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30 changes: 30 additions & 0 deletions docs/book/OGZAF_references.bib
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Expand Up @@ -738,3 +738,33 @@ @ARTICLE{Zhang:1997
month = {December},
pages = {2187-2209},
}

@Article{LMW2023,
author={Li, Delong and Magud, Nicolas E. and Werner, Alejandro},
title={{The long-run impact of sovereign yields on corporate yields in emerging markets}},
journal={Journal of International Money and Finance},
year=2023,
volume={130},
number={C},
pages={},
month={},
keywords={Bonds; Emerging markets; Sovereign risk; Transfer risk; Liquidity premium; JEL Classification Number},
doi={10.1016/j.jimonfin.2022.1},
abstract={We analyze the long-run impact of sovereign yields on corporate yields of the same country, finding that, for emerging markets, the average pass-through is around one. The pass-through is larger in countries with greater sovereign risk and where sovereign bonds are more liquid. The pass-through is also greater for corporate bonds with lower ratings, shorter maturities, and those issued by financial companies and government-related firms. Our results support theoretical arguments that corporate and sovereign yields are linked together through credit risk and liquidity premiums. Consequently, high sovereign risk can slowdown growth by persistently increasing private sector borrowing costs.},
url={https://ideas.repec.org/a/eee/jimfin/v130y2023ics0261560622001516.html}
}

@Article{PRS2020,
author={Pain, Julius and Rapapali, Mpho and Steenkamp, Daan},
title={{Industry TFP estimates for South Africa}},
journal={Occasional Bulletin of Economic Notes},
year=2020,
volume={},
number={},
pages={},
month={November},
keywords={},
doi={},
abstract={},
url={https://econpapers.repec.org/scripts/redir.pf?u=https%3A%2F%2Fwww.resbank.co.za%2Fcontent%2Fdam%2Fsarb%2Fpublications%2Foccasional-bulletin-of-economic-notes%2F2020%2F10412%2FOBEN%25202002%2520%28Industry%2520TFP%2520estimates%2520for%2520South%2520Africa%29%2520-%2520November%25202020.pdf;h=repec:rbz:oboens:10412}
}
4 changes: 2 additions & 2 deletions docs/book/content/calibration/demographics.md
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Expand Up @@ -293,7 +293,7 @@ We discuss the approach to estimating fertility rates $f_{s,t}$, mortality rates
Theoretical steady-state population distribution vs. population distribution at period $t=120$
```

Further, we find that the maximum absolute difference between the population levels $\hat{\omega}_{s,t}$ and $\hat{\omega}_{s,t+1}$ was $1.3852\times 10^{-5}$ after 160 periods. That is to say, that after 160 periods, given the estimated mortality, fertility, and immigration rates, the population has not achieved its steady state. For convergence in our solution method over a reasonable time horizon, we want the population to reach a stationary distribution after $T$ periods. To do this, we artificially impose that the population distribution in period $t=120$ is the steady-state. As can be seen from {numref}`Figure %s <FigOrigVsFixSSpop>`, this assumption is not very restrictive. {numref}`Figure %s <FigImmRateChg>` shows the change in immigration rates that would make the period $t=120$ population distribution equal be the steady-state. The maximum absolute difference between any two corresponding immigration rates in {numref}`Figure %s <FigImmRateChg>` is 0.0028.
Further, we find that the maximum absolute difference between the population levels $\hat{\omega}_{s,t}$ and $\hat{\omega}_{s,t+1}$ was less than $1\times 10^{-4}$ after 160 periods. That is to say, that after 160 periods, given the estimated mortality, fertility, and immigration rates, the population has not achieved its steady state. For convergence in our solution method over a reasonable time horizon, we want the population to reach a stationary distribution after $T$ periods. To do this, we artificially impose that the population distribution in period $t=120$ is the steady-state. As can be seen from {numref}`Figure %s <FigOrigVsFixSSpop>`, this assumption is not very restrictive. {numref}`Figure %s <FigImmRateChg>` shows the change in immigration rates that would make the period $t=120$ population distribution equal be the steady-state. The maximum absolute difference between any two corresponding immigration rates in {numref}`Figure %s <FigImmRateChg>` is very small.

