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Update tax_smoothing_3.md
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lectures/tax_smoothing_3.md

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@@ -62,7 +62,7 @@ import numpy as np
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import matplotlib.pyplot as plt
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```
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## Roll-Over Risk
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## Roll-over risk
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Let $T_t$ denote tax collections, $\beta$ a discount factor,
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$b_{t,t+1}$ time $t+1$ goods that the government promises to
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Specifically, we shut down the government’s ability to borrow in
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one of the Markov states.
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## A Dead End
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## A dead end
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A first thought for how to implement this might be to allow
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$p^t_{t+1}$ to vary over time with:
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Thus, we must represent “roll-over risk” some other way.
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## Better Representation of Roll-Over Risk
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## Better representation of roll-over risk
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To force the government to set $b_{t,t+1} = 0$, we can instead
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extend the model to have four Markov states:

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