### Table 1 Idiosyncratic Endowment Process: Parameter Estimates

1999

"... In PAGE 17: ...e discuss some robustness checks along these lines #28e.g., di#0Berencing and quasi-di#0Berencing the data#29 and #0Cnd the qualitative nature of our results to be relatively stable. Table1 reports parameter estimates obtained using GMM in conjunction with the mo- ments in equations #2812#29. In Panel A we report estimates which constrain #1B H = #1B L and in Panel B we relax this restriction.... In PAGE 18: ... Our estimates incorporate this cross sectional evidence, but only implicitly #28via age-dependence in our moments#29. Our guess is that a more formal treatment of how inequality increases with age would generate an even higher value for the parameter #1A than we report in Table1 #28Storesletten, Telmer, and Yaron #281997#29 investigate this further#29. Finally, providing a frame of reference for our results on heteroskedastic idiosyncratic shocks over the business cycle is more problematic; aside from Heaton and Lucas #281996#29 we are not aware of comparable studies.... In PAGE 19: ...blush, this might seem inconsistent with the values reported in Table1 , where we estimate the increase in the conditional standard deviation of the persistent shock, coincident with a downturn, to be on the order of 126#25. What apos;s going on, however, is that the larger number is associated with the conditional distribution of a given agent apos;s innovation, whereas the smaller number is much more closely associated with the unconditional distribution.... In PAGE 22: ...hose of U.S. females in 1991 and population growth is set to 1.0#25. The process for idiosyncratic labor supply, equation #282#29, is implemented as a discrete approximation to the autoregressive time series model and is parameterized using our point estimates from Table1 . The age dependentintercept terms, #14 h , are chosen so that, on aver- age, our theoretical age-earnings pro#0Cle matches that of the PSID.... In PAGE 22: ... Further details are provided in appendix B. This calibration of our theoretical income process, equation #282#29, su#0Bers from two poten- tial sources of discrepancy relative to the PSID-based estimates from Table1 . The #0Crst is the error induced by approximating an in#0Cnite-state autoregression with a #0Cnite-state Markov chain.... In PAGE 22: ... More to the point, we #0Cnd that if we use our theoretical economy to generate an arbitrarily long sequence of 3 year panel data sets #28which corresponds to our PSID sampling method#29, the application of our GMM estimator #28section 3.2#29 to these data yields estimates which closely match those from Table1 ; our simulated point estimates are 0.... In PAGE 42: ... When we use our methodology we obtain an estimate of 0.931, which is essentially identical to that from the overlapping panels in Table1 . The di#0Berences in our approaches are as follows.... In PAGE 49: ... For our speci#0Ccation, if we ignore the transitory shocks, quot; it , as well as the terms which capture cross sectional variation due to age and education #28see equation #287#29 in section 3.2#29, then our estimation in Table1 boils down to a time series model of the residuals from a regression involving only year-dummy variables. In a large cross section this will be, z it = log c it , ~ E t log c it ; whichhave a cross sectional mean of zero, by construction, and a sample mean of zero, by least squares.... In PAGE 50: ... The quantityofinterest in equation #2820#29 can now be written as, log c i;t+1 =c t+1 c it =c t #11 log #0D i;t+1 , log #0D it = z i;t+1 , z it , 1 2 #10 ~ V t+1 #28log #0D i;t+1 #29 , ~ V t #28log #0D it #29 #11 #2821#29 The term in parentheses | the di#0Berence in the variances | does not vary in the cross section. Consequently, application of the cross sectional variance operator to both sides of equation #2821#29 implies, ~ V t+1 #12 log c i;t+1 =c t+1 c it =c t #13 = ~ V t+1 #28z i;t+1 , z it #29 : Ignoring the transitory shocks, the process underlying the estimates in Table1 is: z i;t+1 , z it =#281,#1A#29z it + #11 i;t+1 ; where the variance of #11 i;t+1 depends on the aggregate shock. For values of #1A close to unity the variance of changes in z it is approximately equal to the variance of #11 i;t+1 .... In PAGE 50: ... For values of #1A close to unity the variance of changes in z it is approximately equal to the variance of #11 i;t+1 . The left side of equation #2820#29 is, therefore, approximately equal to the variance of innovations, #11 i;t+1 , ~ V t+1 #12 log c i;t+1 =c t+1 c it =c t #13 #19 ~ V t+1 #28#11 i;t+1 #29 : In this sense, the estimates of #1B H and #1B L in Table1 provide estimates of what is necessary to calibrate the Constantinides-Du#0Ee model. All that remains are to map our estimates into numerical values for a and b from equation #2820#29.... In PAGE 50: ... Since aggregate consumption growth | the variable on the right side of equation #2820#29 | takes on only two values #283.8 percent and ,0:8 percent#29, computing the parameters a and b simply involves two linear equations: 0:037 = a +0:038b 0:181 = a , 0:008b ; where the values on the left are the cross sectional variances from Table1 . The resulting values are a =0:156 and b = ,3:130.... ..."

