Stocks from flows and the Rate of Return in the Hungarian pension system
7th Global NTA Meeting: Population Aging and the Generational Economy June 11-12, 2010, Honolulu
Róbert I. Gál (
[email protected])
Structure of presentation: * The contribution asset of a PAYG scheme: how to assess it from period values and why is it interesting? * Annual returns in a PAYG scheme * Illustration on Hungarian data
Stocks from flows Let Ac and Ay be the money-weighted average age of consumers and producers, respectively. When Ac < Ay consumers have to borrow against their future labour income and build up a debt or negative wealth. When Ac > Ay a positive wealth is accumulated. Based on Willis (1988) and Lee (1994) we can establish a relationship between a combination of current flows and age profiles and accumulating stocks.
A pension analogy Accumulating contribution asset can be assessed from current contributions and age profiles (Settergren and Mikula 2005): CA ≈ C*TD, Where CA: is contribution asset, the (negative) present value of future net contribution flows C: aggregate contributions in year t TD: turnover duration, Ape – Act (money-weighted average age of pensioners and contributors, respectively) TD is standing for the time contributions (eligibilities) spend in the pension system before they are translated into pensions. TD and ETD
What is the annual return in a PAYG system? CA can be applied in assessing the annual returns in PAYG pension schemes. PAYG pensions are based on past investments in contribution paying capacities. In principle, returns of such investments can be measured. Here the annual return is the rate with which the value of the individual accounts (individual eligibilities) can be raised so that the amount of net pension liabilities should not exceed the value of the contribution asset. This definition (offering a proxy to returns in a PAYG scheme) derives annual returns from long-term sustainability: annual returns are the maximum growth of the value of eligibilities affordable under contribution constraints.
Annual returns (period RR, PRR) Ct1 ⋅ TDt1 − Ct 0 ⋅ TDt 0 + Ft1 ⋅ rt1 PRR = PLt 0 where C is current contributions, TD: is turnover duration, PL: is net pension liabilities, F: is capital fund of the pension system; in the Hungarian case the capital accumulated in the mandatory private funds, r: is the market interest rate on capital, and t0 and t1: are time-indices.
The Hungarian case Some background facts: * A baby boom postponed: no afterwar fertility boom (men in POW camps) but a jump in fertility in the mid-1950s * shortage economy with full employment and a transition from central planning to a market economy in the early 1990s: an employment crisis * explicit electoral cycle in pension expenditures: frequent changes in the pension system
The Hungarian case: ETD 28.0
27.5
27.3
27.4
27.4 27.1
27.0 27.0
26.9
26.9
26.8 26.7
26.4
26.5
26.3
26.3 26.1
26.0 26.0 25.7 25.5 25.2
25.3
25.0 1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
The Hungarian case: C and CA 10.0
250 242 238
240
238 9.5
234 229 230
9.0 220 8.5 210 199 197
200
194 191
191 190
198
198
195
8.0
196
191 188
186
7.5
180 7.0 170 6.5 160
150
6.0 1992
1993
1994
1995
1996
1997
1998
1999
2000
CA (left axis)
2001
2002
C (right axis)
2003
2004
2005
2006
2007
2008
The Hungarian case: PL 80 000
400
70 000
350
60 000
300
50 000
250
40 000
200
30 000
150
20 000
100
10 000
50
0
0 1992
1993
1994
1995
1996
1997
1998
1999
2000
2009 bi llion Ft (left axis)
2001
2002
2003
% of GD P (right axis)
2004
2005
2006
2007
2008
The Hungarian case: PRR 20.0 17.3 13.5
15.0 11.0 10.0
10.9 9.4
9.2
6.6 4.3
5.0
2.6
2.1 -0.1 0.0 1992
1993
1994 -4.2
1995
1996
-5.0 -7.8 -9.9
-10.1 -10.0
-15.0
-20.0
-15.8
1997 -4.5
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
PRR: some conclusions •
Not only funded schemes produce negative returns
•
PRR is a proxy measure for returns in a PAYG scheme
•
There are limits of the applicability/interpretation of the PRR as a return concept: – What if PL is not equal to CA in t0? – What if PL has independent changes?
The overall CA/PL ratio (%) 180
160 154
154
140
143
142
136 120 117 100 1992
1993
1994
1995
1996
80
60
40
20
0
70
66
64
62
63
1997
1998
1999
2000
2001
107 2002
2003 94
2004
2005
83
85
2006 90
2007
114 2008
