Appendix I. The Framework for Long-Term Growth Projections
Total factor productivity:
Hours per employed:
where the circumflex ^ denotes percent change
Y = real GDP
A = total factor productivity, which grows at a constant rate
B = Harrod neutral technical progress, related to total factor productivity by
u = capacity utilization. It is constant after the completion of the current cycle.
C = capital stock
H = total hours worked
hf, hp = hours worked per full-time and per part-time employee
π = share of part-time employment
L = employment
UR = unemployment rate. It is set equal to the NAIRU after the completion of the cycle.
The above model enables us to express GDP growth as the sum of seven components:
where the bracketed term equals average productivity growth.
At the steady state, the following relations hold among the key variables:
Output growth is the sum of growth in labor productivity and hours worked:
The output-capital ratio remains unchanged:
The capital-labor ratio, expressed in efficiency units,
Expressed in physical units, the capital-labor ratio increases at the rate of
Labor productivity per hour worked depends on TFP growth and the labor elasticity of output:
Appendix II. Fiscal Sustainability: Some Theoretical Considerations
43. For analytic purposes it is useful to divide public expenditure into three categories: public pension payments and medical benefits, St; all other expenditure excluding interest, Gt; and interest on public debt, Rt•Dt-1, where Dt denotes the end-of-period level of net debt and Rt is the nominal interest rate on this debt. The distinction between the assets of the public pension system and public debt is only of accounting nature because, ultimately, the public sector will be responsible for the unfunded pension liabilities of the first pillar and, through guarantee schemes, for the second pillar. In view of this, the discussion below is cast in terms of net public debt, i.e. gross debt minus the assets of social security.21
44. Debt dynamics are governed by the one-period government budget constraint:
where Tt denotes tax revenue plus contributions, NTt nontax revenue, including seigniorage, and
45. Since PV is additive in the stream of primary balances
We can use equation (3) to quantify how much each individual component of social security contributes to the increase of public sector’s indebtedness.
46. Because of its additivity, PV can be further decomposed as
That is, the increase on public indebtedness is equal to the present value of the general government primary balance in the absence of aging plus the present value of the change in the primary balance due to aging.
47. Following Blanchard (1990), we define fiscal policy as sustainable if the current policies can be continued in the future without raising the public debt-to-GDP ratio to levels that the market is not prepared to finance at prevailing interest rates. In a partial equilibrium model like the present one, the critical level of debt is determined outside the model and, as a first approximation, it is set equal to the current level of debt. Thus,
48. Neither the metric of the imbalance nor the definition of sustainability is unique. The metric can also be expressed in terms of revenue/expenditure (e.g. by how much should taxes be raised to restore sustainability) or specific measures (e.g. how much is the need to raise contribution rates or cut public pensions to sustain the current generosity of the pension/health care system). The definition of sustainability may be strengthened to ensure that the debt/GDP ratio does not exceed a certain ceiling at all times. Cast in a generational context, policies can be defined as sustainable if their burden is affordable and equitably distributed among generations (e.g., Kotlikoff, 2001).
49. The present value metric of fiscal imbalance is sensitive to the choice of the discount factor. If future fiscal balances are projected to be in deficit, the present value is monotonically decreasing in the discount factor, ζ, since future deficits are discounted at a higher rate. Depending on the choice of the discount factor, this could lead to a situation where the present value of future deficits is low while at the same time future deficit and debt reach levels that could lead to serious downgrading of credit ratings and refinancing problems that, in turn, could trigger a disorderly fiscal adjustment. Thus, the present value metric is not a sufficient summary measure of the fiscal imbalance and a low present value does not obviate the need to look at the future path of debt. A useful supplementary indicator is the number of years it would take for debt to reach a critical threshold beyond which rating agencies are likely to start downgrading the public sector’s creditworthiness.
Appendix III. A Framework for Old Age and Disability Pension Projections
50. The primary expenditure for old age and disability pensions can be modeled as the product of the average pension (which for simplicity and without loss of generality includes also administrative costs) times the number of pensioners, and in percent of GDP can be expressed as22
where a = average nominal pension, including administrative costs. It is based on lifetime earnings (adjusted for inflation), it is subject to a ceiling (2004: SwF 2110 per month for individual pensioner) and the replacement rate for an average income earner is 45 percent. i = I/PO = pensioners in percent of the elderly, which depends on the coverage of the pension insurance and the extent of early retirement. The ratio is boosted by the existence of pensioners, primarily former foreign workers, who live outside Switzerland. ξ = PO/E = old-age dependency, that is the number of elderly per employed. It can be expressed as the share of elderly in the population divided by the activity rate, the participation rate and the unemployment rate: ξ = (PO/POP)·(POP/POPT)·(POPT/LF)·(1+UR) y=Y/E = average labor productivity.
