Labor Market

by Professor Throckmorton
for Intermediate Macro
W&M ECON 304
Slides

Beveridge Curve

• "A Beveridge curve...is a graphical representation of the relationship between unemployment and the job vacancy rate."
• The U.S. job vacancy rate is measured by job openings (reported in the BLS Job Openings and Labor Turnover Survey, or JOLTS) as a share of the labor force.
• A common feature across countries is that job openings are high when unemployment is low (and vice versa), which influences the job finding rate and worker bargaining power over wages.

• Before a recession, unemployment is lowest and job openings are highest, which means workers have the most bargaining power.
• Immediately after a recession, the number of unemployed workers searching for work is highest while job openings is lowest, which means workers have very little bargaining power.
• Thus, worker bargaining power varies over the business cycle and is negatively related to the unemployment rate.

• Job openings as a share of the labor force is known as the job vacancy rate.
• Possible reasons for the BC shifting out: 1) lower matching efficiency or longer search times, 2) decreased turnover/churn in labor market, 3) sectoral/structural mismatch, 4) firms preferring to hire previously employed vs unemployed workers

Nominal Wage

• This series includes salaried workers but earnings do not include benefits.
• Nominal wage growth fell after Great Recession and increased in expansion.
• This series suffers from a composition effect, e.g., during COVID lower-income workers were more likely to become unemployed which drives up the average hourly rate in 2020 and 2021.

• Employment Cost Index (ECI) is a fixed-weight index of nominal employer hourly wage costs (excluding benefits) across a constant “basket” of occupations.
• Thus, it is not affected by composition changes.
• The growth rate of the nominal wage is clearly procyclical, i.e., it falls in recessions and rises in expansions.

• ECI, i.e., the nominal wage, is negatively correlated with unemployment rate.
• From AP/Intro Macro, this looks like an empirical version of the Phillips Curve, which we'll introduce the theory for in Part 4 of this class.

Wage and Price Determination

Wage setting is given by $W = P^e F(u,z)$

• $W$ is the nominal wage rate
• $P^e$ is the expected price level
  • if workers expect the price level to increase by $X\%$
  • $\rightarrow$ they will (eventually) demand an $X\%$ increase in $W$
• $u$ is the unemployment rate
  • In a recession, when $u$ is high, worker bargaining power (BP) is low,
  • $\rightarrow$ workers are willing to accept lower $W$
• $z$ are all other things that affect worker bargaining power, e.g.,
  • minimum wage
  • unemployment insurance benefits
  • laws that affect the collective bargaining power (of unions)
  • employment protections
  • foreign labor supply or automation
• If something besides $u$ leads to higher worker BP, then
  • it represented by $\uparrow z$
  • $\rightarrow$ worker can demand higher $W$

Production Function

• In the Solow Growth model, we assumed a Cobb-Douglas CRS production function, $Y = K^\alpha (AN)^{1-\alpha}$.
• The production function determines a firm's cost function, e.g., factor prices are equal to their marginal products when markets are perfectly competitive.
• For the labor market, we care about labor as an input and capital accumulation is more likely to be important for long-run growth than it is in the short to medium-run. Let's assume:
  • Constant productivity, $A = 1$.
  • Zero output elasticity of capital, $\alpha = 0$
• Thus our short to medium-run production function is $Y = N$, i.e., if $N$ is employment then each worker produces one thing.

Price Setting

• If $N$ is the only factor of production, then $W$ is the only factor price (i.e., marginal cost) paid by the firm.
• If the average firm competes in a monopolistic product market, then they have pricing power and receive positive profits in equilibrium.
• Denote a firm's profit margin (or markup) by the parameter $m$.
• Thus, price setting is given by $P = (1+m)W$, i.e., firms set price at a markup above marginal cost.

Wage-Price Spiral

• After the COVID shutdowns and the expansionary monetary and fiscal policy responses, there was a lot of inflation relative to the 20 years before COVID.
• In the labor market model, that is a situation where $P > P^e$, i.e., the actual price is higher than what worker's expected.
• Wage setting: Workers then begin to expect higher prices, $\uparrow P^e$, which eventually leads to them demanding higher wages $\uparrow W$ to maintain the buying power of their income.
• Price setting: Firms eventually pass the higher costs onto their customers, $\uparrow W \rightarrow \uparrow P$
• But when workers see prices rise again, they $\uparrow P^e$ and the loop repeats, which is the wage-price spiral.
• This is the theory behind a major debate about whether inflation following COVID would be transitory or permanent.

Labor Market Model

• The labor market model consists of wage and price setting equations \begin{gather*} W = P^e F(u,z) \\ P = (1+m)W \end{gather*}

• For equilibrium to exist, $P^e = P$, otherwise wages and prices are moving around (disequilibrium).

• Thus, we can rewrite both equations in terms of the actual real wage rate \begin{gather*} \frac{W}{P} = F(u,z) \\ \frac{W}{P} = \frac{1}{1+m} \end{gather*}

Unemployment

• In AP/intro macro, we learn that unemployment is either frictional, structural, cyclical or seasonal.
• The labor market is a medium-run model (with a 2-5 year horizon), so we can ignore seasonal unemployment.
• In a medium-run equilibrium, that natural unemployment rate ($u_n$) consists of frictional and structural unemployment.
• In the short-run, the unemployment rate fluctuates cyclically and can be less than or greater than the natural unemployment rate, e.g., the short-run unenmployment rate is above $u_n$ in a recession.

Medium-run Equilibrium

• The labor market in equilibrium determines the natural, or medium-run, unemployment rate, $u_n$. \begin{gather*} F({\color{red}u_n},z) = \frac{1}{1+m} \end{gather*}
• The short-run unemployment rate is moving toward $u_n$ in the medium-run.
• In a graph of the labor market, $u_n$ is at the intersection of WS and PS.

• In a recession, $u_{recession}$ is above $u_n$, and $u_{recession} - u_n$ is cyclical unemployment.
• At $u_{recession}$, the real wage offered by firms exceeds the real wage firms are willing to accept.
• Thus firms increase hiring and unemployed workers transition to employment.
• As the unemployment rate falls, workers can demand higher real wages.
• After a few years, the real wage firms offer equals the real wages workers want at $u_n$.

Experiment

• Suppose a policy increases worker bargaining power, $\uparrow z$.
• Workers demand higher real wages reflected by an increase in WS.
• At $u_n$, real wages demand exceed real wages offered, so workers quit to search for higher paying work, or firms layoff workers because they cannot afford to pay them.
• Employed workers transition to unemployment and the short-run unemployment rate increases to the new natural unemployment rate where there is more frictional unemployment in equilibrium than before.