From 0914f94ba67145e3cef791bac7d1bf82c44a10f5 Mon Sep 17 00:00:00 2001 From: Fazeleh Kazemian Date: Tue, 18 Sep 2018 12:59:36 +1000 Subject: [PATCH] fix space and order for a nested list in amss2 --- rst_files/amss2.rst | 15 ++++++--------- 1 file changed, 6 insertions(+), 9 deletions(-) diff --git a/rst_files/amss2.rst b/rst_files/amss2.rst index 1d36bf0d..6f833fdc 100644 --- a/rst_files/amss2.rst +++ b/rst_files/amss2.rst @@ -61,26 +61,23 @@ This lecture studies a special AMSS model in which - 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` - * 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 - - * In this special case - - 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, + - 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, but :math:`\ldots` - - 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` + - 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` - - 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 + - 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 - - 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 \geq 0` + - 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 \geq 0` * In this special case, the Ramsey allocation in the AMSS model agrees with that in a :cite:`LucasStokey1983` model in which the same amount of state-contingent debt falls due in all states tomorrow - - 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 + - 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 * This outcome emerges only when we initialize government debt at a particular :math:`b_0 < 0` @@ -781,4 +778,4 @@ Now let's compute the implied mean time to get to within .01 of the limit print(f"Time to get within .01 of limit = {ttime}") The slow rate of convergence and the implied time of getting within one percent of the limiting value do a good job of approximating -our long simulation above \ No newline at end of file +our long simulation above