Directed Search with Phantom Vacancies

Transcription

1 Directed Search with Phantom Vacancies Jim Albrecht (Georgetown University) Bruno Decreuse (Aix-Marseille U, AMSE) Susan Vroman (Georgetown University) April 2016

2 I am currently on the job hunt and I had a question about applying to jobs online. You know how most websites will tell you the job has been posted 1 day ago, 28 days ago, etc. For some reason, I have concluded that I need to apply to a job the first week they post the position to have the best chances of being hired. Although I heard that it can take up to a month for the company to hire anyone for the position, I feel that applying to a job that was posted 3 weeks ago isn t that promising. What is your take on this situation? AskaManager.com

3 Phantom vacancies Why do job seekers pay attention to vacancy age? obsolete information: some advertised jobs are already filled no one wants to lose time pursuing a phantom vacancy Job seekers observe the age of the advertisement They have to figure out how likely it is that the job is still available

4 Directed search with phantoms With directed search, we focus on the following trade-off: due to phantoms, workers may decide to limit their search to more recent postings however, applying to older postings is also attractive since fewer job seekers apply for these jobs In equilibrium, workers direct their search by the age of the ad so that the job-finding rate is the same for all ages Workers overapply to younger ads finding a job of a given age creates a negative informational externality that only affects cohorts of vacancies after this age

5 Information obsolescence Information obsolescence is a source of matching frictions Chéron and Decreuse (2015): match formation creates phantom traders in a model of random search In this paper, we model agents search behavior when age is observable and search is directed by age endogenous distributions of vacancies, phantoms, and unemployed by age Information obsolescence can account for a substantial fraction of unemployment even though job seekers direct their search by age we calibrate the model using US data phantoms account for about a third of unemployment and two thirds of overall frictions, but the magnitude of the directed search externality is small

6 Plan of the talk 1 Model assumptions 2 Directed search allocation 3 Effi cient allocation 4 Calibration 5 Extensions

7 Model assumptions We focus on the steady state of a continuous time model. General assumptions there are K jobs, v vacancies, u unemployed and v + 1 u = K jobs are homogenous (same output and wage) exogenous separation rate λ Specific assumptions search market is segmented by vacancy age a in each submarket, u(a) unemployed, v(a) vacancies, and p(a) phantoms job seekers cannot distinguish between phantoms and vacancies

8 The flow of new matches is Market segmentation by age M(a) = π(a)m(u(a), v(a) + p(a)), where π(a), the nonphantom proportion, is π(a) = v(a) v(a) + p(a). Two components of the matching function: meeting function m; strictly concave with CRS nonphantom proportion π(a) The job-finding rate by vacancy age is µ(a) = M(a)/u(a), the rate of filling vacancies is η(a) = M(a)/v(a), and submarket tightness is θ(a) (v(a) + p(a))/u(a)

9 Phantoms and vacancies Match formation gives birth to phantoms that die at a constant rate. Vacancies and phantoms evolve according to: v(a)/ a = M(a), p(a)/ a = βm(a) δp(a), with 1 β 0, δ > 0, v(0) = λ(1 u), p(0) = 0, and v = 0 v(a)da. The nonphantom proportion evolves according to: π(a)/ a = M(a) π(a)[1 (1 β)π(a)] + δπ(a)[1 π(a)] v(a) with π(0) = 1. This assumes that vacancies cannot be refreshed or renewed.

10 Closing the model The unemployed are spread over the different submarkets with u = 0 u(a)da and du/dt = M(a)da + λ(1 u) = 0. 0 We need a rule that allocates the unemployed across vacancy ages

11 Plan of the talk 1 Model assumptions 2 Directed search allocation 3 Effi cient allocation 4 Calibration 5 Extensions

12 What directed search means Agents observe vacancy age a and decide which market segment to search in. In equilibrium, the job-finding rate, µ(a) = M (a), must be the u(a) same for all a 0. As µ(a) = π(a)m(1, θ(a)) for all a and π(0) = 1, we have π(a)m(1, θ(a)) = m(1, θ(0)) for all a 0. Differentiating this relationship with respect to age gives: θ α(θ(a)) θ(a) = π π(a) where α(θ(a)) is the elasticity of the meeting function wrt θ(a) and a dot denotes the derivative with respect to age, e.g., θ θ (a).

