Results

ob-Table 2.7. Overview of model parameters

Parameter Value Description

γ 2.000 Relative risk aversion

π -0.003 Liquid asset return

r 0.050 Illiquid asset return

σ_r 0.025 Volatility of the illiquid return

With transitions

Without transitions

β 0.961 0.956 Discount factor

κ 2.822 2.715 Adjustment cost

σ_ε 0.905 0.961 Randomness of adj. cost

served patterns of wealth accumulation over the life cycle to pin down the value of the discount factorβ and the life-cycle evolution of the portfolio composition to estimate the parameters κ and σ_ζ that govern the portfolio adjustment frictions.

Following the approach in Section 2.3, we construct age profiles for the wealth-to-income ratio, the portfolio share of illiquid assets, and the realized return on wealth from the HFCS data for both risk types. Using these empirical targets, we estimate the parameters for two setups: in our baseline setup we allow switching between risk types, while in the alternative case workers have fixed risk types. The result-ing estimated parameters together with the other calibrated parameters are shown in Table 2.7. In the case of our baseline calibration which allows for transitions be-tween risk types, the annual discount factorβis estimated at 0.96. We find that the model requires a non-negligible degree of adjustment frictions to match the empiri-cal data. The adjustment costκis estimated at 2.82 and the standard deviation of the adjustment cost is estimated at 0.91.

either as a low or a high-risk type, but they face a probability to switch between risk types throughout the working life. The switching between types happens according to the probabilities shown in Figure 2.10. In the alternative case, risk types are fixed and workers belong to the same risk type throughout their working lives. We treat the model implied data the same way as we treated the social security data.

Concretely, we assign an average risk type at the end of working life in the simulated data based on the same rules we used for the actual data (see Section 2.2) and allocate workers to the two risk groups using the realized volatility of their income growth rates. The bottom 80% of workers are designated as low risk and the top 20% as high risk. Based on this sample split we can then compare the empirical profiles for wealth accumulation and portfolio composition with the model profiles.

First, we examine the scenario where workers can switch between risk types.

The probability of transitioning between risk types depends on the magnitude of the earnings shock workers experience. For workers of the low-risk type, the probability to switch to the high-risk type is particularly large when they experience a very negative earnings shock. Alternatively, for workers that belong to the high-risk type, their probability to switch to the low-risk type is the largest when they experience a very positive earnings shock. Figure 2.11 shows the resulting life-cycle profiles for the wealth-to-income ratio, liquid share and realized returns.

At first abstracting from differences between risk groups, we find that the esti-mated model is able to replicate the stylized facts on wealth accumulation and port-folio choice over the life cycle. In line with the empirical evidence, workers increase their wealth holdings as they age and the share of the illiquid wealth increases since workers allocate more wealth towards the illiquid asset as they age. Consequently also the return on wealth increases over the life cycle. In terms of quantitative results, we also find that our model matches the data well, although it implies a somewhat more convex profile of wealth accumulation than the data suggests. However, it is important to note that we are able to match the liquid share at the beginning of the working life only by endowing a quarter of workers with an initial endowment of the illiquid asset. In the absence of such an initial endowment, portfolio liquidity would be too high at the start of the working life. Since wealth is held mostly for self-insurance against idiosyncratic income fluctuations at the beginning of working life (Gourinchas and Parker, 2002; Cagetti, 2003), workers start saving in the liquid as-set. Only after a sufficient stock of the liquid asset has been accumulated, they start to invest more into the illiquid asset. Consequently, the model implies that absent any initial endowment of the illiquid asset, portfolios would be composed entirely of liquid wealth at the beginning of working life.

Now turning our attention to the differences between risk groups, we find that the model can match the empirically observed patterns of differences between work-ers to a great extent. First, we find that high-risk workwork-ers hold more liquid portfolios, replicating the empirical finding. Higher volatility of earnings induces workers in the high-risk group to save relatively more in the liquid asset, which can be easily used

Figure 2.11. Results when workers switch between risk types

20 30 40 50

0 1 2 3 4

Low risk (model) Low risk (data) High risk (model) High risk (data)

(a)Wealth-to-income

20 30 40 50

0.2 0.3 0.4 0.5 0.6 0.7 0.8

(b)Liquid share

20 30 40 50

0 0.01 0.02 0.03 0.04

(c)Realized return

Notes: Workers allocated to risk groups on the basis of realized volatility of their income growth rates. The bottom 80% of workers are classified as low-risk and the top 20% as high-risk. Wealth-to-income ratios normalized by the value of the high-risk group in the initial point. Liquid share in the initial point matched by endowing a quarter of workers with an initial stock of the illiquid asset.

to smooth income fluctuations. Asset illiquidity matters a lot for workers with high earnings fluctuations and therefore a higher stock of the liquid asset is required to optimally smooth consumption over time. Second, we also find that our model can replicate the empirical finding that low-risk workers develop higher wealth-to-income ratios than high-risk workers, although model-based differences between risk types are smaller than the empirical ones.

As an alternative, we consider a scenario where switching between risk types is not possible. Workers can belong either to the low-risk type or to the high-risk type, and the risk structure a given worker faces does not change during the working life.

Figure 2.12 shows the life-cycle profiles for the wealth-to-income ratio, liquid share and realized returns for this situation. Similarly to the earlier scenario, where tran-sitions between risk types were possible, the model is able to match the direction of the empirically observed differences in portfolio liquidity and realized returns.

Most importantly, though, the results on wealth accumulation are now inconsistent with the empirical evidence. We find that with fixed worker risk types the model fails to replicate the empirical finding that low-risk workers have relatively more wealth. This version of our model would imply that workers in the high-risk group hold more wealth relative to their income throughout the working life. With a fixed assignment of workers to risk types, earnings are fully mean-reverting and there-fore higher volatility of shocks induces workers to save more in order to smooth the larger deviations around the expected mean throughout the working life. With-out the probability to transition between risk types, there is also no additional pre-cautionary motive to self-insure against the idiosyncratic second-order risk for the initially low-risk type.1⁵

15. In Figure 2.12 workers are split into risk groups based on the realized earnings volatility. In the situation where workers do not switch between risk groups throughout their working life, splitting

Figure 2.12. Results when workers have fixed risk types

20 30 40 50

0 1 2 3 4

Low risk (model) Low risk (data) High risk (model) High risk (data)

(a)Wealth-to-income

20 30 40 50

0.2 0.3 0.4 0.5 0.6 0.7 0.8

(b)Liquid share

20 30 40 50

0 0.01 0.02 0.03 0.04

(c)Realized return

Notes: Workers allocated to risk groups on the basis of realized volatility of their income growth rates. The bottom 80% of workers are classified as low-risk and the top 20% as high-risk. Wealth-to-income ratios normalized by the value of the high-risk group in the initial point. Liquid share in the initial point matched by endowing a quarter of workers with an initial stock of the illiquid asset.