Econometric Testing

for Laws of Demand

Assignment 2

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