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Visualization
of the Road to Chaos for Finance and Economics Majors
--
Cornelis A Los
Efforts
to simulate turbulence in the financial markets include experiments with the logistic
equation: x(t) = kx(t - 1)[1 - x(t - 1)], with 0 < x(t) < 1 and 0 £
k < 4. Visual investigation of the logistic equation shows the various stability
and instability regimes for the various values of the Feigenbaum number k. Visualizations
for t = 20 observations provide clear demonstrations of the stability regimes.
The author algebraically analyzes all these regimes in more detail. For 0 <
k < 3, the process settles to a unique stable equilibrium. For 3 £ k <
3.6, the process bifurcates, or, as colored visualization shows but not black-and-white,
its pitchfork bifurcation branches "bang-bang" switch between two regimes.
For 3.6 £ k =< 4, the process becomes chaotic, i.e., deterministically
random. In this regime are windows of stability, e.g., at k = 3 + 3= 3.8284. At
k = 4, pure chaos, the process is extremely sensitive to initial values, which
is clearly demonstrated visually. The author increases the number of observations
to t = 1000, and computes the homogeneous Hurst exponent of the process at k =
4: H = 0.004, indicating that x(t) is blue noise, i.e., extremely antipersistent.
A histogram shows a highly platykurtic distribution of x(t), with an imploded
"mode", with extremely fat tails higher than the "mode", against
the reflecting values at x = 0 and x = 1. Several plots of the state directory
of the system in the (x(t), x(t - l)) space trace out the parabolic strange attractor.
Although the strange attractor is a well-defined parabole, the points on the attractor
set are deterministically random and unpredictable. ©
2006 IUP . All Rights Reserved. The
Interrelatedness of Malaysian Equity Markets, Money Markets and Foreign Exchange
Market
-- Wan Mansor Wan Mahmood
The
paper examines the relationship among equity markets, money markets and the foreign
exchange market in the Malaysian context. These three markets are proxies by the
3-month treasury bills of the money market, the Kuala Lumpur composite index for
stock market, and the ringgit against Singapore dollar for the foreign exchange
market. The time period for the study covers from January 1998 through December
2002. The results show that these markets are integrated over time in the long
run. As for the short run, the results report the existence of significant bidirectional
short run causal interaction only between exchange rates and money market rates.
The issues are important to look into by investors, multinational companies and
government alike, as disruption of any one market will have an effect on their
strategies in the other markets. ©
2006 IUP . All Rights Reserved. The
Elasticity and Buoyancy of the Botswana Tax System and their Determinants
-- Thuto D Botlhole and Tamunopriye J Agiobenebo
This
study extends the theoretical, methodological and empirical developments in tax
elasticity and buoyancy estimation in several ways. First, rather than assuming
that the tax base is exogenous, it considers the very strong theoretical possibility
that it may be endogenously determined by several factors such as structural shifts
in the domestic economy; developments in the external economy; trends in regional
cooperation and integration; and tax effort and evasion. Using the Botswana tax
system as a case study, it shows that these factors are important determinants
of the tax base, and hence, tax elasticity and buoyancy. Utilizing a Vector Error
Correction Model (VECM), it reveals that the Botswana tax system is income-elastic
and buoyant; trends in regional cooperation and integration are exerting negative
influence on tax revenue via its depleting impact on Southern African Customs
Union (SACU) revenue; tax evasion is revenue-depleting, and hence, dampens the
elasticity and buoyancy of the tax system; openness of the economy has significant
influence on tax revenue yield, thus, trade liberalization and globalization have
serious implications for tax system elasticity and buoyancy; and economic diversification
resulting in dynamic structural shifts have positive effects on both the tax base
and revenue yield. It emphasizes that mineral tax revenue is buoyant and elastic
with respect to mining GDP; non-mineral income tax is buoyant and elastic with
respect to exports; customs and excise duties are neither buoyant nor elastic
with respect to imports and regional integration; and also that government tax
effort is only about 27%, a degree far below its potential. These findings carry
important policy implications. ©
2006 IUP . All Rights Reserved. Housing Finance in India A
Case Study of LIC Housing Finance Limited
-- Fulbag
Singh and Reema Sharma
Housing,
as one of the three basic needs of life, always remains on the top priority of
any person, economy, government and society at large. In India, majority of the
population lives in slums and shabby shelters in rural areas. From the last decade,
the Government of India has been continuously trying to strengthen the housing
sector by introducing various housing loan schemes for rural and urban population.
The first attempt in this regard was the National Housing Policy (NHP), which
was introduced in 1988. The National Housing Bank (NHB) was set up in 1988 as
an apex institution for housing finance and a wholly-owned subsidiary of Reserve
Bank of India (RBI). The main objective of the bank is to promote and establish
the housing financial institutions in the country as well as to provide refinance
facilities to housing finance corporations and scheduled commercial banks. Moreover,
for the salaried section, the tax rebates on housing loans have been introduced.
The paper is based on the case study of LIC Housing Finance Ltd., which analyzes
region-wise disbursements of individual house loans, their portfolio amounts and
the defaults for the last ten years, i.e., from 1995-96 to 2004-05 by working
out relevant ratios in terms of percentages and the compound annual growth rates.
A relevant chart has also been prepared to highlight the results. ©
2006 IUP . All Rights Reserved. Can
there be a Proper Calculation Procedure of the Poverty Line?
-- Aurobindo Ghosh
Poverty
has become a prominent topic for social policy discussions in India. Different
countries have their own methodologies to calculate the poverty line. This is
the reason why they are country-wise unique. In India, it is generally calculated
through calorie intake measure. As the measurement criterion is not very sound
because of the limited access to the technology of food calorie measurement, the
calculation of poverty line in India is invariably with less or no proper validation.
This paper tries to minimize the subjectivity, and aims to convert the poverty
line concept into a realistic line concept by using the 3s-limit of normal distribution
model. The author validates the usual calorie-based measurement by the new 3s-limit
concept. It is shown that within a particular population with varied income groups,
the actual poverty line can be drawn. This line shows that the rich people's data
is not only redundant but should also be eliminated from the actual calculations,
as this will only inflate the data under consideration, resulting in wrong value
of calculated poverty line. The 3s-limit calculation is shown step by step with
examples through which the segments of the population falling under different
categories, like super-rich, rich, average, poor, and very poor, can easily be
located. People falling under very poor category are the people under poverty
line. ©
2006 IUP . All Rights Reserved. |
