Economic Models - Convex Optimization

50 Dipak R. Basu and Alexis Lazaridis
rate and exchange rate. The “New Cambridge” model of the UK economy
(Cripps and Godley, 1976; Godley and Lavoie, 2002; 2007) has postulated
a similar combined consumption-investment function for the UK
as well.
The model was estimated by applying FIML method, using the data
from the Indian economy for the period 1951–1996. The estimated parameters
were then used as the initial starting point for the stochastic control
model. The estimated econometric model can be transformed into a state
variable form (Basu and Lazaridis, 1986), in order to formulate the optimal
control problem, i.e., to minimize the quadratic objective function, subject
to Eq. (4), which is the system transition equation. As already mentioned,
the recursive estimation process of the time-varying response-multipliers
is presented in brief in Appendix A.
3.1. Absorption Function and National Income
Domestic absorption reflects the behavior of both the private and public
sector regarding consumption and investment too. Domestic real adsorption
is influenced by real national income, market interest rate and foreign
exchange rate. We assume a linear relationship.
(A/P) t = a 0 + a 1 (Y/P) t − a 2 (IR) t − a 3 EXR t ,
t = time period.
The relation between the national income and adsorption can be defined
as follows:
Y t = A t + TY t + R t − G t + GBS t − LR t
where A is the value of domestic absorption, P is the price level, Y is the
national income, IR is the market interest rates, EXR is the exchange rate,
TY is the government tax revenue, G is the public consumption, GBS is the
government bond sales, LR is the net lending by the central government to
the states (which is not part of the planned public expenditure) and R is
the changes in the foreign exchange reserve reflecting the behavior of the
foreign trade sector.
The government budget deficit (BD t ) is defined by the following
equation
BD t = (G t + LR t + PF t ) − (TY t + GBS t + AF t + BF t )
where PF is the foreign payments due to existing foreign debts, which
may include both amortization and interest payments, AF is the foreign