The origins of contemporary public pension schemes date back to 19th century when Bismarckian Germany in 1881 first adopted a universal old-age public pension system based on pay-as-you-go (PAYG) funding principle. The principle itself captures full advantages of high (stationary) population growth rate. In the simplest form, PAYG pension scheme is based on the notion of generational solidarity upon which current generations pay mandatory social security contribution into the public scheme. Aggregate contributions are then paid out to current retirees. The cycle is then expanded through generations. However, PAYG funding scheme is sustainable as long as the population growth is high and above the marginal productivity of the capital. Back in 19th century, public pension schemes were adopted under unrealistic assumptions about future population prospects. In 19th century, advanced countries experienced high population growth rate, high fertility rate and an extremely low share of dependent old population that was receiving universal old-age support from PAYG pension schemes. These set of assumptions was crucial to the stability of government-provided old-age support embodied in the public pension schemes.

The sustainability of PAYG pension system requires the equivalence of population growth rate and real interest rate. In the early 20th century, the advanced world shifted towards aging population, declining fertility rates and lower labor market entry rate. In broad terms, a growing old-age dependency ratio led to the pure disequilbrium effects. In a theoretical framework, I re-examined the neoclassical framework of lifecycle hypotheses embodied in Samuelson and Cass-Yaari models of life-cycle utility maximization. The lifecycle hypothesis is based upon the assumption of the three-period model where individuals maximize the consumption in the course of a lifetime. In the first period, individuals do not discount the future consumption since, in this period, individuals acquire the human capital. In the second period individuals enter the working age and discount the future consumption. Hence, in the third period, individuals retire consume the output produced in the working-age period. Since future discounting is compounded, the lifetime consumption increases geometrically. In purely analytical terms, the individuals maximize the utility of consumption through time preference rate.

Considering the abovementioned equivalence between population growth rate and real interest rate, the stability of the equilibria requires the period discount rate to equal the population growth rate. If population growth rate decreases, the stability of the equilibria requires that individuals decrease the future discount rate by the same rate to keep the PAYG pension system within the theoretical limit. The rigorous theoretical formulation of the neoclassical model of lifetime consumption, which essentially captures the necessary conditions for equilibrium stability of public pension schemes, had been put forth by Paul A. Samuelson in his seminal contribution to the theoretical foundations of stationary "PAYG" public pension scheme .

In the course of the last decades, OECD countries have experienced a significant drop in fertility rates, population growth and, under the political climate of social democracy, a widespread adoption of early retirement schemes and generous social security benefits. In addition, labor market exit age dropped significantly, initiating a trend towards the unprecendent growth of generational indebtedness.

The OECD estimated that between 2000 and 2050, old-age dependency ratio is forecast to increase to the largest extent in Japan (193 percent), Spain (136 percent), Portugal and Greece (135 percent). The astonishing increase in the estimated old-age dependency ratio directly reflects the declining fertility rate in OECD countries from 1960s onwards. I estimated the ratio of fertility rate between 1960-1970 and 2000-2006 for OECD countries at around 2, which means that average fertility rate between 1960-1970 was twice the fertility rate between 2000-2006. The highest fertility ratios were found in Spain (2.23), Italy (1.96), Ireland (2.00) while the lowest ratios were found in Denmark (1.37), Netherlands (1.72) and the United States (1.46).

High and stable effective retirement age is the main assumption underlying the stationary stability of PAYG pension system. In the 20th and 21st century, OECD countries have experienced an unprecendent decline in effective retirement age. Blöndal and Scarpetta (2002) estimated the decline in labor market exit age for OECD countries between 1960 and 1995. The female labor market exit age had declined significantly in Ireland (10.7 years), Spain (9.1 years) and Norway (8.8 years). Male labor market exit age exerted persistent decline in all developed OECD countries except for Iceland. The exit age declined significantly in the Netherlands (7.3 years) and Spain (6.5 years).

In a large part, declining labor market exit age has confluenced the rapid growth of unemployment and disability benefits and early retirement incentives from the second half of the 20th century onwards. As the OECD correctly contemplated, in a number of countries, disability pensions and unemployment benefits can be used as de facto early retirement schemes. In a large part, widespread growth of early retirement schemes and implicit incentives for moral hazard in retiring too early via unemployment and disability schemes is held responsible by generous welfare states in the aftermath of the World War II.

