Economic Models - Convex Optimization

58 Dipak R. Basu and Alexis Lazaridis
up, there will be direct pressure on the central bank to provide loans to the
government. The central bank can put pressure on the commercial banks to
extend some loans in public sector and less to the private sector, and the CD
of the commercial banks will be reduced as a result (at the same time reserve
ratio will be increased). While CD goes up in response to government
expenditure (G), the CI will have a similar effect on the currency to deposit
ratio.
Effects of the CD on prices declines rapidly, whereas the effect of the
exchange rate on price level is most prominent and does not vary much. It
demonstrates that although during the initial phase of planning, tight credit
policy may influence prices, in the longer run structural factors, public
expenditure, and import costs reflected through the exchange rate will affect
price levels more significantly. The effect of the CI on the money supply
(MS) will be reduced from −0.005 in period 1 to −0.007 in period 6, and
it will slightly increase in period 7.
The impacts of the public expenditure and tax revenues on the two most
important variables, GNP (Y) and price level (P) can be analyzed as follows.
The increased government expenditure (G) will increase price level and
the impact will be intensified. The impact of the government expenditure
on the GNP will be reduced, which is consistent with the reduced impacts
of the tax revenues on the GNP over the planning period. Tax revenue will
have negative impacts on the GNP as well as on the price level, and the
impacts will decline over time. The negative impacts of the tax revenue on
the GNP is partly explained by the negative effects of tax revenue on the
currency to deposit ratios of the commercial banks, the main indicator for
the private sector activities. The government expenditure also have positive
impacts on the government bond sales and the impact will increase over
time due to the increasing difficulties of raising taxes, which will have
negative impacts on the growth prospects.
The effect of the exchange rate declines gradually, whereas the effect of
the interest rate is cyclical. This is due to the cyclical pattern of the central
discount rate in the optimum path. It is quite obvious that the impacts of
fiscal and monetary policies on output will fluctuate over time depending
on the direction of change of these policies. The variations of the effects are
not unsystematic, as feared by Friedman and Schwartz (1963). However,
here we are analyzing an optimum path not the historical path.
5. Conclusion
The importance of time-varying coefficients was recognized in statistical
literature long ago (Davis, 1941), where frequency domain approach of