Employment, Unemployment and Turnover D. Andolfatto June 2011
Introduction In an earlier chapter, we studied the time allocation problem max { ( ) : = + + =1} We usually assume an interior solution; i.e., 0 ( ) 1 In reality, many people appear be at a corner solution; i.e., ( ) =0 People with =0(over the previous 4 weeks) are labeled nonemployed People with 0 (over the previous 4 weeks) are labeled employed
Over short periods of time, many people make transitions into and out of employment in Canada, roughly 1.5 million workers per month relative to an average employment level of 17 million workers these gross flows of workers largely cancel over time (relative to population growth), but exhibit both cyclical and seasonal variation e.g., in a recession, E N flows (job loss) increase and N E flows (job finding) decrease implies net decrease in employment (with net changes much smaller than gross flows)
Modeling employment turnover For simplicity, assume that time is indivisible; i.e., =0or =1 Then the time allocation problem is simple: choose the action that yields the highest utility payoff Payoff to employment ( =1)is = ( + 0) Payoff to nonemployment ( =0)is = ( 1) There exists a number ( ) that satisfies ( + 0) = ( 1)
Optimal employment decision takes the following form: = ( 1 if ( ) 0 if ( ) ( ) is called a person s reservation wage the minimum wage that would induce a person to work (a measure of choosiness ) theory suggests that reservation wage is an increasing function of (nonlabor income or wealth)
People with different ( ) characteristics will make different employment choices high low individuals more likely to be employed low high individuals more likely to be nonemployed note: theory can be extended to include differences in the valuation of leisure Turnover (gross flows of workers into and out of employment) can be generated by assuming that people experience idiosyncratic shocks to ( ) over time Large gross flows of workers consistent with even a constant level of employment
Policy implications In this model economy, people cannot save or insure themselves In reality, insurance markets hampered by asymmetric information problems (an insurance company may have difficulty in ascertaining the true value of and for individuals, and individuals have an incentive to misreport these values) In this model, the lack of insurance results in too much employment (people are less able to afford home production) In principle, a tax-financed consumption-insurance program could be welfareimproving
Why does average labor productivity sometimes increase in a recession? Unlike other G7 economies, labor productivity actually rose in the U.S. in the last recession (see Figure 4, Andolfatto and Williams) One explanation is that low-skilled workers are more likely to exit employment during a recession (especially in a flexible labor market, like the U.S.) So even if everyone s productivity falls, the average productivity of those whoremainemployedmayincrease This is sometimes referred to as composition bias
Unemployment About 60% of the adult (16+) population is employed; about 40% are nonemployed, or jobless Nonemployment is not the same thing as unemployment Standard labor force surveys ask people whether they ve done any paid work in the previous 4 weeks If answer is no, they then ask questions relating to job search activities Nonemployed persons who are not looking for work are classified as nonparticipants
Job vacancies A job vacancy corresponds to an unemployed job from the perspective of a firm At any given time, job vacancies coexist with unemployed workers Why do firms with vacant positions not hire unemployed workers until unemployment rate falls to zero, or supply of vacant positions is exhausted? Modern view is that labor markets operate more like decentralized marriage markets, as opposed to centralized commodity markets
Jobs and workers need to be properly matched; do not want to match with first partner that comes along Time and resources must be consumed in finding the right partner Some luck is involved, and it generally does not make sense to wait for the perfect partner The typical optimal strategy is to set a reservation quality level (reservation wage is an example) if the partner you contact meets or exceeds a minimum set of criteria, then accept any proposal
A dynamic model of unemployment Imagine a world populated by firms and workers, with time =0 1 2 There are many firms, each with a single job that must be occupied by a worker if output is to be produced At any point in time, firms are either active, vacant, oridle Workers have one unit of time; they use it to work (if employed) or search (if nonemployed) i.e., workers do not value leisure
An employed worker and active firm jointly produce output Wages and profits are determined by a bargaining rule that divides the joint output in some manner; e.g. forsomeexogenous0 1 = = (1 ) Job-worker relationships breakdown with probability 0 1 in each period Firms discount expected future profits by factor 0 1
