### Table 11: Estimation results for the duration model The variables v0 and v1 are mass points of the unobserved heterogeneity distri- bution and p is the probability that the unobserved heterogeneity term equals v0.

2007

"... In PAGE 21: ... Since all houses that are for sale in the first week of the sample period are left-censored with respect to duration, we only include newly arrived houses after the first week of the sample period. Estimation results for the mixed proportional hazard specification are listed in Table11 . As before, we do not list the levels of the neighborhood fixed effects.... In PAGE 21: ... As before, we do not list the levels of the neighborhood fixed effects. First of all, Table11 shows that larger houses, apartments and houses with a garage attached sell faster. Houses have a relatively small probability to be sold in the first four weeks, while the highest probability to sell a house is in between weeks 9 and 13.... In PAGE 22: ... Only after sellers learn about the quality of the house they start to accept bids of potential buyers. An important result in Table11 is that u1 = 0, which means that unobserved heterogeneity is negligible. The possible impact of the murder can be found by comparing the cross effects of time and type I neighborhoods in the quarters before and after the murder.... In PAGE 22: ...e., the time effects times the type I neighborhood effects in Table11 , are large. Note that the present literature on the duration of house sales usually assumes a Weibull distribution for the baseline hazard of the mixed proportional hazards model, see Rutherford et al.... ..."

### Table 7. Estimates of Unobserved Components Models: Discrete Time and Continuous Time

"... In PAGE 28: ... The results are contained in Tables 7 and 8. Table7 contains the results of estimating the discrete time and continuous time trend- plus-cycle models. The discrete time estimates are taken directly from Harvey (1989, p.... In PAGE 30: ...2843 Figures in parentheses are standard errors. misspeci ed in some way, and Harvey (1989) does indeed nd that the discrete time model in Table7 is inferior to a cyclical trend model in which t also depends on t 1 and yt = t+ t. Further investigations with continuous time cyclical trend models may be fruitful, but are beyond the scope of this simple illustration.... ..."

### Table 2: Parameter estimates for simulated data. The MLE estimates are based on the simulated stage time data which are usually unobserved. Other estimates are based on the count data in Table 1. The estimated standard error is given in parentheses.

"... In PAGE 19: ...etween 0.1 and 6. Based on cumulative sums of the generated hatch times, we counted the number of observations in each stage at each sampling time, and these are given in Table 1. Parameter estimates are given in Table2 for various LT and MOM methods, using the count data in Table 1. We used equally spaced cut points about the observation times except that c0 = 0, c15 = 1 for the LT estimates, and c15 = 6:21 for the MOM estimate.... In PAGE 20: ... Note that these s values are rather smaller than the s values in the ad-hoc iterative scheme, but both approaches lead to very similar parameter estimates. The maximum likelihood estimates (MLE) given in Table2 are based on the actual organism-by-organism stage time data: these are usually unobserved, and the di erence in magnitude of the standard errors indicates the loss of e ciency in moving to the censored data. The MOM and LT estimates are all within one standard error of the true value, and generally appear to produce similar estimates of the inverse mean hatch time 2= i in each stage.... ..."

### Table 1e: Average Deductible Derivatives DGP: Mixture model where type depends on unobserved health state, 2-part

2000

"... In PAGE 15: ... To do this in practice we evaluate the conditional expected value at various values of the explanatory variables and calculate the \arc quot; derivatives. Suppose we are interested in calculating the derivatives of the expectation of health care expenses with respect to the level of deductible in the health insurance plan, which we report in Table1 . One way of calculating the average derivative (Average in the tables), is rst to calculate the expected value of expenditures using the estimated distribution function for all observations.... In PAGE 15: ... We also experimented with aggregating these values to construct di erent measures of the overall \average quot; derivative of a covariate. These are reported as Min Variance, Equal Weights, Weight 1, and Weight 2 in Table1 ; these are de ned in detail in Appendix Table A2. Clearly, one 9In our Monte Carlo experiments we randomly draw sets of explanatory variables from sets of covariates for 1219 observations observed in the NMES data set.... In PAGE 18: ... The deductible is that amount of health expenditure dollars that a consumer pays before the insurance company begins sharing the costs. Table1 a contains Monte Carlo evidence when the DGP is a simple OLS model, and the DGPs for Tables 1b through 1e are described in the table titles. We calculate the derivative by numerically di erentiating with respect to the explanatory variable.... In PAGE 19: ... We begin by demonstrating the ability of our quite non-linear conditional density estimation (CDE) technique to uncover the true derivative according to the Monte Carlo experiment. In Table1 a, using OLS to estimate derivatives provides the most e cient estimator. We recover the true mean of -0.... In PAGE 20: ...Table1 a: Average Deductible Derivatives DGP: Yi = 0Xi + i, iid normal errors, OLS OLS OLS OLS Derivative Truth Levels Levels Logs CDE Evaluation point 1st order 4th order 4th order 0 -0.399 -0.... In PAGE 21: ...Table1 b: Average Deductible Derivatives DGP: ln(Yi) = 0Xi + i, iid normal errors, 2-part OLS OLS OLS Derivative Truth Levels Levels Logs CDE Evaluation point 1st order 4th order 4th order 0 -2.632 -0.... In PAGE 22: ...Table1 c: Average Deductible Derivatives DGP: ln(Yi) = 0Xi + i; var( ) E[ln(Y )], 2-part OLS OLS OLS Derivative Truth Levels Levels Logs CDE Evaluation point 1st order 4th order 4th order 0 -2.577 -0.... In PAGE 23: ...Table1 d: Average Deductible Derivatives DGP: ln(Yi) = 0 iXi + i = Xi + ( i ? )Xi + i; random coe cients model OLS OLS OLS Derivative Truth Levels Levels Logs CDE Evaluation point 1st order 4th order 4th order 0 -2.477 -0.... In PAGE 36: ... The only drawback to using the OLS and CDE models with polynomials and interactions of the explanatory variables is the seemingly low precision of the estimates. The standard deviation for the CDE estimator of the deductible derivative in Table1 a, for example, is three times larger... In PAGE 37: ...057); these standard deviations indicate the magnitude of the standard errors of the estimates from these estimators. By using the exible CDE model with the simple linear model DGP in Table1 a (and also Tables A5a, A6a, and A7a, all of which have the same DGP), calculated t-statistics will be about three times smaller for the CDE than for the simple OLS estimator. This \lack of precision, quot; however, is due to the fact that the CDE model allows for the possibility that the e ect of insurance deductible can vary with the level of the deductible and with the levels of the other covariates.... In PAGE 37: ... The OLS model imposes the true restriction, for this DGP, that the deductible e ect is constant across all dimensions. To put the CDE model onto a more level playing eld with the OLS estimator for this DGP, consider imposing the restriction that the CDE estimated deductible derivatives are estimating the same quantity at each level of the deductible that we examined in Table1 a. We do not impose the restriction that these derivative levels are also constant across all values of all of the other covariates, as is imposed by the simple OLS estimator.... In PAGE 37: ... We impose these restrictions ex post by calculating the covariance matrix for the CDE estimators of the derivative at the seven deductible levels displayed in this table and solving for that weighted average of the seven point derivatives that yields the smallest variance. This result is the evaluation point labeled \Min Variance quot; in Table1 a and the other tables of Monte Carlo results. We nd that by imposing this restriction ex post, the standard error of the CDE estimator of the deductible e ect is only 7% higher than that of the OLS estimator.... ..."

