Labor Economics. Basic Job Search Model. Winter 2014/2015. Bonn University

Transcription

1 Labor Economics Basic Job Search Model Petr Sedláček Bonn University Winter 2014/ / 32

2 Motivation Up until now focused on the classical theory of the labor market several important critiques most prominent one is the lack of unemployment has nothing to say about flows cannot explain coexistence of vacancies and unemployed 2 / 32

3 Motivation Search and matching theory provides an alternative with several appealing features taking into account the costly nature of job/worker search vacant jobs and unemployed can coexist unemployment plays a key role equilibrium flows, stocks and wages determined by individual optimization ( micro foundations ) framework for a consistent analysis of policy effects 3 / 32

4 Plan for today basic job search model (taking firm behavior as given) asset values (value functions) of being (un)employed reservation wage comparative statics 4 / 32

5 Setup Value of (un)employment Generalizing with probability of getting job offer Basic setup 5 / 32

6 Setup Value of (un)employment Generalizing with probability of getting job offer Model setup model for decisions of unemployed searching for job workers are risk neutral workers cannot change their intensity of search there is no on-the-job search assume discrete time we will focus on a stationary environment 6 / 32

7 Setup Value of (un)employment Generalizing with probability of getting job offer Model setup Unemployed search for jobs obtain benefits b (can be value of leisure) at the end of the period worker can get an interview firm offers a wage iid draw from wage distribution F (w) distribution is known to workers when worker accepts wage offer wage is constant over duration of job jobs last forever (discount with β = 1/(1 + r) < 1) 7 / 32

8 Setup Value of (un)employment Generalizing with probability of getting job offer Value of employment an unemployed worker has to decide when to accept a wage expected discounted wage income is V e (w) = t=0 βt w V e (w) = w 1 β 8 / 32

9 Setup Value of (un)employment Generalizing with probability of getting job offer Value of unemployment when unemployed get b and get wage offer at the end of the period EO(w) value of being unemployed V u = b + βeo(w) O(w) = max[v u, V e (w)] = max[b + βe[o(w)], w 1 β ] 9 / 32

10 Setup Value of (un)employment Generalizing with probability of getting job offer notice that b + βe[o(w)] does not vary with w w 1 β is increasing in w there is a unique point where both lines intersect, w r worker indifferent between working and not working worker accepts any offer w w r 10 / 32

11 Setup Value of (un)employment Generalizing with probability of getting job offer the reservation wage is defined as V e (w r ) = V u O(w) = wr 1 β for w w r O(w) = w 1 β for w > w r w r = (1 β)b + β 0 max[w, w r ]df (w) 11 / 32

12 Setup Value of (un)employment Generalizing with probability of getting job offer the above is an example of a contraction mapping implies that there is a unique solution to w r = T (w r ) the solution can be found by repeated iteration: wr 1 = T (wr 0 )... wr i = T (wr i 1 ) in the limit wr i T (wr i 1 ) 0 12 / 32

13 Setup Value of (un)employment Generalizing with probability of getting job offer To derive the reservation wage first write the value of unemployment as V u = b + β [V e (w) V u ]df (w) + βv u w r then rewrite the above as w r = b + β [w w r ]df (w) 1 β w r = b + β [1 F (w)]dw (1) 1 β w r 13 / 32

14 Setup Value of (un)employment Generalizing with probability of getting job offer in the Classical theory depends only on non-wage income and the value of leisure in Job search model a broader interpretation of b also includes the value of leisure reservation wage also depends on an additional term this captures the option to search β [V e (w) V u ]df (w) w r by accepting a job, the job seeker forgoes this option premium over the flow income in unemployment 14 / 32

15 Setup Value of (un)employment Generalizing with probability of getting job offer Probability of getting job offer so far we have assumed that jobs arrive every period we can generalize by assuming they arrive with probability λ will be a key element of the full search and matching model 15 / 32

