Tesis para la producción

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Recovery based on panel data

Once I have recovered individual belief and confirmed the assumption of constant relative risk and ambiguity aversion, time preference β, relative risk aversionρ, and relative ambiguity aversionAcan be uniquely recovered according to Proposition11. The recovery result in Proposition11requires a special panel dataset, where I can observe individual zero and non-zero asset demand under the same return of riskfree asset across time. Assum- ing that the return of risk free asset is invariant between 2008 and 2010, I have 148 such observations. Note that the recovery argument in Proposi-

tion 11only applies to an individual being both risk averse and ambiguity averse, since the recovery argument is based on the first order conditions, a necessary and sufficient condition for utility maximization when the utility function is concave, which holds for both risk aversion and ambiguity aver-

sion. From Lemma 6 it is known that a necessary condition for risk and

ambiguity averse individuals to hold risky assets is that the simple excess return of risky asset is positive. As shown in the above analysis, constant relative risk aversion and ambiguity aversion is a good approximation for such a population. So I only recover preference of individuals who ex- pect simple excess return to be positive. Among these 148 observations, I have 65 observations with positive simple excess return. For the remain- ing 83 observations (56%), individuals hold risky assets though they think the simple excess return is negative, so they must be either risk loving or ambiguity loving. A large proportion of people being either risk loving or ambiguity loving is also identified by experimental researchWakker(2010). However, my identification framework can not recover preference of such individuals, and it is not of my interest.

Table 5.12: Recovered risk and ambiguity aversions based on panel data

Time preference Re. risk aversion Re. ambiguity aversion

β ρ A 5% 0.964 0.001 0.296 10% 0.977 0.002 0.385 25% 0.992 0.006 0.777 50% 1.010 0.012 1.581 75% 1.016 0.033 3.958 95% 1.023 0.080 16.383 Min 0.942 0.0003 0.114 Max 1.107 0.114 25.415 Mean 1.004 0.023 3.578 Std. Dev. 0.024 0.026 5.243 Observation 47 47 47

Note: The above recovery assumes the riskfree asset return is invariant across two-year period.

Table 5.12 reports the recovered time preference β, relative risk aver- sion ρ and relative ambiguity aversion A based on 47 panel observations assuming invariant interest rate. The mean of time preference is 1.004 and

the median is 1.010, which is quite consistent with existing empirical re- search. One important feature is that the heterogeneity of time preference across individuals is very moderate, with standard deviation being 0.024. In the following part, when I use cross-sectional data to recover individual risk aversion and ambiguity aversion, I expect that assuming time prefer- ence to be homogeneous across individuals would be without much loss of generality.

Table 5.12 shows that the mean of recovered relative risk aversion is 0.023. It is much smaller than other existing research based on micro data, which only estimates relative risk aversion without considering ambiguity aversion, and suggests that relative risk aversion is larger than 1.8 Although the magnitude is small, the relative risk aversion is different from 0. The

t test rejects risk neutral assumption at significance level 1%. Besides, the risk aversion is heterogeneous across individuals, with standard deviation 0.047.

The parameter which interests me most is relative ambiguity aversion, since current research gives very little evidence. Table 5.12 shows the mean of relative risk aversion is 3.578, with minimum 0.114 and maximum 25.415. The heterogeneity of ambiguity aversion is quite large with a standard deviation of 5.243. Thettest rejects the hypothesis that relative ambiguity aversion is 0 at significance level 1%.

Recovery based on cross-sectional data

The data requirement based on Proposition 11 is too stringent, instead, in this section I assume time preference is homogeneous and is set to be

β = 1. The above analysis suggests that it is a reasonable assumption.

Then from Corollary7, relative risk aversion and ambiguity aversion can be uniquely recovered from one observation of individual saving rate and risky asset share in cross-sectional data. In 2008 data, among 1734 households who report consistent beliefs, 528 households (30.5%) holds risky assets. Since I am only interested in recovering individual preference which is both risk averse and ambiguity averse, I concentrate on the sample with positive simple excess return expectations. In 2008 data, out of 528 households, 259

8_{However, the empirical evidence is far from being conclusive, the estimated relative} risk aversion ranges from 0.05 Binswanger (1981) to over 1000 Schluter and Mount (1976).

households (49.1%) hold expectations that simple excess return of risky assets is positive. In 2010 data, among 1120 households with consistent belief, 344 households (30.7%) report positive risky assets. 112 out of these 344 households (44.2%) expect positive excess return of risky assets, which my analysis focuses on.

Table 5.13: Recovered risk and ambiguity aversions based on cross-sectional data

Individual preference in 2008 Individual preference in 2010

ρ A ρ A 5% 0.001 0.198 0.002 0.131 10% 0.002 0.332 0.003 0.369 25% 0.007 0.792 0.007 0.895 50% 0.019 1.782 0.017 1.349 75% 0.054 3.810 0.034 2.876 95% 0.334 8.355 0.237 6.885 Min 0.0001 0.019 0.0002 0.027 Max 0.861 18.670 0.507 23.966 Mean 0.062 2.90 0.050 2.498 Std. Dev. 0.127 3.070 0.096 3.562 Observation 130 130 67 67

Note: The above recovery assumes homogeneous time preference across individuals.

Table 5.13 reports the recovered relative risk aversion and relative am- biguity aversion based on cross-sectional data from 2008 and 2010 respec- tively. In 2008, among 259 households who hold the expectation that simple excess return of risky assets is positive, 130 households (50.2%) are both risk averse and ambiguity averse. So out of 528 households holding positive risky assets, around 24.6% are both risk averse and ambiguity averse. In 2010, among 112 households who hold positive excess return expectations, 67 households (59.8%) are both risk averse and ambiguity averse. So out of 344 households holding positive risky assets, around 19.5% are both risk averse and ambiguity averse.

In 2008, the mean of relative risk aversion is 0.062. The t test rejects the hypothesis that relative risk aversion is 0 at the 1% significance level.

The mean of relative ambiguity aversion is 2.90. The t test rejects the hypothesis that relative ambiguity aversion is 0 at the 1% significance level. Preference heterogeneity (both in risk aversion and ambiguity aversion) across households can be seen from the standard deviation (0.127 and 3.070 respectively).

In 2010, the mean of relative risk aversion is 0.050. Thettest rejects the hypothesis that relative risk aversion is 0 at significance level 1%. The mean of relative ambiguity aversion is 2.498. The t test rejects the hypothesis that relative ambiguity aversion is 0 at significance level 1%. As in 2008, preference heterogeneity across households is large. The recovery result from cross-sectional data is very similar to the one from panel data, which lessens the concern about the homogeneous time preference assumption.