.- help for ^clad^ .- CLAD estimation with bootstrap standard errors ---------------------------------------------- ^clad^ varlist [^if^ exp] [^in^ range] [^, r^eps^(^#^)^ ^psu(^varname^)^ ^ll^[^(^#^)^] ^ul^[^(^#^)^] ^d^ots ^sa^ving^(^filename^)^ ^replace l^evel^(^#^) qu^antile^(^#^) it^erate^(^#^) wlsi^ter^(^#^)^] Description ----------- ^clad^ calculates Powell's (1984) censored least absolute deviations estimator (CLAD) and bootstrap estimates of its sampling variance. The CLAD estimator is a generalization of the least absolute deviations (LAD) estimator, which is implemented in Stata by @qreg@. Unlike the standard estimators of the censored regression model such as Tobit or other maximum likelihood approaches, the CLAD estimator is robust to heteroscedasticity and is consistent and asymptotically normal for a wide class of error distributions. (See Arabmazar and Schmidt, 1981, and Vijverberg, 1987, for empirical examples of the magnitude of the bias resulting from the Tobit in the presence of non-normal error distributions.) This program sidesteps the issue of programming analytical standard errors and provides instead, bootstrapped estimates of the sampling variance. Rogers (1993) shows that the standard errors reported by Stata for qreg are not robust to violations of homoscedasticity or independence of the residuals and proposes a bootstrap alternative. We follow Rogers for the CLAD estimator and propose two bootstrap estimates of the standard errors. The first is the standard bootstrap which assumes that the sample was selected using a simple random design. The second is a bootstrap estimate which assumes that the sample was selected in two-stages, and which replicates the design by bootstrapping in two stages. An advantage of the two-stage bootstrap estimates available in clad is that if the sample was collected using a two-stage process, then the estimated standard errors will be robust to this design effect. Kish (1995) and Cochran (1997) show the importance of correcting mean values for design effects. Scott and Holt (1982) show that the magnitude of the bias for the estimated variance-covariance matrix for ordinary least squares estimates can be quite large when it is erroneously assumed that the data were collected using a simple random sample if in fact a two-stage design had been used. Options ------- ^reps(^#^)^ specifies the number of bootstrap replications to be performed. The default value is 100. ^psu(^varname^)^ specifies the variable identifying the primary sampling unit. If no variable is specified, then the bootstrap replication is a single-stage, simple random draw on the sample. If specified, the bootstrap replication is two-stage simple random draw on the sample. ^ll(^#^)^ and ^ul(^#^)^ are as in Stata's @tobit@ command and indicate the censoring point. Observations with the dependent variable less than or equal to ll() are left-censored; observations with the dependent variable greater than or equal to ul() are right-censored; remaining observations are not censored. If ll or ul is specified without a specific censoring value, then clad assumes that the lower limit is the minimum observed in the data (if ll is specified) and the upper limit is the maximum (if ul is specified). If nothing is specified for a lower or upper bound, clad assumes that the lower limit is zero. Clad only functions with lower or upper censoring, you can not specify censoring at both the lower and upper bound. ^dots^ prints a dot to the screen for each bootstrap replication thereby allowing the user to estimate, after a few replications, the time to completion. ^saving(^filename^)^ creates a Stata data file (^.dta^ file) containing the bootstrap distribution for each statistics. Then, ^bstat^ can be run on the data in filename to view the bootstrap estimates again. ^replace^ overwrites the Stata data file specified in saving(), if it already exists. All other options are as specified in Stata's @qreg@ command. Remarks ------- The program does not use in calculations observations with missing values of dependent variable or psu-variable. However, the user might want to take care of missing values in exogenous variables to increase effectiveness of the bootstrap procedure. Examples -------- . ^clad lwage exp school^ . ^clad lwage exp school, reps(500) psu(cluster)^ . ^clad lwage exp school if rural==1, reps(500) psu(cluster) ll(1)^ ^level(90) dots saving(c:\stata\data\boot1)^ References ---------- Arabmazar, A. and Schmidt, P. 1981. "Further Evidence on the Robustness of the Tobit Estimator to Heteroskedasticity," ^Journal of Econometrics^, 17: 253-258. Cochran, William, ^Sampling Techniques^, New York: Wiley, Third Edition, 1997. Rogers, W., "Calculation of Quantile Regression Standard Errors," ^Stata Technical Bulletin^, 1993, STB-13: 18-19. Kish, Leslie, ^Survey Sampling^, New York: Wiley Classics Library Edition, 1995. Powell, J.L. 1984. "Least Absolute Deviations Estimation for the Censored Regression Model," ^Journal of Econometrics^, 25: 303-325. Scott, A.J. and Holt, D. 1982. "The Effect of Two-Stage Sampling on Ordinary Least Squares Methods." ^Journal of American Statistical Association^, 77(380): 848-854. Vijverberg, W. 1987. "Non-Normality as Distributional Misspecification in Single-Equation Limited Dependent Variable Models." ^Oxford Bulletin of^ ^Economics and Statistics^, 49(4): 417-430. Also see -------- Manual: ^[R] qreg^, ^bstat^ STB: On-line: help for @qreg@, @bstat@