Question

Consider the labor market model studied in class. Recall that the law of motion for unemployment is given by "u_{t+1} - u_t = s(1 - u_t) - fu_t," where "u_t" denotes the unemployment rate in period "t," "s" is the job separation rate, and "f" is the job finding rate. Assume that the labor force is normalized to one, and hence the unemployment rate is equal to the number of unemployed workers. The job separation rate equals "s = 0.03" per period.

A. Derive formulas for the job finding rate "f" for workers and the vacancy filling rate "q" for firms in terms of labor market tightness "θ = v/u." Is the firm vacancy filling rate "q" increasing or decreasing in market tightness? Provide economic intuition for your answer.

B. Suppose that the value of a filled job is "J = 4," and the cost of posting a vacancy is "c = 2." What is the equilibrium labor market tightness "θ"? Given this value for market tightness, calculate the job finding rate "f" and the steady-state unemployment rate "u."

C. Suppose the economy enters a recession, and the job separation rate increases to "s = 0.05." Calculate the new equilibrium values of unemployment and vacancies. Provide economic intuition for your answers.

D. Evaluate the claim that "recessions are caused by high job separation rates" considering your answers to part (C). [Hint: Think about the movements in market tightness, unemployment, and vacancies and their cross-correlation when the job separation increases. Are the implications consistent with the empirical Beveridge curve we saw in class?]

Answer 1

In the labour market model, the vacancy filling rate q decreases as labor market tightness increases because there are more vacancies than unemployed workers. Calculating exact values for labor market tightness, job finding rate, and steady-state unemployment requires additional specific formulas, which are not provided. High job separation rates, as seen in recessions, can lead to more unemployment but are only one of the many factors contributing to a recession.

Step-by-step explanation:

In the context of the labour market model, the job finding rate f and the vacancy filling rate q can be derived in relation to the labor market tightness θ = v/u. The firm vacancy filling rate q is equal to the ratio of the job finding rate f to the labor market tightness θ, which means q = f/θ. As labor market tightness increases, the vacancy filling rate q for firms decreases because there are more vacancies compared to unemployed workers, making it harder for firms to fill each vacancy. This provides the economic intuition that as vacancies become abundant relative to unemployed individuals, each individual vacancy is less likely to be filled in a given period.

Given a filled job value J = 4, and a vacancy posting cost c = 2, we can infer the equilibrium labour market tightness θ from the ratio J/c. However, since specific formulas or details were not provided in the question or reference material, the exact calculation cannot be made without additional information. Similarly, to calculate the steady-state unemployment rate u, knowledge of how u reacts to changes in f and θ is required. Again, additional models or formulas are needed to proceed.

In a recession, when the job separation rate s increases to s = 0.05, there's a higher rate of workers leaving their jobs, which would typically result in higher unemployment and potentially more vacancies within the economy. However, without a specific model to determine how these values change, an exact numerical answer cannot be provided. Economic intuition suggests that higher separation rates lead to more unemployment and can either increase or reduce vacancies depending on how firms adjust to the economic downturn.

Evaluating the claim that recessions are caused by high job separation rates, this assertion partially fits the model. Increased job separation rates result in higher unemployment, which is characteristic of recessions as represented in the Beveridge curve. However, it is just one of many factors that can contribute to a recession, and so the claim is an oversimplification of the complex dynamics that cause an economy to enter a recession.