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st: Problems of convergence with maximum likelihood estimation in a SFA framework


From   Ngoc Anh Vo Thi <vtnanh@yahoo.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   st: Problems of convergence with maximum likelihood estimation in a SFA framework
Date   Sat, 8 Mar 2008 14:18:42 -0800 (PST)

Dear all,

I’m conducting a study on the comparative cost
efficiency of two types of foreign banks  - those that
enter a domestic market by setting up a greenfield
investment (GRs) and those that enter by mergers and
acquisitions of domestic banks (M&As), and want to
find out which factors explain discrepancies in their
efficiency. To this end, I’ve tried models suggested
by Hung-Jen Wang in his paper  “Heteroscedasticity and
Non-Monotonic Efficiency Effects of a Stochastic
Frontier Model” published in the Journal of
Productivity Analysis (2002) by running his Stata
program as provided in his website. That means I tried
to include factors that are likely to affect the
inefficiency term (u) by parameterizing mu or usigma
or both given the general form fof the distribution of
u: N+(mu, usigma). However, the problem is these
models barely converge with my data.

I would like therefore to aks you why this is the
case? Is it meant these models are not compatible with
my data? Or is it because my zlist is too long (6
variables)?

I would really appreciate your helps. Here is what I
type for the estimation.

*define variables in global macros, so they can be
referred to easily later
global yvar lncostn
global xlist Y1 Y2 P1 P2 Y1Q Y2Q Y1Y2 P1Q P2Q P1P2
Y1P1 Y1P2 Y2P1 Y2P2 lnequit country_2 country_3
YEAR_2-YEAR_11
/* translog cost function with exogenous factors
influencing the shape of the production function */
global zlist lnassets shareinv shareoff sharedep
merger mergage 

**USE THE FOLLOWING FOR M&As VS GREENFIELD

**use the procedure suggested by Wang (2002)
*Run an OLS on the frontier-only function to get
consistent estimates
 *(except the constant). They are used later as
initial values.
capture reg $yvar $xlist if foreign==1
mat b0 = e(b)   /* record the coefficient vectors in a
matrix */

*defining the maximization problem
sfmodel $yvar if foreign==1, cost dist(truncated)
frontier($xlist) mu($zlist) usigmas($zlist) vsigmas()

** (optional) supply initial values
sf_init, frontier(b0) mu(0 0 0 0 0 0 0) usigmas(0 0 0
0 0 0 0) vsigmas(0)

 ** (optional) Search for better starting values for
the specified variables.
 ** Based on Stata's -ml plot- command.
sf_srch, n(2) frontier($xlist) mu($zlist)
usigmas($zlist) fast
   /* "n(2)" cycles through the varaible list twice.
*/
   /* "fast" may speed up the drawing of graphs */

*do the maximization, with the gradients printed
ml max, diff gtol(0.001) gradient

*calculate inefficiency index, and possibly the
marginal effects
sf_predict, bc(bc_Wang) jlms(jlms_Wang)  marginal
   /* Battese & Coelli (1988) efficiency index in
bc_Wang; */
   /* Jondrow et al. (1982) inefficiency index in
jlms_Wang; */
   /* "marginal" calculates the marginal effects of
the zlist varaibles */

Thanks,
Anh



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