The paper "Estimation of Import Demand Functions" is a worthy example of an assignment on macro and microeconomics. This paper is a report covering on the estimation of the import demand function. In order to achieve this objective, textile importation for Qatar and the USA will be used. The equation that will be estimated follows the form: Imports of textile = f (price, income) consequently resulting in two demand equations. Conclusions will be drawn based on the two equations. It is further pertinent to assess the statistical qualities of each model using F-test, t-test, and R-square.
Given the result of the analysis, various published articles on textiles in the US and Qatar will be drawn into the discussion to facilitate comparison and contrast. Textile for Qatar and the USA Imports of textile = f (price, income) After converting data into the log-linear form and by conducting multiple regressions in excel, the estimated demand equation for the two countries follows the form: Qatar: USA: Given the log-linear form, the procedure for obtaining price elasticity of demand is by looking at the absolute values of constants.
However, the negative sign in income elasticity is not eliminated. In this case, income elasticity and the price elasticity of demand for the respective countries are summarized in the table below: Qatar USA Income elasticity of demand 1.401897 2.4419 Price elasticity of demand 1.3349 0.0956 It is apparent from the table above that the price elasticity of demand for textile importation in Qatar is elastic given that 1.3349 is more than 1. At the same time, the price elasticity of demand for textile importation in the US is inelastic since 0.0956 is less than 1. Considering the income elasticity of demand, USA imports are more sensitive to changes in income compared with Qatar.
The income elasticity of demand in both countries is more than 1 thus can be concluded that textile importation is a luxury good. Application of estimated elasticity First, income elasticity helps a business to predict the future demand for a product through estimation if the rate of change in income and the income elasticity of demand is known (Mankiw, 2012). When a business anticipates a change in personal income, it can be able to forecast demand. Secondly, knowledge of income elasticity assists an individual to identify clearly normal from an inferior good.
While normal good has positive income elasticity for any level of income, an inferior good has negative income elasticity when income is increased past a particular level. A business will also be able to use price elasticity of demand to note when to increase prices to register large profits. Often, businesses decide to increase prices because of an increase in the cost of production. In other situations, a business would decide to manipulate prices even when the costs of production have not changed.
In either case, a decision to increase prices is determined by the price elasticity of demand and cross elasticity. The reason behind this assertion is that a rise in the price of a product causes the price of substitutes to become cheaper. Consumers would move in to buy such substitutes. Nonetheless, a rise in price is good for a firm when the demand for the good is inelastic. At the same time, the demand for substitute products should attain a cross-price elasticity of less than 1 (Dwivedi, 2011).
Knowledge of the elasticity helps a business to make wise decisions particularly in generating higher revenue. A business can further deploy knowledge of elasticity of demand to understand factors that affect a product particularly in terms of dependent and independent variables. It is further pertinent to note that elasticity serves the purpose of making estimates of the demand function. An example of a function that gives a relationship between the dependent and independent variables is the estimated demand function: Imports of textile = f (price, income).
A businessperson, therefore, knows that the importation of textiles varies with prices and income. Statistical Adequacy of Equations R-square In the case of the USA, R-square is 0.9864, which indicates that 98.64% of the variation in dependent variables is explained by the regression equation. This percentage is very high which means that the line gives a better fit to the data. Looking at Qatar, R-square is 0.2732. This implies that only 27.32% of the variation in the dependent variable is explained by the regression equation. The conclusion here is that the regression line does not give the best fit. F-test This test is conducted in order to understand the lack of fit.
The F-test is a test on equality of variances. The hypotheses are as follows: The output from excel for the USA are below: F-Test Two-Sample for Variances Variable 1 Variable 2 Mean 16.03579 -0.34344 Variance 0.076672 0.040146 Observations 32 32 df 31 31 F 1.909848 P(F< =f) one-tail 0.038225 F Critical one-tail 1.822132 Conclusion: F > F critical hence we reject the null hypothesis and conclude that variances of the two populations are not equal. The output from excel for Qatar are below: F-Test Two-Sample for Variances Ln (Income) Ln (Price) Mean 10.73226 -0.53771 Variance 0.469133 0.058066 Observations 32 32 df 31 31 F 8.079261 P(F< =f) one-tail 4.45E-08 F Critical one-tail 1.822132 Conclusion: F > F critical hence we reject the null hypothesis and conclude that variances of the two populations are not equal. t-Test A student’ s t-test is conducted to test whether there is a significant relationship between the independent variable and the dependent variable.
