Exogenous Parameters

Exogenous Parameters#

The JSON file ogusa_default_parameters.json provides values for all the model parameters used as defaults for OG-USA. Below, we provide a table highlighting some of the parameters describing the scale of the model (number of periods \(T\), age groups \(S\), productivity types \(J\)) and some parameters of the solution method (dampening parameter \(\xi\) for TPI). The table below provides a list of the exogenous parameters and their baseline calibration values.

Table: List of exogenous parameters and baseline calibration values

Symbol

Description

Value

\(\theta\)

Frisch elasticity of labor supply

0.400

\(g_{y,ann,t}\)

Annual growth rate of labor augmenting technological change

0.020

\(S\)

Maximum periods in economically active individual life

80

\(J\)

Number of lifetime income groups

10

\(T\)

Number of periods to steady-state

320

\(M\)

Number of different production industries

1

\(I\)

Number of different consumption goods

1

\(\lambda_{j}\)

Lifetime income group percentages

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

\(\beta_{j,ann}\)

Annual rate of time preference for households

[0.910…0.995]

\(\sigma\)

Coefficient of constant relative risk aversion

1.500

\(\alpha_i\)

Share parameters for each good in the composite consumption good

[1.000…1.000]

\(c_{min,i}\)

Minimum consumption levels for each good in the composite consumption good

[0.000…0.000]

\(\gamma_m\)

Capital share of income by industry

[0.380…0.380]

\(\gamma_{g,m}\)

Public capital’s share of output in firm production function by industry

[0.000…0.000]

\(\varepsilon_m\)

Elasticity of substitution between capital and labor by industry

[1.000…1.000]

\(\Pi^I\)

Input-output matrix

Too large to report here, see default parameters JSON

\(Z_{m,t}\)

Total factor productivity by industry

Too large to report here, see default parameters JSON

\(\delta_{M,ann}\)

Annual rate of economic depreciation of capital

0.050

\(\delta_{g,ann}\)

Annual rate of economic depreciation of public capital

0.020

\(\tilde{l}\)

Maximum hours of labor supply

1.000

\(r^*_t\)

Exogenous annual world interest rate

[0.040…0.040]

\(D_{f,0}\)

Share of government debt held by foreigners in initial period

0.400

\(\zeta_{D,t}\)

Share of new debt issues purchased by foreigners

[0.400…0.400]

\(\zeta_{K,t}\)

Share of excess capital demand satisfied by foreigners

[0.500…0.500]

\(T_{G1}\)

Model period in which budget closure rule starts

20

\(T_{G2}\)

Model period in which budget closure rule ends

256

\(\alpha^{T}_{t}\)

Transfers as a share of GDP

[0.087…0.100]

\(\alpha^{G}_{t}\)

Government spending as a share of GDP

[0.059…0.050]

\(\alpha^{I}_{t}\)

Exogenous fraction of GDP for infrastructure investment

[0.000…0.000]

\(\alpha^{BS}_{T,t}\)

Proportional adjustment to government transfers relative to baseline amount when budget balance is true

[1.000…1.000]

\(\alpha^{BS}_{G,t}\)

Proportional adjustment to government consumption expenditures relative to baseline amount when budget balance is true

[1.000…1.000]

\(\alpha^{BS}_{I,t}\)

Proportional adjustment to infrastructure spending relative to baseline amount when budget balance is true

[1.000…1.000]

\(\rho_{G}\)

Budget closure rule smoothing parameter

0.100

\(\alpha_{RM,1}\)

Remittances as a share of GDP in initial period

0.00E+00

\(\alpha_{RM,T}\)

Remittances as a share of GDP in long run

0.00E+00

\(g_{RM,t}\)

Growth rate of remittances in initial periods

[0.000…0.000]

\(\bar{\alpha}_{D}\)

Steady-state Debt-to-GDP ratio

1.900

\(\alpha_{D,0}\)

Initial period Debt-to-GDP ratio

1.017

\(\tau_{d,t}\)

Scale parameter in government interest rate wedge

[0.000…0.000]

\(\mu_{d,t}\)

Shift parameter in government interest rate wedge

[-0.005…-0.010]

\(\tau^{c}_{t,s,j}\)

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]

\(\tau^{BQ}_{t}\)

Bequest (estate) tax rate

[0.000…0.000]

\(\tau^{p}_{t}\)

Payroll tax rate

[0.000…0.000]

\(\chi^{b}_{j}\)

Utility of bequests level parameters

[80.000…80.000]

\(\chi^{n}_{s,t}\)

Disutility of labor level parameters

Too large to report here, see default parameters JSON

\(\eta_{j,s,t}\)

Distribution of transfers

Too large to report here, see default parameters JSON

\(\eta_{RM,j,s,t}\)

Distribution of remittances

Too large to report here, see default parameters JSON

\(\zeta_{j,s,t}\)

Distribution of bequests

Too large to report here, see default parameters JSON

\(\texttt{use_zeta}\)

Whether to distribute bequests between lifetime income groups

0.00E+00

\(\texttt{analytical_mtrs}\)

Whether use analytical MTRs or estimate MTRs

0.00E+00

\(\texttt{age_specific}\)

Whether use age-specific tax functions

1.000

\(R\)

Retirement age

[65.000…65.000]

\(\texttt{avg_earn_num_years}\)

Number of years over which compute average earnings for pension benefit

35

\(\texttt{AIME_bkt_1}\)

First AIME bracket threshold

1174.000

\(\texttt{AIME_bkt_2}\)

Second AIME bracket threshold

7078.000

\(\texttt{PIA_rate_bkt_1}\)

First AIME bracket PIA rate

0.900

\(\texttt{PIA_rate_bkt_2}\)

Second AIME bracket PIA rate

0.320

\(\texttt{PIA_rate_bkt_3}\)

Third AIME bracket PIA rate

0.150

\(\texttt{PIA_maxpayment}\)

Maximum PIA payment

4555.000

\(\texttt{PIA_minpayment}\)

Minimum PIA payment

0.00E+00

\(\theta_{adj,t}\)

Adjustment to replacement rate

Too large to report here, see default parameters JSON

\(\texttt{budget_balance}\)

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

\(\texttt{baseline_theta}\)

Flag for use in reform simulations to keep Social Security system replacement rate constant between baseline and reform runs

0.00E+00

\(\texttt{start_year}\)

Initial year

2026

\(\texttt{tax_func_type}\)

Functional form used for income tax functions

HSV

\(\xi\)

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

\(\omega_{s,t}\)

Population by age over time

Too large to report here, see default parameters JSON

\(\bar{\omega}_s\)

Steady-state population distribution

[0.014…0.001]

\(g_{n,t}\)

Population growth rate over the time path

[0.006…-0.004]

\(\bar{g}_n\)

Population growth rate in the steady-state

-3.55E-03

\(i_{s,t}\)

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