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The Mortensen-Pissarides Model on Excel

November 1, 2018

You are asked to simulate dynamic equilibria of the Mortensen-Pissarides on Excel. While we focus almost exclusively on steady-state equilibria in class, dy- namic equilibria are simple to characterize. In any equilibrium, market tightness adjusts instantly to its new steady-state value:

θt = θ ∗ =

( A(y −w)

sk

)2 . (1)

Part I: Due at week 6 discussion section

We want to describe an economy transitioning from an initial steady state to a new steady state following a shock. In order to generate this transitional path, do the following:

1. Enter the exogenous variables corresponding to the initial steady state: A0, y0, w0, s0, and k0. (Assign one cell to each of these parameters in your Excel file.) Compute the initial steady-state equilibrium as:

θ0 =

( A0(y0 −w0)

s0k0

)2 ,

u0 = s0

s0 + A √ θ0 .

2. Take u0 as the initial condition for ut. Enter the new exogenous variables following a shock: A1, y1, w1, s1, and k1 (assign separate cells for parame- ter values following a shock). Compute the new market tightness, θ1, from (1). The law of motion for ut given u0 and the new exogenous variables is described by

∆ut+1 ≡ ut+1 −ut = s1(1 −ut) −utA1 √ θ1. (2)

Generate the sequence for ut and plot it.

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Part II: Due at week 7 discussion section

1. In order to choose realistic parameter values for the model, suppose the period of time is a month. The separation rate is 4%, s = 0.04. Normalize labor productivity to 1, y = 1. Suppose the wage corresponds to 80% of productivity, w = 0.8. We set the entry cost to k = 3. What is the value of A that would generate an unemployment rate of 5%? Take this list of parameter values as your initial steady state.

2. By how much would y have to fall to raise steady-state unemployment rate to 10%? Plot the transition.

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