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fix arellano (#141)
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lectures/arellano.md

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@@ -709,8 +709,8 @@ The first figure shows the bond price schedule and replicates Figure 3 of
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Arellano, where $ y_L $ and $ Y_H $ are particular below average and above average
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values of output $ y $.
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![https://python-advanced.quantecon.org/_static/lecture_specific/arellano/arellano_bond_prices.png](https://python-advanced.quantecon.org/_static/lecture_specific/arellano/arellano_bond_prices.png)
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```{figure} _static/lecture_specific/arellano/arellano_bond_prices.png
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```
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- $ y_L $ is 5% below the mean of the $ y $ grid values
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- $ y_H $ is 5% above the mean of the $ y $ grid values
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The next figure plots value functions and replicates the right hand panel of Figure 4 of {cite}`Are08`.
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![https://python-advanced.quantecon.org/_static/lecture_specific/arellano/arellano_value_funcs.png](https://python-advanced.quantecon.org/_static/lecture_specific/arellano/arellano_value_funcs.png)
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```{figure} _static/lecture_specific/arellano/arellano_value_funcs.png
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```
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We can use the results of the computation to study the default probability $ \delta(B', y) $
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defined in {eq}`equation13_4`.
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The next plot shows these default probabilities over $ (B', y) $ as a heat map.
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![https://python-advanced.quantecon.org/_static/lecture_specific/arellano/arellano_default_probs.png](https://python-advanced.quantecon.org/_static/lecture_specific/arellano/arellano_default_probs.png)
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```{figure} _static/lecture_specific/arellano/arellano_default_probs.png
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```
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As anticipated, the probability that the government chooses to default in the following period
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increases with indebtedness and falls with income.
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The grey vertical bars correspond to periods when the economy is excluded from financial markets because of a past default.
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![https://python-advanced.quantecon.org/_static/lecture_specific/arellano/arellano_time_series.png](https://python-advanced.quantecon.org/_static/lecture_specific/arellano/arellano_time_series.png)
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```{figure} _static/lecture_specific/arellano/arellano_time_series.png
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```
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One notable feature of the simulated data is the nonlinear response of interest rates.
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Periods of relative stability are followed by sharp spikes in the discount rate on government debt.
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## Exercises
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```{exercise-start}
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:label: arellano_ex1
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```
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```{exercise-end}
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```
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```{solution-start} arellano_ex1
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:class: dropdown
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```
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Solution to this [exercise](https://python-advanced.quantecon.org/arellano.html#arella_ex1).
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Compute the value function, policy and equilibrium prices
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```{code-cell} ipython3

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