13 Solving The objective is to show how market tightness varies with age. Substitution yields [ ] m(1, θ(0)) α(θ(a)) θ = 1 (δθ(a) m(1, θ(a)) βm(1, θ(0)) m(1, θ(a)) We need to find θ(0). To do this, we use the resource constraint 1 u + m(1, θ(0)) v(a)da = K where 1 u = 0 λ + m(1, θ(0)) and v(a) solves v=. m(1, θ(a)) v(a) with v(0) = λ(1 u). θ(a)

14 Directed search allocation The directed search allocation is characterized by the function θ ds (a) that solves [ α(θ ds (a)) θ ds = 1 m(1, θ ] ds (0)) [δθ ds (a) m(1, θ ds (a)] m(1, θ ds (a)) βm(1, θ ds (0)) { m(1, θ ds (0)) [ a 1 + λ exp λ + m(1, θ ds (0)) 0 0 ] } m(1, θ ds (b)) db da = K. θ ds (b)

15 Some properties The job-finding rate µ(a) = m(1, θ ds (0)) is constant over vacancy age. The nonphantom proportion π(a) = v(a)/(v(a) + p(a)) decreases with a. Tightness θ(a) = (v(a) + p(a))/u(a) increases with a. The rate of filling vacancies η(a) = m(1, θ ds (a))/θ ds (a) decreases with a.

16 Random Search Allocation We can compare the directed search allocation to one in which workers do not observe the age of job listings and so can only apply at random. In the random search allocation, market tightness is constant across age, i.e., θ = 0 or θ(a) = (v(a) + p(a)) u(a) = θ for all a 0 The random search allocation is characterized by the unique θ rs such that m(1, θ rs ) + λθ rs m(1, θ rs ) + λ + λ(β/δ)m(1, θ rs )/θ rs = K

17 Plan of the talk 1 Model assumptions 2 Directed search allocation 3 Effi cient allocation 4 Calibration 5 Extensions

18 Social Planner Problem The social planner allocates job seekers across vacancy ages to minimize aggregate unemployment. Since 1 u + v = K, the SP problem can be expressed as max θ(.) v(a)da 0 This maximization is constrained by 1 The laws of motion for v(a) and p(a) 2 The resource constraint: (1 u) + v = K.

19 Details subject to max θ(.) v(a)da p(0) = 0 v(a) + p(a) da + v(a)da = K θ(a) 0 v = η(θ(a))v(a) ( ) v(0) = λ K v(a)da ṗ = βη(θ(a))v(a) δp(a) 0

20 Effi cient allocation In the effi cient allocation for all a, we have θ(a) = ( which implies. α 1 α(θ(a)) α(θ(a)) θ θ(a) = 1 [1 α(θ(a))]π(a) )( 1 α(θ(0)) α(θ(a))π(a) 1 α(θ(a)) )θ(0) π π(a) θ + (1 α(θ(a)))(1 π(a)) θ(a). This differs from the expression that characterizes the directed search allocation in two ways:

21 Effi cient allocation (cont d). α 1., the added term on the LHS, reflects the fact that 1 α(θ(a)) what matters to the social planner is the marginal productivity of vacancies, i.e., (1 α(θ(a)))π(a)m(1, θ(a)) rather than π(a)m(1, θ(a)), which is kept constant in directed search. θ 2. (1 α(θ(a)))(1 π(a)), the added term on the RHS, θ(a) reflects the intertemporal externality that is internalized in the effi cient allocation.

