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rickecon committed Oct 30, 2023
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### Elasticity of labor supply

As discussed in the [OG-Core household theory documentation](https://pslmodels.github.io/OG-Core/content/theory/households.html), we use the elliptical disutility of labor function developed by {cite}`EvansPhillips:2017`. We then fit the parameters of the elliptical utility function to match the marginal disutility from a constant Frisch elasticity function. `OG-USA` users enter the constant Frisch elasticity as a parameter. {cite}`Peterman:2016` finds a range of Frisch elasticities estimated from microeconomic and macroeconomic data. These range from 0 to 4. Peterman makes the case that in lifecycle models with out an extensive margin for employment, such as `OG-USA`, the Frisch elasticity should be higher. We take a default value of 0.4 from {cite}`Altonji:1986`.
As discussed in the [OG-Core household theory documentation](https://pslmodels.github.io/OG-Core/content/theory/households.html), we use the elliptical disutility of labor function developed by {cite}`EvansPhillips:2017`. We then fit the parameters of the elliptical utility function to match the marginal disutility from a constant Frisch elasticity function. `OG-ZAF` users enter the constant Frisch elasticity as a parameter. {cite}`Peterman:2016` finds a range of Frisch elasticities estimated from microeconomic and macroeconomic data. These range from 0 to 4. Peterman makes the case that in lifecycle models without an extensive margin for employment the Frisch elasticity should be higher. For `OG-ZAF` we take a default value of 0.4 from {cite}`Altonji:1986`.

### Intertemporal elasticity of substitution

The default value for the intertemporal elasticity of substitution, $\sigma$, is taken from {cite}`ABMW:1999`. We set $\sigma=1.5$.

### Rate of time preference

We take our default value for the rate of time preference parameter, $\beta$ from {cite}`Carroll:2009`. We set the value of to $\beta=0.96$ (on an annual basis).
We take our default value for the rate of time preference parameter, $\beta$ from {cite}`Carroll:2009`. We set the value to $\beta=0.96$ (on an annual basis).


## Economic Assumptions

As the default rate of labor augmenting technological change, $g_y$, we use a value of 3%. The average annual growth rate in GDP per capita in the United States since 1948 is 2% per year.
As the default rate of labor augmenting technological change, $g_y$, we use a value of 3%. The average annual growth rate in GDP per capita in South Africa between 1961 and 2021 is 0.7% per year.

## Aggregate Production Function and Capital Accumulation

The [OG-Core firm theory documentation](https://pslmodels.github.io/OG-Core/content/theory/firms.html) outlines the constant returns to scale, constant elasticity of substitution production function of the representative firm. This function has two parameters; the elasticity of substitution and capital's share of output.

### Elasticity of substitution

`OG-USA`'s default parameterization has an elasticity of substitution of $\varepsilon=1.0$, which implies a Cobb-Douglas production function.
`OG-ZAF`'s default parameterization has an elasticity of substitution of $\varepsilon=1.0$, which implies a Cobb-Douglas production function.

### Capital's share of output

The historical value in U.S. is about 0.33, but {cite}`EHS:2013` find capital's share is increasing. We therefore use the slightly higher value of $\gamma =0.35$. Note that the mean of capital's share of income from 1950 onwards is 0.38 from the Penn World Tables.

Here, we use a default value of $\gamma =0.61$.

## Open Economy Parameters

### Foreign holding of government debt in the initial period

The path of foreign holding of domestic debt is endogenous, but the initial period stock of debt held by foreign investors is exogenous. We set this parameter, `initial_foreign_debt_ratio` to 0.4, consistent with data from the Financial Accounts of the United States for 2019.
The path of foreign holding of domestic debt is endogenous, but the initial period stock of debt held by foreign investors is exogenous. We set this parameter, `initial_foreign_debt_ratio` to 0.26, consistent with data from the World Bank WDI.


### Foreign purchases of newly issued debt

We set $\zeta_D = 0.4$. This is the average share of foreign purchases of newly issued government debt found from the Financial Accounts of the United States.
We set $\zeta_D = 0.26$. This is the average share of foreign purchases of newly issued government debt found from the World Bank WDI.

### Foreign holdings of excess capital

We set $\zeta_K = 0.1$.
We set $\zeta_K = 0.9$.


## Government Debt, Spending and Transfers
Expand All @@ -57,12 +56,10 @@ The path of government debt is endogenous. But the initial value is exogenous.

### Aggregate transfers

Aggregate (non-Social Security) transfers to households are set as a share of GDP with the parameter $\alpha_T$. Using the [OMB Fiscal Year 2017 Historical Tables](https://www.whitehouse.gov/sites/default/files/omb/budget/fy2017/assets/hist.pdf), we define transfers as:
<center>Transfers = VA Benefits and Services (700) + Income Security (600) + Medicare (570) + Healthcare Services (551)</center>

We exclude Social Security from transfers since it is modeled specifically. With this definition, the share of transfers to GDP in 2015 is 0.09.
Aggregate (non-Social Security) transfers to households are set as a share of GDP with the parameter $\alpha_T$. We exclude Social Security from transfers since it is modeled specifically. With this definition, the share of transfers to GDP in 2015 is 0.04 according to Federal Reserve Economic Data (FRED).

### Government expenditures

Government spending on goods and services are also set as a share of GDP with the parameter $\alpha_G$. Using the [OMB Fiscal Year 2017 Historical Tables](https://www.whitehouse.gov/sites/default/files/omb/budget/fy2017/assets/hist.pdf), we define government spending as:
Government spending on goods and services are also set as a share of GDP with the parameter $\alpha_G$. We define government spending as:
<center>Government Spending = Total Outlays - Transfers - Net Interest on Debt - Social Security</center>
With this definition, the share of government expenditure to GDP is 0.27 based on FRED.

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