Technical Overview of PWBM Dynamic OLG Model

Overlapping generations, general equilibrium, incomplete markets model

Published 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.

Household demographics

  • 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

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.


  • 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.


  • Expenditures:
  • 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.