Mismatch. Robert Shimer. (American Economic Review, 2007) Presented by Ismael Gálvez. January 23, 2018

Transcription

1 Mismatch Robert Shimer (American Economic Review, 2007) Presented by Ismael Gálvez January 23, 2018

2 Motivation Broad questions: (1) Why do unemployed and job vacancies coexist? (2) What determines the job-finding rate? Two complementary theories: (1) Mismatch: Former steel workers remaining near a closed plant in the hope that it reopens. (2) Search: Former steel workers moving to a new city to look for positions as nurses. Goal of the paper: Develops a dynamic model of mismatch. Unemployed workers attached to an occupation/location.

3 This paper This model solves two search and matching shortcomings: (1) No matching function is assumed. (2) Wages are set competitively. Main contribution: Develop a model of mismatch: (1) Quantitatively consistent with data. (2) Make the notion of labor market explicit. Main finding: (1) Consistent with Beveridge curve and the reduced-form matching function. (2) Consistent with the BC comovement of u, v and JFR.

4 Economic Agents M workers and a large number of firms. Time is continuous. Agents are risk neutral, infinitely lived. Each firm may have zero, one, or more jobs. N(t): total number of jobs. Each worker/job is assigned to one of L labor markets (LM) N =N/L; M = M/L Wage setting. Let i(j): number of workers (jobs) in some LM: i > j = Unemployment = wage equals home production z. i < j = Job vacant = wage equals MPL p(t). i = j = Nor unemployment,vacant. Assume wage = p(t). Two shocks following a Poisson process: Quit shock q: worker leaves LM and move to a random one. Layoff shock l: job leaves LM and disappears.

5 Stocks and Flows Number of unemployed and vacancies: U(N) = i=1 i (i j)π(i, j; N) ; V (N) = j=0 j=1 j (j i)π(i, j; N) where π(i, j; N) is the fraction of LM with i workers and j jobs. Firms may create a new job by paying k > 0. Share of LM with i workers π(i; M) and with j jobs π(j; N(t)) evolves: π(i; M) = q[(i + 1) π(i + 1; M) + M π(i 1; M) (i + M) π(i; M)] π(j; N(t)) = l[(j + 1) π(j + 1; N(t)) + n(t) π(j 1; N(t)) (lj + n(t)) π(j; N(t))] Independent birth-death process = number of workers and jobs in a LM are independent Poisson random variables at each instant. i=0

6 Aggregate Shock and Equilibrium Single shock: fluctuations in aggregate productivity p(t) (wp λ). HJB of the Value of a job: rj p (N) = (p z)s(n) lj p (N) + J p(n)ṅ + λ(e p J p (N) J p (N)) where S(N) is the share of LM with unemployment Equilibrium is characterized by a sequence of targets Np : If N(t) < Np = Firms create Np N(t) jobs. If N(t) = Np = Gross job creation = Gross job destruction. If N(t) > Np = No jobs are created. HJB equation can be written as follows: rj p(n) = (p z)s(n) lj p(n) J p (N)lN + λ(epj p (N) Jp(N)) if N N P rj p(n) = rk if N < N p Propositions 1 and 2 There is a unique equlibrium. In it, the targets N p are increasing. The equilibrium maximizes the present value of net output.

7 Theory UR and VR depend only on the number of workers per market M and number of jobs per market N. Propositions 3 The unemployment rate u is increasing in M and decreasing in N. The vacancy rate v is decreasing in M and increasing in N. Implications: (1) p = N = u and v. (2) A proportional increase in M and N reduce both u and v. (3) Data on u and v pin down N and M.

8 Measurement

9 Volatility of the V-U Ratio If λ = 0 = HJB: (r + l)k = (p z)s(n p ) PROPOSITION 5 log(v (Np )/U(Np ( )) V (Np ) = logp V (Np ) U (Np ) ) U(Np U (Np ) p ) U (Np ) p z > 0. Given consistent values of M and N, a 1% increase in p will rise v-u ratio by 4.25p/(p z). In matching model: 1.03p/(p z). Why is v-u ratio more responsive in a mismatch model? (1) Vacancy cost is sunk. (2) Structure of mismatch: wages and market shift.

10 Job Finding and Separation Rates Probability that a quit leads to a UE transition: ρ UE q (N) = 1 i 1 jπ(i, j; N) + u(n) π(i, j; N) = (1 u(n)) M i=1 j=0 i=0 j=i+1 Probability that a job entering leads to a UE transition: ρ UE n (N) = S(N) Probability that a job layoff leads to a EU transition: i=0 i π(i, j; N). j=0 ρ EU l (N) = 1 N j=1 jπ(i, j; N) = i=j j=0 i=j+1 π(i, j; N) = ρ UE n (N) JFR f (N) = qmρue q (N)+lNρUE(N) n U(N) ; SR s(n) = qmρeu q (N)+lNρEU(N) l M U(N)

11 Job Finding and Separation Rates N = u and v = f. Relation between f and V/U: Insensitive to the composition of q+l. Nearly isoelastic. When p is high, more jobs per LM = more likely to find a new job immediately = s.

12 Calibration Procedure Nine parameters: Number of workers per LM: M = to match Beveridge curve. Quit and layoff rates: q = l = to match SR in ss. r = 0.012, z = 0.4 for comparability and k = Stochastic process (3 parameters: η, λ and ).

13 Results The model is able to match: Both negative correlation V and U and autocorrelation of V and U. 40% and 31% of the volatility in V and U. Correlation between f and v-u ration ( reduced-form matching funtion ) 26% and 43% of the volatility of f and s.

14 Duration Dependence Not all unemployed are equally likely to find a job. Why? Individual JF probability depends on i and j in her LM. Thus Duration dependence in the JFR. JF probability declines sharply during the unemployment spell. Accounting for duration dependence: (1) Lowers the level of Job finding probability. (2) Does not affect the reduced-form matching function.

15 Mobility Benchmark model: mobility is random. Now: mobility is bounded by δ: i j δ. Beveridge curve and reduced-form matching function are quite insensitive to δ. Fit of the BC is better when mobility is more random. High δ to have constant elasticity in the reduced-form matching function.

16 Conclusions Simple mismatch model to highlights major forces. Must deliver right slope of the Beveridge Curve. Beveridge Curve unaffected by cyclical fluctuations in q+l. Explains much of the volatility of v and u. JFR declines with unemployment spell. Generate reduced-form matching function.