Pension System Provisions

There follows a short description of the basic provisions of the Polish pension benefit system.^2/ Three conditions must be met before a worker is eligible to receive a retirement pension. First, one must have contributed for 25 (20)^3/ qualifying years. Reduced benefits are available under certain circumstances to those who have worked only 20 (15) qualifying years. Second, recipients must cease full-time working. Note that this constraint hardly binds since it is possible to work almost a full working week while still drawing a pension. Third, recipients must be older than 65 (60).

For large sections of the workforce the third, age requirement does not apply. Groups deemed to be in hazardous or otherwise demanding occupations may retire at 60 (55). Such groups include miners, firemen, teachers, journalists, academics, customs officers and artists. In addition, women with 30 qualifying years may retire at 50, while men in disability groups 1 or 2 (see below) with 25 qualifying years may retire at 60. Some professions, including teachers and miners, have the right to retire if they have accumulated enough qualifying years (30 for teachers, 25 for underground miners) whatever their age. The exceptions to the age requirement apply to such a substantial fraction of the population that the average age for new retirees in 1990 was 58 for men and 57 for women.^4/

Once eligible for a pension, a worker’s benefit level depends on earnings and the number of qualifying years he has accumulated. Under the Social Insurance Act of October 1991, the pension entitlement equals 24 percent of the national average wage plus, for each qualifying year during which contributions were made, 1.3 percent of the worker’s pension base.^5/ The pension base is the average of labor earnings in the best three of the last 12 years of work.^6/ The authorities intend to increase the averaging period each year by one year until the pension base for a new retiree equals the average of the best 10 years out of the last 20.^7/

Workers are given partial credit for periods during which no contributions were made (for example, periods spent in higher education, military service or childcare), receiving 0.7 percent of their pension base for each non-contributory year.

Under the new income tax law of July 1991,^8/, pension benefits are fully taxable. There is a minimum pension equal to 35 percent of the average wage, and a maximum implied by the fact that the pension base applicable for benefit calculations has an upper limit of 2.5 times the average wage. Pensions are subject to a simple earnings test in that those earning more than 120 percent of the average wage receive no benefits, while pensioners earning 60-120 percent lose the flat-rate part of the pension, i.e., 24 percent of the average wage.

The indexing provisions in the pension system have changed substantially over the last few years. Rapid inflation in the 1980s seriously eroded pensioners’ purchasing power. In 1988 and 1989, benefit levels were adjusted on an ad hoc basis to ameliorate this problem. In 1990, pension payments were indexed by average wages. Entitlements continued to depend on the nominal wage received in the last year before retirement, however, leading to wide disparities between the benefits received by those who had retired before and after the hyperinflation. The law of October 1991 remedied the situation by implementing the benefit formula described above according to which both the pension base and flat-rate components of the pension are indexed by average wages.

Disability Pensions

In Poland, the disability pension system is relatively generous. Eligibility requires little more than a doctor’s certificate. Three levels of disability are recognized. Group 1 are severely disabled persons, unable to look after themselves, Group 2 consists of those unable to work, while Group 3 is individuals with long-term medical problems who, due to disability, can only work part-time. As with old age pensions, disability pension recipients are not permitted to work full-time but working for a substantial fraction of the full working week is allowed. Group 3 benefit levels equal 75 percent of the old age pension. Group 2 receives an amount calculated just like the old-age pension (i.e., taking account of previous earnings and qualifying contributory years), while Group 1 receive the old age pension plus a supplement equal to 30 percent of the minimum pension.

The Unemployment Benefit System

Unemployment has increased extremely rapidly since Poland’s reform process began, rising from negligible levels at the start of 1990 to 2.2 million or 12.2 percent of the workforce by March 1992.^9/ The latest information suggests that this increase has leveled off. Table 1 gives a breakdown of unemployment by sex, age and level of education. Clearly, a substantial youth unemployment problem has developed, while the unemployment rate among 25 to 54 year old is also relatively high. The proportion of the female unemployed is much higher than one would find in a Western European country.^10/ From the educational breakdown, it appears that, while there is very little white-collar unemployment, unemployment is not so concentrated among the unskilled as in other countries.

Table 1:

Polish Pension Recipients by Sex and Age in 1990

Source: Social Insurance Office (ZUS) and Barr (1992).

Table 1:

Polish Pension Recipients by Sex and Age in 1990

	Pensioners (thousands)
	Old Age			Disability
Age	Men	Women	Total	Men	Women	Total
0-19	-	-	-	0.0	0.0	0.0
20-24	-	-	-	6.9	1.9	8.8
25-29	-	-	-	19.1	5.0	24.1
30-34	-	-	-	34.2	22.7	56.9
35-39	-	-	-	68.4	38.9	107.3
40-44	-	-	-	89.9	65.6	155.5
45-49	19.0	15.9	34.9	107.8	67.4	175.2
50-54	44.5	57.9	102.4	159.7	153.5	313.2
55-59	129.7	184.5	314.2	207.3	200.2	407.4
60-64	264.8	286.9	551.7	201.1	162.5	363.6
65-69	280.5	287.5	568.0	108.8	134.3	243.1
70-74	145.4	150.2	295.6	53.1	73.9	127.0
75-79	120.3	128.8	249.1	39.3	70.2	109.5
80+	101.5	110.3	211.8	31.5	67.1	98.6
Total	1105.7	1222.0	2327.7	1127.1	1063.2	2190.3

Source: Social Insurance Office (ZUS) and Barr (1992).

