are characterized by large levels of net job destruction by existing firms.

1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 New Business Start-ups and the Business Cycle Evidence on New Business Start-ups Net job creation in the U.S. economy 6000000 4000000 2000000 0-2000000 -4000000-6000000 -8000000 Net Job Change - Startups Net Job Change - Existing Firms

The model The model builds on conventional equilibrium unemployment framework with discrete time and an infinite time horizon; e.g. Pissarides (2000). The main difference is the business start-up process. Time is discrete (monthly) with infinite horizon. There is a unit mass of equally productive workers who are infinitely lived. Workers are either employed or unemployed. Let u t denote the number unemployed at date t and v t denotes the number of vacancies at time t. Total Job Matches in period t is m t = m(u t, v t ) where m(.) is positive, increasing, concave and homogenous of degree one.

The model The start-up process The start-up process: The conception stage. In time period t each entrepreneur has one independent business idea and invests in it whenever a business idea has positive value; i.e. when Jt P x > 0 where Jt P is the expected value of a project and x is the investment cost. The start-up process. A new project is transformed into a new business, an unfilled vacancy with productivity P t and with corresponding value J v t, with probability of α. The expected start-up time, time-to-build, for any project is α 1 1 (and is zero when α = 1).

The model Timeline Each period is divided into 5 stages: Stage I [new realizations]: given (p t 1, δ t 1 ) from the previous period, new values of p t, δ t are realized according to stochastic process described below; Stage II [bargaining and production]: the wage w t is determined by Nash bargaining. Production takes place so that a firm with a filled job enjoys one period profit p t wt while an employed worker enjoys payoff w t : Each unemployed worker enjoys payoff z; Stage III [project investment]: entrepreneurs invest in it new projects. If I t 1 denotes the stock of projects inherited from the previous period then α[i t + i t ] describes new vacancy creation while I t = (1 α)[i t + i t ] determines the number of projects which continue into the next period;

The model Timeline Stage IV [matching]: let ut,vt denote the stock of unemployed job seekers and vacancies at the start of this stage. Matching takes place so that mt = m(ut; vt) describes the total number of new matches; Stage V [job destruction]: each vacancy and each filled job is independently destroyed with probability δ t : If a job is destroyed, the firms s continuation payoff is zero and the worker becomes unemployed.

The model Equilibrium Dynamics Equilibrium Dynamics(1) Unemployment and vacancy evolve accoring to: u t = u t 1 + δ t 1 (1 u t 1 ) (1 δ t 1 )m t 1 (1) v t = (1 δ t 1 )[v t 1 m t 1 ] + α[i t 1 + i t ] Once (p t, δ t ) are realised, it is useful to define the intermediate measure of vacancies v t = (1 δ t 1 )[v t 1 m t 1 ] Define the stage II state vector Ω t = {p t, δ t, I t 1, u t, v t, } where I t 1 is the number of continuing projects inherited from the previous period, u t is the number unemployed and v t is the continuing number of vacancies.

The model Equilibrium Dynamics Stage II determines wages according to a standard Nash bargaining procedure: below we show this yields a wage rule of the form w t = w N (Ω t ). Stage III then determines optimal investment in new projects: below we show this also takes the form i t = i(ω t ). As the matching and separation dynamics ensure Ω t evolves as a first order Markov process, then Ω t is indeed a sufficient statistic for optimal decision making in period t.

The model Equilibrium Dynamics Equilibrium Dynamics(2) let: Jt P = J P (Ω t ) denote the entreprenueur s expected value of a project; J V t Jt F Vt U = J V (Ω t ) denote the expected value of a vacancy; = J F (Ω t ) denote the expected value of a filled job; = V U (Ω t ) denote the worker s expected value of unemployment; = V E (Ω t ) denote the worker s expected value of employment. V E t

The model Equilibrium Dynamics The firms value functions are defined recursively by: } Jt P = αjt V + (1 α)βe {Jt+1 Ω P t (2) { Jt V m(ut, v t ) = c + β(1 δ t )E Jt+1 F + [1 m(u } t, v t ) ]J V v t v t+1 Ω t t J F t = p t w t + β(1 δ t )E{J F t+1 Ω t } where the interpretation is standard and follows the timing of the model described above. The worker value functions are also defined recursively: V U t V E t = z + βe = w t + βe [ V U t+1 + (1 δ t ) m(u t, v t ) [ V E u t [ ] Vt+1 E + δ t+1 [Vt+1 U Vt+1] Ω E t t+1 V U t+1 ] Ω t ] (3)

The model Equilibrium Dynamics As Diamond entry implies the reservation cost rule - invest if and only if cost x Jt P - then equilibrium investment i t = i(ω t ) is given by i t = BH(Jt P ) where Jt P = J P (Ω t ). we adopt functional form i t = B [ Jt p ] ξ and ξ then describes the elasticity of project investment with respect to the value of a new project.

