Title:  Least Squares Estimation Subject to Monotonicity and Concavity
Constraints, with an Application to Cost Functions

Author:  Paul A. Ruud

Keywords:  restricted least squares, nonparametric regression,
monotonicity and concavity constraints, cost and profit functions,
quadratic programming

Reference:  P. A. Ruud, "Least Squares Estimation Subject to
Monotonicity and Concavity Constraints," Invited Symposium on
Computationally Intensive Methods In Econometrics, 1995.

Description:  This entry contains Matlab programs for computing the
least squares, nonparametric, fit of cost functions using data on
factor demands, factor prices, and output levels.  Both factor demands
and outputs may be multi-dimensional.

The algorithm is a specialized quadratic programming method based on
applying Gauss-Seidel to the dual program.  The Gauss-Seidel steps
include projection onto the cone of constraints that require each
observation to be the least cost factor demands for that output level
and input prices and a projection that imposes all monotonicity
constraints.  In addition, when the active constraints are stationary
over two iterations, the program attempts to jump to a final solution.

The computational example included is the re-estimation of the cost
function for electricity utilities from the Christensen-Greene study
(JPE, 84(4), 1976, 655-676).

The attached technical paper used these programs for the calculations:
P. A. Ruud, "Least Squares Estimation Subject to Monotonicity and
Concavity Constraints," Invited Symposium on Computationally Intensive
Methods In Econometrics, 1995.

Platforms:  Matlab

Support:  Please contact the author with questions or suggestions at
ruud@econ.Berkeley.EDU.

Manifest:
  3837 Aug 17 09:24 CG.out
  6336 Jul 31 10:57 Christensen.dat
  6543 Aug 17 09:17 Estimation.m
  2202 Aug 17 09:37 abstract.txt
  1873 Aug 17 09:11 active.m
  3636 Jul 31 12:30 avgcost.m
   521 Jul 31 10:48 feq.m
   527 Jul 31 10:48 fle.m
   517 Jul 31 10:48 flt.m
  1553 Jul 31 11:00 intpolfactor_p.m
  2591 Jul 31 14:57 install.txt
   744 Jul 31 10:55 load_Christensen.m
  4376 Aug 17 09:01 project.m
  8011 Aug 17 09:22 results_cg.mat
204594 Aug 17 10:27 tokyo1.ps