When I examined various features affecting early retirement choices, I came across an interesting finding. I regressed labor market exit age and marginal tax rate in a cross section of 23 OECD countries in 2007. I estimated the relationship between exit age and marginal tax rate using a classical OLS linear regression model. The estimate suggests that, holding all other factors constant, if marginal tax rate increases by 1 percentage point, average labor market exit age decreases by 1.88 months. Surprisingly, 51.74 percent of sample variation is explained by marginal tax rate alone. The sample constant is statistically significant, suggesting that if the hypothetical marginal tax rate were zero, the average labor market exit age in randomly chosen country from OECD sample would be 69.65 years. The sample constant is consistent with a prior theoretical expectations since it concurs with the "substitution effect" hypothesis that higher marginal tax rate leads to lower labor supply and fewer working hours.

The cost of early retirement in OECD countries

Source: T.T. Herbertsson & J.M. Orszag, The Cost of Early Retirement in OECD, 2001. OECD, Pensions at Glance, 2009.

Fiscal imbalances arising from unsustainable PAYG public pension systems in OECD countries cannot be assessed without a sufficient estimate of economic costs of unfunded pension liabilities. I approximated the cost of early retirement using Auerbach-Kotlikoff-Gokhale (1999) methodology that directly estimates the size of generational imbalances created by public social security systems. Large and rapidly unsustainable net pension liabilities occured in late 1980s. Van den Noord and Herd (1993) estimated the size of net pension liabilities in seven major OECD countries. The results suggest that continental European countries have had the largest net pension liabilities in terms of GDP. The size of pension liabilities in France and Italy had been about 2.5 times the size of their respective GDPs and twice the stock of the public debt.

Gokhale (2008) directly estimated fiscal imbalances arising from unfunded pension liabilities to current and prospective generations. The size of generational fiscal imbalance, as a share of the GDP, is extremely large and rapidly unsustainable in all OECD countries. In fact, the size of the imbalance is the most severe in Greece (875 percent of the GDP), France, Finland and the Netherlands (500 percent of the GDP) while it is more than twice the size of the GDP in all OECD countries except for the United States, Canada, Australia and New Zealand.

Fiscal imbalance in OECD countries

I built the econometric model of public pension expenditure for a cross section of 23 OECD countries in 2007 to assess which variables might explained the cross-country variation in public pension expenditures. I've been aware of the possible drawbacks of choosing a cross-section model since it might be vulnerable to specification errors and the unbiasedness of regression coefficients. To account for possible specification bias, I conducted Kolmogorov-Smirnov, Shapiro-Wilk and Jarque-Bera normality tests. By performing normality tests, I have examined whether the normality assumption of normally distributed error terms is valid in the studied sample of 23 OECD countries considering error terms as identically and independently distributed.

In the set of explanatory variables that might yield consistent and robust estimates of regression coefficients I chose 10 various demographic, economic and institutional independent variables. Apart from demographic and economic variables, institutional variables are dichotomous since the institutional features can be captured by binary modes of choice. The dependent variable is the size of public pension expenditures in the share of the GDP.

The results suggest that public pension expenditures are positively correlated with the share of population aged 65 and older (0.746**), difference in life expectancy after age 65 between 1960 and 2005 (0.477*) and dichotomous variable for continental European countries (0.697**) where * and ** indicate the statistical significant of the sample correlation coefficient at the 5% and 1% level. The estimates suggests that the probability of higher pension expenditures in the share of the GDP is likely to occur in a continental European country known for a relatively large share of older population and a high difference in life expectancy after age 65 between 1960 and the present. On the other hand, public pension expenditures are negatively correlated with average effective retirement age (-0.475**), private pension funds as a share of GDP (-0.658**), labor market exit age (-0.523**), dichotmous variable for Anglo-Saxon countries (-0.544**) and a dichotomous variable for private pension system (-0.672**), where ** denotes the statistical significant of the sample correlation coefficient at the 1% level. Again, the estimates suggest that the probability of lower pension expenditure is likely to occur if a randomly chosen country from the OECD sample is Anglo-Saxon and has a high effective retirement age, large private pension funds as a share of the GDP, high labor market exit age and a mandatory private pension system. The coefficients suggest that in repeated sampling, the estimated sample correlation coefficient will include the true or correct population value in 99 percent of cases.

I conducted the econometric model which consisted of 8 regression specifications. I chose double-logarithmic model which yields direct elasticities as regression coefficients. However, I added two exceptions. In regression specifications 5 and 6, I chose a mixed specification mostly due to the inclusion of private pension funds (assets) variable in the regression specification. Unfortunately, but the share of private pension funds in Greece in 2007 equals 0 percent of the GDP which does not enable the researcher to apply double-logarithmic model as the basis of regression specification.

