Technical Overview of PWBM Dynamic OLG Model

Published January 3, 2019

Overview

Discrete-time, year periods.
Bewley Model
- Households subject to idiosyncratic labor productivity shocks
- No risk-sharing due to incomplete markets
Profit maximizing firms: Corporate and pass-through.
Openness of the Economy
Government Debt and Investment Crowd-out
Unanticipated policy shock

Households

Maximize discounted lifetime utility from consumption and leisure
State: age, wealth, productivity, avg. lifetime earnings, immigration status
Save into portfolio of physical capital and government debt
- Portfolio composition exogenous to household
- Corporate debt holdings are implicit
10 idiosyncratic labor productivity shocks (per period)
- Life-cycle profile
- Markov transitions
- Productivity lower for illegal immigrants
Labor supply choice is continuous and labor supply is zero after retirement.

Household demographics

Households taxation

Tax treatments in the model:
1. Ordinary rates
2. Preferred rates
3. Payroll
4. Consumption
Tax functions from the PWBMsim and Tax Module (PWBM-TM) and reflect demographics
- Time-varying
- Cumulative tax liability from a piecewise-linear tax rate function

Social Security

Average earnings (AIME model equivalent)
- Labor earnings increased by growth in average earnings in the economy from the year of work until the year household turns 60
- Taxable maximum indexed by average wage inflation
- Indexed labor earnings capped to the indexed taxable maximum
- Calculate the average of capped indexed labor earnings
Benefits (PIA model equivalent)
- Cohort-specific and time-varying bend points to create brackets for the AIME
- Benefit formula: Sum of the separate portions of AIME multiplied by their respective replacement rates
All OASI parameters from the PWBMsim and Social Security Module (PWBM-SS) and reflect demographics.

Firms

Single-firm Cobb-Douglas production
All tax parameters from PWBMsim and PWBM-TM and reflect composition of sector.
Exogenous split: corporations & pass-throughs
Capital adjustment costs, other expenses
Time-varying cost of capital
Business debt:
- Interest deductibility
- Calibrated “cost of leverage”
- Endogenous from tax-benefit
Time-varying detailed tax treatment:
- Credits, deductions
- Investment expensing (in NPV)
- Other expenses

Openness

Allow closed, small open, and partially open economies.
Exogenous time-varying take-up of government debt by foreigners.
- Percent of each dollar of new debt issued.
Exogenous time-varying foreign investment in capital:
- “World rate” must equal net of taxes capital returns + capital gains.
- Percent of additional investment comes from foreigners
  (small open economy = 100%)
Foreigners pay tax on capital returns (in addition to implicit taxation at the entity level).
- Separate time-varying tax rates on corporate and pass-through incomes.

Government

Expenditures:
- Endogenous OASI benefits
- Remainder is exogenous from PWBMsim and Expenditure Modules.
- Only benefits affect welfare.
Revenues:
- Endogenous from household, business, foreigners
- Remainder is exogenous from PWBMsim and PWBM-TM.
Interest rates on debt are partially endogenous, determined from maturity composition of debt and projected yield curve (exogenous).
Debt held by households and foreigners 🡪 crowds out domestic investment in real capital.
Closure rule:
- Fix debt/GDP at some year via “magic money”.
- Cuts in discretionary spending, but need more cuts than available in budget.

Unanticipated policy shock

Run baseline model
Save full state prior to shock year (including relevant history, e.g., wages for wage indexes)
State includes next period choices of investment (locked in).
Run counterfactual policy from saved new initial state.
Validation: “Non-shock” counterfactual within convergence tolerance of baseline.