Technical Overview of PWBM Dynamic OLG Model
Overlapping generations, general equilibrium, incomplete markets modelPublished January 3, 2019
- 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
- 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.
- Population data from Penn Wharton Budget Model Microsimulation (PWBMsim)
- Born into model at age 20
- Age-dependent survival probability
- Death probability equals 1 at age 100
- Age-dependent immigration (legal & illegal)
- Retirement age is exogenous and cohort-specific
- Tax treatments in the model:
- Ordinary rates
- Preferred rates
- Tax functions from the PWBMsim and Tax Module (PWBM-TM) and reflect demographics
- Cumulative tax liability from a piecewise-linear tax rate function
- 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.
- 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
- 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.
- 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.