51. Thus, the change of primary pension expenditure (in percent of GDP) relative to base period expenditure is given by
Pension expenditure increases when (i) the average pension rises faster than inflation plus labor productivity growth, (ii) the share of pensioners in the elderly rises, and (iii) old age dependency rises. In the past quarter century, average pensions increased at an annual rate of 2.7 percent, practically at the same rate as the growth of the GDP deflator plus labor productivity, leaving the bracketed term roughly unchanged.23 As a result, the evolution of expenditure has been driven by the rise in old-age dependence (ξ) and early retirement (i). Higher immigration reduces pension expenditure in percent of GDP to the extent that it reduces old-age dependence (ξ). Similarly, an increase in the effective retirement age reduces pension expenditure by raising the participation rate.
Annual average rate of change in 1980-2003
Annual average rate of change in 1980-2003
|Old age and survivor pensions||2.7|
Annual average rate of change in 1980-2003
|Old age and survivor pensions||2.7|
52. Primary revenue of the pension system comprise contributions and earmarked VAT rates:
W= average nominal wage
B= persons contributing to the pension system (includes also Swiss working abroad)
v = the VAT rate that is earmarked for the financing of pensions, and
h= incidence of VAT.
53. If, as it has been the case in Switzerland, real wages increase in line with labor productivity (leaving the labor share practically unchanged) and the ratio of contributors to employment remains constant, revenue dynamics are driven by the evolution of contribution and earmarked VAT rates. An increase in the effective retirement age or immigration would raise revenue in absolute terms but not in percent of GDP. Hence, in the absence of measures the evolution of the primary balance of the first pillar is driven exclusively by expenditure.
54. The projected increases in the deficit of old age and disability pensions, along with the evolution of the number of pensioners and the ratio of benefits vis-à-vis productivity growth, are given in Figure I-6.
Appendix IV. A Framework for Health Care Projections
55. Primary health care expenditure is modeled as the product of the average expenditure per insured times the number of insured persons and, in percent of GDP, is expressed as
and the evolution of expenditure relative to the base period is given by
h = average health care expenditure per insured person. It depends on inflation in the health care sector, the generosity of the health care system (how extensive is the list of covered diagnostic procedures and treatable illnesses) and the average age of the insured (expenditure increase rapidly for persons over 50 and for octogenarians they are four times the expenditure for person under 50).
i= insured individuals in percent of the population.
e = employment as percent of the population, which equals the product of the activity rate, participation rate and the unemployment rate.
56. Primary revenue is modeled as the product of the contribution rate, c (which is defined to include co-payments by insured), times the number of insured persons. In percent of GDP, revenue are given by
57. Thus, the operating balance and its evolution relative to the base year are given by
58. The evolution of the deficit (Figure I-7) is driven primarily by the shortfall of the contribution rate from per capita expenditure (c–h) and employment rate e. The projections assume that the contribution rate and the government subsidy (in percent of GDP) remain unchanged at their present level.
Appendix V. Data Sources
59. Population and working-age population: OECD Analytical Data Base (ADB) until 2000. From 2001 onwards, the two growth rates are set equal to the ones reported in BfS’ baseline scenario.
60. The labor force series is constructed as the sum of employment and registered unemployment. Employment figures up to 2003 are obtained from ADB. The 2004 estimate is based on the rate of change reported in the BfS employment statistics. From 2005 onward, employment is linked to GDP and is based on the assumption that labor productivity will grow at an average rate of 1.1 percent per year. The registered unemployment series is from ADB. Unemployment is projected to decline to the NAIRU (2.3 percent) by 2010.
61. Data on hours worked, with a breakdown between full- and part-time employed, are available since 1991 from the Federal Statistical Office, BfS. The series are backcasted using the product of the number of work-weeks per year times the average contractual hours per week as reported by BfS. In 1991-2002, full-timers worked 2.5 times more hours than part-timers. This ratio, which has been fairly stable, is used to link the hours of full- and part-time workers in earlier years.