A situation that depicts a significant relationship will not result in a slope of zero. Hypotheses are stated as follows: Excel output for the USA: t-Test: Paired Two Sample for Means Ln (Income) Ln (Price) Mean 16.03579 -0.34344 Variance 0.076672 0.040146 Observations 32 32 Pearson Correlation 0.867306 Hypothesized Mean Difference 0 df 31 t Stat 645.8526 P(T< =t) one-tail 7.13E-66 t Critical one-tail 1.695519 P(T< =t) two-tail 1.43E-65 t Critical two-tail 2.039513 Conclusion: there is a significant difference between ln(income) and ln(price) given that t-statistic is > p-value for a one-tail test. Excel output for Qatar: t-Test: Paired Two Sample for Means Ln (Income) Ln (Price) Mean 10.73226 -0.53771 Variance 0.469133 0.058066 Observations 32 32 Pearson Correlation 0.763621 Hypothesized Mean Difference 0 df 31 t Stat 121.5425 P(T< =t) one-tail 2.13E-43 t Critical one-tail 1.695519 P(T< =t) two-tail 4.25E-43 t Critical two-tail 2.039513 Conclusion: there is a significant difference between income and price gave that t-statistic is > p-value for a one-tail test. Comparison with published work According to the Qatar Statistics Authority (2012), the consumer price index for textile increased from 94.9 in 2006 to 113.1 in 2011.
Notwithstanding the fact that prices were rising, the importation of textiles in Qatar also increased from 23498 million to 25359 million in 2011.
This indicates that price elasticity of demand is inelastic since demand is increasing even though the price is rising. This case presented by Qatar Statistics Authority is not reflected in the assessment conducted above which found out that textile importation is elastic to the price. The American Apparel and Footware Association (2011) investigated the movement of apparel importation in the United States. Their findings demonstrated that apparel importation between 2002 and 2011 increased from 56,962 million to about 77,659 million in 2011. This was the period when the price of textiles was also rising.
The conclusion that can be derived from this observation is that textile importation in the US is inelastic given that it keeps rising even though the price is rising. This case was as well alluded to by the United States International Trade Commission (2013) that found out that price changes did not affect the importation of textiles. Conclusion The estimated import demand function for the US and Qatar are: Qatar: USA: It is apparent from the equations above that price elasticity of demand for textile importation in Qatar is elastic. At the same time, the price elasticity of demand for textile importation in the US is inelastic.
Considering the income elasticity of demand, USA imports are more sensitive to changes in income compared with Qatar. The income elasticity of demand in both countries is more than 1 thus can be concluded that textile importation is a luxury good. The paper further assessed the statistical qualities of each model using the F-test, t-test, and R-square.
American Apparel and Footware Association. (2011). U.S. Apparel Imports - 2002 – 2011. Retrieved from https://www.wewear.org/assets/1/7/usimportsapparel1112.pdf.
Dwivedi, D. N. (2011). Microeconomics, 2/e. New Delhi: Pearson Education India.
Harmon, M. (2011). t-Tests in Excel - The Excel Statistical Master. Mark Harmon.
Mankiw, GN 2012, Principles of Microeconomics, South-Western Cengage Learning, Florence KY.
Qatar Statistics Authority. (2012, 25 April). Qatar Economic Statistics at a Glance. Retrieved from http://www.qsa.gov.qa/eng/publication/economic_publication/2012/Qatar%20Economic %20Statistics%20at%20Glance.pdf.
United States International Trade Commission. (2013). Textile and Apparel Imports from China: Statistical Reports. New York: USITC Publication.