Update money_inflation.md #440
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This updates lecture money_inflation.md according to #437. In particular, it involves, ## Code - Remove the grid in the plot - Use `solve` to calculate the inverse ## Content - Change bold non-definition words to italics - $m_{t+1}^d/p_t =\gamma_1 - \gamma_2 \frac{p_{t+1}}{p_t}, \quad t \geq 0$ -> $\frac{m_{t+1}^d}{p_t} =\gamma_1 - \gamma_2 \frac{p_{t+1}}{p_t}, \quad t \geq 0$ where $\gamma_1$ and $\gamma_2$ are positive parameters. - Remove the repetition of definition of $b_t$ and $R_{t-1}$ - Remove the $()$ in 26.6 - Check capitalization for titles - gross rates of return on currency -> gross rates of return on currency and real balance - $\bar R < 1$ -> $\bar R \le 1$ - $\bar R \in [\frac{\gamma2}{\gamma1}, 1] \equiv [\underline R, \overline R]$ -> $\bar R \in [\frac{\gamma_2}{\gamma_1}, 1] \equiv [\underline R, \overline R]$ - $R_t \in \bar R = [\underline R, \overline R], \quad t \geq 0$ -> $R_t \in [\underline R, \overline R], \quad t \geq 0$ - two values of $R$ -> Two steady-state values of $R$ - $R_l$ ->$R_\ell$ - An equilibrium sequences are not unique -> equilibrium sequences are not unique - Remove the repetitive ``` $$\begin{aligned} b_t & = b_{t-1} R_{t-1} + g \cr R_t^{-1} & = \frac{\gamma_1}{\gamma_2} - \gamma_2^{-1} b_t \end{aligned}$$ ``` - "code plot outcomes" -> "code plot to outcomes" - Set $ \Lambda= \begin{bmatrix} {R_l}^{-1} & 0 \cr 0 & {R_u}^{-1} \end{bmatrix}$ - $Q y_0 = y^*_0 = \begin{bmatrix} y^*_{1,0} \cr 0 \end{bmatrix}$ -> $Q^{-1} y_0 = y^*_0 = \begin{bmatrix} y^*_{1,0} \cr 0 \end{bmatrix}$.
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@longye-tian will this close #437? @jstac this is ready for review |
Hi @mmcky, Some comments remain unresolved, but I think I need to submit another pull request for that as it might related to the content. Best, |
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| **Remark 1:** method 1 uses an indirect approach to computing an equilibrium by first computing an equilibrium $\{R_t, b_t\}_{t=0}^\infty$ sequence and then using it to back out an equilibrium $\{p_t, m_t\}_{t=0}^\infty$ sequence. | |||
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| **Remark 2:** notice that method 1 starts by picking an **initial condition** $R_0$ from a set $[\frac{\gamma_2}{\gamma_1}, R_u]$. An equilibrium $\{p_t, m_t\}_{t=0}^\infty$ sequences are not unique. There is actually a continuum of equilibria indexed by a choice of $R_0$ from the set $[\frac{\gamma_2}{\gamma_1}, R_u]$. | |||
| **Remark 2:** notice that method 1 starts by picking an **initial condition** $R_0$ from a set $[\frac{\gamma_2}{\gamma_1}, R_u]$. Equilibrium $\{p_t, m_t\}_{t=0}^\infty$ sequences are not unique. There is actually a continuum of equilibria indexed by a choice of $R_0$ from the set $[\frac{\gamma_2}{\gamma_1}, R_u]$. | |||
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@mmcky , is there a suitable environment for these remarks?
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@jstac there is a remark admonition available in sphinx-proof but they are pretty in your face styling.
I think it would be good to migrate to them and them update the styling perhaps?
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Yeah, +1 on that @mmcky . These admonitions need simple styling.
Then definitions, theorems, etc. can have stronger styles, so they stand out.
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Many thanks @longye-tian, much appreciated! Just some very minor comments above that need to be addressed. |
update bold to italics and typos
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Many thanks @longye-tian @mmcky , please see my comments above and merge when ready. |
Dear John @jstac ,
I have update lecture money_inflation.md according to #437. In particular, it involves,
Code
solveto calculate the inverseContent
Best 👻
Longye