A State-Wise Empirical Investigation of The Income-Demand Relationship - Research Paper Example

A State-wise Empirical Investigation of The Income-Demand Relationship Abstract This paper attempts to investigate how variations in average household income levels affect the general price level. Using state wise data on average income levels and cost of living index values, the paper identifies a positive dependence of the price index on average household incomes. We obtain evidence for the fact that US states with higher average household income also have the highest average prices. This in all probability reflects that high income households tend to bid up demands for typical merchandise and this leads to higher average price levels in states with higher average household incomes. I. Introduction This paper seeks to investigate how household income levels influence prices. In particular, we are interested in investigating whether increases in average household earnings lead to higher costs of living. We use state wise data to explore the question. Given the nature of the data, the specific query that we seek to answer is: Does more affluent states tend to have relatively higher costs of living? The secondary questions are regarding the nature of dependence, i.e., is there a linear dependence or is there in fact a non-linear relationship among our variables of interest? I. The economic model In this section we discuss the basic economic theory that we intend to validate and then develop the hypothesis to test using the data. Economic theory establishes that other things remaining the same, higher income leads to higher demand. That is, if there is an increase in the income of the consumer, ceteris paribus, at each price the consumer will demand more of the good, provided it is not an inferior good (Varian, 2006). Now, given the market supply curve is fixed, such a rise in demand always results in higher prices for the good (Sullivan and Sheffrin, 2003). This is elaborated in the diagram below: Figure 1: The effect of increase in income on equilibrium prices In the diagram above, E1 is the initial equilibrium price. Now if there is an increase in income of the consumer, the quantity demanded at each price increases. As a result, the demand curve shifts from D1 to D2. Given the supply, curve remains unchanged, this results in the new equilibrium point E2. Clearly, the new equilibrium price P2 is higher than the initial price P1. Therefore, we find that higher incomes tend to boost up equilibrium prices. Extending this logic implies that localities where more affluent individuals reside should witness higher relative prices. This is because people with higher incomes will bid up prices of general merchandise and, thus, the cost of living could potentially be higher for such places. It is precisely this claim that we intend to investigate in this paper. Therefore, we are claiming that cost of living is a function of average household income and that an increase in average household income leads to an increase in the average cost of living index, CLI, i.e., and that >0. II. The econometric model(s) However, although we can anticipate a positive relationship, i.e., higher prices tend to be associated with higher income states, and thus such states have higher costs of living, there is nothing to ensure that the dependence will be linear. Thus, we shall estimate both a linear (additive) and a non-linear model. The linear model is specified as follows: … (1) Here, CLI­i represents the average cost of living index for the ith state, Avg_Inci represents the average household income in the ith state, and is the random disturbance term. represents the part of the cost of living that is independent of average household income and is the coefficient that measures the extent of influence average income has on the cost of living. To test the possibility of a nonlinear dependence we shall also estimate the following multiplicative model: … (2) For convenience we shall utilize the following logarithmic transformation: … (3) Observe that in all three cases, our fundamental hypothesis is that higher average income states have higher cost of living index, i.e., the coefficient on the variable representing average household income is positive. Therefore, the hypothesis we intend to test for both specifications is essentially: > 0. III. Data and Methodology The data used in this empirical investigation is the US Census bureau data on average household incomes and cost of living across the 51 US states. We utilize a standard ordinary least squares regression methodology to estimate the models specified above. Since there is essentially only one parameter of interest, testing its individual significance and the joint significance of the model will yield similar results. Therefore, we shall use t-tests of significance to establish whether there is any impact of income level variations on the costs of living. The direction of the impact will be clear from the signs of the estimated coefficients. IV. The Empirical Results In this section, the empirical results will be presented. However, before progressing on to the actual regression results we start off by exploring the characteristics of the data. Table 1 presents the summary statistics of the variables included in our data set. Table 1: Descriptive Statistics Average Income Average Cost of Living Mean 50,738 105.19 Median 50,504 97.95 Std Dev. 7558.40 17.03156623 Sample Variance 57129390.57 288.7677403 Range 29,453 77.48 Min 36,850 90.35 Max 66,303 167.83 Sum 2,587,649 5364.89 Count 51 51 From Table 1 we find that there