16 Setup Value of (un)employment Generalizing with probability of getting job offer Probability of getting job offer the structure of the value of a job remains unchanged value of unemployment changes V u = b + λβ [V e (w) V u ]df (w) + βv u w r reservation wage changes accordingly 16 / 32

17 Changes in unemployment benefits Changes in the wage offer arrival rate 17 / 32

18 Changes in unemployment benefits Changes in the wage offer arrival rate response of reservation wage unemployment duration to changes in unemployment benefits job offer arrival probability 18 / 32

19 Changes in unemployment benefits Changes in the wage offer arrival rate Changes in unemployment benefits Assume increase in b reservation wage, i.e. workers become more picky reduces the probability that a given wage offer is accepted 19 / 32

20 Changes in unemployment benefits Changes in the wage offer arrival rate Changes in unemployment benefits one can write the reservation wage as w r = b + using Leibniz s rule we get dw r db = 1 + λβ [1 F (w)]dw 1 β w r λβ w r [1 F (w)]dw dw r 1 β w r db w r [1 F (w)]dw = (1 F (w r )) w r dw r db = λβ 1 β (1 F (w r )) > 0 20 / 32

21 Changes in unemployment benefits Changes in the wage offer arrival rate Changes in unemployment benefits What about unemployment duration? h = λ(1 F (w r )): probability of finding a job D = 1/h: expected duration of unemployment dd db? df (wr ) dw r > 0 dd dw r dd df (w r ) > 0 > 0 dd db > 0 21 / 32

22 Changes in unemployment benefits Changes in the wage offer arrival rate Changes in wage offer arrival rate An increase in λ (more frequent wage offers) directly decreases expected duration but, also an indirect effect via the reservation wage workers become more choosy increases reservation wage this in turn increases expected duration overall impact unclear? 22 / 32

23 Changes in unemployment benefits Changes in the wage offer arrival rate Changes in wage offer arrival rate Overall impact of changes in probability of job offer dw r dλ = β 1 β dh dλ = 1 F (w r ) λf (w r ) dw r dλ (1 F (w))dw w r λβ 1 β (1 F (w r )) dw r dλ dh dλ = 1 F (w β w r ) λf (w r ) r (1 F (w))dw 1 β + λβ(1 F (w r )) for most distributions, 1 F (w r ) > λf (w r ) β (1 F (w))dw wr 1 β+λβ(1 F (w r )) an increase in λ increases w r, but decreases the D 23 / 32

24 Job destruction 24 / 32

25 in reality accepted jobs of course do not last forever in the US the average job duration is 5 years in France, Germany and the UK it is 12, 11.1 and 8.8 years easily adjust the model to allow for this jobs are destroyed with probability ρ 25 / 32

26 expression for value of unemployment is unchanged the value of employment can now be written as V e (w) = w + β(1 ρ)(v e (w) V u ) + βv u 26 / 32

27 reservation wage now depends also on ρ an increase in ρ leads to a decrease in w r, because the option of searching decreases affects expected duration of unemployment, which falls 27 / 32

28 Basic idea Discouraged workers 28 / 32

29 Basic idea Discouraged workers Classical theory workers were either employed or not participating Job search theory workers either employed or unemployed (seeking employment) but there is no option to leave the labor market it is straight-forward to allow for this option 29 / 32

30 Basic idea Discouraged workers let V N be value of a non-participation let R N be the flow income derived from non-participation decision to participate compare the values of (non-)participation whenever V N V u, worker will participate and search for a job i.e. if w r R N the worker participates 30 / 32

31 Basic idea Discouraged workers participation depends on all the labor market characteristics increases in unemployment benefits lead to higher participation consistent with our model: dw r /db > 0 a decrease in λ associated with lower participation consistent with our setup: dw r /dλ > 0 31 / 32

32 Basic idea Discouraged workers Discouraged workers among non-participants distinguish between those who do not want to work for the current wage those who do, but give up - discouraged workers denote average wage offer as E[w] = wdf (w) discouraged workers characterized by w r R N E[w] 32 / 32