1 Job Search Models

2 In economics we have a general rule of behavior that says engage in an activity up to the point where the marginal benefit is equal to the marginal cost. When you first saw this rule it was probably related to how much output a firm should make. Here we want to look at a variant of the rule that guides folks in understanding how many firms they should search in an attempt to land a job. The Fixed Sample Search Model. COST – It is assumed that the cost to a job searcher of each firm searched is a constant amount c. The total cost of searching n firms is cn and the marginal cost of searching another firm is c. Let’s look at the marginal cost in a graph on the next screen.

3 Number of firms searched $ Marginal expected cost = mec =c (the constant) What does it cost you to check out a firm for a job? You have to research the company and maybe drive there. Maybe you even send a resume. It is assumed the cost is the same for each firm searched.

4 BENEFITS To explore the benefits of the job search we will look at an example. Say there are two types of companies out there. Half have starting pay of 20,000 and half have starting pay of 30,000. The job applicant does not know what type of firm each firm is until the potential worker has checked out the company. The expected (yearly) wage from searching only one firm is.5(20,000) +.5(30,000) = 25,000. By the way, the expected wage is the probability that each type of firm would be found times its pay and add the multiplications across all firms. The expected wage from searching only two firms is.25(20,000) +.75(30,000) = 27,500. Let’s think about how we obtained this amount. On the next slide we start with the possible wage offers the worker could get when two firms are searched.

5 (20,000 20,000) (20,000 30,000) (30,000 20,000) (30,000 30,000) If a person checks two firms, and if they pick the job that pays more between the two, then only 25% of the time will they get a 20,000 job. 75% of time they would get a 30,000 job. Next I have a table where we list the expected wage for various numbers of firms searched.

6 Firms searchedprob. Of prob. Of expected wage meb 20k offer 30k offer 1 ½ ½ ½(20k) +1/2(30k) = 25,000 xxx 2 ¼ ¾ 1/4(20k) +3/4(30k) = 27,500 2, /8 7/8 1/8(20k) +7/8(30k) = 28,750 1, /16 15/16 1/16(20k) +15/16(30k) = 29, The last column, meb, or marginal expected benefit, is the additional wage the person can expected if they expanded their job search by 1 additional firm. As you can see the amount is not the same for each firm added to the search. Note, I said the cost of search per firm searched was a constant. In that sense it is known with certainty, but I mentioned the marginal expected cost because on the benefit side we have uncertainty. Let’s graph both the mec and meb on the next slide.

7 Number of firms searched $ mec n* is the optimal number of firms searched because after that point the expected benefits of additional search are outweighed by the cost of the search. meb n*

8 What happens to the optimal number of jobs searched if the cost of job search rises? Well, in the graph the mec would rise and thus the curves would cross at a lower point – search less firms. This makes sense because if the cost of additional search rises then you would expect fewer of the searches to have high enough additional benefits to overcome the cost. Some dude named Stigler – a university of Chicago chap, dead now a few years – showed if wage offers follow a normal distribution with mean offer wmean, and standard deviation sigma, then the meb =.24(sigma)/n raised to the power On the next slide let’s see a graph when sigma = 1 and the cost of searching a firm is a little over 7 cents.

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10 Here I show that if the standard deviation of the distribution is larger the marginal expected benefit curve shifts right and the optimal number of firms search would rise. The basic logic behind this result is that when the standard deviation rises the probability of getting a high paying job rises. When you look back at our table the expected wage is sensitive to the probability of a high paying job. If the probability goes up then the meb will go up as well.

11 Some have criticized the fixed search model as unrealistic. Their logic is that although there is a distribution of wages, some will get a high wage relatively early in the search and thus stop way short of searching n* firms. The criticism suggests that the search should really stop after a certain wage has been offered. We turn to this idea next. Sequential Search Model We are going to look at an example here to motivate our discussion. Say you have 10 weeks in your summer vacation and you will go to a resort area to get a job. The time line below shows your ten weeks. If you take a job at time zero you will work the whole ten weeks. If you wait and not take a job until time 1 you will only have 9 weeks left to work, and so on

12 In our example say you will get one job a week and if you reject it you will have to wait a week for another offer. Say there are four types of jobs. The difference is that the pay per week over your room and board will be either 100, 120, 130, or 140 and the probability of getting any type of job is ¼. Before you take a job at time zero, let’s think about the expected value of continuing the job search until time period 1 (the beginning of the second week). Job typeincome over the 9 weeks 100 job job job job1260 The expected value of continuing the job search is ¼(900) + ¼(1080) + ¼(1170) + ¼(1260) =

13 The $ is called the reservation wage at time zero by the authors. This wage makes you indifferent between accepting a job at time zero and continuing the search into the next period. On a weekly basis the reservation wage is So, the only offer that should be rejected at time zero is the offer of 100. Ways the reservation wage - wr -can change 1) If there are out-of-pocket costs when not working then wr would be lower. In our example, if room and board is $100 per week then you would subtract the 100 from the ) Sources of nonlabor income like unemployment benefits increase wr. Say your parents pay your room and board the first week and give you 20. wr = ) wr changes if the payment distribution changes – we need to see the changes before more can be said about the impact. 4) wr changes if the probability distribution changes - wr rises if the distrubution becomes more disperse – similar to the Stigler story. 5) Wr is lower the longer you are unemployed. Consider waiting until time 2 to take a job The expected wage is then 980.

14 Because of the criticism of the fixed sample search model we said the focus should be on the wages offered and not the number of firms searched. In our graph we will switch from the number of firms searched on the horizontal axis to the value of the reservation wage. Our behavioral rule is still the same – continue to search until the mec = meb, but the connecting point is the reservation wage not the number of firms searched. More formal model Assume Searchers are unemployed No unemployment bennies or welfare Looking for a lifetime job Each period one firm is searched at a constant cost c Same wage offer distribution and cost occurs each period

15 Digress: the uniform distribution The uniform distribution is one where the probability of any set interval within the distribution is the same no matter where the interval is placed. As an example, say the arrival time of a plane from Chicago is uniform over the time period 1 hour after take-off to 1 hour and 30 minutes after take-off. The probability of landing between 1 hour and 5 minutes to 1 hour ten minutes after take-off would be the same as from 1 hour ten minutes to 1 hour 15 minutes after take-off = 1/6. minutes density 1/30 Probabilities are areas here. 5 minute intervals have an area = 1/6

16 Say wage offers are uniformly distributed over the range 0 to $1. In the graph below I have put in a value for wr arbitrarily, but we use it as a reference point. The probability a wage is above wr is 1-wr. The average wage above wr is (1+wr)/2, so the marginal expected benefit is (1-wr)(1+wr)/2 = ((1-wr)^2)/2. dollars 0 1 density 1 wr wr 1-wr

17 So in our example, if meb = ((1-wr)^2)/2 and if we have mec = c, then the point of equality is the wr where ((1-wr)^2)/2 = c, so wr* = 1-sqrt(2c). Remember this is just for the uniform distribution. We switch to the graph for the more general setting. $ wr c ((1-wr)^2)/2 wr*

18 Impact on the optimal reservation wage to changes in the world 1) Higher search cost – means wr* would be lower because the mec shifts up. 2) Bringing in nonlabor income and unemployment bennies here is like a lowering of the search cost – wr* rises. 3) If a wider distrubution of wage offers occurs then the probability of getting a high paying job rises and meb shifts right – so wr* rises. Implications for unemployment Some unemployment may be voluntary and may be good in the sense that the job ultimately taken has higher marginal product – meaning more output results.