Engel's Law: Calculating Regression Parameters and Interpreting Statistical Measures, Assignments of Statistics

Download Engel's Law: Calculating Regression Parameters and Interpreting Statistical Measures and more Assignments Statistics in PDF only on Docsity! Economics 105 Davidson College Aug - Dec 2008 Mark C. Foley Graded Homework #201 There are very few empirical laws in economics. One such law that seems to hold most of the time is Engel’s law. Engel’s law simply states that the share of household income devoted to food should decline as income rises. Consider the following sample of 10 households. i Food Share (fsi) Log income (ln Ii) 1 0.54 9.2 2 0.67 8.9 3 0.36 9.4 4 0.55 9.2 5 0.61 8.8 6 0.39 9.4 7 0.47 9.2 8 0.29 9.5 9 0.62 9.0 10 0.52 9.1 If PF is the price of a unit of food, and QFi is the number of units of food purchased by household i, then food share of household i is given by fsi = (PFQFi)/Ii, where Ii is income of household i. A simple specification of the “Engel curve” is give by iii Ifs εβα ++= )(lnln , where ),0(...~ 2σε Ndiii . (a) Compute the ordinary least squares estimate of the parameters α and β “by hand,” that is, use Excel like you would a calculator. Check your results using Excel’s built-in regression function (Tools-Data Analysis-Regression). (b) Calculate, “by hand,” and interpret the R2 for this regression. (c) Calculate, “by hand,” and interpret the standard error of the model. 1 Example is taken from problem 10.2 of Ashenfelter, Levine, and Zimmerman (2003), Statistics and Econometrics: Methods and Applications.