An Overview of CBO's Life-Cycle Growth Model

CONGRESSIONAL BUDGET OFFICE
An Overview of CBO’s
Life-Cycle Growth Model
February 2019

1
CBO
CBO uses several models to analyze the effects of fiscal policy. In CBO’s view, changes in fiscal
policy affect the economy in both the short and long term:
 Short-term effects are driven by changes in the demand for goods and services (such as
consumption and investment) and changes in supply-side factors (such as growth in productivity
and the supply of labor), as well as by the interactions between them.
 Long-term effects are primarily driven by changes in supply-side factors such as national saving,
productivity, and people’s incentives to work, save, and invest.
The life-cycle growth model (also called an overlapping-generations, or OLG, model) is one model
that CBO uses to estimate the long-term effects of changes in fiscal policy.
CBO’s Fiscal Policy Models

2
CBO
CBO uses the model to analyze the effects of fiscal policy on the following:
 People’s incentives to work and save;
 The distribution of income, wealth, consumption, and taxes across households; and
 The well-being of different generations of households.
For example, the model can analyze the effects of changes to the Social Security system.
Key Purposes of the Life-Cycle Growth Model

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CBO
The model has several useful features for analyzing changes in fiscal policy:
 The effects of government spending and taxation on households’ behavior vary with their age,
income, and wealth, allowing the effects of fiscal policy to be broken down by generation and
different demographic groups.
 Households of different ages have different marginal propensities to consume, which is important
in analyzing the effects of transfer payments.
 Households’ work decisions vary with their age, income, and wealth, which is important in
understanding the effects of changes in tax rates.
Features of the Model

4
CBO
 A Macroeconomic Analysis of the President’s Budget (2016)
 A Macroeconomic Analysis of the President’s Budget (2015)
 The Costs to Different Generations of Policies That Close the Fiscal Gap,
CBO Working Paper 2015-10
 Fiscal Policy Effects in a Heterogeneous-Agent Overlapping-Generations Economy
With an Aging Population, CBO Working Paper 2013-07
 Economic Impacts of Waiting to Resolve the Long-Term Budget Imbalance,
CBO Economic and Budget Issue Brief 2010-12
CBO Analyses Using the Life-Cycle Growth Model

5
CBO
Structure of the Life-Cycle
Growth Model

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CBO
 Households in the model optimally choose consumption, saving, and labor
supply over their lifetime. Households are rational and forward-looking.
 Firms purchase households’ labor and rent capital to maximize profits.
 The government collects income, payroll, and consumption tax revenues and
runs public programs, including a Social Security system and other transfer
programs. It finances budget deficits through borrowing.
 The rest of the world in the model interacts with the domestic economy
through financial markets.
Four Components of the Model

7
CBO
Interactions in Life-Cycle Growth Model
Payments flow between
households, firms, the
government, and the
international economy.

8
CBO
 Shinichi Nishiyama and Felix Reichling,The Costs to Different Generations of Policies That Close
the Fiscal Gap, Working Paper 2015-10 (Congressional Budget Office, December 2015),
www.cbo.gov/publication/51097.
 Shinichi Nishiyama and Kent Smetters, “Analyzing Fiscal Policies in a Heterogeneous-Agent
Overlapping-Generations Economy,” in Karl Schmedders and Kenneth L. Judd, eds., Handbook of
Computational Economics, vol. 3 (Elsevier, 2014), pp. 117–160.
 Shinichi Nishiyama, Fiscal Policy Effects in a Heterogeneous-Agent Overlapping-Generations
Economy With an Aging Population, Working Paper 2013-07 (Congressional Budget Office,
December 2013), www.cbo.gov/publication/44941.
Model Details

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CBO
In each period a new cohort of households is born. As households age, their mortality risk increases
independently of their income, wealth, and other household characteristics. Households live to a
maximum age of 100.
Structure of Households Over Time

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CBO
 Households are differentiated not just by their age but also their wage rate, wealth, and average
lifetime earnings.
 Those differences mean that different households of the same age can respond differently to the
same policy change.
 That has important effects on the overall macroeconomic response to fiscal policy changes.
Structure of Households Over Time

11
CBO
These figures depict the life-cycle behavior of an average household in the model. Vertical axes
show internal model values and are useful only for comparisons of relative size over the life cycle.
Retirement is set at age 65.
Life-Cycle Behavior of Individuals
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
20 30 40 50 60 70 80 90
Age
Private Consumption
0.00
0.20
0.40
0.60
0.80
1.00
1.20
20 30 40 50 60 70 80 90
Age
Hours Worked
-2.00
0.00
2.00
4.00
6.00
8.00
10.00
12.00
20 30 40 50 60 70 80 90
Age
Private Wealth
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
20 30 40 50 60 70 80 90
Age
Income Taxes Paid

12
CBO
Fiscal Policy in the Model

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CBO
 There are four types of taxes in the model:
– Progressive income tax
– Flat payroll tax
– Flat consumption tax
– Lump-sum tax
 The model has four types of government outlays:
– Spending on goods and services
– Old-Age, Survivors, and Disability Insurance (OASDI) and Medicare transfer payments
– Other lump-sum transfer payments to households
– Interest payments made on outstanding debt
Key Features of Fiscal Policy in the Model