View Table

Table 1:

Polish Pension Recipients by Sex and Age in 1990

	Pensioners (thousands)
	Old Age			Disability
Age	Men	Women	Total	Men	Women	Total
0-19	-	-	-	0.0	0.0	0.0
20-24	-	-	-	6.9	1.9	8.8
25-29	-	-	-	19.1	5.0	24.1
30-34	-	-	-	34.2	22.7	56.9
35-39	-	-	-	68.4	38.9	107.3
40-44	-	-	-	89.9	65.6	155.5
45-49	19.0	15.9	34.9	107.8	67.4	175.2
50-54	44.5	57.9	102.4	159.7	153.5	313.2
55-59	129.7	184.5	314.2	207.3	200.2	407.4
60-64	264.8	286.9	551.7	201.1	162.5	363.6
65-69	280.5	287.5	568.0	108.8	134.3	243.1
70-74	145.4	150.2	295.6	53.1	73.9	127.0
75-79	120.3	128.8	249.1	39.3	70.2	109.5
80+	101.5	110.3	211.8	31.5	67.1	98.6
Total	1105.7	1222.0	2327.7	1127.1	1063.2	2190.3

Source: Social Insurance Office (ZUS) and Barr (1992).

Under the Polish unemployment benefit system, instituted in December 1989, unemployed workers received 70 percent of their previous wage for 3 months, followed by 60 percent for the subsequent 6 months, and 40 percent thereafter.^11/ The benefit entitlement was in nominal terms and hence decreased more rapidly than the above percentages suggest when inflation accelerated. The minimum and maximum benefit levels were the minimum and average wages. Since these were indexed, this introduced some safety net in the face of large price movements.

Unemployment benefit eligibility initially did not depend upon past labor market participation and a large proportion of applicants in the first year of the scheme were not unemployed in an economic sense. In July 1990, eligibility was tightened by requiring that unemployed had worked for 180 days in the past year. The minimum benefit was also slightly reduced and some special extra payments to unemployed graduates were reduced. Despite these measures, the high unemployment totals undoubtedly still contain many people who are not genuinely members of the workforce. The high proportion of women among the unemployed, commented on above, may well reflect unemployment claims by housewives not really in search of work.

The October 1991 Employment Law introduced an indexed, flat-rate unemployment benefit of 36 percent of the average wage in the previous quarter (with a supplement of 15 percent of the average wage for those in training programs). An important feature of the new benefit was that it was only payable for 12 months except to workers approaching retirement. Claimants ceased to receive benefits if they turned down two job offers and tighter rules were adopted to discourage work in the private sector particularly in agriculture at the same time as claiming benefits.

Table 2:

Polish Unemployment by Sex, Age and Education

Source: Boeri and Keese (1992).Note: sex and education breakdowns refer to November 1991. Age breakdowns refer to October 19911988 employment data is used in the calculation of unemployment rates.

Table 2:

Polish Unemployment by Sex, Age and Education

Shares in Total Unemployment
	Sex		Age			Education
	Women	Men	≤24	25 to 54	≥55	Primary	Vocational	Secondary	Higher
Shares in Total Unemployment	52.8	47.2	36.3	53.6	10.1	29.7	37.0	30.3	3.0
Unemployment Rates	12.8	10.6	26.4	10.7	3.7	9.8	13.3	11.7	4.2

Source: Boeri and Keese (1992).Note: sex and education breakdowns refer to November 1991. Age breakdowns refer to October 19911988 employment data is used in the calculation of unemployment rates.

View Table

Table 2:

Polish Unemployment by Sex, Age and Education

Shares in Total Unemployment
	Sex		Age			Education
	Women	Men	≤24	25 to 54	≥55	Primary	Vocational	Secondary	Higher
Shares in Total Unemployment	52.8	47.2	36.3	53.6	10.1	29.7	37.0	30.3	3.0
Unemployment Rates	12.8	10.6	26.4	10.7	3.7	9.8	13.3	11.7	4.2

Source: Boeri and Keese (1992).Note: sex and education breakdowns refer to November 1991. Age breakdowns refer to October 19911988 employment data is used in the calculation of unemployment rates.

Demographic Pressures

Barr (1992) argues^12/ that, extrapolating past trends, the current population age structure implies that the number of pensioners should be constant over the next few years. Hambor (1992) analyzes population trends for several Central and Eastern European countries. Under a number of strong simplifying assumptions, he derives potential worker/retiree ratios. Of the countries he examines, Poland shows the worst proportional deterioration, with the relevant ratio falling from 2.9 in 1990 to 2.0 in 2020, although the ratio in Hungary falls to an even lower level of 1.6 by 2020 from the 1990 level of 2.1.^13/ Hambor’s simulations, however, suggest that demographic pressures on pension expenditure will not become serious until well into the first decade of the next century. Given reasonable assumptions about real wage growth, Hambor suggests that indexing on prices rather than wages would largely eliminate future demographic pressure on pension expenditures.