Cited by 14

### Table 1 Idiosyncratic Endowment Process: Parameter Estimates

1999

"... In PAGE 17: ... After presenting our benchmark estimation results we discuss a number of modi#0Ccations intended to incorporate a non-degenerate distribution of initial conditions and#2For agent speci#0Cc #0Cxed e#0Bects. Table1 reports parameter estimates obtained using GMM in conjunction with the mo- ments in equations #2812#29. In Panel A we report estimates which constrain #1B H = #1B L and in Panel B we relax this restriction.... In PAGE 18: ... Our estimates incorporate this cross sectional evidence, but only implicitly #28via age-dependence in our moments#29. Our guess is that a more formal treatmentofhow inequality increases with age would generate an even higher value for the parameter #1A than we report in Table1 #28Storesletten, Telmer, and Yaron #281997#29 investigate this further#29. Finally, providing a frame of reference for our results on heteroskedastic idiosyncratic shocks over the business cycle is more problematic; aside from Heaton and Lucas #281996#29 we are not aware of comparable studies.... In PAGE 18: ... The largest increase associated with an economic downturn is roughly 12#25, which is associated with the recession in the early 1980 apos;s #28the same answer is obtained using the cross sectional standard deviation#29. At #0Crst blush, this might seem inconsistent with the values reported in Table1 , where we estimate the increase in the conditional standard deviation of the persistent shock, coincident with a downturn, to be on the order of 126#25. What apos;s going on, however, is that the larger number is associated with the conditional distribution of a given agent apos;s innovation, whereas the smaller number is much more closely associated with the unconditional distribution.... In PAGE 21: ...hose of U.S. females in 1991 and population growth is set to 1.0#25. The process for idiosyncratic labor supply, equation #282#29, is implemented as a discrete approximation to the autoregressive time series model and is parameterized using our point estimates from Table1 . The age dependentintercept terms, #14 h , are chosen so that, on aver- age, our theoretical age-earnings pro#0Cle matches that of the PSID.... In PAGE 21: ...Further details are provided in appendix B. This calibration of our theoretical income process, equation #282#29, su#0Bers from two poten- tial sources of discrepancy relative to the PSID-based estimates from Table1 . The #0Crst is the... In PAGE 22: ... More to the point, we #0Cnd that if we use our theoretical economy to generate an arbitrarily long sequence of 3 year panel data sets #28which corresponds to our PSID sampling method#29, the application of our GMM estimator #28section 3.2#29 to these data yields estimates which closely match those from Table1 ; our simulated point estimates are 0.... In PAGE 50: ... For our speci#0Ccation, if we ignore the transitory shocks, quot; it ,aswell as the terms which capture cross sectional variation due to age and education #28see equation #287#29 in section 3.2#29, then our estimation in Table1 boils down to a time series model of the residuals from a regression involving only year-dummyvariables. In a large cross section this will be, z it = log c it , ~ E t log c it : whichhave a cross sectional mean of zero, by construction, and a sample mean of zero, by least squares.... In PAGE 51: ...Table1 correspond to, z i;t+1 , z it =#281, #1A#29z it + #11 i;t+1 For values of #1A close to unity the variance of changes in zit is approximately equal to the variance of #11 i;t+1 . The left side of equation #2820#29 is, therefore, approximately equal to the variance of innovation, #11 i;t , ~ V t+1 #12 log c i;t+1 =c t+1 c it =c t #13 #19 ~ V t+1 #28#11 i;t+1 #29 In this sense our estimates of #1B H and #1B L provide estimates of the quantity needed to calibrate the Constantinides-Du#0Ee model.... In PAGE 51: ... Since aggregate consumption growth | the variable on the right side of equation #2820#29 | takes on only twovalues #283.8 percent and ,0:8 percent#29, computing the parameters a and b simply involves two linear equations: 0:037 = a +0:038b 0:181 = a , 0:008b; where the values on the left are the cross sectional variances from Table1 . The resulting values are a =0:156 and b = ,3:130.... ..."

