Econometric commodities in the economy: Tobacco and Gas.

Econometric Testing
for Laws of Demand

Assignment 2

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ABSTRACT

 

The basic
economic theory states that for a normal good there exists a positive relation
between demand of good and income, ceteris paribus. We aim to assert and
examine such economic theory related to the consumer by using an annual time
series data of the US and have a critical examination with respect to two
commodities in the economy: Tobacco and Gas. The effects of price, income and
the sensitivity of the data with respect to these factors and the population is
taken into account. As we try to test various hypothesis related to consumer
behavior using OLS and assume that the demand equation takes a log linear
preference form. Also, a lag adjusted model is tested for both the commodities
and the trend values are checked for significance in the later parts of the
project.

 

Basic Demand Model

 

Hence, we
run OLS regression on the above equation and obtain the estimates of both the commodities.
It is interesting to note that the individual estimates actually represent the
elasticities.

 

Thus, the
income and own price elasticity of the commodities are as follows:

Income
elasticity: Gas:
0.82549

                              Tobacco: 0.50197

Own-price
elasticity: Gas: 0.00238

                                   Tobacco: -0.5165

 

Thus, we
can infer that the demand for both the commodities has a strong positive
relationship with income changes while it is interesting to note that the
economic theory of reduction in demand with increase
in price is fact and is thus the elasticity is reflected for gas. However, as
tobacco is a substance with hardly any substitutes its highly inelastic and
thus the changes in price has a low or no effect on the demand for tobacco.
But, since gas has relatively number of substitutes it is seen to be more
elastic than tobacco.

 

Thus,
taking a 5% level of significance, we form a confidence interval for these
elasticities. Thus, computing the intervals with a value of 1.96 critical
value.

 

Income elasticity: 0.597209 ? Gas ? 1.05377

                              0.408690 ?
Tobacco ? 0.595246

 

Own-price
elasticity: -0.081110
? Gas ? 0.085870

                                   -0.568832 ?
Tobacco ? -0.464168

 

Now we test the law of demand: the null hypothesis
?p = 0, against the alternative ?p 0.05, thus we do not reject the null
hypothesis and can comment that the population is insignificance in terms of
affecting the demand for Tobacco.

 

Thus, in
line with economic theory, we see that there exists an inverse
relationship between elasticity and impact of population on the demand.
Greater elasticity reduces the impact of the population
due to the availability of alternate
substitutes.

 

Now, we
have also run another test for coefficients of the population to be equal to that of 1-

 . The underlying theory being that whether
this is the best form of expression of the variables or not. For Tobacco we see
the p value is greater than 0.05, hence we see that the per capita form is
significant in this case. Theoretically it confers with economics of data as it
is easier to measure for tobacco as only a portion of the population has a
specific demand for Tobacco. However, the converse is true for Gas. As we have
already seen Gas acts as a necessary good and thus almost is demanded by the whole
population of an economy. Hence, as per our earlier results population affects
the demand for gas and hence per capita form can be asserted to be
insignificant and to be not represented by this form for expenditure and
income.

 

CHECKING FOR
STABILITY OF PARAMETERS:

The Chow test is
used to determine whether the independent variables have a structural break and
have different impacts on two subgroups of the population. Thus, we check the
stability of values over the whole period between 1981 to 2003 by dividing it
into two halves of 22 and 23 samples.

From TSM output of
Gas., we observe the stability test equals 32.0769 which is greater than the
critical value of F-test (4 and 37 degrees of freedom): 2.62605 and the p-value
of 0 is less than 0.05 at 5% significance
level.

32.0769 > 2.62605

0 2.62605

0