journal={arXiv preprint arXiv:2410.16076},

year={2024}

}

@article{MaCurdy1982,

title={The use of time series processes to model the error structure of earnings in a longitudinal data analysis},

author={MaCurdy, Thomas E.},

journal={Journal of Econometrics},

volume={18},

number={1},

pages={83--114},

year={1982},

publisher={Elsevier}

}

@article{Meghir2004,

title={Income variance dynamics and heterogeneity},

author={Meghir, Costas and Pistaferri, Luigi},

journal={Econometrica},

volume={72},

number={1},

pages={1--32},

year={2004},

publisher={Wiley Online Library}

}

- file: mccall_model_with_separation

- file: mccall_model_with_sep_markov

- file: mccall_fitted_vfi

- file: mccall_correlated

- file: mccall_persist_trans

- file: career

- file: jv

- file: odu

where $\psi$ is the standard normal density.

Here we are thinking of $v_u$ as a function on all of $\RR_+$.

Here we are thinking of $v_u$ as a function on all of $\mathbb{R}_+$.

### Fitting

```{exercise}

:label: mfv_ex2

Let us now consider how the agent responds to an increase in volatility.

To try to understand this, compute the reservation wage when the wage offer distribution is uniform on $(m - s, m + s)$ and $s$ varies.

The idea here is that we are holding the mean constant and spreading the support.

(This is a form of *mean-preserving spread*.)

Use `s_vals = jnp.linspace(1.0, 2.0, 15)` and `m = 2.0`.

State how you expect the reservation wage to vary with $s$.

Now compute it - is this as you expected?

```

```{solution-start} mfv_ex2

:class: dropdown

```

Maybe add an exercise that explores a pure increase in volatility.

```{solution-end}

```

```{exercise}

:label: mfv_ex3

Create a plot that shows how the reservation wage changes with the risk aversion parameter $\gamma$.

Use `γ_vals = jnp.linspace(1.2, 2.5, 15)` and keep all other parameters at their default values.

```

```{solution-start} mfv_ex3

```{solution-start} mfv_ex2

:class: dropdown

```

---

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(mccall_with_sep_markov)=

</div>

```

+++

# Job Search III: Search with Separation and Markov Wages

\right]

$$

+++

## Computational Approach

2. Substitute into the unemployed agent's Bellman equation to get:

+++

$$

v_u(w) =

The optimal policy turns out to be a reservation wage strategy: accept all wages above some threshold.

+++

## Code

Can you provide an intuitive economic story behind the outcome that you see in this figure?

+++

## Employment Simulation

via $P(w, \cdot)$, and positive correlation means that a high current $w$ is

often leads a high new draw.

+++

## The Ergodic Property

Often the second approach is better for our purposes, since it's easier to parallelize.

+++

## Cross-Sectional Analysis