This section evaluates the quantitative performance of our asset pricing model in the absence of FTTs with subjective price beliefs given by equations (2.8) and (2.9). Performance is evaluated in terms of the ability to match the stylized facts presented in section 2.4. The effects of introducing FTTs will be studied in section 2.9.
We parameterize our model using the model parameters employed in Adam, Beutel and Marcet (2014), which are summarized in table 2.5. Table 2.5 also lists the value for the support of stock supply shocks, which is a new parameter and set such that the amount of trade caused by these shocks amounts to less than 0.3% of the average trading volume in a setting without FTTs. Since trading volume is only weakly affected for the considered range of FTTs, the same holds approximately true for the case with FTTs. Furthermore, we verify that in the absence of FTTs, stock supply shocks affect the model moments in almost non-noticable ways.
Motivated by the evidence in table 2.4, we consider a model with 5 agent types, each of which has mass 1/5, and assign to them the point estimates of the updating gains from table 2.4.28
Parameter Value Calibration Target
βD 1.0048 average quarterly real dividend growth
σD 0.0192 std. deviation quarterly real dividend growth ρ 22 average consumption-dividend ratio
σDW −3.74·10−4 jointly chosen s.t. corrt(Ct/Ct−1, Dt/Dt−1) = 0.2
σW 0.0197 and stdt(Ct/Ct−1) = 17stdt(Dt/Dt−1)
σε 0.0816 std. deviation of quarterly real stock price growth δ 0.995 average PD ratio
γ 2 - none -
u 1·10−5 - none -
Table 2.5: Model calibration
Table 2.6 compares the model generated moments in the absence of FTTs to those in the data.29 The model moments for our baseline calibration are reported in the third column, while the fourth column reports the associated t-ratios for each considered data moment.30 Overall, our asset pricing model does a good job in replicating the pure stock price moments, i.e., the first
28
Recall that we chose the experience groups in table 2.4 so as to have approximately the same number of investors in each group.
29
All simulation results are based on 100.000 quarters of simulated data, where the first 10.000 quarters are considered as a burn-in and discarded when calculating model moments. Also, to make results from different simulations more comparable, we use fixed sequences for the exogenous driving processes (wages, dividends, stock supply shocks).
2.7. QUANTITATIVE MODEL PERFORMANCE
five moments reported in the table. It matches particularly well the mean and autocorrelation of the PD ratio, as well as the mean of quarterly real stock returns. It produces, however, too much volatility for the PD ratio and for returns. The model also does a good job in capturing the observed high positive correlation between the PD ratio and average return expectations in the survey data (corr(P Dt, EtRt+1)).
Regarding the newly added moments, the model generates a high positive autocorrelation in trading volume (corr(T Vt, T Vt−1)), albeit the model cor- relation is too high relative to the one found in the data. The model also manages to quantitatively capture the positive correlation between trading volume and (normalized) absolute price changes (corr(T Vt,|Pt/Pt−1 − 1|)). When looking at the correlation between trading volume and the PD ratio (corr(T Vt, P Dt)), the model produces a fairly weak positive correlation, but
one that is stronger than in the data. The model also generates a positive cor- relation between trading volume and cross sectional dispersion of return expec- tations (corr(T Vt, std(EetiRt+1))), but again overstates this correlation relative
to the data.31 The latter should not be surprising, given that in our simple model belief dispersion is the only reason why agents want to trade.
Since the baseline model produces an ‘anti-puzzle’ in the form of too much stock price volatility relative to the data, we also consider a model version in which we dampen the extrapolative component in belief updating. This is motivated by the fact that the updating gains in table 2.4 are themselves estimated with uncertainty. Specifically, we reduce the point estimates from table 2.4 by 2.5 times the estimated standard deviation of the point estimate32, leaving all other parameters unchanged. The resulting model moments are reported in the second to last column in table 2.6 below, with the last column reporting the associated t-ratios. Price and return volatility are now in line with data, while all other moments remain largely unaffected.
Overall, we find that the model does a good job in quantitatively replicating the joint behavior of stock price, trading volume and price expectations.
measure of uncertainty. Since the data moments in table 2.6 are not truly data moments, but functions of such moments, we estimate the standard deviation using the so-called delta method, as described in Cox (1998) or in the online appendix to Adam, Marcet and Nicolini (2016).
31
The data moment reported in table 2.6 is the one pertaining to the UBS survey, which has also been used to computecorr(P Dt, EtRt+1) in the data.
32We use for each gain parameter the gain specific standard deviation reported in the last
U.S. Data Baseline t-ratio Reduced t-ratio
Model Gain
(no tax) (no tax)
E[P D] 139.77 135.77 0.16 117.16 0.91 std(P D) 65.17 122.13 -3.84 92.96 -1.88 corr(P Dt, P Dt−1) 0.98 0.98 0.84 0.98 -0.13 std(rs) 8.00% 11.63% -9.05 8.27% -0.68 E[rs] 1.89% 2.11% -0.47 1.84% 0.11 corr(P Dt, EtRt+1) 0.79 0.84 -0.78 0.84 -0.73 corr(T Vt, T Vt−1) 0.89 0.97 -4.29 0.97 -4.14 corr(T Vt, P Dt) -0.07 0.37 -5.79 0.47 -7.09 corr(T Vt,|Pt/Pt−1−1|) 0.34 0.25 1.12 0.28 0.78 corr(T Vt, std(EetiRt+1)) 0.41 0.95 -3.67 0.92 -3.50
Table 2.6: Quantitative match of the asset pricing model