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Generation. G1. G2. G3. G4. Time t1. +$1. -$1. Time t2. +$1. -$1. Time t3. +$1. -$1. Time t4. +$1. Intergenerational problem. Intergenerational problem. Each generation lives for two periods (young and old). The initial generation (G1) is old at time t1.
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Generation G1 G2 G3 G4 Time t1 +$1 -$1 Time t2 +$1 -$1 Time t3 +$1 -$1 Time t4 +$1 Intergenerational problem
Intergenerational problem • Each generation lives for two periods (young and old). • The initial generation (G1) is old at time t1. • They receive $1 per head by taxing generation G2 at time t1. • Similarly, G2 receives $1 by taxing G3 in t2. G3, in turn, gets $1 in t3 by taxing G4. • This process continues indefinitely.
Intergenerational problem • Let us now consider two systems: pay as you go and a switch to privatized system. We will consider the outcomes in turn. • Pay as you go: It is easy to see that each generation (except the generation G1) pays $1 in one period and gets $1 in the following period. For example generation G2 pays $1 in t1 and gets $1 in t2. Therefore, the rate of return is zero.
Intergenerational problem • Privatized scheme: Let us assume that the investors are only allowed to invest in bonds under a privatized individual account system. Let us suppose that the system starts at t2. Suppose the rate of return on the bond is 5%.
Intergenerational problem • It might seem that the individuals in generation G3 would now get $1.05 in period t3 rather than $1 in the pay as you go regime. Note that the $1 that is owed to G2 has to be paid from somewhere. Suppose that the government pays G2 by selling bonds in t2. The only way the government can sell the bonds is to offer a market interest rate of 5%. In other words, the government owes $1.05 in t3.
Intergenerational problem • If the government simply wants to keep the principal of the loan at $1, it has to pay for the interest payment in t3. If this five cents ($0.05=$1.05-$1.00) is to be paid for by taxes, it is likely to tax the younger generation. Thus, the net gain of G3 would be $1.05 (from bond holding) minus $0.05 (from tax payment). Thus, once the interest cost (through taxes) is included, G3 does not gain anything from the new privatized system.
Intergenerational problem • Once the government has borrowed that $1, private accounts do not generate any additional national savings. The $1 extra in private accounts is exactly offset by $1 extra borrowed by the government. With no added savings at the national level, there would be no additional capital formation and therefore no increased wealth for future generations. In future years, nobody in the society will have more income than they would under a pay as you go system.
Intergenerational problem • The result can be worse for the retired old. If the taxes are paid (at least in part) by the old, they will be worse off. Instead, if the benefits are cut, the retired generation will be worse off as well.
Intergenerational problem • There is one way of making future generations better off by privatization. Suppose young people direct their $1 contribution to privatized individual accounts. The $1 hole is now "financed" in two parts. The government cuts the benefits of the current old generation by $0.50 and imposes an additional tax of $0.50 to the current young generation. This means no new borrowing is necessary to finance anything else in the future. Future generations will be able to enjoy the 5% without offsetting taxes.
Intergenerational problem • Of course, there is no free lunch. The above process will make the current old generation worse off. They will see their benefits dwindle by $0.50. In addition, even though the current young people will get a 5% rate of return on their investment, they will also pay an additional tax of $0.50.
Intergenerational problem • The essential nature of this argument does not change if we have other forms of financing schemes. For example, if all generations hold diversified portfolios (with bonds and stocks), it does not alter the conclusion. The main insight is that higher rates of return for stocks also have higher risk.
Intergenerational problem • In summary, privatization of accounts by itself does not have any effect on the economy as a whole. Benefits from privatization only comes from raising taxes or cutting benefits (or both) which might then be used to raise national saving.
Consider a worker who earns ws at time s, assumed to grow exponentially at rate g: • (1) ws = w0egs. • The tax rate on these earnings is t. There is a proportional front-load charge of f, so that t(1-f) w0egs is deposited at time s.
This accumulates until retirement age T. • The accumulation occurs at rate r-c, where r is the rate of return and c is the management charge per dollar under management. • Thus deposits made at time s have accumulated to t(1-f) w0egs e(r-c)(T-s) at time T.
The total accumulation at time T is the integral of this expression from time 0 until time T. Integrating, the accumulation depends on f and c and (for g+c unequal to r) is equal to: • (2) A[f, c] = t(1-f)w0e(r-c)T{e(g+c-r)T - 1}/(g+c-r).
For g+c=r, the accumulation satisfies • (3) A[f, c] = t(1-f)w0e(r-c)T T. • How do we get (3) from (2)?
For r unequal to both g+c and g, the ratio of the accumulation to what it would be without any charges satisfies: • (4) AR[f, c] = A[f, c]/A[0, 0] =(1-f)e-cT{(e(g+c-r)T - 1)/(e(g-r)T - 1)}{(g-r)/(g+c-r)}. • The charge ratio is one minus the accumulation ratio: • (5) CR[f, c] = 1 - AR[f, c].
Let Vt denote the value of the fund at the end of time t. The contribution during time t is denoted by Ct (we will assume that the entire payment occurs at the beginning of the period so that the interest earned by the contribution is the same as interest earned by the balance Vt-1 brought in from the previous period).
The rate of return between time t-1 and time t is denoted by rt. There are two types of fees charged by the AFOREs: fees on flow and fees on saldo. We denote the fee on flow at period t by ft and the fee on saldo at period t by st.
Therefore, we can write the value of the fund at time 1 as follows: • V1 = [V0 + c1(1 - f1)](1 + r1)(1 – s1) • Similarly, the value of the fund at time 2 can be written as follows: • V2 = [V1 + c2(1 –f2)](1 + r2)(1 – s2) • In general, we can write this recursive relation that connects period t-1 and t as follows: • Vt = [Vt-1 + ct(1 – ft)](1 + rt)(1 – st)
There is an additional contribution by the government in the form of a cuota social. • According to the law, cuota social is not subject to fees on flow. Thus, we need to add the cuota social in the formula ensuring that it stays outside the fees ft. Let us denote the cuota social at time t by cst. Then, the modified formula takes the following form: • Vt = [Vt-1 + cst + ct(1 – ft)](1 + rt)(1 – st)
AFORE 2003 Spreadsheet • Comparison with IMSS
CONSAR Comisiones Equivalentes sobre saldo a 25 años Junio 2004 (Porcentaje anual) Enero 2001 (Porcentaje anual) Disminución de 34%
Comparar ambos resultados • El Reforma dice 19% de las aportaciones • La CONSAR calcula sobre el saldo • El Reforma dice que ha sucedido hasta ahora • La CONSAR calcula con una proyección a 25 años • Ademas, CONSAR supone que cada persona se mantiene con la misma AFORE durante 25 años • La verdadera competencia debe permitir la posibilidad de cambiar de AFORE sin castigo
Costos fiscales comparativos Miles de milliones de pesos
Scenario 1: Affiliate with three minimum salary (flat profile with the assumption of the salario minimo at 16,931 per year), 5% real interest rate (we assume it is the same for all AFORES), 0% inflation, 0 initial quantity brought into the system
Scenario 2: Suppose we keep all the other assumptions the same as in scenario 1 but simply change the amount of money an affiliate brings into the system. (3 times salario minimo and 5% real return with 0% inflation but an initial amount of 50,000.)
Impact of the real interest rate: If the real interest rate is high and stays high (for example, 10%), the charges of Inbursa begin to have a bigger bite by the twenty-seventh year. Azteca becomes the best AFORE.
