# The cyclically adjusted federal budget and federal debt: revised and updated estimates.

The Cyclically Adjusted Federal Budget and Federal Debt: Revised and
Updated Estimates

THE cyclically adjusted budget is an estimate of what the Federal budget would be after removing the automatic responses of receipts and expenditures to enconomic fluctuations. The uses of the cyclically adjusted budget and the methods to measure it have been discussed in several earlier BEA publications.1

1. See Frank de Leeuw and Thomas M. Holloway, "Cyclical Adjustment of the Federal Budget and Federal Debt,' SURVEY OF CURRENT BUSINESS 63 (December 1983): 25-40 and Thomas M. Holloway, Cyclical Adjustment of the Federal Budget and Federal Debt: Detailed Methodology and Estimates, Bureau of Economic Analysis staff paper no. 40 (Washington, DC: U.S. Government Printing Office, 1984).

This article presents revised and updated estimates of the cyclically adjusted budget, cyclically adjusted debt, and trend GNP. The revisions are primarily due to the comprehensive revisions of the national income and product accounts (NIPA's) that became available in December 1985. The first section focuses on how the NIPA revisions affect the estimates. The second section presents revised and updated estimates of the cyclically adjusted budget and debt, based on middle-expansion trend GNP. The final section presents revised and updated estimates of a variant of the cyclically adjusted budget, based on 6-percent unemployment rate trend GNP.

Effects of the NIPA revisions

The NIPA revisions affect the estimates of the cyclically adjusted budget in three important ways. First, because cyclically adjusted receipts and expenditures are derived by subtracting estimates of the automatic cyclical responses from actual receipts and expenditures, revisions in the actual measures result in a dollar-for-dollar change in the corresponding cyclically adjusted measures, ceteris paribus.2 The same methodological approach applies to the income components --wages and salaries, corporate profits, etc.--used to estimate cyclically adjusted tax bases. Because of the way the cyclically adjusted tax bases are used in the model, the net effect on cyclically adjusted receipts of revisions in the actual income components is much smaller than the effect of revisions in actual receipts.

2. The methodological approach is referred to as the "gross-up method.' It is described in detail in Frank de Leeuw, Thomas M. Holloway, Darwin G. Johnson, David S. McClain, and Charles A. Waite, "The High-Employment Budget: New Estimates, 1955-80,' SURVEY 60 (November 1980): 15-16, 18-19.

The second way the NIPA revisions affect the estimates is through trend GNP. Trend GNP--the reference path from which cyclical fluctuations are measured--depends on actual constant-dollar GNP. In the case of middle-expansion trend GNP, geometric means of actual GNP for each middle expansion are connected to form the series. In the case of 6-percent unemployment rate trend GNP, regression results based on actual GNP are used to construct the series. In both cases, NIPA revisions affect the trends, the gaps between actual and trend GNP, and the cyclical adjustment corresponding to the gaps.

The third way the NIPA revisions affect the estimates is through reestimated regression equations. The most important regression equations include those used to estimate cyclically adjusted income components, cyclical tax elasticities, and the cyclical adjustment of net interest paid. In most cases, the specifications of the regression equations were not changed; however, partly as a result of the NIPA revisions, some of the equations were respecified to improve their performance. An example of a respecified equation is the one used to estimate the cyclical adjustment of net interest paid.

Chart 4 shows the revised and previously published estimates of the cyclically adjusted surplus or deficit as percentages of middle-expansion trend GNP. The chart illustrates that there is little difference between the two series in most quarters. Table 1 shows the sources of the revisions in selected quarters when there is a noticeable difference in chart 4. In the table, "data revisions' reflect the first two ways the NIPA revisions affect the cyclically adjusted surplus or deficit; "reestimated equations' reflect the third way. In all quarters, data revisions are the major source of revision. The effects of reestimated equations are sometimes more important for specific categories of receipts and expenditures than is suggested by the net effect on the surplus or deficit.3

3. An example occurs in the second quarter of 1982. Reestimated equations caused decreases in cyclically adjusted receipts and expenditures of about $2.5 billion and $1.6 billion, respectively. The net effect on the deficit was a $0.9 billion increase.

