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# APPLIED ECONOMETRICS ECON 446

Rice University

GPA 3.53

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This 3 page Class Notes was uploaded by Destany Daniel on Monday October 19, 2015. The Class Notes belongs to ECON 446 at Rice University taught by Robin Sickles in Fall. Since its upload, it has received 71 views. For similar materials see /class/225021/econ-446-rice-university in Economcs at Rice University.

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Date Created: 10/19/15

Econ 446 Spring 2000 MIDTERM REVIEW answer key for 2007 MT R Sickles Answer all of the following questions The questions are weighted equally You have 50 minutes You may use a calculator and an 8 12 X 11 sheet of paper with notes etc on both sides 1 Labor economists study the determination of labor earnings using a statistical earnings function A simple example of such a regression estimated using data for 31093 men is logYi 758 0070 X 6 000160 Here Y denotes earnings and X is years of education log denotes a natural logarithm The value in parentheses is the estimated standard error a Using your knowledge of logarithmic functional forms explain the interpretation of the coefficient on education ANSWER The dlogYiin 1Yi in dXi 07 So if years of education increase by 1 then earnings will increase by about 7 It is essentially the rate of return for education b What does this equation predict would be the ea1nings of a hypothetical person with no education ANSWER Iin0 then Yiexp7581959 c Obtain a 90 confidence interval for the rate of return to education bziseb2tc1 1u2 gt007l00160tc31091r05 gt CI0670726 2 Answer true or false and state why a The power of a test increases as the sample size increases ANSWER TRUE The power ofthe test is given by l where Paccept HoH1 is true b The size ofatest increases as the sample size increases ANSWER FALSE The size of the test is constant it is chosen by the experimenter c The independent variables in a bivariate regression model needs to be constant to estimate the slope coefficient ANSWER FALSE Regressors should change across observations d In large samples the usual standardized ratios follow the tdistribution ANSWER FALSE They followthe standardized normal distribution e If we rescale the dependent variable in a regression by dividing by 100 the new coefficients and their estimates will be multiplied by 100 ANSWER FALSE They are divided by 100 see page 95 in HGL f R2 always decreases as we add variables to a regression ANSWSER FALSE They either increase or leave the R2 the same 3 Consider the bivariate regression model y A zxzyl 1 for il n Explain the key assumptions needed in order to establish the desirable properties of best linear unbiasedness of the ordinary least squares estimates of A and z ANSWER Assumptions SRlSRS of the linear regression model see page 16 ofHGL 4 In the macroeconomics literature there are two competing theories concerning consumption behavior According to Keynes aggregate consumption is determined by aggregate income Alternatively the classical economists feel that consumption should be inversely related to interest rates The results below are based on observations on US consumption expenditures in billions of 1982 dollars disposable personal income in billions of 1982 dollars and the real interest rate for the years 195586 Based on the econometric evidence below what are your conclusions relative to the validity of the two hypotheses Keynes Theory An economic model that relates consumption to income using a linear relationship is Q Bl 82M The corresponding statistical model is C2 B1BzM2ez where we will assume the e are independent random variables with e N 06 Classical Economist39s Theory In this case we specify the linear economic model relating consumption to interest rate as Q 001 octh The corresponding statistical model is C a1 0sz v with the v assumed to be v N 063 and independent The two least squares estimated equations with standard errors in parentheses are C 737744 09085 M C 13707 59859 R 13527 00076 1154 29488 Note that the standard error of b in the first equation is very small so doing the hypothesis testing whether b20 will be rejected at any level of signi cance of 11 Also the pvalue is almost zero which makes us reject the null hypothesis On the other hand in the second equation the tratio is 203 and we can find a to reject the alternative hypothesis especially in small samples In summary the aggregate consumption is likely to be determined by the aggregate income and Keynes theory seems to be valid in many cases

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