1. Lifetime Wealth Constraint

where P_t is the price of the consumption good, W_t is bequests received in period t, w_t is the wage rate, Z_t is lump sum transfers, r_t is the gross interest rate, τ_wt, τ_st τ_c and τ_h are tax rates on labor and savings income, consumption goods and inheritances respectively, all at time t. Here, total labor endowment in each period is normalized to unity. Q_t is a composite price index based on the value of full consumption and involving the parameters of the agents utility function.

2. Liquidity Constraints

where S_t is liquid private sector savings at period t and equals the partial sum of the budget constraint.

3. Employment Constraints

where $L_t^{*}=1,2,\dots T$ are fixed constants that represent the minimum leisure that the household can consume in given periods.

The solution of this program is considerably complicated by the presence of all the various constraints. Let us start by considering the simple case in which π_t = 1 for t = 1,2,…T and there are no liquidity or labor supply constraints and no bequest motive. One may then obtain the optimal paths for the decision variables by solving the following system of equations.

where t_r is the date of retirement from the workforce, and where ${\left\{{\lambda }_t\right\}}_{t=1}^T$ is a vector of marginal utilities of wealth in each period. In each pair of adjacent periods, t, and t+1, the marginal utilities of wealth satisfy the relation: λ_t=λ_t+l/(1+r_t(1+τ_st). In other words, there is effectively just a single discounted Lagrange multiplier for the agent’s program, associated with the single life-time wealth constraint. The last degree of freedom in the problem is then resolved by choosing λ₁ such that savings at the end of life are zero.

Introducing the possibility of early death and a bequest motive implies two changes to the approach one must take to solving the problem. First, the formula for updating λ_t takes the more complicated form:

and second the terminal condition required to pin down the single degree of freedom in the λ_t’s is:

i.e., that the marginal utility of an extra unit of bequests in the final period of life divided by the price of bequests is equal to the terminal utility of wealth.

The inclusion of labor supply and liquidity constraints substantially complicates matters. For each period, two additional complementary slackness conditions must be added to the basic maximization problem. As far as the above equations are concerned, these imply, first, that we must replace λ_t by λ_t + γ_t where γ_t is a Lagrange multiplier that is strictly positive in periods in which the liquidity constraints bind and otherwise zero. Second, w_t (l−T_wt) must be replaced by w_t (1−T_wt)+η_t where η_t is a Lagrange multiplier which is strictly positive in periods in which the employment constraints bind and otherwise zero. Suppose one knows in advance in which periods the constraints bind. One may then compute the optimal path by substituting out consumption and leisure in the periods in which the constraints bind using respectively the liquidity and labor supply constraints. The additional equations that one then has can be used to find the values of the additional Lagrange multipliers.

In the case of the labor supply constraints, it does not matter that one does not know in advance in which periods the constraints bind since one can write a solution algorithm in which the algorithm checks as it runs through the household’s optimal program to see if the constraint is contravened and then changes the calculation accordingly. However, the fact that one does not know in advance in which periods the liquidity constraints bind leads to major computational complications. In principle, one may employ brute force methods, solving the problem for different combinations of binding Lagrange multipliers and then taking the solution to be the one that yields the maximum utility without contravening the constraints. But, such methods are not feasible using conventional computers. The approach taken in the algorithms employed in this paper is to assume that the constraints bind at the start of the household’s ‘life’ and then hold continuously until some date at which the household becomes unconstrained. While this is not a general solution technique, it works well for commonly observed lifetime wage patterns.

Polish households face a wide range of minimum retirement ages, depending, for example, on the industry in which they work or their health status. For the purpose of simulating the model, I shall assume that households can retire when their age is in the range 57 to 65 years old. It should be recalled that the rules on retirement do not oblige pensioners to cease supplying labor after retirement, although full-time working is not possible. I, therefore, assume that there is a limited loss of earnings upon retirement, say, because of the need to change industries or places of employment. Thus, the wage profile is assumed to shift down after retirement by a factor of 0.7 compared to what it would be if the household had not retired. In principle, this cut in wages could induce households to retire after the age of 57, but in practice, for most simulations, the lower bound on retirement ages binds and they retire at 57. Some of the measures I review below, most notably benefit cuts for households that retire early and income tests on total retirement income, do induce later retirement and indeed this is the principal mechanism through which they influence total lifetime tax payments net of benefits.

One may compare the above framework with other models that have been developed for the study of savings behavior and pensions and unemployment benefit systems. The main strength of the model described above is the inclusion of a range of constraints upon household choices, over and above the budget constraint equating expenditures to total lifetime wealth, most notably the limits on borrowing and labor supply. Given the deteriorating labor markets and primitive state of consumer lending in Eastern Europe, these features are clearly important. Hubbard and Judd (1986) set up a relatively simple model of a liquidity constrained household in order to study the impact of such constraints on savings and consumption decisions. The present model, with numerous complications such as endogenous retirement decisions and bequests, concentrates more on public finance aspects.