Revised estimates based on middle-expansion trend GNP

Table 2 shows revised estimates of middle-expansion trend GNP and the companion middle-expansion trend unemployment rate. The growth rates in middle-expansion trend GNP are lower than those previously published because the revised growth rates in actual constant-dollar GNP are lower.4 The table also shows the unemployment rate gap and the GNP gap. These gaps play a key role in determining the size and sign of the cyclical adjustment to the actual budget. A positive GNP gap is associated with a positive adjustment to actual receipts in estimating cyclically adjusted receipts; a positive unemployment rate gap is associated with a positive adjustment to actual expenditures in estimating cyclically adjusted expenditures.

4. The middle-expansion trend GNP growth rates by period were revised for 1956-62 from 3.5 to 3.4 percent, for 1962-72 from 4.0 to 3.8 percent, for 1972-77 from 2.9 to 2.6 percent, for 1977-81 from 2.7 to 2.5 percent, and for 1981-85 from 2.5 to 2.1 percent.

The cyclically adjusted budget based on these trends and gaps is shown in table 3. The table shows receipts, expenditures, and the surplus or deficit in billions of dollars and as percentages of trend GNP. The table also decomposes changes in the cyclically adjusted budget into those resulting from the automatic effects of inflation and those resulting from discretionary policy changes and other factors. The revised estimates confirm several points that had been apparent in the previously published estimates:

Starting in the fourth quarter of 1982, the deficit-to-GNP ratio matched or exceeded the ratio in all previous quarters except for the second quarter of 1975.5

5. In the second quarter of 1975, the Tax Reduction Act of 1975 caused a sharp one-quarter decline in receipts and resulted in the increase in the deficit.

The rise in the deficit-to-GNP ratio in recent years has been the result of a decline in the receipts-to-GNP ratio in combination with an increase in the expenditures-to-GNP ratio.

The automatic inflation effects tend to move the budget toward surplus. With the deceleration of inflation, the magnitude of these effects declined in recent years from those in the late 1970's and early 1980's.

The rise in the cyclically adjusted deficit-to-GNP ratio contributed to a rise in the cyclically adjusted debt-to-GNP ratio. In earlier articles, it was suggested that the debt-to-GNP ratio has important effects on macroeconomic developments.6 Specifically, an increase in the cyclically adjusted debt-to-GNP ratio is associated with an increase in interest rates and a decline in the capital-output ratio.

6. See de Leeuw and Holloway, "Cyclical Adjustment of the Federal Budget and Federal Debt,' pp. 37-40. Also see Frank de Leeuw and Thomas M. Holloway, "The Measurement and Significance of the Cyclically Adjusted Federal Budget and Debt,' Journal of Money, Credit, and Banking 17 (May 1985): 232-42.

Changes in the cyclically adjusted debt-to-GNP ratio are related to cyclically adjusted receipts and expenditures in the following way:7

7. Using the definitions in the text following equation (1) and letting the numerical subscripts represent time lags, the debt-to-GNP ratio can be factored as follows:

(D/Y) = DY-1/YY-1 - D-1Y/Y-1Y

= (D-1 D) Y-1 - D-1 (Y-1 Y)/YY-1

= D/Y - (D-1/Y) Y/Y-1

From the definitions of the variables, D = E - T L Z; substituting for D gives:

= E/Y - T/Y L/Y Z/Y - (D-1/Y) g,

the equition shown in the text.