Cited by 14

### Table 1 Idiosyncratic Income Process: Parameter Estimates

1997

"... In PAGE 11: ... After presenting our benchmark estimation results we discuss a number of modi cations intended to incor- porate a non-degenerate distribution of initial conditions and/or agent speci c xed e ects. Table1 , panel A reports parameter estimates obtained using GMM in conjunction with the moments in equations (11). Our point estimate of is 0.... In PAGE 12: ... We estimated the parameters of our time series process using a GMM estimator analogous to that outlined in equations (11). The results for the rst-di erenced data, which handles what we view as the most important omission | xed e ects | are reported in Table1 , panel B. We see that the the conditional variances are qualitatively very similar to those from panel A, whereas the estimates of are, not surprisingly, somewhat smaller at .... In PAGE 13: ... The solid-dotted graph in Figure 3 reports the age-dependent cross-sectional variance of log of idiosyncratic earnings, yit, which would apply in a life cycle economy with no aggregate shocks and a large number of agents of each generation, where each agent derives their earnings from the process (9). Population moments are evaluated at the point estimates from Table1 , panel A. When estimating this process we controlled for some characteristics, in particular education.... In PAGE 13: ... We x the ratio of the transitory to the permanent standard deviation at 1.44 (corresponding to Table1 , panel A). We then choose the remaining three parameters, , and to match the cross-sectional standard deviation of the young (0.... In PAGE 14: ...5 Benchmark processes We have chosen to explore the implications of two di erent processes for log of indi- vidual earnings: 1. Based on our GMM estimates from Table1 we set = 0:9345, 2 = 0:061, and 2 = 0:0172. When estimating this process we controlled for some character- istics, in particular education.... ..."

### Table 1 Idiosyncratic Endowment Process: Parameter Estimates

"... In PAGE 17: ... Further details on the exact composition of our panel are available in Storesletten, Telmer, and Yaron (1998). In Table1 , row 1, we reproduce point estimates from our previous paper for the the following time series process, yit = git(yt) + uit (19) uit = zit + quot;it ; quot;it N(0; 2 quot;) (20) zit = zi;t?1 + it ; it N(0; 2 ) ; (21) where yit is the logarithm of the i apos;th household apos;s labor market endowment and git(yt) is the portion of yit comprising of aggregate shocks as well as deterministic components of household-speci c earnings such as unobservable ` xed e ects apos; and deterministic variation attributable to household age, education level and so on. In Storesletten, Telmer, and Yaron (1998) we discuss our particular parameterization of g (which follows closely a number of studies in the labor market dynamics literature), provide estimates and discuss how sensitive our results are to alternatives.... In PAGE 17: ... In Storesletten, Telmer, and Yaron (1998) we discuss our particular parameterization of g (which follows closely a number of studies in the labor market dynamics literature), provide estimates and discuss how sensitive our results are to alternatives. The rst row of Table1 shows that the autocorrelation coe cient is relatively large, at 0.935, and that the conditional standard deviation of the persistent shock process is roughly 90% larger than that of the transitory shocks.... In PAGE 18: ... First, we simply choose the variance of the distribution from which an agent draws their intercept term at birth so that the average, theoretical cross-sectional variance matches that of the data. Values represented by this procedure are reported in Table1 , row 2. The resulting age-pro le for cross-sectional variance is represented by the dotted line in Figure 1.... In PAGE 18: ... Loosely speaking, we chose to match the cross-sectional variation associated with the youngest age-cohort, to match the slope required to hit the variation associated with agents just ready to retire (the 60 year olds), and to match the curvature of the age-pro le. The values which result are reported in the third row of Table1 and the theoretical age-pro le is represented by the dashed line in Figure 1. Note that the implied value for is substantially higher, at 0.... In PAGE 19: ....S. females in 1991 and population growth is set to 1.0%. The process for idiosyncratic labor income, equation (2), is implemented as a discrete approximation to the autoregressive time series model and is parameterized using our point estimates from Table1 . In order to highlight the implications of the xed e ects, i, we begin by setting them to zero for our benchmark economy.... In PAGE 19: ...section 6.4) we allow them to be non zero and implement them as an i.i.d. two state bino- mial process, with variance chosen to match our estimates in Table1 . The age dependent intercept terms, h, are chosen so that the age-dependent mean of the logarithm of labor income in our theory matches our measure from the PSID.... In PAGE 30: ...escribed in sections 5.1 and 5.2. Speci cally, we modify the idiosyncratic risk process to include xed e ects according to the parameter values from the second line of Table1 . We then conduct several experiments designed to isolate pure risk sharing e ects (i.... In PAGE 43: ...7 Age Cross Sectional Variance The solid line represents estimates of the cross-sectional variance of PSID labor market in- come (inclusive of `transfers apos;), described in detail in Storesletten, Telmer, and Yaron (1997). The dash-dot line represents population moments associated with the time series process (19), evaluated at parameter estimates obtained by GMM (the rst row of Table1 ). The dotted line represents the incorporation of apos; xed e ects, apos; where we choose the variance of the distribution from which these parameters are drawn in order to match average disper- sion across ages (the second row of Table 1).... In PAGE 43: ... The dash-dot line represents population moments associated with the time series process (19), evaluated at parameter estimates obtained by GMM (the rst row of Table 1). The dotted line represents the incorporation of apos; xed e ects, apos; where we choose the variance of the distribution from which these parameters are drawn in order to match average disper- sion across ages (the second row of Table1 ). The dashed line incorporates xed e ects by choosing parameter values in order to match the initial cross sectional dispersion, and the slope and curvature of the age-pro le (the third row of Table 1).... In PAGE 43: ... The dotted line represents the incorporation of apos; xed e ects, apos; where we choose the variance of the distribution from which these parameters are drawn in order to match average disper- sion across ages (the second row of Table 1). The dashed line incorporates xed e ects by choosing parameter values in order to match the initial cross sectional dispersion, and the slope and curvature of the age-pro le (the third row of Table1 ). Speci cally, we choose 2 to match the initial variance, 2 to match the slope (or, equivalently, the end-point), and to match the curvature.... ..."