Table 3:

Baseline Parametrization

Table 3:

Baseline Parametrization

Utility Function Parameters
Parameter	Symbol	Value
Subjective discount rate	δ	0.04
Elasticity of intertemporal substitution	α	0.80
Consumption-leisure elasticity of substitution	ρ	0.80
Consumption-leisure parameter	α0	0.20
Bequest-full-consumption parameter	α1	0.10
Bequest substitution elasticity	μ	0.80
Maximum life-span (assuming adult life begins at 20)	T	80.0
Tax Parameters
Parameter	Symbol	Value
Tax on consumption goods	τc	0.08
Wage tax rate	τw	0.25
Savings tax rate	τs	0.23
Inheritance tax rate	τh	0.00
Social security contribution rate	τp	0.31
Prices
Parameter	Symbol	Value
Real interest rate	rt	0.05
Average per period wage rate	$\overline{w}$	2.79
Consumer goods price	Pt	1.00
Official average wage	wav	2.23

View Table

Table 3:

Baseline Parametrization

Utility Function Parameters
Parameter	Symbol	Value
Subjective discount rate	δ	0.04
Elasticity of intertemporal substitution	α	0.80
Consumption-leisure elasticity of substitution	ρ	0.80
Consumption-leisure parameter	α0	0.20
Bequest-full-consumption parameter	α1	0.10
Bequest substitution elasticity	μ	0.80
Maximum life-span (assuming adult life begins at 20)	T	80.0
Tax Parameters
Parameter	Symbol	Value
Tax on consumption goods	τc	0.08
Wage tax rate	τw	0.25
Savings tax rate	τs	0.23
Inheritance tax rate	τh	0.00
Social security contribution rate	τp	0.31
Prices
Parameter	Symbol	Value
Real interest rate	rt	0.05
Average per period wage rate	$\overline{w}$	2.79
Consumer goods price	Pt	1.00
Official average wage	wav	2.23

Probably the greatest weakness of the model employed in this paper is the limited role played by uncertainty. Time of death is stochastic in this model but no other sources of randomness are introduced. The study by Rust (1989) (and the slightly less rigorous implementations of similar ideas by Lazear and Moore (1988) and Stock and Wise (1990)) shows just how stringent are the simplifying assumptions required if one is to incorporate stochastic elements. The largely deterministic nature of the model is particularly a problem in the treatment of unemployment which is here treated simply as a constraint on labor supply. Fears of future unemployment among households still fully employed have probably contributed greatly to the surge in early retirements mentioned in the introduction. Here these can only be examined through fully anticipated employment constraints.

Liquidity Constraints

The simulation results are presented in two forms. First, Tables 4 and 5 summarize total lifetime quantities such as utility and consumption of goods and leisure. Second, Charts 5 to 21 show the profiles for these same variables over the adult life of the household. Eight basic simulations were performed, in each case with and without liquidity constraints.

Table 4:

SUMMARY SIMULATION RESULTS (W/O Liquidity Constraints)

Table 4:

SUMMARY SIMULATION RESULTS (W/O Liquidity Constraints)

	Goods Cons.	Leis. Cons.	Life Util.	Total. Sav.	Tax Paid	M.U.of Wealth	Ret. Age
Simulation 1.	74.09	25.85	−114.33	46.35	28.18	16.49	57
Simulation 2.	74.50	26.04	−114.14	13.77	25.71	16.37	57
Simulation 3.	74.54	26.27	−114.05	−5.05	23.93	16.36	57
Simulation 4.	70.70	34.44	−114.62	98.60	12.21	17.48	57
Simulation 5.	72.95	25.90	−114.63	80.06	30.83	16.81	65
Simulation 6.	74.11	25.96	−114.29	23.85	26.82	16.48	61
Simulation 7.	68.84	28.83	−114.81	1.49	25.41	17.28	63
Simulation 8.	70.48	34.42	−114.71	101.60	12.65	17.55	57
Details of Simulations
Simulation 1.	Averaging Over Whole Pre-Retirement Period
Simulation 2.	Averaging Over Ten Best Years Out of Last Twenty
Simulation 3.	Averaging Over Three Best Years Out of Last Twelve
Simulation 4.	Ten Year Averaging With Unemployment
Simulation 5.	Ten Yr. Avg. + Benefit Cuts for Early Retire.
Simulation 6.	Ten Yr. Avg. +Existing Income Tests
Simulation 7.	Ten Yr. Avg. +50% Taper on Retire. Income
Simulation 8.	Ten Yr. Avg. + Unemp.+Inc. Tests+Unem. Ben. Cut
NB: lifetime utility is the subjectively discounted sum of period by period utilities. Other variables are simply period by period quantities summed over the lifetime.