```{figure} ./images/OrigVsAdjImm.png
---
Expand All @@ -303,7 +303,7 @@ We discuss the approach to estimating fertility rates $f_{s,t}$, mortality rates
Original immigration rates vs. adjusted immigration rates to make fixed steady-state population distribution
```

The most recent year of population data come from {cite}`Census:2015` population estimates for both sexes for 2013. We those data and use the population transition matrix {eq}`EqPopLOMstatmat2` to age it to the current model year of 2015. We then use {eq}`EqPopLOMstatmat2` to generate the transition path of the population distribution over the time period of the model. {numref}`Figure %s <FigPopDistPath>` shows the progression from the 2013 population data to the fixed steady-state at period $t=120$. The time path of the growth rate of the economically active population $\tilde{g}_{n,t}$ is shown in {numref}`Figure %s <FigPopDistPath>`.
We begin with 2023 population data and use the population transition matrix {eq}`EqPopLOMstatmat2` to age it to the start year of the model (e.g., 2024 or 2025). We then use {eq}`EqPopLOMstatmat2` to generate the transition path of the population distribution over the time period of the model. {numref}`Figure %s <FigPopDistPath>` shows the progression from the 2023 population data to the fixed steady-state at period $t=120$. The time path of the growth rate of the economically active population $\tilde{g}_{n,t}$ is shown in {numref}`Figure %s <FigPopDistPath>`.

```{figure} ./images/pop_distribution.png
---
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103 changes: 78 additions & 25 deletions docs/book/content/calibration/exogenous_parameters.md
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Expand Up @@ -21,33 +21,86 @@ kernelspec:
```{code-cell} ogzaf-dev
:tags: [hide-cell]
from myst_nb import glue
import ogzaf.parameter_tables as pt
from ogzaf import Specifications
import ogcore.parameter_tables as pt
from ogcore import Specifications
import ogzaf
import importlib
import json
p = Specifications()
table = pt.param_table(p, table_format=None, path=None)
with importlib.resources.open_text(
"ogzaf", "ogzaf_default_parameters.json"
) as file:
defaults = json.load(file)
table = pt.param_table(p, table_format="md", path=None)
glue("param_table", table, display=False)
```
-->

```{list-table} **List of exogenous parameters and baseline calibration values.**
:header-rows: 1
:name: TabExogVars
* - **Symbol**
- **Description**
- **Value**
* - $S$
- Maximum periods in economically active household life
- 80
* - $E$
- Number of periods of youth economically outside the model
- $\text{round} \frac{S}{4}$=20
* - $T_1$
- Number of periods to steady state for initial time path guesses
- 160
* - $T_2$
- Maximum number of periods to steady state for nonsteady-state equilibrium
- 160
* - $\nu$
- Dampening parameter for TPI
- 0.4
```
| Symbol | Description | Value |
|:---------------------------------|:------------------------------------------------------------------------|:------------------------------------------------------|
| $\texttt{start_year}$ | Initial year | 2025 |
| $\omega_{s,t}$ | Population by age over time | Too large to report here, see default parameters JSON |
| $i_{s,t}$ | Immigration rates by age | Too large to report here, see default parameters JSON |
| $\rho_{s,t}$ | Mortality rates by age | Too large to report here, see default parameters JSON |
| $e_{j,s,t}$ | Deterministic ability process | Too large to report here, see default parameters JSON |
| $\lambda_{j}$ | Lifetime income group percentages | Too large to report here, see default parameters JSON |
| $J$ | Number of lifetime income groups | 7 |
| $S$ | Maximum periods in economically active individual life | 80 |
| $E$ | Number of periods of youth economically outside the model | 20 |
| $T$ | Number of periods to steady-state | 320 |
| $R$ | Retirement age | [65.000...65.000] |
| $\tilde{l}$ | Maximum hours of labor supply | 1.000 |
| $\beta$ | Discount factor | [0.960...0.960] |
| $\sigma$ | Coefficient of constant relative risk aversion | 1.500 |