### Table 3 Idiosyncratic Consumption Process: Parameter Estimates

2003

"... In PAGE 10: ... For many questions, most notably asset pricing, we are equally interested in consumption and how its cross-sectional distribution is related to aggregate variation. Table3 replicates the estimation in Panels C, D and F of Table 2 using data on food expenditure from the PSID (the only consumption data available).... ..."

Cited by 5

### Table 5: Idiosyncratic Term Descriptive Statistics Germany Sweden Spain Euro

"... In PAGE 23: ...3.1 RBF Residuals - Descriptive Statistics Table5 presents the descriptive statistics for country-level idiosyncratic residual returm obtained by the application of the Kajiji-4 spillover model. At four significant digits, the results show a mean of zero and a relatively s~nall to near-zero variance measurement.... ..."

### Table 6: Second-Order Approximation Using Idiosyncratic Data

"... In PAGE 27: ...8. Table6 presents the results when the corresponding experiment is performed in my model under the baseline set of parameter values, and under several alternative parametric... In PAGE 31: ... These are eminently testable propositions.18 Given the results of Table6 , it even seems worthwhile to attempt to estimate an equation of the form of the second-order approximation to the Euler equation (but only if idiosyncratic data are used). The point of the earlier discussion of Table 6 was that the coe cient on Ei;t 2 i;t+1 didnotyieldanunbiasedestimateof .... In PAGE 31: ...arameter values). These are eminently testable propositions.18 Given the results of Table 6, it even seems worthwhile to attempt to estimate an equation of the form of the second-order approximation to the Euler equation (but only if idiosyncratic data are used). The point of the earlier discussion of Table6 was that the coe cient on Ei;t 2 i;t+1 didnotyieldanunbiasedestimateof . From a less structural point of view, however, the lesson of the table is that for any tested set of parameter values the model implies a hugely statistically signi cant relationship between consumption growth and Ei;t 2 i;t+1.... ..."

### Table 4 Idiosyncratic and systematic risks: median regression controlling for size and

"... In PAGE 20: ...erformance. The results are quite similar. The #0Crst regression I run is: PPS = #0B + #0C 1 ID RISK + #0C 2 SY S RISK + #0C 3 YEAR DUMMY + CONTROL+ #0F #283.21#29 Table4 reports the median regression result. I report three di#0Berent measures of risk esti- mated using the market model.... ..."

### Table 5 Idiosyncratic and systematic risk: OLS regression controlling for firm size and

"... In PAGE 20: ... 16 Second, I add the control for #0Crm size to control for size-related heterogeneity. Table5 reports the OLS regression results for the same regression. Here, in addition to the control for #0Crm size and CEO e#0Bort productivity, I control for the year and #0Crm #0Cxed 16 When I employ #0Crm age and Tobin apos;s Q as proxy for CEO e#0Bort productivity respectively, or use all three proxies, the results are similar.... ..."