Merge pull request #40 from NHgit213/doc-book-content-calib-macro

docs/book/content/calibration/macro.md

@@ -5,48 +5,47 @@
 
 ### 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
@@ -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.