View Table

Table 4:

SUMMARY SIMULATION RESULTS (W/O Liquidity Constraints)

	Goods Cons.	Leis. Cons.	Life Util.	Total. Sav.	Tax Paid	M.U.of Wealth	Ret. Age
Simulation 1.	74.09	25.85	−114.33	46.35	28.18	16.49	57
Simulation 2.	74.50	26.04	−114.14	13.77	25.71	16.37	57
Simulation 3.	74.54	26.27	−114.05	−5.05	23.93	16.36	57
Simulation 4.	70.70	34.44	−114.62	98.60	12.21	17.48	57
Simulation 5.	72.95	25.90	−114.63	80.06	30.83	16.81	65
Simulation 6.	74.11	25.96	−114.29	23.85	26.82	16.48	61
Simulation 7.	68.84	28.83	−114.81	1.49	25.41	17.28	63
Simulation 8.	70.48	34.42	−114.71	101.60	12.65	17.55	57
Details of Simulations
Simulation 1.	Averaging Over Whole Pre-Retirement Period
Simulation 2.	Averaging Over Ten Best Years Out of Last Twenty
Simulation 3.	Averaging Over Three Best Years Out of Last Twelve
Simulation 4.	Ten Year Averaging With Unemployment
Simulation 5.	Ten Yr. Avg. + Benefit Cuts for Early Retire.
Simulation 6.	Ten Yr. Avg. +Existing Income Tests
Simulation 7.	Ten Yr. Avg. +50% Taper on Retire. Income
Simulation 8.	Ten Yr. Avg. + Unemp.+Inc. Tests+Unem. Ben. Cut
NB: lifetime utility is the subjectively discounted sum of period by period utilities. Other variables are simply period by period quantities summed over the lifetime.

Table 5:

SUMMARY SIMULATION RESULTS (With Liquidity Constraints)

Table 5:

SUMMARY SIMULATION RESULTS (With Liquidity Constraints)

	Goods Cons.	Leis. Cons.	Life Util.	Total. Sav.	Tax Paid	M.U.of Wealth	Ret. Age
Simulation 1.	77.94	26.55	−114.63	155.04	27.65	17.05	57
Simulation 2.	78.44	26.58	−114.60	151.56	26.98	16.98	57
Simulation 3.	78.51	26.84	−114.51	131.52	25.02	16.97	57
Simulation 4.	73.65	34.36	−114.94	188.88	13.60	17.86	57
Simulation 5.	76.34	26.37	−115.03	197.02	31.78	17.34	64
Simulation 6.	77.79	26.46	−114.75	157.33	28.24	17.08	61
Simulation 7.	72.00	29.58	−115.22	123.54	26.30	17.78	64
Simulation 8.	73.38	34.33	−115.02	190.22	14.01	17.92	57
Details of Simulations
Simulation 1.	Averaging Over Whole Pre-Retirement Period
Simulation 2.	Averaging Over Ten Best Years Out of Last Twenty
Simulation 3.	Averaging Over Three Best Years Out of Last Twelve
Simulation 4.	Ten Year Averaging With Unemployment
Simulation 5.	Ten Yr. Avg. + Benefit Cuts for Early Retire.
Simulation 6.	Ten Yr. Avg. + Existing Income Tests
Simulation 7.	Ten Yr. Avg. +50% Taper on Retire. Income
Simulation 8.	Ten Yr. Avg +Unemp.+Inc. Tests+Unem. Ben. Cut
NB: lifetime utility is the subjectively discounted sum of period by period utilities. Other variables are simply period by period quantities summed over the lifetime.

View Table

Table 5:

SUMMARY SIMULATION RESULTS (With Liquidity Constraints)

	Goods Cons.	Leis. Cons.	Life Util.	Total. Sav.	Tax Paid	M.U.of Wealth	Ret. Age
Simulation 1.	77.94	26.55	−114.63	155.04	27.65	17.05	57
Simulation 2.	78.44	26.58	−114.60	151.56	26.98	16.98	57
Simulation 3.	78.51	26.84	−114.51	131.52	25.02	16.97	57
Simulation 4.	73.65	34.36	−114.94	188.88	13.60	17.86	57
Simulation 5.	76.34	26.37	−115.03	197.02	31.78	17.34	64
Simulation 6.	77.79	26.46	−114.75	157.33	28.24	17.08	61
Simulation 7.	72.00	29.58	−115.22	123.54	26.30	17.78	64
Simulation 8.	73.38	34.33	−115.02	190.22	14.01	17.92	57
Details of Simulations
Simulation 1.	Averaging Over Whole Pre-Retirement Period
Simulation 2.	Averaging Over Ten Best Years Out of Last Twenty
Simulation 3.	Averaging Over Three Best Years Out of Last Twelve
Simulation 4.	Ten Year Averaging With Unemployment
Simulation 5.	Ten Yr. Avg. + Benefit Cuts for Early Retire.
Simulation 6.	Ten Yr. Avg. + Existing Income Tests
Simulation 7.	Ten Yr. Avg. +50% Taper on Retire. Income
Simulation 8.	Ten Yr. Avg +Unemp.+Inc. Tests+Unem. Ben. Cut
NB: lifetime utility is the subjectively discounted sum of period by period utilities. Other variables are simply period by period quantities summed over the lifetime.

The presence of liquidity constraints did not affect optimal retirement dates, nor did it influence the total lifetime tax payments in a systematic way. However, liquidity constraints had a very substantial impact on savings and welfare. The relative generosity of the Polish retirement income system effectively removes the standard life-cycle motive for saving, i.e., that of providing for retirement consumption. In the absence of liquidity constraints, high pension benefits together with upward sloping lifetime wage profiles typically lead to consumption patterns that require heavy borrowing early in life. Thus, in our eight simulations without liquidity constraints, households only begin to have positive net financial wealth late in life, after the age of forty.^14/

Imposing constraints on borrowing restores the more conventional hump-shape for life cycle saving, with liquidity constraints ceasing to bite when households are in their early thirties. An important implication of this analysis is that the current Polish benefit system, with its relatively generous replacement ratios, would have an extremely deleterious impact on aggregate saving if consumer credit were freely available. Since financial liberalization, while not yet achieved, will presumably be implemented before too long, one could expect aggregate savings to suffer greatly unless changes are made in the current system such as some reduction in the generosity of retirement benefits relative to pre-retirement incomes.

