Statistics for Decision Making

The following demand for housing function was estimated using ordinary least squares techniques with data on 250 households

Q A (Y (P u

where A is the regression constant , Q is quantity demanded ,

is price Y is personal income and u is the error term . The results of double log estimation were

In Q 19 .21 0 .98 In Y - 1 .13 In

, R2 0 .83

What are the price and income elasticities estimated

On the basis of the estimated regression equation (ln Q ) shown above the estimated price

elasticity is 1 .13 and the estimated income elasticity is 0 .98 . These are notably the regression coefficients of the predictor variables income and price in the estimated regression equation

Are these values significantly different from zero ? How do you know

Income . With the number of households equal to 250 , one can assume that this sample size is sufficiently large and therefore the critical value to which the computed test statistic value will be compared will be approximated by a Z critical value instead of the a t critical value If we use a level of significance equal to 5 , the critical value is 1 .96

To determine if the estimated income elasticity is significantly different from zero , compare the computed test statistic value with the Z critical value . If the former is higher than the latter , then one can safely conclude that the estimate is significantly different from zero Hence , with income elasticity , it can be concluded that the estimate is significantly different from zero since 8 .91 is higher than 1 .96

Price . Since 2 .17 is higher than 1 .96 , the data provides sufficient evidence to conclude that the estimated price elasticity is significantly different from zero . This conclusion stands for a level of significance equal to 5

Note that for both t tests to determine if price and income elasticity are significantly different from zero , if for instance the level of significance set by a researcher or an economist is 10 instead of 5 the critical value becomes 1 .645 , not 1 .96 . Therefore , in this case once can still safely say that both estimates are significantly different from zero

It is often important for policy purposes to know if demand is inelastic , unitary elastic , or elastic , i .e , is the elasticity greater than , equal to , or less than one

Based from the sample regression equation , the income elasticity of demand is 0 .98 which is less than one . This implies that demand is inelastic . A 1 percent income increase will result to a 0 .98 increase in quantity demanded

The price elasticity of demand , on the other hand is equal to -1 .13 which means that price is also inelastic . A one percent increase in price will result to a 1 .13 percent decrease in quantity demanded

For the above equation , test this question for the price elasticity and tell the level of significance of the result using Normal Distribution

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