Job Search Part 3: Modeling A Recession with Unemployment Insurance Benefits

Let's look at what happens in a recession spurred on by an adverse financial shock (most of the search literature would say that recessions are caused by productivity shocks which fits in nicely with labor market dynamics.  I have chosen to instead attribute this recession to a financial shock which is substantially more realistic and at least graphically still consistent within this framework). Say that a financial shock occurs, maybe a series of bank failures makes financial institutions more risk adverse and less likely to lend.  Firms that have to borrow money from commercial banks in the commercial paper market may find themselves in a squeeze as liquidity dries up (Some  companies maintain day to day operations by borrowing from the commercial paper market).
Figure A: Downward shift in Vacancy-Suppy curve Lowers Labor Market Tightness, θ

Businesses have to cut back and hire less people than previously anticipated. This can be witnessed in Figure A where the vacancy-supply curve shifts downward from VS1 to VS2. We move from point A to B and workers face a lower market wage (w* to w1). As Figure B demonstrates the decrease in labor market tightness rotates the job creation curve clockwise from JC to JC1.
Figure B: Downward Rotation of the Job Creation curve increases Unemployment

The rotation happens because the job creation curves slope which is labor market tightness θ, is now less than before so we move along the Beveridge curve from point A1 to B1. The vacancy rate declines from V* to V1 and the unemployment rate increases from U* to U1.

          In recessions, more workers find themselves in the pool of unemployed and tap into unemployment insurance to sustain their consumption levels while searching for new employment. With unemployment insurance benefits workers find themselves in a better position when unemployed which allows them to negotiate a higher wage. As a result, firms have a lower incentive to open vacancies because they would make lower profits off of them. As witnessed in Figure C this results in a rightward shift of the wage-setting curve from WS1 to WS2 and movement along VS2 from B to C. The resulting increase in unemployment benefits increases wages but reduces market tightness from θ1 to θ2. Workers claim a higher wage because the cost of unemployment is lower. Higher wages induce firms to create fewer jobs and lead to reduced labor market tightness. 
Figure C: Rightward Shift of Wage-Setting Curve

As Figure D demonstrates the job creation line rotates clockwise from JC1 to JC2 as we move along the Beveridge curve from B1 to C1 thus reducing vacancies and increasing the unemployment rate. Wages increased from w1 to w2 and the unemployment rate increased from U1 to U2. 
Figure D: Clockwise Rotation of JC curve and an Outward Shift of the Beveridge curve

Increases in the generosity of benefits, either through increases in benefit levels or the duration of benefits, seem to lengthen the unemployment spells of unemployment insurance recipients (for more information on Unemployment Insurances effects on unemployment please refer to Babcock, Congdon, Katz, and Mullainathan (2010)).
          As previously stated, more generous unemployment benefits like extending unemployment insurance to 99 weeks, also slows down the time it takes to match workers and firms. Individuals may not be all too optimistic when they form expectations about wages and consider their possible employment opportunities. This negative bias will cause many unemployed workers to be more lackadaisical when searching for a job and search with a lower intensity because they have more time till their income stream dies out (empirical work by Krueger and Mueller (2008) supports this claim as they find, using time use data, that across the 50 states and D.C. job search intensity is inversely related to the generosity of unemployment benefits with and elasticity between -1.6 and -2.2).
Furthermore, workers tend to set inefficiently high reservation wages in response to more generous unemployment benefits. When given the false sense of confidence and self worth brought on by more generous benefits the unemployed become more selective in terms of the type of job and wage they will accept (although, Krueger and Mueller (2008) find that the predicted wage is a strong predictor of time devoted to job search with an elasticity in excess of 2.5).
          Because of these effects the Beveridge curve BC1 shifts outward to BC2 along the job creation curve JC2.  This means that for the given labor market tightness θ2 we have a greater number of vacancies and a higher unemployment rate.  In Figure D above we move from C1 to D1 as unemployment increases from U2 to U3 and the vacancy rate settles back at its previous level, V2. One important fact to realize is that the shift to BC2 is only temporary because those unemployment insurance benefits can't last indefinitely.  When unemployment insurance benefits get close to expiring, logic would suggest that the unemployed would pick up their searching intensity as they realize that time is running out. In fact, research by Krueger and Mueller (2008) tells us that job search intensity for those on unemployment insurance increases prior to benefit exhaustion. This increase in search intensity would shift the Beveridge curve back to BC1.