The magnitude of these effects can be seen by comparing the total lifetime savings in Tables 4 and 5. If the population was stationary, then one could regard the volume of savings in these tables as scaled down versions of those pertaining in steady state equilibria for the economy as a whole. Comparing simulation 1 with and without liquidity constraints, one can see that the total level of savings is roughly six times larger in the latter case. While such differences clearly exaggerate the actual impact of liquidity constraints, they still point to the potential seriousness of the problem.

As a last point, the presence of liquidity constraints radically alters the time profile of household consumption which instead of declining monotonically as in the unconstrained case, rises sharply through the twenties before falling from the early thirties onward. Liquidity constraints also have spill-over effects in the labor market since households supply more labor in an attempt to alleviate the constraint on liquid resources.

Averaging Periods

Turning now to the individual model runs, the first three simulations analyze the impact of different averaging periods for the derivation of the wage base from which pension entitlements are calculated. As noted in a previous section, the Polish authorities intend to increase the averaging period gradually from the best three of the last twelve years before retirement to the best ten out of the last twenty. Simulation 1 assumes an averaging period of the whole working life,^15/ while simulations 2 and 3 suppose three and ten year averaging periods. Note that the principal economic impact of calculating pension entitlements based on labor income earlier in life is to reduce the effective tax rate on wages. Given the heavy burden of taxation on wage income in Poland, this would seem to be highly desirable.

Comparing Charts 6 and 7 with Chart 5, it is clear that averaging over a short period provides a strong incentive for intertemporal substitution of labor supply. Tax payments are significantly boosted during the short averaging periods.^16/ The simulation result summaries in the tables show, however, that cutting the length of the averaging period significantly reduces the household’s total lifetime tax payments less benefits. In the liquidity constrained case, net taxes less benefits paid over the life cycle fall from 27.65 to 26.98 and 25.02 respectively for ten and three year averaging periods. The decline occurs for the simple reason that the household’s wage base calculated as an average of the best three years of labor income is higher than an average based on a larger number of years. Total lifetime leisure falls for shorter averaging periods while consumption rises slightly, as does total utility.

To assess the welfare impact of the change, one may use the figures for the average marginal utility of wealth also given in Tables 4 and 5. To illustrate such a calculation, consider the rise in lifetime utility of 0.12 units for a switch from lifetime to three year averaging. Using the average marginal utility of wealth for simulation 1, this translates into a money equivalent of 17.05×0.12=2.05. In weighing the utility change by the lifetime average marginal utility of wealth, we are effectively calculating what sum of money that, if spread evenly over the household’s life in the form of a flow of lump sum income, would give the same change in lifetime utility. Given that expenditure on consumption over the life cycle is 74 in simulation 1,^17/ this represents a significant welfare gain.

The welfare gain for a shorter averaging period may be attributed, first, to the fact that tax net of benefits paid over the life cycle is lower. This effect is partly illusory since we have not included in the model any role for exhaustive public spending which would presumably be cut if the government’s tax receipts fell, reducing utility derived from public goods output. Second, the welfare gain is an example of the increases in steady state utility that are always available to governments in overlapping generations models when the interest rate exceeds the growth rate of the economy. To see this, suppose the economy has zero population growth with a stationary age structure and that r>0. Then the government can obtain the same steady state net tax revenue while switching tax from young to old, whereas steady state household utility will increase with such a switch since discounted lifetime income will rise. Again, such steady state welfare gains are somewhat illusory since they ignore the welfare losses of the transitional generation that is old when the new policy is enacted.

These caveats about the welfare effects implied by our analysis of averaging periods suggest that, from a practical, policy perspective, it is more important to consider the positive effects of cutting the averaging period, namely a sharp fall of 15.2 percent in aggregate saving in the more empirically relevant liquidity-constrained case, and the 15.1 percent decline in total tax receipts net of benefit payments. Both effects run counter to what one could regard as sensible policies given Poland’s current predicament. Thus, averaging over a longer period would be preferable in the current Polish situation.

Unemployment

Simulation 4 shows the impact on the household of unemployment. Unemployment takes the form of a constraint on per-period household labor supply of 0.7. One way to think of this is to suppose that the household contains two working individuals of whom one works part-time. When the labor supply constraint binds, we assume that the full-time worker supplies zero labor and the household receives unemployment benefit from the state.

The charts for simulation 4 show that being unemployed depresses savings as the constrained household dissaves in an attempt to maintain its consumption level, in anticipation of the pension benefits it will receive after retirement which significantly exceed unemployment benefit. However, anticipation when young of unemployment later in life generates substantial extra saving by households at the start of the life cycle leading to a large positive impact on total saving. To some degree, this result points to a weakness in our modelling of unemployment which here is taken to be fully anticipated by households in their youth. In the current Polish case, households now unemployed are very unlikely to have anticipated their present situation and hence to have build up savings balances. Nevertheless, in the newly reformed Polish economy with unemployment that is likely to persist for the foreseeable future, it is reasonable to expect quite significant precautionary saving by households, and the model is at least useful in underlining this fact.