(D/Y) = E/Y - T/Y L/Y Z/Y - g (D-1/Y)

where:

D = cyclically adjusted Federal debt held by the public at the end of the period;

Y = middle-expansion trend GNP in current dollars;

E = cyclically adjusted expenditures;

T = cyclically adjusted receipts;

L = Federal direct loans at the end of the period;

Z = other debt-deficit discrepancy items equal to the change in debt minus the deficit minus the change in loans ( D - (E - T) - L);8

8. The other discrepancy items include net purchases of land, timing differences between NIPA and unified budget receipts, and changes in U.S. Treasury operating cash. A complete list of the items is shown in table 10 of de Leeuw and Holloway, "Cyclical Adjustment of the Federal Budget and Federal Debt,' p. 39.

g = the growth rate of Y, which is Y/ Y-1.

The first two terms on the righthand side involve receipts and expenditures and together represent the deficit-to-GNP ratio. The next two terms involve direct loans and other discrepancy items between the NIPA Federal sector deficit and the change in debt. The final term, referred to as the "trend GNP growth factor,' basically measures the effects of growth in trend GNP on the denominator of the debt-to-GNP ratio.

Table 4 shows the terms of equation (1) and the changes in the cyclically adjusted debt-to-GNP ratio annually for 1956-85. An addendum to the table presents the debt-to-GNP ratio. Chart 5 shows quarterly estimates of the cyclically adjusted receipts- and expenditures-to-GNP ratios, and the debt-to-GNP ratio. Table 5 shows quarterly estimates of actual debt, cyclically adjusted debt, and the cyclically adjusted debt-to-GNP ratio. The revised estimates confirm several points that had been apparent in the previously published estimates:

The debt-to-GNP ratio declined during most quarters from 1955-74, was relatively flat from 1974-82, then increased every quarter starting with the third quarter of 1982.

The debt-to-GNP ratio declined or remained flat during many quarters when the cyclically adjusted budget was in deficit (i.e., when the expenditures line is above the receipts line in chart 5).

Given conditions at 1985 levels, a cyclically adjusted deficit-to-GNP ratio of about 1.2 percent would halt the increase in the cyclically adjusted debt-to-GNP ratio. At 1985 levels, that implies about a $48 billion cyclically adjusted deficit.

Revised estimates based on 6-percent unemployment rate trend GNP

A variant of the cyclically adjusted budget is based on a trend GNP series associated with a constant 6-percent unemployment rate. Table 6 shows, for 1970-85, estimates of the 6-percent unemployment rate variant and the underlying measures of 6-percent unemployment rate trend GNP.9 Compared with the revised and updated estimates of the cyclically adjusted budget based on middle-expansion trend GNP, the deficit-to-GNP ratio of the 6-percent unemployment variant was higher in the early 1970's, about the same in 1974-75, then lower in all subsequent years. The difference has been about 0.9 percentage point in recent years. The pattern of the differences followed the pattern of the differences between the middle-expansion trend unemployment rate and 6.0 percent.

9. The growth rate in constant-dollar 6-percent unemployment rate trend GNP is derived with regression estimates and is 3.4 percent for 1970-74, 3.0 percent for 1974-81, and 2.1 percent for 1981-85.

Table: 1.--Revisions in Estimates of the Cyclically Adjusted Surplus or Deficit Based on Middle-Expansion Trend GNP, Selected Quarters

Table: CHART 4 Cyclically Adjusted Surplus or Deficit, Percent of Trend GNP

Table: 2.--Trend and Actual Unemployment Rate and GNP

Table: 3.--Cyclically Adjusted Federal Receipts and Expenditures

Table: 4.--Relationship of Cyclically Adjusted Receipts and Expenditures to Changes in the Ratio of Debt Held by the Public at Par Value to Trend GNP: Percentage of Trend GNP

Table: 5.--Actual and Cyclically Adjusted Federal Debt Held by the Public at Par Value

Table: CHART 5 Cyclically Adjusted Federal Receipts, Expenditures, and Debt Held by the Public at Par Value, Percent of Trend GNP

Table: 6.--Cyclically Adjusted Federal Receipts and Expenditures Based on 6-Percent Unemployment Rate Trend GNP

