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# st: RE: disequilibrium model

 From "Schaffer, Mark E" To "statalist@hsphsun2.harvard.edu" Subject st: RE: disequilibrium model Date Mon, 22 Apr 2013 11:21:32 +0000

```Matt,

-movestay- by Lokshin and Sajaya estimates the kind of "switching-regression" model you are working with - see description below.  Playing with the -findit- turned up some other options, e.g., switchr (Zimmerman) and  ssm (Miranda and Rabe-Hesketh).

HTH,
Mark

movestay uses the maximum likelihood method to estimate the endogenous
switching regression model.  It is implemented using the d2 evaluator to
calculate the overall log likelihood together with its first and second
derivatives.

movestay estimates all of the parameters in the model:

(regression equation for regime 1: y1 is depvar1, x1 is varlist1)
y1 = x1 * b1 + e_1

(regression equation for regime 2: y2 is depvar2, x2 is varlist2)
y2 = x1 * b2 + e_1

(selection equation: Z is varlist_s)
y1 observed if Zg + u > 0
y2 observed if Zg + u <= 0

where:
e_1 ~ N(0, sigma1)
e_2 ~ N(0, sigma1)
u ~ N(0, 1)
corr(e_1, u) = rho_1
corr(e_2, u) = rho_2

Here depvar1, depvar2 and varlist1, varlist2 are the dependent variables
and regressors for the underlying regression models (y1, y2 = xb), and
varlist_s specifies the variables Z thought to determine which regime is
observed.

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Matt
> Sent: 22 April 2013 11:05
> To: statalist@hsphsun2.harvard.edu
> Subject: st: disequilibrium model
>
> Hi,
>
> I'm current working on the disequilibrium model as in the Maddala and
> Nelson (1974).
>
> Quantity of demand (qDt) = B1X'1t + u1t
> Quantity of supply (qSt) = B2X'2t + u2t
> Quantity observed (qt) = min (qDt, qSt)
>
> the model consists of a demand equation qDt, a supply equation qSt, and a
> transaction equation qt.
> the vectors X'1t and X'2t are exogenous, independent variables, B1 B2 are
> their coefficients, u1t and u2t are their disturbances.
>
> qDt and qSt in this model are the amount of bank debt demanded and
> supplied, but they are not observed by any external party.
> Only the amount of bank debt which was actually received, the transaction
> amount qt can be perceived.
> But we don't know if this transaction amount of debt is the agrees to the
> amount demanded by the firm or whether it is limited by bank. We don't
> know whether the firms in the sample face credit rationing - unknown
> sample separation.
>
> So, to avoid writing the complicated ML programme, i uses 3-stage least
> square to estimate the demand and supply model, but i'm confused about
> the dependent variable should be used for estimation of demand and supply
> equation. Indeed, for the quantity observed (qt) is the short-term bank loans
> of the firm as in the balance sheet. But what should be the dependent
> variable for qDt and qSt?
>
> Also, how can i do conditional probability in stata?
>
> Many thanks if you can answer my query.
>
> Matt
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