The two other substantial effects of unemployment are, as one would expect, first, a big shift from consumption to leisure expenditure (one could think of this as due to a large fall in the shadow price of labor) and, second, a big decline in net tax payments. Unemployment, of itself, does not affect the retirement date, but this is only because the household already retires at the minimum age of 57. Simulations not reported here in which rule changes such as benefit cuts for early retirees induce later retirement show that unemployment can shift the retirement date back in time quite significantly.

Simulation 8 shows the effect of cutting the unemployment benefit level by 20 percent and introducing the current system of income tests (i.e., reductions in benefits when a retired household’s income exceeds 60 and 120 percent of the average wage. This package of measures has little impact on total tax revenue net of benefits which rise from 13.6 to 14.0 in the liquidity constrained case. Lifetime welfare falls by a monetary equivalent of 1.4 while consumption and leisure show small movements in intuitively reasonable directions.

Pension Benefit Cuts

Simulations 5, 6 and 7 look at different approaches to cutting pension benefits. Simulation 6 is a simulation of the current system with step reductions in benefits at earnings thresholds of 60 and 120 percent of the average wage. As one may see by comparing simulations 2 and 6 in Tables 4 and 5, for the household considered here, the income tests do not bite very much whether or not liquidity constraints apply. In the liquidity constrained case, taxes rise by 1.2, while savings are up 5.8 and utility falls by a monetary equivalent of 4.1.

Simulation 7 yields what might appear a surprising result. Imposing a 50 percent taper on total retirement income (i.e. an additional 50 percent tax on pension income over and above existing taxes) actually reduces total tax revenue in the case without liquidity constraints (compare 7 with simulation 2). Adding a 50 percent additional levy to what is already a quite high burden of taxation on labor income generates Laffer effects as the very large decline in labor supply swamps, in its effect on tax receipts, the gains due to the higher tax rate. The magnitude of the distortionary effects may be gauged by looking at the charts for simulation 7 which show both substantial declines in labor supply by the old and a quite distorted pattern of consumption as the higher tax rate on interest income induces intertemporal substitution. Note that despite its small impact on total tax receipts, the taper in simulation 7 significantly reduces the attractiveness of early retirement, pushing the optimal retirement age up from 57 to 62.

Simulation 5 shows what appears to be the preferred way of cutting pension benefits, namely reducing benefit levels for each year before the age of 65 that the household is retired. A 5 percent cut in benefits for each year of early retirement has a big impact on retirement decisions, increasing the optimal retirement age to 65. Total taxes paid increase by 4.8, a quite significant amount. Total lifetime savings rises by 30 percent. Although welfare, of course, decreases, it does so by less than in the case of simulation 7.

Sensitivity Analysis

Table 6 shows a sensitivity analysis for the simulations with binding liquidity constraints. I report the elasticities of the Table 5 simulation results with respect to various utility function parameters. Since these parameters are hard to guess given the paucity of econometric evidence, it is important to examine the impact changes in their levels have on the results.

Table 6:

SENSITIVITY ANALYSIS WITH LIQUIDITY CONSTRAINTS

Table 6:

SENSITIVITY ANALYSIS WITH LIQUIDITY CONSTRAINTS

	Goods Cons.	Leis. Cons.	Life Util.	Total. Sav.	Tax Paid	M.U. of W
Elasticity α
Simulation 1.	0.03	0.00	6.76	0.46	0.04	−0.89
Simulation 2.	0.04	0.00	6.76	0.49	0.03	−0.89
Simulation 3.	0.03	0.00	6.77	0.50	0.02	−0.88
Simulation 4.	0.06	−0.01	6.74	0.49	0.13	−0.90
Simulation 5.	0.04	0 00	6.73	0.35	0.03	−0.90
Simulation 6.	0.04	0.00	6.75	0.46	0.03	−0.89
Simulation 7.	0.00	0.02	6.72	0.12	−0.03	−0.90
Simulation 8.	0.06	−0.01	6.73	0.49	0.12	−0.90
Elasticity ρ
Simulation 1.	0.27	−0.60	1.58	−0.14	0.84	1.59
Simulation 2.	0.27	−0.60	1.58	−0.27	0.81	1.59
Simulation 3.	0.27	−0.60	1.58	−0.17	0.93	1.59
Simulation 4.	0.19	−0.25	1.59	−0.11	0.85	1.61
Simulation 5.	0.26	−0.59	1.58	−0.10	0.73	1.59
Simulation 6.	0.27	−0.60	1.58	−0.26	0.77	1.59
Simulation 7.	0.24	−0.50	1.58	−0.90	0.78	1.59
Simulation 8.	0.19	−0.25	1.59	−0.11	0.83	1.61
Elasticity δ
Simulation 1.	−0.03	−0.00	−0.16	−0.58	−0.07	−0.14
Simulation 2.	−0.04	−0.01	−0.16	−0.50	−0.03	−0.14
Simulation 3.	−0.04	−0.01	−0.16	−0.60	−0.04	−0.14
Simulation 4.	−0.05	0.00	−0.16	−0.48	−0.12	−0.14
Simulation 5.	−0.04	−0.01	−0.16	−0.42	−0.03	−0.14
Simulation 6.	−0.03	−0.01	−0.16	−0.51	−0.04	−0.14
Simulation 7.	−0.03	−0.02	−0.16	−0.57	−0.02	−0.15
Simulation 8.	−0.05	0.00	−0.16	−0.48	−0.12	−0.14
Elasticity α0
Simulation 1.	−0.17	0.37	0.22	−0.14	−0.52	0.21
Simulation 2.	−0.17	0.37	0.22	−0.09	−0.51	0.21
Simulation 3.	−0.17	0.37	0.22	−0.21	−0.60	0.21
Simulation 4	−0.13	0.14	0.21	−0.28	−0.56	0.18
Simulation 5.	−0.17	0.37	0.22	−0.12	−0.46	0.21
Simulation 6.	−0.17	0.37	0.22	−0.09	−0.49	0.21
Simulation 7.	−0.17	0.39	0.22	−0.08	−0.70	0.21.
Simulation 8.	−0.13	0.14	0.21	−0.27	−0.55	0.18