22 Effi cient allocation (cont d) As we did in the directed search case, we can substitute for π(a) and use the resource constraint to solve for θ(0), giving us a differential equation for θ(a). We can use this to show that in the effi cient allocation: 1. θ(a) is increasing in a 2. π(a) is decreasing in a 3. µ(a) is decreasing in a 4. η(a) is decreasing in a

23 Ineffi ciency 1 The random search allocation coincides with the effi cient allocation if and only if β = 0; 2 The directed search allocation generically differs from the effi cient allocation when β > 0.

24 Plan of the talk 1 Model assumptions 2 Directed search allocation 3 Effi cient allocation 4 Calibration 5 Extensions

25 The meeting technology is Cobb-Douglas, i.e., Calibration m(u, v + p) = m 0 u 1 α (v + p) α, m 0 > 0, α (0, 1) JOLTS and BLS data for the period monthly job-finding probability: µ m = 0.4 (1 exp( µ)) = 0.4 so µ = ln(1 0.4) 0.5 monthly job-loss probability: λ m = 0.03 λ = ln(1 0.03) 0.03 this implies that u = λ/(λ + µ) mean vacancy-to-unemployed ratio x = v/u = 0.5 Each match gives birth to a phantom that reaches one month with probability 0.5 β = 1.0 and δ m = 0.5 δ = ln(1 0.5) 0.7, i.e., phantoms live for 1.4 months on average

26 Calibration (cont d) Aggregate matching technology is M = m 0 0 π(a)u(a)θ(a)α da the elasticity of this function wrt overall tightness is larger than α We use α = 0.2, which implies a matching function elasticity of 0.4. We set m 0 so that u = and we set K = to match x = 0.5. This implies that u is in the absence of meeting frictions and phantoms

27 job seeker density Baseline Calibration φ u ds φ u eff φ u rs vacancy age in months Densities of Job Seekers by Vacancy Age

28 tightness θ ds θ eff θ rs vacancy age in months Market Tightness by Vacancy Age

29 job finding rate µ ds µ eff µ rs vacancy age in months Job-finding Rates by Vacancy Age

30 vacancy proportion π ds π eff π rs vacancy age in months Nonphantom Proportion by Vacancy Age (in months)

31 Quantitative implications Effi ciency gains achieved by the effi cient allocation are modest search strategies that produce more matches also produce more phantoms the average nonphantom proportion varies little across allocations: π rs = 42.9%, π ds = 40.7%, π eff = 39.1% Contribution of information obsolescence to unemployment is nonetheless large nonfrictional unemployment rate is min(1 K, 0) = unemployment rate with β = 0 is directed search unemployment rate (β = 1) is u ds = phantoms account for 0.020/ % of overall frictions and 0.020/ % of unemployment

32 Alternative Parameterizations We now look at how the magnitude of ineffi ciency varies with α and δ To do this, we calibrate the directed search allocation so that the predicted u remains at a bit over The next two figures illustrate how the the unemployment rates in the random search allocation and the effi cient allocation then vary with α and with δ

33 unemployment rate Alternative Parameterizations u ds u eff u rs elasticity α of the meeting technology Unemployment rates as functions of α

34 unemployment rate u Alternative Parameterizations u ds u eff u rs phantom death rate δ Unemployment rates as a function of δ

35 Plan of the talk 1 Model assumptions 2 Directed search allocation 3 Effi cient allocation 4 Calibration 5 Extensions

36 Some Additional Results Vacancy renewals Lemons Wages determined by Nash bargaining

37 Vacancy Renewals Some websites destroy ads after a fixed time, e.g., Craigslist - one month; Monster - two months. Others offer the possibility of renewing offers. To capture this idea, we assume that vacancies automatically renew at age A and are randomly renewed at exogenous rate γ for a (0, A). By renewed, we mean that the existing ad is withdrawn and the vacancy is reposted with age a = 0 Vacancies now evolve by age according to. v = M(a) γv(a) v(0) = λ(1 u) + γv + v(a) The equation for the nonphantom proportion becomes. ( ) π m(1, θ(a)) m(1, θ(a)) = (1 π(a)) δ βπ(a) π(a) θ(a) θ(a) γ(1 π(a))