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### Table 3 may be biased because of the correlation between these unobservables and the SE

1999

"... In PAGE 23: ...The details can be found in the Appendix. The estimation results for model (15) are reported in Table3 . Durations are measured in months.... In PAGE 23: ... The matching estimators of Section 4 suggested that SE decreases the exit rate from welfare. Table3 , which corrects for the timing of selection and the resultant lower exit rate due to the duration dependence of the exit rate, leads to the opposite conclusion: participation in SE increases the exit rate by a factor 1.... In PAGE 26: ...The GLS estimates for regression equation (18) and the regression equations for the other transitions are reported in Table 4. A comparison with the results in Table3 shows, that the parameter estimates for the destination states welfare without SE and welfare with SE are almost identical in the two tables. Also the duration effects in the transition intensity to the state out-of- welfare do not differ by much between these tables.... In PAGE 26: ... This is reassuring given the structurally weaker economy of the Walloon Provinces. More importantly, the effect of SE is negative in Table 4, while it was significantly positive in Table3 . Note that the GMM test statistic for the null hypothesis of regressor-error orthogonality only rejects at a significance level of more than 27%.... In PAGE 29: ... If we cor rect for selection on observables only (Section 5.3, Table3... ..."

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### Table 7 Median Survival Times (Weeks) For an Unobserved Center When Observed Centers are Excluded Exponential Mixture Changepoint

"... In PAGE 17: ... The six models were rerun 5 times, each time excluding one treatment center. The impact of the exclusion is summarized in Table7 . This table presents the median survival time for an unobserved center, again denoted Center F.... In PAGE 18: ...ncluded is 34. Hence the di erence is 29-34=-5. Di erence B presents the error in our prediction if we used the median for an unobserved center to predict the Kaplan-Meier median for the excluded center. Table7 about here The table shows that median survival times for an unobserved center were most a ected by the exclusion of Centers D and E. The largest increase in median survival under each of the 6 models occurred when Center E was excluded, the largest decreases when Center D was excluded.... In PAGE 18: ... If we used this value to predict Center A apos;s median survival we would miss by 20 weeks. This is the Di erence B reported in Table7 . We see di erences for other centers ranging from -40 to +49.... ..."

### Table 8. Estimates of Continuous Time Unobserved Components Model with Di erential-Di erence Equation Cycle

"... In PAGE 28: ...3 years compared to 7 years.15 The estimates in Table8 , for the di erential-di erence equation cycle, are based on three choices of truncation parameter for the spectrum. Using the same method as in the simulations in the previous section, the truncation parameter M is determined by M = [T ] + 1(T 62 N ) for = f0:25; 0:50; 0:75g (the corresponding values of M are 3, 8 and 22 respectively).... ..."

### Table 5 Duration Model Estimates Off-Welfare Spell: No Unobserved Heterogeneity

"... In PAGE 20: ... The evidence also indicates that the first quarter hazard is higher than the last quarter hazard. The next-to-last row of Table5 provides an estimate of the... In PAGE 21: ... Beyond that point, the survival function becomes relatively flat and about 60% of ex-clients are still off welfare after 4 years. The estimates of the proportional hazard models for off-welfare spells are presented in Figure 6 and Table5 . We report results for only the two specifications that do not control for UH.... In PAGE 22: ...The remaining proportional hazard coefficients are in Table5 . The baseline hazard with controls for both schooling implies a mean off-welfare spell length of 32 months if one assumes a constant hazard beyond the sample period.... In PAGE 38: ... Table5 (continued) Number of Past Months on Welfare /10 1.017 1.... ..."

### TABLE 3: CONTROLLING FOR UNOBSERVABLES (1)

2000

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