62. The share of part-time employment in total employment is derived from the hours statistics.
63. In the absence of official estimates, capital stock is computed from investment at constant prices (excluding residential construction)24 using as starting value the 1968 capital stock estimate in Lüscher and Ruoss (1996) and applying exponential depreciation. Depreciation rates are based an expected life of 50 years for structures, 15 years for machinery and equipment, and 4 years for software. These values are similar to those used by the Federal Statistical Office. In addition to ordinary depreciation, additional depreciation is applied in years of extensive restructuring, such as in the period after the oil shocks and the protracted recession in the 1990s. With the composition of investment changing over time, the average depreciation rate rose gradually from 4 percent in early 1970s to 5 percent in the early 2000s.
64. Capacity utilization in industry is obtained from the KOF data bank. Due to a break in the series, pre-1999 values are reduced by 3 percentage points.
Blanchard, O., 1990, “Suggestions for a New Set of Fiscal Indicators,” OECD Economics and Statistics Department Working Paper No. 79
Borgmann, C. and B. Raffelhüschen, 2004, “Zur Entwicklung der Nachhaltigkeit der schweizerischen Fiskal- und Generationenbilalzen 1995-2001”, Swiss Economic Swcretariat (seco), Bern.
Bundesamt für Sozialversicherung, 2003, “Finanzierungsbedarf in der AHV (inkl. EL)”, Beiträge zur Sozialen Sicherheit, Forschungsbericht Nr. 10/03, Bern.
Commission of the European Communities, 2005, “Green Paper ‘Confronting demographic change: a new solidarity between generations’”, COM (2005) 94 final.
Duval, R., 2003, “The Retirement Effects of Old-Age Pension and Early Retirement Schemes in OECD Countries”, OECD, Economics Department Working Paper No. 370.
Frederiksen, Niels, 2001, “Fiscal Sustainability in the OECD: A Simple Method and Some Preliminary Results”, Working Paper No. 3/2001, Finansministeriet, Denmark.
Hall, R., 1988, “The Relation between Price and Marginal Cost in U.S. Industry,” Journal of Political Economy, vol. 96 (October), pp. 921–47.
Keel, A., K. Frauendorfer and U. Jacoby, 2003, #x201C;Studie über die kurz- und mittelfristigen Finanzierungsrisiken von Vorsorgeeinrichtungen—Schlussbericht”, Instut für Unternehmensforschung, Universität St. Gallen.
Lüscher, B. and E. Ruoss, 1996, “Entwicklung der Potentiellen Produktion in der Schweiz,” Swiss National Bank, Quarterly Bulletin, No. 14(1).
Olivera Martins, J., S. Scarpetta and D. Pilat, 1996, “Mark-up Pricing, Market Structure and the Business Cycle”, OECD Economic Studies, No. 27.
Prepared by Anastassios Gagales.
To the extent that a drop in asset prices will be accompanied by higher yields, it would become more difficult to fund any fiscal deficit.
To facilitate international comparisons, the discussion in this section is based on the World Bank’s multicountry population projections.
Product market reforms could add ½ percentage point to growth in the medium term: Gagales (2002) estimates that reducing markups to the OECD average could boost productivity growth by 0.1-0.3 percentage point. The OECD (2002) estimates an even stronger effect (a cumulative increase of 4-7 percent of GDP over a ten-year period) from the liberalization of the health, agriculture, electricity, and gas sectors. These results are confirmed by growth regressions, which suggest that, had Switzerland pursued structural reforms more vigorously and maintained its relative rank in terms of market openness, average annual growth could have been ½ percent faster over a five-year period.
The Cobb-Douglas production function fitted the data (1972–2004) reasonably well but the estimated parameters were not very precise. The confidence interval for the labor elasticity of output ranged from 60 to 90 percent but estimates across alternative specifications were centered on 70 percent.
Euler’s theorem for homothetic functions implies that, in the case of Cobb-Douglas production functions, labor elasticity is equal to θ=(w·L)/(c·Q), where w and c stand for the wage rate and the marginal cost (the latter equals price in perfect competition). If market power introduces a wedge between the price of output and its marginal cost, 1+µ = p/c, then θ=SL· (1+ µ), where SL=(w·L)/(p·Q) is the estimate of the labor share in the national accounts.
The primary deficit of social security is defined as the difference between noninterest expenditure and revenue from contributions, co-payments, and earmarked taxes. It is financed with subsidies from the federation and the cantons, plus a run-down of assets.