Simulation Model Calibration Model Calibration We adopt the parameter values in Mortensen and Nagypal (2007), with a Cobb-Douglas matching function m = Au γ v 1 γ. Parameters Values γ elasticity parameter on matching function 0.6 φ worker bargaining power 0.6 z worker outside value of leisure 0.7 β monthly discount factor 0.9967 ρ p productivity autocorrelation 0.978 ρ δ separation autocorrelation 0.925 σ p st. dev. productivity shock 0.0064 σ δ st. dev. separation shock 0.031 σ pδ covariance of shocks -0.60

Simulation Model Calibration Stochastic Process: ln p t = ρ p ln p t 1 + ɛ t ln δ t = ρ δ ln δ t 1 + (1 ρ δ ) ln δ + η t where (ɛ t, η t ) are white noise innovations drawn from the Normal distribution with mean zero and covariance matrix Σ; and δ > 0 is the long-run (average) job destruction rate. Note p = 1: Calibrate these processes to Shimer s (2005) data.

Simulation Impulse Responses Unemployment Response to Separation Rate Shock 0.05 0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 Responses to Separation Rate Shock Unemployment FE Unemployment DE Unemployment DE + TTB 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 Months

Simulation Impulse Responses Vacancies response to Separation Rate Shock Responses to Separation Rate Shock 0.03 nemployment FE 0.02 nemployment DE nemployment 0.01 DE + TTB Vacancies FE Vacancies DE Vacancies DE + TTB 0-0.01-0.02 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 Months -0.03-0.04-0.05 33 36 39 42 45

Simulation Impulse Responses The introduction of the time-to-build constraint, α = 1/13; instead implies vacancies immediately fall in response to the job separation shock. The separation innovation generates a rising tide of unemployed workers who rematch with the existing vacancy stock. As it takes time to increase new vacancy creation rates, the original stock of vacancies becomes depleted by the increased number of job seekers. The increased inertia implies unemployment grows more and it takes longer for the economy to recover. This in turn yields larger variations in unemployment, the vacancy stock and the vacancy/unemployment ratio over the cycle.

Simulation Volatilities Volatilities Volatility of unemployment and vacancies. Volatility Data Free Entry Diamond Diamond+TTB σ u 0.19 0.08 0.15 0.18 σ v 0.20 0.05 0.14 0.18 σ v/u 0.38 0.07 0.28 0.36 Persistence in unemployment and vacancies. Serial Persistence Data Free Entry Diamond Diamond+ttb autocorr(u) 0.94 0.85 0.95 0.96 autocorr(v) 0.94 0.77 0.96 0.96 corr (u,v) -0.89 0.33-0.93-0.97

Simulation Relationship with adjustment cost models Relationship with adjustment cost models Another alternative to free entry is employment adjustment costs (See Yashiv(2006)). Assuming no time-to-build and following Merz and Yashiv (2007) cubic estimate for the employment adjustment cost function, yields a new vacancy creation, i t = B[J V t ] 1/2. function. Volatility with an adjustment cost specification. Volatility Data AC Diamond Diamond ξ = 1/2, no TTB ξ = 1/2 +TTB σ u 0.19 0.08 0.17 0.19 σ v 0.20 0.04 0.17 0.21 σ v/u 0.38 0.05 0.34 0.40

Conclusion Conclusion This paper considers new business start-up activity within a stochastic equilibrium model of unemployment. The resulting job creation process is both natural and tractable, and generates equilibrium unemployment and vacancy dynamics which match the volatility and persistence observed in the data. The advantage of the two-shock extension is that an aggregate productivity shock would seem a poor metaphor for the recent financial crisis. Tying ones hands to a single source of aggregate shocks would seem unnecessarily restrictive.

Conclusion The insight is that the standard Diamond-Mortensen-Pissarides matching framework works beautifully once the free entry of vacancies assumption is replaced by a model of business start- up activity. The approach is particularly important as it is demonstrated that a large part of net job creation in the U.S. economy can be attributed to new business start-ups.