Re: [Gretl-devel] Lags in gretl's probit
On Thu, 26 May 2016, Sven Schreiber wrote:
Hi,
I've just noticed that it is possible to add (in the GUI) lags of the binary
dependent variable in the built-in Probit routine. However, there are some
subtleties involved in this context, so I'm wondering whether this has always
been possible? Could somebody provide some background on gretl's
implementation?
For example, there is this quite recent paper:
ROBERT M. DE JONG, TIEMEN WOUTERSEN
DYNAMIC TIME SERIES BINARY CHOICE
Econometric Theory, 27, 2011, 673–702.
doi:10.1017/S0266466610000472
From the abstract: "... it shows in a time series setting the validity of
the dynamic probit likelihood procedure when lags of the dependent binary
variable are used as regressors ..."
Does gretl rely on this particular paper's findings?
Well, in a way.
Section 3 states quite clearly that maximising the standard log-likelihood
gives you perfctly standard inference. Most of the paper is concerned with
the MSCORE estimator (that we don't have) in a dynamic setting.
It is true that what happens if you stick the --robust option hasn't been
thought out particularly thoroughly. From De Jong and Woutersen (2013):
"Note that given the weak dependence property of Theorem 2, it is also
possible to set forth conditions such that for weakly dependent u_n with
arbitrary distribution,
N^1/2 (b − ) −→ N (0J)
for some matrix J and a β∗ thatuniquely minimizes the objective function.
Here of course β∗ does notnecessarily equal the true parameter value β."
But of course we're sailing the treacherous QMLE seas here, so I doubt
that anybody really knows what happens when :)
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------