Topic 3.2: Job Search (Labour Economics) Fall 2023 PDF

Topic 3.2: Job Search Labour Economics Jeanne Tschopp University of Bern Fall 2023 Motivation The standard neoclassical model is unsatisfactory because it does not generate involuntary unemployment - The data...

Topic 3.2: Job Search Labour Economics Jeanne Tschopp University of Bern Fall 2023 Motivation The standard neoclassical model is unsatisfactory because it does not generate involuntary unemployment - The data shows that unemployment and open vacancies co-exist - There are substantial job and worker flows in the economy Standard neoclassical framework - Workers and firms instantaneously adjust to shocks to the labor market - Workers decide whether or not to work, and if they decide to work, how many hours to supply at the equilibrium wage; there is no need for job search - Firms decide how many workers to hire at the equilibrium wage; there is not need to post vacancies and search for workers Jeanne Tschopp Topic 3.2: Job Search 1/ 29 Motivation (con’t) In practice however, the labor market is characterized by search frictions - It takes time and effort for both sides of the market to find a suitable match - These frictions generate (frictional) equilibrium unemployment Over the next lectures, we are going to think about the labour market as a search and matching environment - Workers are searching for a job - Firms are searching for a worker to fill their open vacancies - A worker and a firm might meet and, if it is mutually optimal, they will form a job match bargain Nash over the wage rate (through bargain Jeanne Tschopp Topic 3.2: Job Search 2/ 29 Motivation This lecture will begin building towards an equilibrium search and matching model by modeling the behaviour of job seekers - Model that formalizes the behaviour of job seekers is called the “Job Search Model” The model will help us understand/answer questions that the standard neoclassical model is unable to answer: - Why does unemployment co-exist alongside open vacancies? - If a job offer is received, how does the job seeker decide whether to accept it or reject it? In other words, what is the optimal job search strategy? - How is the reservation wage determined within this richer search environment? - What is the job finding rate and average unemployment duration of an unemployed individual? How do they relate to the reservation rate? - What are the determinants of unemployment? Reading: Cahuc et al textbook: Chapter 5 memple Job/Ending rate so opnial job search Retemation - - - - rate Jeanne Tschopp smategy Topic 3.2: Job Search 3/ 29 Job Search Model Job Search Model The job search model considers the behaviour of an individual in a context of imperfect information about jobs and wages, also known as search frictions The benefit of spending time searching for a job is the possibility of finding a good (high paying) job Searching for a job may also be required in order to collect unemployment benefits But spending time searching for a job is also costly - Opportunity costs: lost leisure, foregone earnings from rejecting a low wage offer (if available) - Direct costs: employment agency fees, transportation to and from job interviews Jeanne Tschopp Topic 3.2: Job Search 4/ 29 Model Assumptions no differences in obs. Charactenshis (nahonality , educahon , gender )... r " "inuncbs. (abilines) Workers are homogeneous (and so are firms) -> representative firm, no duff. In from producibly Only unemployed workers search for jobs ) no on-the-job search seven though There are many different jobs (employers) that pay different wages job-to-jobGo a es ↳ - Different wages can co-exist because of frictions in the labor market ↳ - Wages in a given job are fixed forever Ifrm=1 jab 4 no renegociation ww H(w) Job seekers know the overall distribution of wages (potential job offers) that exist Job seekers and potential employers are randomly matched - No directed search; no way of targeting the high-paying jobs · Ich offers arrive at an arnual rate - ↳ f After receiving an offer, the job seeker decides whether to accept or reject it rejectsgobe i - Cannot collect several job offers before making a decision; must decide on the spot pool Jobs can exogenously disappear with probability q (separation rate) ↳ if the pr is destroyed disappears Jeanne Tschopp · Dynamic world Topic 3.2: Job Search 5/ 29 The Optimal Search Strategy Job seekers’ optimal strategy: accept any job offer that pays at least their (optimally determined) reservation wage Formalized as follows: Ve (w): expected discounted utility of being employed at wage w Vu : expected discounted utility of unemployment ""of job offer (F Ve(w) " Since Vi : a The optimal job-search strategy is: you can reject a job offer) - If the job-seeker receives no offer at date t, she continues to search. - If the job-seeker receives a wage offer w, she accepts if Ve (w) Vu. If Ve (w) < Vu , she continues to search. Jeanne Tschopp Topic 3.2: Job Search 6/ 29 Expected Utility of Being Employed: Ve (w) ↑) wilely accepted Assume an instantaneous utility function U(w) = w (risk neutrality and no preferences for leisure, in order to keep things simple) The worker discounts the future at a rate 1/(1 + r) A worker who is employed at wage w today will receive a wage payment equal to w at the end of the period At the end of the period, the worker’s job ends with exogenous probability q or continues with probability 1 q The expected discounted utility Ve (w) of a person employed at wage w is then equal to the following Bellman equation: 1 Ve (w) = [w + (1 q)Ve (w) + qVu ] 1+r Jeanne Tschopp Topic 3.2: Job Search 7/ 29 Illustration: Ve (w) Employed at w t wage - work V. n tancos nig ncwi - wi t + 1 destroyed - the is (1-q) : 9 proba job proba the / the ob is : not destroyed L join the pool of unemployment denie and stay emploed and search and denie unily Vu Unily Ve (w) - Hence , the expected discounted rnhly of empl , is summated as follows : BECRAN Evan - Ve (w) = =Er(N+ (1 - 9) Ve (w) +qUnd V-time Lust periment s etpenodz  Ve(w) it (w (1-q)Ve(w7+qVn] Reservation Wage - + (AriVe(w = w + (/-q)Ve(w)+qVe ↳ Multiplying the two sides by 1 + r and rearranging the terms of this expression, we find that: rVe (w) = w + q [Vu Ve (w)] This implies: r[Ve (w) -Vn] = w - q[Ve(w)-Yn]-wV 3 w rVu 7 Ve (w) Vu = (1) = r+q Recall that a job seeker accepts a job offer if Ve (w) Vu (think of Un as the outsole From Equation (1), Ve (w) Vu implies: sprion if you don't ↓ w rVu accept the offer) Accept if Ve(w) Un e - reservatou we wage which means Jeanne Tschopp Topic 3.2: Job Search 9/ 29 Reservation Wage This implies that the worker will accept a job offer at wage w if w is greater than rVu , i.e. if the value of remaining unemployed is lower than the value of becoming employed The reservation wage can therefore be defined as: x = rVu (2) If the incoming job offers entail wages below the reservation wage ) optimal to keep searching (and hence remain unemployed) Jeanne Tschopp Topic 3.2: Job Search 10/ 29 Example Reserverhou wage There is an St% proba that a worker accept the offer Jeanne Tschopp Topic 3.2: Job Search 11/ 29 Expected Utility of an Unemployed Worker: Vu We saw that x = rVu , so the reservation wage depends on the value of being unemployed. What is Vu equal to? In any given period, an unemployed worker may: unemployment - Receive unemployment benefits and enjoy utility from leisure 3 Z benefits : - But also has to pay costs related to the search for a new job - search costs All these costs and benefits are summarized by z, which denotes the net “income” for the unemployed Jeanne Tschopp Topic 3.2: Job Search 12/ 29 Expected Utility of an Unemployed Worker (con’t) Suppose that with probability , a worker gets a job offer at the end of a period: - The value of this job offer is V - Note that this is the value of a job offer, not the value of being employed With probability 1 the worker does not receive a job offer - Continues to be unemployed - Receives Vu Therefore, the expected discounted utility Vu of an unemployed person is: 1 Vu = [z + V + (1 )Vu ] 1+r mempl benefits. ↓ rVu = z + [V Vu ] (3) e ↑ cursibleoption arnual rate of pbs reservenon wage = Jeanne Tschopp Topic 3.2: Job Search 13/ 29 Illustration: Vu Unemployed -> t V collect memp! benefits and pay the costs related to the Karch - tt1 Z ↳ : job offer aunual rate 1- EOGENOUS ~ L ngrejectV offer the Stay andune en Ac on : : Hence, be summanted the expected discounted miling of unemployment cam by the flowing Bellman equation : v me Un = Er [z + (1-3) Va + x - Vx] Expected Utility of an Unemployed Worker (con’t) What is the value of a job offer V ? Not necessarily the value of employment as a job offer may be rejected w ⇠ H(w), where H(w) is the wage distribution If the job offer entails a wage w < x, the worker: - rejects the offer - remains unemployed If the job offer entails a wage w > x, the worker: - accepts the offer - receives the value of employment at wage w: Ve (w) Z resou Wage. x Z +1 ) V = Vu dH(w) + Ve (w)dH(w) (4) - 0 0x - of releching · job offers... Disc eap Value.. of accepting Jeanne Tschopp job offers Topic 3.2: Job Search 15/ 29 Expected Utility of an Unemployed Worker (con’t) Plugging (4) into (3) gives: Z x Z +1 rVu = z + Vu dH(w) + Ve (w)dH(w) Vu 0 x  Z +1 rVu = z + H(x)Vu + Ve (w)dH(w) Vu x Z +1 rVu = z + Ve (w)dH(w) (1 H(x))Vu x Z +1 Z +1 rVu = z + Ve (w)dH(w) Vu dH(w) x x Z +1 rVu = z + [Ve (w) Vu ] dH(w) (5) x This shows that the value of unemployment depends on the net income received while unemployed z, on the probability of receiving a job offer and on the value of different acceptable job offers (i.e. offers with a wage above x). Jeanne Tschopp Topic 3.2: Job Search 16/ 29 Reservation Wage Plugging (2) into (1) we have: w x Ve (w) Vu = (6) r+q And plugging (6) into (5) and using the fact that rVu = x we have: Z +1 x=z+ (w x)dH(w) (7) r+q x It is possible to show that there is a single value of x that solves the above equation; thus there is a unique solution for the reservation wage Intuition: the reservation wage depends on the: - Utility obtained while unemployed z - Expected value of what the job search can yield above the reservation wage Jeanne Tschopp Topic 3.2: Job Search 17/ 29 Reservation Wage: Comparative Statics Let the following implicit function define the reservation wage (comes from 7): Z +1 (x, z, r, , q) ⌘ x z (w x)dH(w) = 0 r+q x The partial derivatives of the function possess the following properties: x > 0, z < 0, r > 0, < 0, q >0 The condition = 0 implies that @x/@i = i/ x, i = z, r, , q, and using the implicit function theorem we get: @x @x @x @x > 0, > 0, < 0, 0: A higher utility from unemployment z (for example due to higher unemployment benefits) increases the reservation wage @x @r < 0: A higher discount rate r, meaning that people value the future less, decreases the reservation wage; people want to start earning a wage sooner rather than searching for longer @x @ > 0: A higher probability of receiving a job offer increases the reservation wage, because it increases the value of searching for a job @x @q < 0: A higher rate of job loss q decreases the reservation wage: - When q is high, jobs are at a higher risk of being destroyed: the value of waiting for a good job offer is lower, because the good job will not last long - When q is low, jobs are expected to last for a very long time: there is a stronger incentive to keep searching in the hopes of getting a very good wage offer Jeanne Tschopp Topic 3.2: Job Search 19/ 29 Hazard Rate and Unemployment Duration Hazard rate f : exit rate from unemployment, or equivalently job finding rate A worker will exit unemployment if: 1 She receives a job offer ! occurs with probability 2 The job offer is above her reservation wage ! occurs with probability [1 H(x)] (i.e. probability that w > x) ) Hazard rate: f = [1 H(x)] The average duration of unemployment is inversely proportional to the hazard rate (since loss of work follows a Poisson process): 1 Tu = [1 H(x)] E.g.: If an individual has a one in ten chance of exiting unemployment in any given week, she will on average remain unemployed for ten weeks Everything else equal, a higher reservation wage reduces the hazard rate and increases unemployment duration Jeanne Tschopp Topic 3.2: Job Search 20/ 29 Aside: How Is the Unemployment Duration Obtained Instead of considering continuous time, assume time is discrete (McCall model) Proba of getting a job : f Proba of being unemployed for n periods: P(duration = n = (1 f )n 1 f Expected unemployment duration: 1 X 1 E(duration) = n(1 f )n 1 f = f n=0 In continuous time, job offers arrive at a rate ↵ following a Poisson distribution and we get 1 Tu = [1 H(x)] Jeanne Tschopp Topic 3.2: Job Search 21/ 29 Link with Job Finding Rate Recall that the job finding rate in this model is given by: f = [1 H(x)] Increases in z, decreases in r, and decreases in q increase the reservation wage, and would therefore decrease the job finding rate and increase unemployment duration. An increase in has an ambiguous effect on the job finding rate and on unemployment duration, because it increases the probability of receiving a job offer, but it also increases the reservation wage, which decreases the probability that an offer is accepted. Jeanne Tschopp Topic 3.2: Job Search 22/ 29 Link with Unemployment Rate Recall from the previous class that the steady state unemployment rate is given by: q u⇤ = q+f where q is the separation rate and f is the job finding rate In the job search model: q is exogenously given f is endogenous; as discussed above, it