THE cyclically adjusted budget is an estimate of what the Federal budget would be after removing the automatic responses of receipts and expenditures to enconomic fluctuations. The uses of the cyclically adjusted budget and the methods to measure it have been discussed in several earlier BEA publications.1

1. See Frank de Leeuw and Thomas M. Holloway, "Cyclical Adjustment of the Federal Budget and Federal Debt,' SURVEY OF CURRENT BUSINESS 63 (December 1983): 25-40 and Thomas M. Holloway, Cyclical Adjustment of the Federal Budget and Federal Debt: Detailed Methodology and Estimates, Bureau of Economic Analysis staff paper no. 40 (Washington, DC: U.S. Government Printing Office, 1984).

This article presents revised and updated estimates of the cyclically adjusted budget, cyclically adjusted debt, and trend GNP. The revisions are primarily due to the comprehensive revisions of the national income and product accounts (NIPA's) that became available in December 1985. The first section focuses on how the NIPA revisions affect the estimates. The second section presents revised and updated estimates of the cyclically adjusted budget and debt, based on middle-expansion trend GNP. The final section presents revised and updated estimates of a variant of the cyclically adjusted budget, based on 6-percent unemployment rate trend GNP.

Effects of the NIPA revisions

The NIPA revisions affect the estimates of the cyclically adjusted budget in three important ways. First, because cyclically adjusted receipts and expenditures are derived by subtracting estimates of the automatic cyclical responses from actual receipts and expenditures, revisions in the actual measures result in a dollar-for-dollar change in the corresponding cyclically adjusted measures, ceteris paribus.2 The same methodological approach applies to the income components --wages and salaries, corporate profits, etc.--used to estimate cyclically adjusted tax bases. Because of the way the cyclically adjusted tax bases are used in the model, the net effect on cyclically adjusted receipts of revisions in the actual income components is much smaller than the effect of revisions in actual receipts.

2. The methodological approach is referred to as the "gross-up method.' It is described in detail in Frank de Leeuw, Thomas M. Holloway, Darwin G. Johnson, David S. McClain, and Charles A. Waite, "The High-Employment Budget: New Estimates, 1955-80,' SURVEY 60 (November 1980): 15-16, 18-19.

The second way the NIPA revisions affect the estimates is through trend GNP. Trend GNP--the reference path from which cyclical fluctuations are measured--depends on actual constant-dollar GNP. In the case of middle-expansion trend GNP, geometric means of actual GNP for each middle expansion are connected to form the series. In the case of 6-percent unemployment rate trend GNP, regression results based on actual GNP are used to construct the series. In both cases, NIPA revisions affect the trends, the gaps between actual and trend GNP, and the cyclical adjustment corresponding to the gaps.

The third way the NIPA revisions affect the estimates is through reestimated regression equations. The most important regression equations include those used to estimate cyclically adjusted income components, cyclical tax elasticities, and the cyclical adjustment of net interest paid. In most cases, the specifications of the regression equations were not changed; however, partly as a result of the NIPA revisions, some of the equations were respecified to improve their performance. An example of a respecified equation is the one used to estimate the cyclical adjustment of net interest paid.

Chart 4 shows the revised and previously published estimates of the cyclically adjusted surplus or deficit as percentages of middle-expansion trend GNP. The chart illustrates that there is little difference between the two series in most quarters. Table 1 shows the sources of the revisions in selected quarters when there is a noticeable difference in chart 4. In the table, "data revisions' reflect the first two ways the NIPA revisions affect the cyclically adjusted surplus or deficit; "reestimated equations' reflect the third way. In all quarters, data revisions are the major source of revision. The effects of reestimated equations are sometimes more important for specific categories of receipts and expenditures than is suggested by the net effect on the surplus or deficit.3

3. An example occurs in the second quarter of 1982. Reestimated equations caused decreases in cyclically adjusted receipts and expenditures of about $2.5 billion and $1.6 billion, respectively. The net effect on the deficit was a $0.9 billion increase.

