Economic Models - Convex Optimization

Time Varying Responses 49
equations should be updated accordingly so that adaptive control rules may
be derived.
Once we estimate the model (described in the next section), using the
full information maximum likelihood (FIML) method, we can obtain both
the structural model and the probability density functions along with all
associated matrices mentioned above. We first convert the structural econometric
model to a state-variable form according to Eq. (1). Once we specify
the targets for the state and control variables, the objective function is to be
minimized, the weights attached to each state and control variables, then
we can calculate the results of the optimization process for the entire period
using Eqs. (6)–(13). Thereafter, we can update all probability density functions
and all other associated matrices using Eqs. (20)–(23). These will
effectively update the coefficients of the model in its state-variable form.
We can repeat the optimization process over and over as we update the
model, its associated matrices, probability density functions and use these
as new information. When the process will converge, i.e., the difference
between the old and new estimates are insignificant according to some preassigned
criteria, we can obtain the final updated coefficients of the model
along with the results of the optimization process. The dynamics of the
time-varying coefficients (in terms of response-multipliers) are described
later in Section 4. This mechanism is a great improvement compared to the
fixed-coefficient model as we can incorporate in our calculation, changing
information sets derived from the implementation of the optimization
process.
3. Monetary-Fiscal Policy Model
We describe below a monetary-fiscal policy model, which was estimated
with data from the Indian economy. The model accepts the definition of
balance of payments and money stock according to monetary approach
of balance of payments (Khan, 1976; Khan and Montiel, 1989; 1990).
The decision to choose this particular model is influenced by the fact that
it is commonly known as the fund-bank adjustment policy model, used
extensively by the World Bank and the International Monetary Fund (IMF).
In the version adopted for this paper, there is no explicit investment
or consumption function, because the domestic absorption can reflect the
combined response of both private and public investment and consumption,
to the planned target for national income set by the planning authority
and to various market forces reflected in the money market interest