PACC6007 Economics
Task:
In this project you will be using data to determine appropriate values of parameters to use in the Pissarides model of equilibrium unemployment. The data is taken from a recent paper by Elsby, Michaels and Ratner (Sept. 2015 issue of the Journal of Economic Literature). Taking the parameter values estimated from the data, you will then simulate the model and examine its implications for the unemployment rate, vacancy creation, the job filling probability and the job finding probability in response to particular shocks that hit the labour market.
Consider the Pissarides model of equilibrium frictional unemployment that we studied in class. Suppose that the job separation rate, δ, is constant over time. In the version of the model studied in this project, labour productivity will vary across time. In addition, the matching function takes on a Cobb-Douglas form so that ξ follows an AR(1) process and the shocks to this AR(1) process are normally distributed with mean zero and variance We will also assume that labour productivity is exogenous.
In solving the model numerically, we will discretize the state-space for A and ξ so that instead of A ∈ R, we will have A ∈ A where A := {A1, A2, ..., AnA}. Similarly, ξ ∈ Ξ with Ξ := {ξ1, ξ2, ..., ξnξ }. Both A and ξ will evolve following a Markov-chain. Let ΠA denote the matrix of transition probabilities for A while Πξ denotes the matrix of transition probabilities for ξ. The typical element of ΠA will be π(A0, A) which is the probability that given a level of productivity a = e A in the current period, labour productivity will equal a 0 = e A0 in the following period. There is a similar interpretation for the typical element of Πξ, π(ξ 0ξ). Letting θt , q(θt) := m(ut,vt) vtis the vacancy-filling probability. The job finding probability is then θtq(θt). As is derived in the class notes.