Revised estimates based on middle-expansion trend GNP

Table 2 shows revised estimates of middle-expansion trend GNP and the companion middle-expansion trend unemployment rate. The growth rates in middle-expansion trend GNP are lower than those previously published because the revised growth rates in actual constant-dollar GNP are lower.4 The table also shows the unemployment rate gap and the GNP gap. These gaps play a key role in determining the size and sign of the cyclical adjustment to the actual budget. A positive GNP gap is associated with a positive adjustment to actual receipts in estimating cyclically adjusted receipts; a positive unemployment rate gap is associated with a positive adjustment to actual expenditures in estimating cyclically adjusted expenditures.

4. The middle-expansion trend GNP growth rates by period were revised for 1956-62 from 3.5 to 3.4 percent, for 1962-72 from 4.0 to 3.8 percent, for 1972-77 from 2.9 to 2.6 percent, for 1977-81 from 2.7 to 2.5 percent, and for 1981-85 from 2.5 to 2.1 percent.

The cyclically adjusted budget based on these trends and gaps is shown in table 3. The table shows receipts, expenditures, and the surplus or deficit in billions of dollars and as percentages of trend GNP. The table also decomposes changes in the cyclically adjusted budget into those resulting from the automatic effects of inflation and those resulting from discretionary policy changes and other factors. The revised estimates confirm several points that had been apparent in the previously published estimates:

Starting in the fourth quarter of 1982, the deficit-to-GNP ratio matched or exceeded the ratio in all previous quarters except for the second quarter of 1975.5

5. In the second quarter of 1975, the Tax Reduction Act of 1975 caused a sharp one-quarter decline in receipts and resulted in the increase in the deficit.

The rise in the deficit-to-GNP ratio in recent years has been the result of a decline in the receipts-to-GNP ratio in combination with an increase in the expenditures-to-GNP ratio.

The automatic inflation effects tend to move the budget toward surplus. With the deceleration of inflation, the magnitude of these effects declined in recent years from those in the late 1970's and early 1980's.

The rise in the cyclically adjusted deficit-to-GNP ratio contributed to a rise in the cyclically adjusted debt-to-GNP ratio. In earlier articles, it was suggested that the debt-to-GNP ratio has important effects on macroeconomic developments.6 Specifically, an increase in the cyclically adjusted debt-to-GNP ratio is associated with an increase in interest rates and a decline in the capital-output ratio.

6. See de Leeuw and Holloway, "Cyclical Adjustment of the Federal Budget and Federal Debt,' pp. 37-40. Also see Frank de Leeuw and Thomas M. Holloway, "The Measurement and Significance of the Cyclically Adjusted Federal Budget and Debt,' Journal of Money, Credit, and Banking 17 (May 1985): 232-42.

Changes in the cyclically adjusted debt-to-GNP ratio are related to cyclically adjusted receipts and expenditures in the following way:7

7. Using the definitions in the text following equation (1) and letting the numerical subscripts represent time lags, the debt-to-GNP ratio can be factored as follows:

(D/Y) = DY-1/YY-1 - D-1Y/Y-1Y

= (D-1 D) Y-1 - D-1 (Y-1 Y)/YY-1

= D/Y - (D-1/Y) Y/Y-1

From the definitions of the variables, D = E - T L Z; substituting for D gives:

= E/Y - T/Y L/Y Z/Y - (D-1/Y) g,

the equition shown in the text.

(D/Y) = E/Y - T/Y L/Y Z/Y - g (D-1/Y)

where:

D = cyclically adjusted Federal debt held by the public at the end of the period;

Y = middle-expansion trend GNP in current dollars;

E = cyclically adjusted expenditures;

T = cyclically adjusted receipts;

L = Federal direct loans at the end of the period;

Z = other debt-deficit discrepancy items equal to the change in debt minus the deficit minus the change in loans ( D - (E - T) - L);8

8. The other discrepancy items include net purchases of land, timing differences between NIPA and unified budget receipts, and changes in U.S. Treasury operating cash. A complete list of the items is shown in table 10 of de Leeuw and Holloway, "Cyclical Adjustment of the Federal Budget and Federal Debt,' p. 39.

g = the growth rate of Y, which is Y/ Y-1.