depends on: i. the probability of receiving a job offer, : ambiguous effect on f ii. the probability that the job offer will be acceptable, which is a function of the reservation wage x: " x ) # probability of receiving an acceptable job offer ) # f Jeanne Tschopp Topic 3.2: Job Search 23/ 29 Link with Unemployment Rate (con’t) Implications: " z ) " x ) # f ; no effect on q, so " u⇤ " r ) # x ) " f ; no effect on q, so # u⇤ " : effect oon u⇤ is ambiguous " q: " q ) # x ) " f ) # u⇤ But " q ) " u⇤ Total effect on u⇤ is ambiguous Jeanne Tschopp Topic 3.2: Job Search 24/ 29 Extension: Directed Search Directed Search The model that we have just discussed is known as a random search model, because workers cannot target specific jobs. Workers only randomly receive job offers from different firms that pay different wages. An analogous model can be obtained allowing for directed search, i.e. the idea that workers target specific jobs. - Workers choose which jobs to apply for. - Applying is costly, so workers can only apply for one job. - Employers receive applications from the workers, and since all workers are homogeneous and equally qualified for the job, they pick a candidate randomly out of the pool of applicants and offer them the job. Jeanne Tschopp Topic 3.2: Job Search 23/ 29 Directed Search The probability that any given worker is offered the job that they apply for depends on the total number of applicants for that job. The expected value of an application depends on the probability of getting the job and the payoff from that job (wage). What will happen in equilibrium? - Workers would like to get the job that pays the highest wage, but since all workers want this job, it will attract a lot more applicants. - Therefore, if a worker chooses to apply to a high paying job, the probability that they will get a job offer is low. - Meanwhile, if a worker chooses to apply to a low paying job, the probability that they will get a job offer is high. - In equilibrium, the number of applicants for each job will adjust until the point where the expected value from all jobs is the same and workers are indifferent between applying to any given job. Jeanne Tschopp Topic 3.2: Job Search 24/ 29 Directed Search In equilibrium workers, even though workers have the option of directing their search, there is no incentive to actually do so, as they are indifferent between all jobs. Hence this setup can be thought of as being equivalent to the random search model. The implications discussed earlier about the reservation wage are the same in this context. Jeanne Tschopp Topic 3.2: Job Search 25/ 29 Extension: On-the-Job Search On-the-Job Search So far, we assumed that unemployed people can look for a job, but employed workers cannot look for a new job In practice, people often move from one job to another without ever becoming unemployed: there is on-the-job search We now extend the model to allow for on-the-job search For simplicity, we assume that searching for a job is costless for employed workers, so all employed workers have a chance of receiving job offers Jeanne Tschopp Topic 3.2: Job Search 26/ 29 On-the-Job Search An employed person receives a job offer with probability e As before, her current job may end with exogenous constant probability q Ve (w) now becomes: Z +1 rVe (w) = w + q [Vu Ve (w)] + e [Ve (⇠) Ve (w)] dH(⇠) w Jeanne Tschopp Topic 3.2: Job Search 27/ 29 On-the-Job Search Let u denote the arrival rate of job offers for a job seeker As before, Vu satisfies: Z +1 rVu = z + u [Ve (⇠) Vu ] dH(⇠) x This implies: Z +1 x=z+( u e) [Ve (⇠) Vu ] dH(⇠) x Compared to the basic model, this equation indicates that the value of search is proportional to the difference ( e u ) of the rates with which job offers arrive Jeanne Tschopp Topic 3.2: Job Search 28/ 29 On-the-Job Search Intuitively, the reservation wage will be lower if we allow for on-the-job search In the model with no on-the-job search, one of the advantages of being unemployed is the option of searching To the extent that job seekers can take a job and continue to search, this reduces the value of unemployment and makes it more appealing to take a job, even if it is low-paying In the limiting case where u = e, we will have that x = z In the case where e > u, the reservation wage falls below z - If it is easier to find jobs when you are already employed, individuals will have an incentive to take any job in order to have a higher change of “climbing up the ladder” to better jobs Jeanne Tschopp Topic 3.2: Job Search 29/ 29