Econometric Testingfor Laws of DemandAssignment 2 ABSTRACT The basiceconomic theory states that for a normal good there exists a positive relationbetween demand of good and income, ceteris paribus. We aim to assert andexamine such economic theory related to the consumer by using an annual timeseries data of the US and have a critical examination with respect to twocommodities in the economy: Tobacco and Gas. The effects of price, income andthe sensitivity of the data with respect to these factors and the population istaken into account.
As we try to test various hypothesis related to consumerbehavior using OLS and assume that the demand equation takes a log linearpreference form. Also, a lag adjusted model is tested for both the commoditiesand the trend values are checked for significance in the later parts of theproject. Basic Demand Model Hence, werun 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 theelasticities. Thus, theincome and own price elasticity of the commodities are as follows:Incomeelasticity: Gas:0.82549 Tobacco: 0.50197Own-priceelasticity: Gas: 0.00238 Tobacco: -0.
5165 Thus, wecan infer that the demand for both the commodities has a strong positiverelationship with income changes while it is interesting to note that theeconomic theory of reduction in demand with increasein price is fact and is thus the elasticity is reflected for gas. However, astobacco is a substance with hardly any substitutes its highly inelastic andthus 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 moreelastic than tobacco. Thus,taking a 5% level of significance, we form a confidence interval for theseelasticities. Thus, computing the intervals with a value of 1.96 criticalvalue. Income elasticity: 0.
597209 ? Gas ? 1.05377 0.408690 ?Tobacco ? 0.595246 Own-priceelasticity: -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.
In this, we try to find out if our commodities areperfectly inelastic in terms of their own price elasticity or not. From our computations, we check the t-ratio. This is aone-tailed test with 5% significant level, from t-tables we get a criticalvalue of -1.68.Hence, wefail to reject our null hypothesis for tobacco as the absolute value of thet-ratio is greater than the critical value:|19.345| ? | 1.68 |and thus,confers to our initial assertions about tobacco being inelastic. However, wereject the null hypothesis for gas as0.
029 | ? -1.68 Testthe homogeneity restriction In the nextexercise we test the homogeneity restrictions for the existence of money illusionfor the demands of the specific commodities, i.e., we check H0: againstthe alternative that H1: Thus, onobservation of the both the Wald test and the variable replacement significancetest (relative price is now regressed instead of price) on the quantity of eachcommodity and we find that for both the commodities the t-ratio:Gas: -3.273and Tobacco: -6.077, is rejected for the critical value of 1.678.
Hence, wereject the null hypothesis implying that there exists no money illusion and thetests are insignificant. Note, both the tests provide the same result as in theWald test we check the same equation’s complimentary transposed version .As even in Wald test the p-value is less than 0.5 for both the commodities thuswe reject the null hypothesis in the latter as well.
FORECAST OF DEMAND FOR 2003In the next section we create a model forecasting of demand usingthe actual price and income data for that year – in other words, we fit themodel to 1959-2002 and check the Chow test to test that the sample has beendrawn from the same distribution as the residuals. Figure forecast for Gas 2003: Figureforecast for Tobacco 2003: The actualforecast error computed by TSM for the commodities are:Gas:-0.14019 and Tobacco: 0.017695UsingP-value approach we see that the Chow forecast test rejects the null hypothesisfor Gas which in this case is that the sample isdrawn from the same population as the residuals. As 0.023 is less than 0.05SIGNIFICANCE OFPOPULATION ON THE DEMAND OF COMMODITIES Now weanalyze how does the addition of another variable to the demand equation affectthe demand.
The regression is carried out with the underlying assumption of thenull hypothesis being that the population doesn’t affect the demand. However, forboth our commodities we observe that the p-values and also the t-ratios withbounds of |1.96|. It isobserved that for Gas the t-ratio is obtained as -3.
045 which lies beyond theacceptance region. Also, the p-value is 0.04 < 0.
05, thus we reject the nullhypothesis and can comment that the population has a significance in terms ofaffecting the demand for Gas. Similarly,it is observed that for Tobacco that the t-ratio obtained as -0.198 which lies within the acceptanceregion. Also, the p-value is 0.844 > 0.05, thus we do not reject the nullhypothesis and can comment that the population is insignificance in terms ofaffecting the demand for Tobacco.
Thus, inline with economic theory, we see that there exists an inverserelationship between elasticity and impact of population on the demand.Greater elasticity reduces the impact of the populationdue to the availability of alternatesubstitutes. Now, wehave also run another test for coefficients of the population to be equal to that of 1- . The underlying theory being that whetherthis is the best form of expression of the variables or not.
For Tobacco we seethe p value is greater than 0.05, hence we see that the per capita form issignificant in this case. Theoretically it confers with economics of data as itis easier to measure for tobacco as only a portion of the population has aspecific demand for Tobacco.
However, the converse is true for Gas. As we havealready seen Gas acts as a necessary good and thus almost is demanded by the wholepopulation of an economy. Hence, as per our earlier results population affectsthe demand for gas and hence per capita form can be asserted to beinsignificant and to be not represented by this form for expenditure andincome. CHECKING FORSTABILITY OF PARAMETERS:The Chow test isused to determine whether the independent variables have a structural break andhave different impacts on two subgroups of the population. Thus, we check thestability of values over the whole period between 1981 to 2003 by dividing itinto two halves of 22 and 23 samples. From TSM output ofGas.
, we observe the stability test equals 32.0769 which is greater than thecritical value of F-test (4 and 37 degrees of freedom): 2.62605 and the p-valueof 0 is less than 0.05 at 5% significancelevel. 32.0769 > 2.626050 < 0.05 Similarly, from TSM output of Tobacco, we observe thestability test equals 15.
1298 which is greater than the critical value ofF-test (4 and 37 degrees of freedom): 2.62605 and the p-value of 0 is less than 0.05 at 5% significance level. 15.1298 > 2.626050 < 0.05 This implies bothGas and Tobacco is unstable over the 10-year period of the sample. Note: Here our Ho is that our model is stable whereas H1 isthat our model is unstable.
Thus, we rejected Ho for Gasand Tobacco. TREND EFFECT Testing foran adjusted model that changes systematically with time. Thus, weobserve that for both Gas and Tobacco the inclusion of the trend values givesus non-sensical parameter outputs as for example the effect of price and incomeis seen to be insignificant for tobacco (p-value < 0.05) and similarly forGas as well. This might be due to the well-known factor of time series data tobe suffering from multicollinearity. There may not beenough independent variation in the variables to measure the elasticities effectively,once the linear trend is taken into account.
Thus, the income and price effect arenot reflected in the demand equation when taken into account. Conclusion Regression analysis estimates the effect ofeach independent variable by seeing how much effect the independent variableshas on the dependent variable when other independent variables are held constant.We recognise that not all of the econometric test statistics are adequatelyconclusive and entirely satisfactory. Alternative specifications or refinementsmay further improve on the present results. This may partly be due tomulticollinearity between most price variables. But still, we obtain a significant empirical evidence of economic dataof demand theory using real economy values, which give still a better proofthan most other models.