The first two terms on the righthand side involve receipts and expenditures and together represent the deficit-to-GNP ratio. The next two terms involve direct loans and other discrepancy items between the NIPA Federal sector deficit and the change in debt. The final term, referred to as the "trend GNP growth factor,' basically measures the effects of growth in trend GNP on the denominator of the debt-to-GNP ratio.

Table 4 shows the terms of equation (1) and the changes in the cyclically adjusted debt-to-GNP ratio annually for 1956-85. An addendum to the table presents the debt-to-GNP ratio. Chart 5 shows quarterly estimates of the cyclically adjusted receipts- and expenditures-to-GNP ratios, and the debt-to-GNP ratio. Table 5 shows quarterly estimates of actual debt, cyclically adjusted debt, and the cyclically adjusted debt-to-GNP ratio. The revised estimates confirm several points that had been apparent in the previously published estimates:

The debt-to-GNP ratio declined during most quarters from 1955-74, was relatively flat from 1974-82, then increased every quarter starting with the third quarter of 1982.

The debt-to-GNP ratio declined or remained flat during many quarters when the cyclically adjusted budget was in deficit (i.e., when the expenditures line is above the receipts line in chart 5).

Given conditions at 1985 levels, a cyclically adjusted deficit-to-GNP ratio of about 1.2 percent would halt the increase in the cyclically adjusted debt-to-GNP ratio. At 1985 levels, that implies about a $48 billion cyclically adjusted deficit.

Revised estimates based on 6-percent unemployment rate trend GNP

A variant of the cyclically adjusted budget is based on a trend GNP series associated with a constant 6-percent unemployment rate. Table 6 shows, for 1970-85, estimates of the 6-percent unemployment rate variant and the underlying measures of 6-percent unemployment rate trend GNP.9 Compared with the revised and updated estimates of the cyclically adjusted budget based on middle-expansion trend GNP, the deficit-to-GNP ratio of the 6-percent unemployment variant was higher in the early 1970's, about the same in 1974-75, then lower in all subsequent years. The difference has been about 0.9 percentage point in recent years. The pattern of the differences followed the pattern of the differences between the middle-expansion trend unemployment rate and 6.0 percent.

9. The growth rate in constant-dollar 6-percent unemployment rate trend GNP is derived with regression estimates and is 3.4 percent for 1970-74, 3.0 percent for 1974-81, and 2.1 percent for 1981-85.

Table: 1.--Revisions in Estimates of the Cyclically Adjusted Surplus or Deficit Based on Middle-Expansion Trend GNP, Selected Quarters

Table: CHART 4 Cyclically Adjusted Surplus or Deficit, Percent of Trend GNP

Table: 2.--Trend and Actual Unemployment Rate and GNP

Table: 3.--Cyclically Adjusted Federal Receipts and Expenditures

Table: 4.--Relationship of Cyclically Adjusted Receipts and Expenditures to Changes in the Ratio of Debt Held by the Public at Par Value to Trend GNP: Percentage of Trend GNP

Table: 5.--Actual and Cyclically Adjusted Federal Debt Held by the Public at Par Value

Table: CHART 5 Cyclically Adjusted Federal Receipts, Expenditures, and Debt Held by the Public at Par Value, Percent of Trend GNP

Table: 6.--Cyclically Adjusted Federal Receipts and Expenditures Based on 6-Percent Unemployment Rate Trend GNP

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Author: | Holloway, Thomas M. |
---|---|

Publication: | Survey of Current Business |

Date: | Mar 1, 1986 |

Words: | 1975 |

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