update functions edit

docs/functions.md

@@ -26,49 +26,45 @@ We hold the assumption that total compensation from the employer to the employee
 
 Under this assumption, an increase on the employer side payroll tax rate will result in a decrease in the employee's wages. The decrease of wages will then result in a decrease of tax revenue from the employee side, both income tax revenue and payroll tax revenue.
 
-$\
 Total Compensation = Wage + Employer Side Payroll Tax Liability + Non-Taxable Benefit
-$
 
-
 Note:
 - Pension is included in the Wage variable  
 - Payroll tax is consisted of OASDI social security tax and HI medicare hospital insurance tax
 - Non-taxable benefit is not considered in our model, because our data sets (PUF & CPS) do not capture the information of this item. (The overall contribution from non-taxable benefit to the value of total compensation should also not be very significant). 
 
 
-So we consider the following components for total compensation calculation: 
+So we consider wage and employer side payroll for total compensation calculation.
 
-$$\
-Wages: wages and pension, from employer paid to employee
-FICA_ss_employer: employer side OASDI social security tax liability 
-FICA_mc_employer: employer side HI medicare hospital insurance tax liability
-$$
+Total Compensation = Wage + Employer side FICA Social Security Tax Liability + Employer side FICA Medicare Tax Liability 
 
-$$\
-Total Compensation = Wage + FICA_ss_employer + FICA_mc_employer
-$$
+
+Wages: wages and pension, from employer paid to employee
+OASDIrate: employer side OASDI social security tax rate
+HIrate: employer side HI medicare hospital insurance tax rate
+OASDImax: OASDI social security tax maximum taxable value
 
 To be noticed, OASDI social security tax have a maximum taxable value, $118500 in 2016. For wages below this value, the wages will be taxed by the actual value of the wages; for wages above this value, the employee will be taxed by this OASID maximum taxable value.
 
+
 (1) For employee whose wage is below the OASDI taxable maximum value:
 
 Under the baseline policy:
 
 $$
-Total Compensation_{base} = Wage_{base} + Wage_{base} * FICA_ss_employer tax rate_{base} + Wage_{base} * FICA_mc_employer tax rate_{base}
+Total Compensation_{base} = Wage_{base} + Wage_{base} * OASDIrate_{base} + Wage_{base} * HIrate_{base}
 $$
 
 Under the reform policy:
 
 $$
-Total Compensation_{policy} = Wage_{policy} + Wage_{policy} * FICA_ss_employer tax rate_{policy} + Wage_{policy} * FICA_mc_employer tax rate_{policy}
+Total Compensation_{policy} = Wage_{policy} + Wage_{policy} * OASDIrate_{policy} + Wage_{policy} * HIrate_{policy}
 $$
 
 By combining the two equations above, we have:
 
 $$
-Wage_{policy} = \frac{Wage_base * (1 + FICA_ss_employer tax rate_base+ FICA_mc_employer tax rate_base)}{1 + FICA_ss_employer tax rate_policy + FICA_mc_employer tax rate_policy}
+Wage_{policy} = \frac{Wage_base * (1 + OASDIrate_{base}+ HIrate_{base})}{1 + OASDIrate_{policy} + HIrate_{policy}}
 $$
 
 
@@ -77,19 +73,19 @@ $$
 Under the baseline policy:
 
 $$
-Total Compensation_{base} = Wage_{base} + OASDI max taxable amount * FICA_ss_employer tax rate_{base} + Wage_{base} * FICA_mc_employer tax rate_{base}
+Total Compensation_{base} = Wage_{base} + OASDImax * OASDI_{base} + Wage_{base} * HI_{base}
 $$
 
 Under the reform policy:
 
 $$
-Total Compensation_{policy} = Wage_{policy} + OASDI max taxable amount * FICA_ss_employer tax rate_{policy} + Wage_{policy} * FICA_mc_employer tax rate_{policy}
+Total Compensation_{policy} = Wage_{policy} + OASDImax * OASDI_{policy} + Wage_{policy} * HI_{policy}
 $$
 
 By combining the two equations above, we have:
 
 $$
-Wage_{policy} = \frac{Total Compensation - FICA_ss_employer tax rate_policy * OASDI max taxable amount}{1 + FICA_mc_employer tax rate_policy}
+Wage_{policy} = \frac{Total Compensation - OASDI_{policy} * OASDImax}{1 + HI_{policy}}
 $$