# Calibration of labor market frictions parameters

I want to refer to the following paper A Three State Model of Worker Flows.

My questions are regarding the calibration of parameters. First, I would appreciate any help when on p. 11 it says that $$\alpha$$ (disutility of work) is set so that the steady state value of employment is equal to 0.632.

Second, loosely speaking, let $$\sigma$$ be the exogenous job separation rate and $$\lambda_w$$ the exogenous arrival rate. This model is a variation of the standard growth model. In the calibration section, they mention the following: "We choose $$\lambda_w$$ so that the steady state unemployment rate in our model is equal to 0.083" (p. 11) and also that "for our benchmark case we target the flow rate from employment to unemployment of 0.021 [to pin down the value of $$\sigma$$]" (p. 12). My question is, how is this procedure done? Since the model kind of combines some features of the Pissarides model, I tried following the same logic, that in the steady state the number of people that go from employment to unemployment is equal to the number of people that go from employment to unemployment, but I don't think this is the correct approach.

I would appreciate any help/guide you can provide me.

Update: Now I understand that when it says that they target the flow rate from employment to unemployment of 0.021, it means the following:

$$\begin{gather} EU_t=\sigma(1-\lambda_w)E_t \\ \frac{EU_t}{E_t} = \sigma(1-\lambda_w) \\ \sigma(1-\lambda_w)=0.021 \quad \quad \text{(1)} \end{gather}$$

So this is one equation that must hold. In regard to a second equation, given that the paper uses a steady state value of employment of 0.632 and the unemployment rate $$U/(E+U)$$ of 0.083, one can derive that $$U=0.057$$. Given that $$N_t=1-E_t-U_t$$, I though that in steady state we could also get the value of $$N=0.311$$. Thus, the law of motion of unemployed people would be as follows:

$$$$U_{t+1} = \sigma(1-\lambda_w)E_t + (1-\lambda_w)U_t + (1-\lambda_w)N_t \quad \quad \text{(2)}$$$$

Intuitively, this means that the stock of unemployed people would be equal to those workers who lost their job and did not find one in $$t+1$$ + those who were unemployed and continued to being so in $$t+1$$ with probability $$1-\lambda_w$$ + those who were out of the labor forcein $$t$$, decided to enter in $$t+1$$, but did not find a job with the same probability $$1-\lambda_w$$.

So with these two equations I tried estimating the parameters, but I failed. I pressume Equation (2) is somehow wrong, so I would appreciate any comments on that. Also, I still don't know how to calibrate $$\alpha$$. Thank you in advance.