38 Vacancy Renewals The model calibration involves two new parameters, A and γ. We set A = 2, i.e., vacancies (and phantoms) can last for at most 2 months. We also set δ = 0 so ads deterministically last 2 months. To set γ, we use data from Craigslist, which indicate that 55% of a new cohort of ads consists of new vacancies. We then vary α from 0 to 1 keeping λ(1 u) λ(1 u) + γv + v(2) = 0.55 and u = This gives us the values for γ and m 0. γ lies between 0.5 and 0.8 (ads are renewed on average every ten days) and m 0 is about 1.

39 Vacancy Renewals If we look at the unemployment rates for the three allocations varying α from 0 to 1, we get a similar picture to our earlier one, but the unemployment differential between the directed search allocation and the random search allocation is larger. Random search is more costly with renewal. When α = 0.2, as in the baseline calibration, γ 0.6 and u eff = < u ds = < u rs = The corresponding nonphantom proportions are π eff = 35.5%, π ds = 34.8%, π rs = 44.9% In this case, phantoms account for about 64% of overall frictions and about 32% of unemployment

40 Lemons Next we consider the possibility that some jobs may be lemons so that workers who meet them won t take them. Lemons are another reason that workers pay attention to vacancy age. Let l(a) be the number of lemons of age a with total lemons of l = l(a)da. Let l (a) = δl(a) and set l(0) = δl. 0 Unlike phantoms, lemons are created at age zero, and no new lemons are created after this.

41 Lemons Lemons create an ineffi ciency because when a match is formed, there is a compositional externality a job seeker responding to an ad is less likely to find a vacancy. Quantitatively, the effect of lemons is small. To see this, we set β = 0 (no phantoms) and choose l 0 so that the lemon proportion among new ads is 10%. Again, we adjust m 0 to keep the unemployment rate associated with the directed search allocation equal to 5.6%. Using δ = 0.5, the magnitude of the externality associated with lemons is small relative to the one associated with phantoms. The reason is that matching does not generate the kind of intertemporal frictions that arise when there are phantoms.

42 Age-Dependent Wages Fixed-wage contracts cannot internalize the vacancy-age-dependent informational externality caused by phantoms. One could imagine firms posting sophisticated contracts advertising a wage that varies with the length of time it takes to fill the vacancy, but contracts of this sort are not realistic. Instead, and as an approximation to these more sophisticated contracts, we consider Nash bargaining over the wage.

43 Nash-Bargained Wages With Nash bargaining, workers receive a share υ [0, 1] of the match surplus, S(a) and the firm receives the remaining 1 υ. Workers in directed search then allocate themselves over job listings so that π(a)m(1, θ(a))s(a) = m(1, θ(a)(0))s(0) for all a 0. Taking derivatives of both sides yields. θ. α θ(a) = ( π π(a) +. S S(a) ).

44 Nash-Bargained Wages (continued) The match surplus increases with vacancy age because the value of a vacancy falls with age as workers are less likely to apply to older vacancies. Since match surplus increases with vacancy age, the wage does the same. Workers then have more incentive to apply for older jobs even though the job-finding rate falls with age. Then market tightness increases less rapidly when wages depend positively on vacancy age. Quantitatively (work in progress), Nash-bargained wages move the directed search allocation towards the almost-effi cient allocation but don t internalize the effect of phantoms completely.

45 Summing Up When vacancies are filled, the ads that were posted are often not withdrawn creating phantom vacancies. Directed search by workers who observe the age of job listings then leads workers to overapply to young ads. Thus filling a vacancy of a given age creates a negative informational externality that affects all cohorts of vacancies that are older. We calibrate our model of directed search with phantoms to US data and find that phantoms contribute significantly to unemployment and market frictions. The externality, however, is not large if the social planner is unable to eliminate the phantoms.