By Daniela Viana Costa
U.S. federal debt is projected to grow substantially faster than GDP over time, increasing the federal debt-to-GDP ratio over time. At some date in the future, the cost of servicing that debt will absorb the entire GDP of the economy. However, capital market investors are forward-looking and, based on past experience, will respond well before that future date, including requiring additional compensation (a larger “risk premium”) for investing.
Modern economic models that incorporate this forward-looking behavior, therefore, will fail to solve, without an additional assumption how Congress will eventually stabilize the debt-to-GDP ratio at a sustainable level. This assumption is commonly known as the “closure rule” because it “closes” the model mathematically rather than leaving the stabilizing decision open and unsettled.
PWBM’s Closure Rule
In recent analyses, PWBM begins stabilizing the debt-to-GDP ratio in 2050 (or later) at a maximum of the debt-to-GDP value that the policy being analyzed generates by 2050. So, for example, if a particular policy generates a debt-to-GDP ratio of 110 percent by 2050, PWBM does not allow the debt-to-GDP ratio to exceed 110 percent in the years after 2050.
This stabilization is achieved by assuming that a change in policy (the “closure rule”) occurs in 2050 to maintain stabilization. There are a variety of different potential closure rules that could be used to achieve this stabilization. Because capital market participants are forward-looking, the exact choice of closure rule has an impact on the analysis of the economy even before 2050.
PWBM's Dynamic OLG model mitigates the impact of the closure rule in two primary ways. First, our choice of 2050 is typically well beyond the time window of interest to policymakers, which often focuses on the first 10 or 20 years. However, for some programs, like Social Security, a longer time window is desirable. In these cases, a later closure rule date, like 2100 might be desirable. Unfortunately, such a long date might be impossible to achieve if debt has exploded before then, making it mathematically impossible to meet the debt payments.
Second, to stabilize the debt-to-GDP ratio, PWBM cuts government spending, except for spending on entitlement programs (Social Security, Medicare, and Medicaid) or public capital projects such as roads. While this choice attempts to minimize the economic disruption produced by the closure rule, this choice avoids other--and potentially even more realistic--choices that could be more disruptive on the economy prior to the closure date, including increasing taxes.1 Put differently, while PWBM’s analysis demonstrates a considerable negative impact of debt on the economy, the choice of closure rule is still more favorable to debt than alternatives.
The experts at CBO also use a closure rule with three key differences. First, besides a reduction in government spending, CBO also reports the impact of stylized tax increases to stabilize the debt-to-GDP ratio. Second, CBO phases in the federal debt stabilization over a 10-year period, producing smoother results around the closure year. In contrast, PWBM intentionally imposes the closure rule at the stated targeted closure-rule date (e.g., 2050) without smoothing. PWBM’s position is that the closure rule is an artificial device that should not be confused with actual policy under current law. Put differently, PWBM’s position is that the bluntness of the closure rule correctly highlights the “bug” of an unsustainability policy instead of allowing the closure rule to be confused as a “feature” of that policy. Third, CBO’s closure rule generally starts to be implemented within 16 years.
How Important is Closure Rule Year on PWBM Projections?
To assess the importance of the choice of the closure year, Table 1 shows the debt-to-GDP ratio over time for three different choices of closure years under present law: 2050, 2060, and 2070. Consistently, the later the choice of closure year, the larger the debt that is allowed to accumulate relative to GDP.
| Closure Rule Year | |||
|---|---|---|---|
| Year | 2050 | 2060 | 2070 |
| 2020 | 0.88 | 0.88 | 0.88 |
| 2030 | 1.33 | 1.33 | 1.33 |
| 2040 | 1.93 | 1.93 | 1.93 |
| 2050 | 2.65 | 2.72 | 2.71 |
| 2060 | 2.65 | 3.73 | 3.82 |
| 2070 | 2.65 | 3.73 | 5.34 |
Note: Consistent with our previous dynamic analysis and the empirical evidence, the dynamic projections above assume that the U.S. economy is 40 percent open and 60 percent closed. Specifically, 40 percent of new government debt is purchased by foreigners.
Figure 1 shows that until 2040, all three closure years choices generate very similar projections for key macroeconomic variables. However, after 2040, sharp differences emerge. Because 2050 and 2060 allow for more debt,2 these choices of closure rules produce a larger crowd-out of investment, thereby producing a smaller capital stock and GDP relative to the choice of 2040. Table 2 summarizes differences in macroeconomic variables at decade-level increments.
Metric
Note: Consistent with our previous dynamic analysis and the empirical evidence, the dynamic projections above assume that the U.S. economy is 40 percent open and 60 percent closed. Specifically, 40 percent of new government debt is purchased by foreigners.
| Debt (% Change) | GDP (% Change) | Capital Services (% Change) | ||||
|---|---|---|---|---|---|---|
| Year | 2050 | 2070 | 2050 | 2070 | 2050 | 2070 |
| 2020 | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% |
| 2030 | 0.00% | 0.00% | -0.04% | 0.00% | -0.07% | -0.01% |
| 2040 | 0.06% | -0.02% | -0.20% | 0.06% | -0.41% | 0.07% |
| 2050 | -2.76% | -0.10% | -0.20% | 0.29% | -0.17% | 0.53% |
Note: Consistent with our previous dynamic analysis and the empirical evidence, the dynamic projections above assume that the U.S. economy is 40 percent open and 60 percent closed. Specifically, 40 percent of new government debt is purchased by foreigners.
In conclusion, each closure year assumption delivers similar results for macroeconomic variables over the next two decades. However, for policies in which policymakers are interested in a longer time horizon (e.g., Social Security), the choice of the closure rule becomes more material. Ideally, the assumed closure year would occur outside of the time window of interest since the closure rule itself is artificial and not actual policy. But, a closure year that occurs very far into the future might be mathematically impossible to solve, reflecting the unsustainable nature of policy up until that closure year.
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See, for example, Shinichi Nishiyama and Felix Reichling, 2015, “The costs to different generations of policies that close the fiscal gap,” Working Paper 2015--10, Congressional Budget Office. ↩
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Debt is higher in 2040 with earlier closures because forward-looking agents anticipate the closure and do less to mitigate the debt. ↩