Let denote the value of an active firm at date = + (1 ) +1 + 2 (1 ) 2 +2 + = + (1 ) +1 Since =(1 ) it follows that = +1 = (constant); solving... = " 1 1 (1 ) # The value of a worker to a firm is: increasing in decreasing in increasing in and decreasing in Note: is labor share of income (bargaining power of labor); expected duration of employment is 1 ; real interest rate is =1 1
The matching process Unmatched workers and firms must search for each other (recall marriage market) Let denote unemployed workers and let denote vacant jobs, and define (labor market tightness) Assume that there is an aggregate matching technology that relates aggregate search intensity ( ) to aggregate matches ; i.e., = ( ) where is increasing in ( ) and displays constant returns to scale (CRS)
CRS implies = ( 1) ( ) = (1 1 ) ( ) Can interpret and as match probabilities is an increasing function of while is a decreasing function of Note: these properties reflect congestion effects e.g., it becomes more difficult for firms to find workers when there are a lot of vacancies (relative to available workers)
Recruiting intensity Because workers do not value leisure, nonemployed workers choose to search for work (which is what makes them unemployed); hence, measures aggregate search effort for workers Let me now describe how is determined Assume that idle firms generate zero value An idle firm can decide to become a vacant firm at some cost (a recruiting cost)
What is the expected payoff to vacancy creation? Contact an unemployed worker with probability ( ) Begin producing output in period +1 So creating a vacancy makes sense if ( ) Assume that idle firms will continue to enter (as vacancies) until it is no longer profitable to do so; i.e., ( ) =
The condition above (free-entry condition) determines equilibrium = is an increasing function of and a decreasing function of Since is predetermined as of date once is determined, we can then determine equilibrium recruiting intensity =
Employment/unemployment dynamics Let denote labor force; = + The level of employment at a point in time is predetermined (like the capital stock) We can derive a stock-flow equation to describe employment/unemployment dynamics Beginwithstock add flow in (job creation) ( )( ) subtract flow out (job destruction) +1 = ( ) +(1 ( ))
If 1 (1 ( )) 1 then employment dynamics are stable for any given 0 employment converges to a steady-state If 1 (1 ( )) 0 then the dynamics oscillate If 0 (1 ( )) 1 then the dynamics converge monotonically The natural level of employment can be solved by setting = +1 = = Ã ( ) + ( )!
Similarly, the natural rate of unemployment is Ã! = Ã + ( )! depends directly on and also on whatever parameters influence the equilibrium depends on and depends on etc. Easy to verify that is a decreasing function of Can interpret as any factor that influences the business sector s expectation of the return to job creation (e.g., productivity, tax policy, etc.)
Some observations Unemployment here has nothing (directly) to do with wage inflexibility or labor markets that do not clear unemployment is the natural byproduct of search and matching the nature of the wage bargain may influence the equilibrium unemployment, but is not the direct cause of unemployment Zero unemployment is not socially optimal In general, the equilibrium unemployment may be either higher or lower than the socially optimal rate
The Beveridge Curve Refers to an alleged negative correlation that exists between and (interpreted as the byproduct of cyclical shocks ) Movements off the (alleged) Beveridge curve are often interpreted as the consequence of structural shocks
Cyclical asymmetry in unemployment rate dynamics Unemployment rates typically spike up sharply in recession, and decline only slowly during recovery/expansion
Unemployment duration Most unemployment spells are relatively short...but long duration spells have been increasing since the past recession
Current policy debate over the labor market Employment has slumped in the U.S. and shows little sign of recovery A similar phenomenon for Canada in early 1990s
People almost universally believe that employment is too low but does anyone really know what the socially optimal employment rate is? In any case, if employment is too low (unemployment too high), then why is this the case? Keynesian interpretation is that aggregate demand is too low Why? Private sector is (irrationally) afraid to invest and recruit Policy prescription: government should step in and create demand
There are many alternative interpretations depressed expectations are rational expectations of bad policy structural rearrangement of sectoral demands takes time to work through (cannot transform construction workers into nurses) Warnings against Keynesian policies government demand largely crowds out private demand requires raising taxes and/or debt, providing a further drag on private incentives to invest Nobody really knows for sure, so some degree of caution (and humility) is in order