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Copy file name to clipboardExpand all lines: rst_files/amss2.rst
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@@ -61,26 +61,23 @@ This lecture studies a special AMSS model in which
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- the one-period gross interest rate :math:`R_t(s^t)` on risk-free debt converges to a time-invariant function of the Markov state :math:`s_t`
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* For a **particular** :math:`b_0 < 0` (i.e., a positive level of initial government **loans** to the private sector), the measurability constraints **never** bind
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* In this special case
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- the **par value** :math:`b_{t+1}(s_t) = \bar b` of government debt at time :math:`t` and Markov state :math:`s_t` is constant across time and states,
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- the **par value** :math:`b_{t+1}(s_t) = \bar b` of government debt at time :math:`t` and Markov state :math:`s_t` is constant across time and states,
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but :math:`\ldots`
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- the **market value** :math:`\frac{\bar b}{R_t(s_t)}` of government debt at time :math:`t` varies as a time-invariant function of the Markov state :math:`s_t`
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- the **market value** :math:`\frac{\bar b}{R_t(s_t)}` of government debt at time :math:`t` varies as a time-invariant function of the Markov state :math:`s_t`
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- fluctuations in the interest rate make gross earnings on government debt :math:`\frac{\bar b}{R_t(s_t)}` fully insure the gross-of-gross-interest-payments government budget against fluctuations in government expenditures
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- fluctuations in the interest rate make gross earnings on government debt :math:`\frac{\bar b}{R_t(s_t)}` fully insure the gross-of-gross-interest-payments government budget against fluctuations in government expenditures
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- the state variable :math:`x` in a recursive representation of a Ramsey plan is a time invariant function of the Markov state for :math:`t \geq0`
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- the state variable :math:`x` in a recursive representation of a Ramsey plan is a time invariant function of the Markov state for :math:`t \geq0`
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* In this special case, the Ramsey allocation in the AMSS model agrees with that in a :cite:`LucasStokey1983` model in which
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the same amount of state-contingent debt falls due in all states tomorrow
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- it is a situation in which the Ramsey planner loses nothing from not being able to purchase state-contingent debt and being restricted to exchange only risk-free debt debt
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- it is a situation in which the Ramsey planner loses nothing from not being able to purchase state-contingent debt and being restricted to exchange only risk-free debt debt
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* This outcome emerges only when we initialize government debt at a particular :math:`b_0 < 0`
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@@ -781,4 +778,4 @@ Now let's compute the implied mean time to get to within .01 of the limit
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print(f"Time to get within .01 of limit = {ttime}")
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The slow rate of convergence and the implied time of getting within one percent of the limiting value do a good job of approximating
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