View Table

Table 6:

SENSITIVITY ANALYSIS WITH LIQUIDITY CONSTRAINTS

	Goods Cons.	Leis. Cons.	Life Util.	Total. Sav.	Tax Paid	M.U. of W
Elasticity α
Simulation 1.	0.03	0.00	6.76	0.46	0.04	−0.89
Simulation 2.	0.04	0.00	6.76	0.49	0.03	−0.89
Simulation 3.	0.03	0.00	6.77	0.50	0.02	−0.88
Simulation 4.	0.06	−0.01	6.74	0.49	0.13	−0.90
Simulation 5.	0.04	0 00	6.73	0.35	0.03	−0.90
Simulation 6.	0.04	0.00	6.75	0.46	0.03	−0.89
Simulation 7.	0.00	0.02	6.72	0.12	−0.03	−0.90
Simulation 8.	0.06	−0.01	6.73	0.49	0.12	−0.90
Elasticity ρ
Simulation 1.	0.27	−0.60	1.58	−0.14	0.84	1.59
Simulation 2.	0.27	−0.60	1.58	−0.27	0.81	1.59
Simulation 3.	0.27	−0.60	1.58	−0.17	0.93	1.59
Simulation 4.	0.19	−0.25	1.59	−0.11	0.85	1.61
Simulation 5.	0.26	−0.59	1.58	−0.10	0.73	1.59
Simulation 6.	0.27	−0.60	1.58	−0.26	0.77	1.59
Simulation 7.	0.24	−0.50	1.58	−0.90	0.78	1.59
Simulation 8.	0.19	−0.25	1.59	−0.11	0.83	1.61
Elasticity δ
Simulation 1.	−0.03	−0.00	−0.16	−0.58	−0.07	−0.14
Simulation 2.	−0.04	−0.01	−0.16	−0.50	−0.03	−0.14
Simulation 3.	−0.04	−0.01	−0.16	−0.60	−0.04	−0.14
Simulation 4.	−0.05	0.00	−0.16	−0.48	−0.12	−0.14
Simulation 5.	−0.04	−0.01	−0.16	−0.42	−0.03	−0.14
Simulation 6.	−0.03	−0.01	−0.16	−0.51	−0.04	−0.14
Simulation 7.	−0.03	−0.02	−0.16	−0.57	−0.02	−0.15
Simulation 8.	−0.05	0.00	−0.16	−0.48	−0.12	−0.14
Elasticity α0
Simulation 1.	−0.17	0.37	0.22	−0.14	−0.52	0.21
Simulation 2.	−0.17	0.37	0.22	−0.09	−0.51	0.21
Simulation 3.	−0.17	0.37	0.22	−0.21	−0.60	0.21
Simulation 4	−0.13	0.14	0.21	−0.28	−0.56	0.18
Simulation 5.	−0.17	0.37	0.22	−0.12	−0.46	0.21
Simulation 6.	−0.17	0.37	0.22	−0.09	−0.49	0.21
Simulation 7.	−0.17	0.39	0.22	−0.08	−0.70	0.21.
Simulation 8.	−0.13	0.14	0.21	−0.27	−0.55	0.18

What is perhaps reassuring is that, changing most of the parameters affects all the simulations in a uniform manner. So, for example, a perturbation in the rate of subjective time preference, δ, alters all the simulation results proportionally in the same way.

There are a few exceptions to this, however. For example, perturbing the coefficient of intertemporal substitution, α, has much less of an effect on saving in Simulation 7 than it does on other simulations. Hence, if a is much lower than the baseline level, the savings impact of the Simulation policies might appear rather better than they do in Table 5.

Another example of a case in which parameter perturbations affect simulations differently is with the leisure-consumption substitution parameter, ρ. Leisure is less sensitive to changes in this parameter in Simulations 4 and 8. But, of course, this is because these simulations include binding constraints on labor supply as an approximation to unemployment so this is not surprising.

In general, the sensitivity results do not lead us to question out basic conclusions and are reassuring about the robustness of our findings.