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INVESTING RETIREMENT WEALTH: A LIFE-CYCLE MODEL - Other parametersAs an empirical measure for the excess return on our stylized risky asset, we use CRSP data on the New York Stock Exchange value-weighted stock return relative to the T-bill rate. For all education groups, the regression coefficients are strikingly low and insignificant. To allow for potential lags in the realization of labor income, we repeat the exercise with the excess stock return lagged one year. The relationship becomes much stronger: the regression coefficient now varies from 0.06 to 0.10, and the correlation coefficient from 0.32 to 0.52, as reported in Table 1. Interestingly, the correlation of labor income with the stock market is larger and more significant for households with higher education.
In our portfolio choice model, allowing for lags in the relationship between innovations in stock returns and permanent shocks to labor income unfortunately requires an additional state variable. We therefore assume the correlation is contemporaneous. The model requires the variances of both 1, the aggregate permanent labor income shock that is correlated with stock market risk and шц, the idiosyncratic permanent shock to labor income. The first variance is obtained immediately as the variance of Alog(Y*). Subtracting this variance from the total variance of uit gives then the variance of wit.
The riskless real interest rate is assumed to be constant at 2%. We set the equity premium > equal to 4%. This is well below the long-run historical average, but represents a reasonable compromise between that average and lower forward-looking estimates based on the observation that stock prices have tended to increase in recent years relative to corporate earnings (Blanchard 1993, Campbell and Shiller 1998). We set the standard deviation of innovations to the risky asset j to 0.157. Recall that the classic formula for the risky asset portfolio share, under power utility with iid returns and no labor income, is >/7 j. With these parameters the implied risky asset share would be about 1/3 at the benchmark risk aversion of 5; we find higher optimal shares in our model only because of the presence of labor income. We set the fixed cost of equity market participation to zero in the benchmark case, but we go on to consider a $10,000 fixed cost.
The proportion of labor income W that is added to retirement wealth is equal to 10% of current labor income when retirement wealth accumulates at the riskless rate. This value implies an average replacement ratio at age 65 of 60%. When retirement wealth is also invested in stocks we either fix W at the same 10% value, or adjust it so as to maintain the replacement ratio at 60%. We will show that the value of W has a very important effect on our results. Table 1 summarizes the parameters used in the baseline case.