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CBO
 The government operates a budget based on the tax revenues it collects from households and
its outlays.
 In the short run, the government does not have to balance its budget in each period and can
finance deficits through debt issuance or run a surplus.
 In the long run, the government adjusts fiscal policy to stabilize the debt-to-GDP ratio.
Key Features of Fiscal Policy in the Model

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CBO
 Debt evolves over time as revenues differ from outlays.
 In each period, the next period’s debt is current debt plus
– Spending on goods and services,
– OASDI and Medicare transfer payments,
– Other lump-sum transfer payments to households, and
– Interest payments made on outstanding debt
and minus
– Income taxes collected,
– Payroll taxes collected,
– Consumption taxes collected, and
– Lump-sum taxes collected.
Government Debt Over Time

16
CBO
Simulating the Effects of
Fiscal Policy Changes

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CBO
Effects of fiscal policy changes are assessed by examining the differences between a baseline
simulation and an alternative simulation:
 A baseline simulation is a set of projections for macroeconomic variables produced under the
assumption that current law will remain unchanged over the period of interest, followed by a policy
change that stabilizes the debt-to-GDP ratio in the long run.
 The alternative simulation incorporates the policy changes in question during the period of
interest, followed by a policy change that stabilizes the debt-to-GDP ratio in the long run.
Baseline and Alternative Simulations

18
CBO
Simulation Procedure
Select Model Parameters
For each period, the model
 Solves for households’ optimal work and saving decisions,
 Solves for the firms’ optimal investment and hiring decisions,
 Implements the government’s taxation and outlay policies, and
 Finds the market-clearing wage and interest rate.
The model produces a time series of projected values for
 Saving, consumption, labor supply, taxes paid, and transfers received for all households;
 Capital holdings, labor, and output (GDP) for firms;
 Total government revenue, outlays, borrowing, and debt; and
 The market-clearing wage and interest rate.

19
CBO
 In the model, budget deficits adjust in the long run to ensure that fiscal policy changes do not
result in an unsustainable path for government debt.
 Those adjustments are implemented through a closure rule and usually consist of changes in
various types of outlay and/or tax policies.
 CBO sets the closure rule to ensure a stable solution to the model for each simulation and to
minimize interference with the effects of the fiscal policies that underlie those simulations.
The Closure Rule

21
CBO
This example quantifies the economic effects of stabilizing the debt-to-GDP ratio earlier rather than
later. Those effects are assessed by comparing the economic outcomes under two illustrative
policies:
 Policy 1 starts reducing federal deficits in 2025 to stabilize the debt-to-GDP ratio by 2035.
 Policy 2 starts reducing federal deficits in 2035 to stabilize the debt-to-GDP ratio by 2045.
Because the policy starts later, the deficit reductions are larger.
Under each policy, the debt-to-GDP ratio is stabilized in the long run by an equal cut to government
spending on goods and services and increase in lump-sum taxes.
Households and firms have perfect foresight and alter their behavior in anticipation of future policy
changes.
Effects of Waiting to Stabilize the Debt-to-GDP Ratio

22
CBO
Because Policy 2 starts reducing deficits 10 years later than Policy 1, the debt-to-GDP ratio is higher
in the long run under Policy 2.
0
40
80
120
160
200
2018 2028 2038 2048 2058 2068 2078 2088
Percentage of GDP Debt
Policy 1 (2035 Closure) Policy 2 (2045 Closure)

23
CBO
Stabilizing the debt-to-GDP ratio in 2045 instead of 2035 results in the following:
 Lower levels of capital and GDP due to more crowding out of private investment driven by a higher
level of debt relative to GDP;
 A lower level of labor supply driven by lower wages and the later increase in lump-sum taxes; and
 An increase in private consumption in the short term but a substantial decrease in private
consumption in the long run. That is driven by the later increase in lump-sum taxes and a relatively
lower wage rate in the long run.

24
CBO
These figures show the estimated effects of stabilizing the debt-to-GDP ratio in 2045 instead of
2035. The effects are expressed as changes from what each variable would equal in a given year if
stabilization occurred in 2035.
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
2018 2028 2038 2048 2058
Percentage
Capital Stock
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
2018 2028 2038 2048 2058
Percentage
GDP
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
2018 2028 2038 2048 2058
Percentage
Labor Supply
-3,500
-3,000
-2,500
-2,000
-1,500
-1,000
-500
0
500
1,000
1,500
2018 2028 2038 2048 2058
2017DollarsperHousehold
Private Consumption

25
CBO
These slides were prepared to enhance the transparency of the work of the Congressional Budget
Office and to encourage external review of that work. In keeping with CBO’s mandate to provide
objective, impartial analysis, this document makes no recommendations.
Jaeger Nelson and Kerk Phillips prepared this document with guidance from Jeffrey Werling and
Devrim Demirel. Wendy Edelberg and Jeffrey Kling reviewed the document, and Rebecca Lanning
edited it. An electronic version is available on CBO’s website (www.cbo.gov/publication/54985).
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An Overview of CBO's Life-Cycle Growth Model

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