are 51 observations for each variable (since the data is state-wise and there are 51 US states). The mean and median average household incomes lie quite close although the median lies slightly to the left of the mean. This is true for the cost of living index values as well. The other point to notice from the table above is that there are substantial variations in both set of observations (see standard deviations and sample variances). Therefore, a regression framework which works best when there are such variations is aptly suited. Now, to gain an idea about the nature of association between the variables, we present the scatter plot of the data below: Figure 2: Scatter plot From figure 2 above, it does seem that there is an apparent positive relationship between the two variables. The correlation coefficient is calculated as being 0.61. Therefore, at the outset, we find that there is a positive association between these variables. That is, if one increases the other also is expected to increase. Although the correlation coefficient indicates the direction and degree of the association, one should be careful and note that correlation does not say anything about causality. Therefore, although we do find evidence of a strong association here, the relationship could be non-causal. It is precisely to investigate whether there is a causal dependence or not, that we need the regression methodology. The final step before looking at the estimation results is to look at the following diagram which seems to indicate a close relationship between the two variables: Figure 3: co-movements of data across states From the diagram above (Figure 3), we find that both series follow very similar patterns. The diagram, therefore, does indicate a strong possible association. This confirms the evidence obtained in the scatter plot. With such strong evidence of a potential dependence it is time to turn to the actual regression results. Table 1 presents the results of estimating the specification denoted by equations (1) (model 1) and (3) (model 2)1. Table 2: Results Variable Model 1 Model 2 Intercept 35.60** (2.73) 0.89* (1.70) Average Household Income 0.001*** (5.39) 0.62*** (5.57) Adjusted R-Squared 0.372 0.375 Notes: t-statistics in parenthesis, *** if significant at 1%, ** if significant at 5% and * if significant at 10% Recall that for each estimate the reported t-statistic is computed under the null hypothesis of assuming the coefficient to be zero. If the test finds the null hypothesis is rejected, then the coefficient is said to be significant, i.e., there is evidence to establish that the coefficient is statistically significantly different from zero. Whenever a variable has a significant coefficient, this implies that it has an effect on the dependent variable. From table above, we find that in both models the effect of average household income on the cost of living is positive and significant even at the 1% level. Though, the intercept is significant at 5% in the first model but significant only at the 10% level in the second model. However, for the first model, the estimate of the impact of average household income is very small, albeit positive. This implies that a rise in average household income leads to a very small rise in the cost of living. For the second model however, we get a much stronger coefficient. It should be noted that since the second model is a logarithmic specification, the coefficient actually measures the income elasticity of cost of living indices. This is found to be 0.62. The Adjusted R-squared is also higher for the second model. Thus it is safe to conclude that the non-linear specification fits the data better. Therefore, we finally conclude that the relationship is non-linear and a higher average household income leads to a higher cost of living. V. Conclusions This study explored the relationship between household income and cost of living. Both linear and non-linear relationships were explored. It was found that average household incomes do influence the cost of living. This is quite possibly due to the fact that higher incomes translate to higher demands which, in turn, boost up prices. VI. Works Cited Varian, Hal. Intermediate Microeconomics: A modern approach. W.W. Norton & Co. 2006. p. 754. Print. Sullivan, A. and Steven M. Sheffrin. Economics: Principles in action. Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. 2003. p. 80. print. VII. APPENDIX: Detailed estimation output Table 3: Estimation output for specification (1) Table 3.a Regression Statistics Multiple R 0.61008 R Square 0.372198 Adjusted R Square 0.359386 Standard Error 13.60106 Observations 51 Table 3.b ANOVA   df SS MS F Significance F Regression 1 5373.936 5373.936 29.05006 2.01E-06 Residual 49 9064.451 184.9888 Total 50 14438.39       Table 3.c: Estimated coefficients and tests of significance   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 35.60075 13.05169 2.727673 0.008828 9.372389 61.8291 Average Household Income 0.001372 0.000254 5.389811 2.01E-06 0.00086 0.001883 Table 4: Estimation results for equation (3) Table 4.a Regression Statistics Multiple R 0.622653 R Square 0.387697 Adjusted R Square 0.375201 Standard Error 0.050423 Observations 51 Table 4.b: ANOVA   df SS MS F Significance F Regression 1 0.078883 0.078883 31.02568 1.07E-06 Residual 49 0.124583 0.002543 Total 50 0.203467       Table 4.c: Estimated coefficients and tests of significance   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -0.89263 0.522435 -1.70859 0.093854 -1.9425 0.157244 Log(Average Household Income) 0.619004 0.11113 5.57007 1.07E-06 0.395679 0.842329 Read More