
                       =============================================
                                INFORMATION ON CVM PROGRAM
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4/94

Joseph Cooper and Daniel Hellerstein
USDA/ERS/Resources and Technology Division
1301 New York Ave. NW, rm. 508
Washington DC, 20005-4788
(202) 219-0403


CVM is a collection of dichotomous choice and double bounded
CVM related routines.  It is designed to be run with the Gauss 3.1, or
with the GAUSS 3.1 run-time module.  To facilitate ease of use by the
typical researcher, CVM uses a menu-based system with limited on-
line help, and can read ASCII input data sets (e.g. the *.prn files
created in Lotus 123) or GAUSS data files.

The GAUSS 3.1 run-time module is available separately.  Contact us
at the above adress for more information on the GAUSS 3.1 runtime
module.


The following lists the options available in the CVM program:

  BOXCOX          :  Use BOX COX to deduce distribution of data
  BOOT            :  Logit, using BOOTSTRAP methods to compute C.I.
  JACK            :  Logit, using JACKKNIFE methods to compute C.I.
  LOGIT           :  Logit, using Krinsky & Robb methods to compute
                  C.I.
  WEIBIT          :  Weibit, using K & R ...
  DBLOGIT         :  Double Bounded Logit
  DWEABS          :  Find optimal # of bid values (symmetric distribution)
  DWEABS2         :  Find optimal # of bid values (Asymmetric
                  distribution)
  NONPARA         :  Non-parametric estimation of WTP using survival
                  function.
  OUTPUT          :  Select output file
  TITLE           :  Write TITLE to output file
  EXIT            :  Exit Program
  HELP            :  Description of options

======================================================================
                   Description of options available in the CVM program.

BOXCOX

     BOXCOX is used to estimate the distribution of a variable, using
     a BOX-COX approach.  A test for log-normality is also
     performed.

BOOT

     This program uses the maximum likelihood logit model to
     estimate the dichotomous choice  coefficients. Confidence
     intervals are then calculated using the bootstrap approach
     developed by the author.

     This approach, is analogous in most steps to the bootstrap for
     OLS models in that coefficient estimates are re-estimated using
     pseudo residuals  drawn from an unspecified distribution.  Monte
     Carlo results show the results to be close to the jackknife
     approach.  It performs better in  large samples (i.e.  1000
     observations or more) than in small samples  (i.e.  approximately
     100 observations).

   The rest of the instructions and sample data set are the same as
LOGIT.

JACK

     This program uses the logit model to estimate the dichotomous
     choice coefficients.   Confidence intervals are then calculated
     using the jackknife approach.

     In this approach, a new data set is created for each repetition by
     randomly drawing N observations, with replacement, from the
     original data  set.  The welfare point estimate is then calculated
     for this new data set.  This process is very time consuming
     compared to the Krinsky and Robb or Cameron approaches but is
     superior to these two for large samples (1000 observations or
     more).

      The rest of the instructions and the sample data set are the same
     as LOGIT

LOGIT

     This program produces LOGIT estimates for DC CVM using the
     maximum likelihood procedure (specifically, the method of
     scoring, see Judge, et al., The Theory and Practice of
     Econometrics: Second Edition, p. 765). CONFIDENCE
     INTERVALS around the welfare measure are then performed
     using the Krinsky and Robb approach (Loomis, Park, and Creel,
     Land Economics, 1991) and Cameron's approach (Land
     Economics, 1992).

     Your input data set (either an ASCII or GAUSS file) must contain
     a dependent variable and a bid (price) variable.  The dependent
     variables  must be a zero/one variable.  You can also select
     independent variables  to include (a constant is always included).

     If you use an ASCII data file, be sure you know the number of
     rows (observations) and number of columns (variables).

         Sample data set: LOGITEX.PRN, which contains a (300 X 4)
         dimensional  matrix.

WEIBIT

     Similar to LOGIT except that the underlying distribution for the
     MLE estimator is the Weibull (a slightly asymmetric distribution,
     where the random variable is greater than or equal to 0).  Hence,
     this model can be named the WEIBIT estimator.

        Instructions and sample data set are the same as for LOGIT

DBLOGIT

     This program uses maximum likelihood estimation with the
     analytic  first and second derivatives from Hanemann, Loomis,
     and Kanninen (American  Journal of Agricultural Economics,
     1991) to estimate DOUBLE-BOUNDED LOGIT coefficient
     estimates.  CONFIDENCE INTERVALS around the associated
     willingness to pay measure are constructed using the Krinsky and
     Robb Method.

     Your data set must contain a special dependent variable, which
     must be coded as:
          Yes-Yes = 1, Yes-No = 2, No-Yes = 3, and No-No = 4.