The estimates suggest that the share of population aged 65 and older is statistically singificantly positively related to the share of public pension expenditures in the GDP. Hence, the elasticity of public pension expenditures with respect to effective retirement age ranges from -1.465 to -4.935, suggesting that an increase in effective retirement age by an additional year leads to per unit increase in public pension expenditures by more than a unit increase in the share of the GDP. The coefficient of private pension funds is highly statistically significant. The elasticity of public pension expenditures with respect to private pension funds (as a share of the GDP) ranges from -0.34 to -0.38 and is statistically significant at the 1% level. The elasticity suggests that a 10 percentage point increase in the share of private pension funds reduces the share of public pension expenditures in the GDP, on impact, by 3.4-3.8 percent, holding all other factors constant. In addition, the estimates of coefficients for dichotomous variables suggest the following: the probability of higher public pension expenditures (as a share of GDP) is likely to occur in continental European countries with mandatory private pension system. Five estimates of dichotomous coefficients are statistically significant at the less than 10% level.

The significance of dichotomous (dummy) coefficients has been tested by beta coefficient analysis to rank the magnitudes of separate effects of explanatory variables on public pension expenditures as dependent variable. The results suggest that continental European countries are significantly more likely to face higher public pension spending in the share of GDP compared to Anglo-Saxon countries.

Earlier I mentioned the necessity of normality assumption in yielding robust, consistent and unbiased estimates of regression coefficients. The assumption has been questioned by conducting Kolmogorov-Smirnov test (K-S), Jarque-Bera test (J-B) and Shapiro-Wilk (S-W) normality test. The aim of the testing the normality assumption is to observe whether error terms distribute normally so that estimated test statistics, standard errors and confidence intervals are reliable. In setting test statistic, I set the normality assumption as null hypothesis. The results from K-S, J-B and S-W tests show that the null hypothesis cannot be rejected at 5% level, suggesting that the normality assumption is valid in the studied sample. Hence, test statistics, standard errors and confidence intervals are both valid and reliable.

The meaningful question to evaluate the prospects of the coming public pension crisis is how to reverse the growth of fiscal imbalances and reform public pension system as to avoid erratic generational indebtedness. Aging population and the growth of old-age dependency ratio trigger an enormous future burden on public finances in OECD countries. Lower fertility rate and population growth shall place an incurable burden on the stability of PAYG public pension systems. The estimates suggest that life-expectancy after the age of 65 is likely to increase by 2050 and gradually approach the age of 90 for both male and female. Assuming the effective retirement age is 65, the remaining life expectancy is 25 years or almost one-third of the average lifetime. As Alemayehu and Warner (2004) suggest: "Old-age health care costs thus will impose increasingly severe pressure on private finances and government coffers. Indeed, applying our age-specific estimates to the age distribution anticipated for the year 2030, we find that if nothing is done to alter current patterns of health care, per capita health care expenditures will rise by one-fifth due to population aging alone."

The long-term pension reform that aging societies of the West should undertake is a complementary measures of three key policy features of the reform.

First, the transition to fully-funded retirement savings accounts is the only viable and sound pension reform that can alleviate the damage generated by the growing fiscal imbalances. The theoretical foundation of the transition from public pension systems to fully-funded pension system has been laid down by Feldstein and Liebman (2001). The authors derived an algebraic solution which suggests that keeping a PAYG public pension system does not attenuate the persistence of a growing demographic pressure on the stability of public pension system. As I discussed earlier, PAYG system crucially depends on three key assumptions: high fertility rate, very low share of population older 65+ and high population growth. These assumptions are incompatible with actual demographic parameters and, hence, OECD countries should undertake a drastic transition towards fully-funded pension systems based on individual savings accounts. Otherwise, the growing demographic pressure will inevitably result in the exponential growth of generational debt, creating an enormous deadweight loss for current and prospective generations.

Fully-funded pension system is based on the premise of investing pension contributions into the capital market, earning a compound interest over time. The stock of individual's lifetime earnings is paid in the form of annuities upon individual's withdrawal from the labor market. In addition, there is a growing disparity between the implicit return of PAYG public pension system and real rate of return in the capital market. Under realistic assumptions, such as that the marginal product of capital (MPK) is below the welfare-maximizing level and the real rate of return exceeds the implicit return from PAYG system, fully-funded pension system would not create a deadweight consumption loss to the working-age population. In fact, Feldstein and Liebman (2001) derived an analytic solution for the transition to fully-funded pension system in which the transition induces a short-term consumption loss in the next period while, at the same time, it creates a geometrically-growing future consumption for both retired and working-age population.