For a detailed discussion on the growing costs of health care, see Chapter II on “The Need for Health Care Reform.”
The proceeds from the sale of excess gold reserves that were transferred to the federation and cantons in 2005 could reduce public debt by up to 4.6 percent of GDP.
The projections incorporate, in addition to the aging-related assumptions outlined in Section I-C, the following assumptions:
The nominal interest rate is set at 0.4 percentage point over nominal GDP growth, the average differential in the past 20 years.
The general government runs a structural primary surplus (excluding transfers to the first pillar and health care) of 6 percent of GDP, its level at the base year of the projections adjusted for the effect of ongoing fiscal consolidation measures.
Benefits in the first-pillar pension system grow at half the rate of productivity growth and the incidence of early retirement and disability declines after 2015 (Appendix III).
In health care (Appendix IV), expenditure on health per insured person (deflated by GDP) grows faster than productivity, reflecting (i) a unitary income elasticity of health care demand; (ii) health care costs that grow at a faster pace than inflation; and (iii) the increasing share of elderly in the population (evidence from other industrial countries suggests that the health care expenditure of persons in the 75+ and 55-74 age cohort are, respectively, about four and two times higher than the expenditure of persons in the 0-54 cohort). These assumptions are considerably more optimistic than the baseline projections on health expenditure presented in the accompanying health care chapter. Underpinning these assumptions is the assessment that the rapid increase so far reflects the transition to a new, more technologically intensive environment, and the expectation that benefits from the bilateral agreements with the EU and further progress in strengthening competition will temper price increases in the health care sector. Nevertheless, a more difficult outcome cannot be excluded.
The authorities recently proposed a phased rise in the VAT rate of a cumulative 2.5 percentage points, but this was rejected in a referendum.
These calculations abstract from the adverse effects that such a fiscal measures would have on output.
The debt-brake rule, which was introduced in 2002 in response to the doubling of federal debt in the 1990s, requires the federal accounts to be in balance after adjusting for the business cycle. In operational terms, expenditure is set equal to projected cyclically-adjusted revenue. Unanticipated deficits must be reversed in the following years. The ceiling under the debt-brake rule can be over-ridden in exceptional circumstances if supported by a majority of members in both chambers of parliament. This was done in 2004, when loans to the Unemployment Insurance (ALV) were excluded from the ceiling under the debt-brake rule in an effort to allow automatic stabilizers to operate fully.
Between May 2000 and March 2005, and in coordination with the ECB and European national central banks, the SNB sold 1,300 tons of gold raising SwF 21 billion or 4.6 percent of GDP. The parliament has decided to allocate ⅓ of these proceeds to the federal government and ⅔ to the cantons.
This compares with 40 percent in the Netherlands, 25 percent in the United kingdom, 13 percent in the United States, and only 5 percent in Germany. See Deutsches Institut für Altersvorsorge (http://www.dia-vorsorge.de).
This compares with 95 percent in the United Kingdom, 84 percent in the United States, 7 percent in Germany, 5 percent in France, and 4 percent in Austria. See Deutsches Institut für Altersvorsorge (http://www.dia-vorsorge.de).
Currently, the Federal Social Security Service (Bundesamt für Sozialversicherung) prepares an annual report on the state of social security, including prospects for the next five-ten years. This horizon, however, fails to capture the problem since the effects of population aging are expected to peak around 2040. Occasional reports cover longer horizons—for instance, Bundesamt für Sozialversicherung 2003, 2004a, 2004c, Keel et.al. 2003, and Borgmann and Raffelhüschen 2004—but these are not an integral part of long-term budgetary planning.
The aggregation of assets and liabilities into net debt is not innocuous when the return on assets differs from the interest rate paid on government debt. However, with assets amounting to only 10 percent of net debt and return on the public pension system’s portfolio being moderate owning to a conservative investment strategy, the quantitative implications of this simplifying assumption are of second order of importance. The relation between the interest rates on net and on gross debt and assets (respectively, RN, RD, RA) is given by RN=RD+(RD-RA) · A / (D-A).
Alternatively, expenditure can be expressed in terms of per capita GDP and the share of pensioners in the population:
Pensions are adjusted every two years for the increase in consumer prices and inflation, each with 50 percent weight, which is equivalent to full indexation for inflation plus half the increase in real wages. However, average pensions increase is faster due to wage drift.
Pre-1980 investment figures are obtained by linking the ESA78 and ESA95 series. Figures on residential construction are from the ADB.