| $\nu$ | Frisch elasticity of labor supply | 0.400 |
| $b$ | Scale parameter in utility of leisure | 0.573 |
| $\upsilon$ | Shape parameter in utility of leisure | 2.856 |
| $\chi^{n}_{s}$ | Disutility of labor level parameters | Too large to report here, see default parameters JSON |
| $\chi^{b}_{j}$ | Utility of bequests level parameters | [80.000...80.000] |
| $\texttt{use_zeta}$ | Whether to distribute bequests between lifetime income groups | 0.00E+00 |
| $\zeta$ | Distribution of bequests | Too large to report here, see default parameters JSON |
| $Z_{t}$ | Total factor productivity | Too large to report here, see default parameters JSON |
| $\gamma$ | Capital share of income | [0.401...0.401] |
| $\varepsilon$ | Elasticity of substitution between capital and labor | [1.000...1.000] |
| $\delta$ | Capital depreciation rate | 0.050 |
| $g_{y}$ | Growth rate of labor augmenting technological progress | 0.00E+00 |
| $\texttt{tax_func_type}$ | Functional form used for income tax functions | linear |
| $\texttt{analytical_mtrs}$ | Whether use analytical MTRs or estimate MTRs | 0.00E+00 |
| $\texttt{age_specific}$ | Whether use age-specific tax functions | 0.00E+00 |
| $\tau^{p}_{t}$ | Payroll tax rate | [0.000...0.000] |
| $\tau^{BQ}_{t}$ | Bequest (estate) tax rate | [0.200...0.200] |
| $\tau^{b}_{t}$ | Entity-level business income tax rate | Too large to report here, see default parameters JSON |
| $\delta^{\tau}_{t}$ | Rate of depreciation for tax purposes | Too large to report here, see default parameters JSON |
| $\tau^{c}_{t,s,j}$ | Consumption tax rates | Too large to report here, see default parameters JSON |
| $H$ | Coefficient on linear term in wealth tax function | [0.100...0.100] |
| $M$ | Constant in wealth tax function | [1.000...1.000] |
| $P$ | Coefficient on level term in wealth tax function | [0.000...0.000] |
| $\texttt{budget_balance}$ | Whether have a balanced budget in each period | 0.00E+00 |
| $\texttt{baseline_spending}$ | Whether level of spending constant between the baseline and reform runs | 0.00E+00 |
| $\alpha^{T}_{t}$ | Transfers as a share of GDP | [0.041...0.041] |
| $\eta_{j,s,t}$ | Distribution of transfers | Too large to report here, see default parameters JSON |
| $\alpha^{G}_{t}$ | Government spending as a share of GDP | [0.267...0.267] |
| $t_{G1}$ | Model period in which budget closure rule starts | 20 |
| $t_{G2}$ | Model period in which budget closure rule ends | 256 |
| $\rho_{G}$ | Budget closure rule smoothing parameter | 0.100 |
| $\bar{\alpha}_{D}$ | Steady-state Debt-to-GDP ratio | 1.200 |
| $\alpha_{D,0}$ | Initial period Debt-to-GDP ratio | 0.740 |
| $\tau_{d,t}$ | Scale parameter in government interest rate wedge | [0.245...0.245] |
| $\mu_{d,t}$ | Shift parameter in government interest rate wedge | [-0.034...-0.034] |
| $\texttt{avg_earn_num_years}$ | Number of years over which compute average earnings for pension benefit | 35 |
| $\texttt{AIME_bkt_1}$ | First AIME bracket threshold | 749.000 |
| $\texttt{AIME_bkt_2}$ | Second AIME bracket threshold | 4517.000 |
| $\texttt{PIA_rate_bkt_1}$ | First AIME bracket PIA rate | 0.00E+00 |
| $\texttt{PIA_rate_bkt_2}$ | Second AIME bracket PIA rate | 0.00E+00 |
| $\texttt{PIA_rate_bkt_3}$ | Third AIME bracket PIA rate | 0.00E+00 |
| $\texttt{PIA_maxpayment}$ | Maximum PIA payment | 0.00E+00 |
| $\texttt{PIA_minpayment}$ | Minimum PIA payment | 0.00E+00 |
| $\theta_{adj,t}$ | Adjustment to replacement rate | [1.000...1.000] |
| $r^{*}_{t}$ | World interest rate | [0.040...0.040] |
| $D_{f,0}$ | Share of government debt held by foreigners in initial period | 0.237 |
| $\zeta_{D, t}$ | Share of new debt issues purchased by foreigners | [0.237...0.237] |
| $\zeta_{K, t}$ | Share of excess capital demand satisfied by foreigners | [0.900...0.900] |
| $\xi$ | Dampening parameter for TPI | 0.400 |
| $\texttt{maxiter}$ | Maximum number of iterations for TPI | 250 |
| $\texttt{mindist_SS}$ | SS solution tolerance | 1.00E-09 |
| $\texttt{mindist_TPI}$ | TPI solution tolerance | 1.00E-05 |
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