The only remaining question is whether the real rate of return would compensate the consumption loss of working-age population and, hence, increase the stock of future consumption to all generations. According to Feldstein and Liebman (2001), assuming 6.5 percent inflation-adjusted rate of return, the payroll cost of fully-funded pension system would represent only 27 percent of the payroll cost incured under PAYG public pension system. Tax rate, required to bear the cost of current stock of pension liabilities is 12.4 percent respectively.

According to Congressional Budget Office, the average real rate of return for large-company stocks between 1926 and 2000 is 7.7 percent, 9.0 percent of small-company stocks and 2.2 percent for long-term Treasury bonds. Feldstein (1997) estimated that PAYG implicit rate of return is 2.6 percent.

Assume an individual wants to maximize the lifetime earnings in the capital market. An individual is offered 2.6 percent implicit return from PAYG system. The individual enters the labor market at certain age, say 25, and intends to retire upon the age of 65. Assume he invests $10.000 annually in the capital market to create retirement annuities upon labor market withdrawal. Assuming the implicit rate of return (2.6 percent), the stock of overall annuity would be 10 times the initial investment in 90 years. Assuming the average long-run real rate of return from large-company stocks (7.7 percent), the the overall annuity would be 10 times the initial stock of investment in 31 years. Therefore, the individual would reach the desired level of lifetime earnings at the age of 56 or 9 years before the targeted retirement age.

I assumed the distribution of lifetime investment portfolio is weighted average of availible asset types: large-company stocks (33 percent), small-company stocks (19 percent), long-term corporate bonds (20 percent), long-term Treasury bonds (20 percent) and 3-month Treasury bills (8 percent). According to the average annual real rates of return in the United States (1926-2000), I calculated the weighted average real rate of return (5.247 percent). Investing $10.000 annually at the age of 25 would buy $100.000 annuity at 5.247 real rate of return in 45 years (the age of 70) compared to 90 years (the age of 115) under the PAYG implicit rate of return (2.6 percent). Of course, the time to buy the annuity would shift alongside the changing composition of portfolio.

In addition, OECD countries should immediately increase the effective retirement age. I believe the solution suggested by Gary Becker is both meaningful but sustainable in reversing the growth of generational debt. Becker (2010) suggested "One simple and attractive rule would be to raise retirement age by an amount that makes the

**ratio**of years spent in retirement to years spent working equal to the ratio that existed at the beginning of the social security system."

When President Roosevelt signed the notorious Social Security Act in 1935, the normal retirement age was 65. However, life expectancy after the age of 65 was significantly lower than is today. In 1940, average life expectancy after 65 in the U.S was 13.7 years. In 2006, it stood at 18.6 years, according to OECD. In 1935, the average life expectancy at birth in the United States was 61.7 years. We assume that individuals in 1935 worked for 35 years and spent 12 years in retirement. The ratio is thus 0.4 (12/ 35=0.34). Today, if individuals retire at the age of 65, they can expect further 18.6 years in retirement. To equalize the ratio to the 1935 level, (18.6/x=0.34), individuals should spend 54.7 years working. The estimate time is an equivalent measure of years required to spend working if PAYG public pension system is left intact. Assuming the individuals enter the labor market at the age of 25, then the expected effective retirement age is the age of 80.

In the long run, PAYG public pension system is unsustainable since demographic parameters do not suffice the assumptions under which the PAYG system is possible without distortions of labor supply incentives. The future of OECD countries will be marked by aging population, lower fertility rates and a growing demographic pressure on public finances. Without bold and decisive pension reform, OECD countries will experience increasing pension deficits and, hence, an explosive growth of generational indebtedness.

Parametric pension reforms are not a substitute for the postponement of paradigmatic pension reform. Thus, implementing the transition to fully-funded pension system essentially requires higher effective retirement age. A comprehensive pension reform cannot be made possible without these measures. At last, but not least, the major challenge in the systematic pension reform in OECD countries to address the burden of global aging, is whether political courage will withstand the pressure of interest groups to maintain the status quo of early retirement incentives. Nonetheless, eliminating early retirement incentives is the essential step towards creating retirement system without perverse incentives to retire too early. Unless political leaders encourage a transition to fully-funded pension system, OECD countries will be unable to withstand the deadly consequences of an enormous generational indebtedness.

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