        You must specify 3 bid (price) variables.
                  BID1 = The first bid amount.
           BIDLOW = The low bid amount (if first answer is NO)
                  BIDHIGH = The high bid amount (if first answer is
                  YES)

     You may also include other explanatory variables. Note that a
     constant is automatically included.

     Sample data set: DOUBLEB.PRN,
                    which is (265 X 6 : Dep,Bid1,Bidlow,Bidhigh,X1,X2).


DWEABS and DWEABS2

     These models, for a given set of pre-test data and total sample
     size N, use an iterative technique to find the Mean Square Error
     minimizing sample design for a dichotomous choice CVM survey
     (see Cooper, Journal of Environmental Economics and
     Management, January 1993, for details).  DWEABS assumes
     WTP or WTA has a symmetric distribution. DWEABS2 assumes
     WTP or WTA has an asymmetric distribution.

     The models require you to select a variable from an ASCII, or
     GAUSS, input file of open-ended pre-test data.  The programs are
     self-explanatory. Note though, that the iterative procedure can be
     time consuming if N is large.

     Sample (ASCII) data set: DWEABDAT.PRN (DWEABDAT.PRN
     is nX1)

NONPARA

     This program produces coefficient estimates using the generalized
     least squares procedure found in Judge et al., Page 758 (second
     edition). Therefore, it is a NONPARAMETRIC estimator. Based
     on the coefficient estimates, the consumer surplus estimate is
     calculated under the survival function. The procedure is similar to
     Kristom's (Land Economics, 1990) and should return similar
     results.  The CONFIDENCE INTERVALS around the welfare
     estimate are calculated using the Krinsky and Robb approach.

      Note: Repeat observations for each BID variable are required.

     The rest of the instructions and sample data set are the same as
     those for LOGIT.

OUTPUT

     Use this option to:
     1) View the current output file.  Use this to scan results of just
     completed     regressions.
     2) Change the name of the output file.  U

TITLE

     Use this to write a title to the output file.  The title can have as
     many as 10 lines in it.  If you are running several regressions in a
     row, you can changed selected lines of the title -- permitting you
     to retain information that does not change across models.

EXIT

     EXIT is used to exit the program.

=========================================================================
                                 CVM: Miscellaneous Notes

NOTE 1:
     This program attempts to read all the data into memory.  If there
     is not enough memory, it will fail. If you have the GAUSS 3.1
     run time module, you can work around this problem by setting up
     virtual memory (see VMRUNI.BAT). Also, for some models,
     numeric integration is attempted, which  requires a lot of memory.
     Again, the program may fail if there is not enough memory
     available.

NOTE 2:
     Given the output of the welfare estimate repetitions, the
     confidence intervals are found using Efron's percentile method
     (Canadian Journal of Statistics, 1981, Vol. 9, p.139-172; Journal
     of the American Statistical Association, Vol. 82, p. 171-185).  In
     this approach, the  welfare estimates are sorted in ascending order,
     forming an empirical distribution for the welfare estimate.  Next,
     to find a  (1 - alpha) confidence interval, where 0 <= alpha <= 1,
     the welfare estimates corresponding tothe alpha/2 percentile and
     the (1 - alpha/2) percentile of the sorted welfare estimate output
     distribution are pulled from this empirical   distribution.  The
     former value is the lower bound of the (1-alpha) distribution and
     the latter is the upper bound.  For example, if alpha =.1 and the
     number of repetitions is 1000, then the fiftieth value and the nine
     hundred and fiftieth value form the endpoints of the 90%
     confidence interval.

Note 3:
     For calculation of the confidence intervals around the welfare
     estimate, we recommend that you do at least a THOUSAND.
     According to Efron, this number should be sufficient.

Note 4:
     The functional form for the welfare estimator in the confidence
     interval programs assume that the bid variable is LINEAR.  If
     demand is sufficient, future versions of this package may allow
     the welfare estimate to be estimated with nonlinear forms, such as
     the log of bid.

Note 5:
     Monte Carlo results suggest that when the CVM data set is large
     (i.e. 1000 observations, CVMBOOT and CVMJACK are most
     likely to be the most accurate. For small samples the Krinsky and
     Robb or Cameron algorithms(such as 100) in the LOGIT and
     WEIBIT routines are likely to be the most accurate, though they
     have a tendency to produce confidence intervals that are too
     narrow.

Note 6:
     It is possible, if the data fit is lousy enough, that the welfare point
     estimate could fall outside the bounds of the estimated confidence
     interval. This situation is possible as the confidence intervals cut
     some percentage of the lowest and highest values, which may be
     quite extreme,from the tails of the empirical distribution of the
     welfare estimates.
