University of Hong KongIntroductory Econometrics (ECON0701), Spring 2014

Assignment #1: Due February 14, 2014

1. Let 1 2 be independent random variables that all have the same probability distrib-ution, with mean and variance 2. Let = 1

P=1 .

(a) Show that [] = .(b) Show that 1+22 = 22 .(c) Show that () = 2 .

2. (2.2) The following table contains the ACT scores (the ACT test is a pre-matriculationexamination that some American college students take instead of the SAT) and the GPA(grade point average) for 8 college students. Grade point average is based on a four pointscale and has been rounded to one digit after the decimal.

Student GPA ACT1 2.8 212 3.4 243 3.0 264 3.5 275 3.6 296 3.0 257 2.7 258 3.7 30

(a) Estimate the relationship between GPA and ACT using OLS; that is, obtain the interceptand slope estimates in the equation

[ =c0 +c1Comment on the direction of the relationship. Does the intercept have a useful inter-pretation here? Explain. How much higher is the GPA predicted to be if the ACTscore is increased by 5 points?

(b) Compute the fitted values and residuals for each observation, and verify that the residuals(approximately) sum to zero.

(c) What is the predicted value of GPA when ACT = 20?

(d) How much of the variation in GPA for these 8 students is explained by ACT? Explain.

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3. (2.9) In the linear consumption function

d =c0 +c1the (estimated) marginal propensity to consume (MPC) out of income is simple the slope,c1, while the average propensity to consume (APC) is d = c0 +c1. Using observationsfor 100 families on annual income and consumption (both measured in dollars), the followingequation is obtained: d = 12484 + 0853

= 100 2 = 0692(a) Interpret the intercept in this equation, and comment on its sign and magnitude.

(b) What is the predicted consumption when family income is $30,000?

(c) With on the x-axis, draw a graph of the estimated MPC and APC.4. (2.11) The data set bwght.dta contains data on births to women in the United States. Twovariables of interest are the dependent variable, infant birth weight in ounces (bwght), andan explanatory variable, average number of cigarettes the mother smoked per day duringpregnancy (cigs). The following simple regression was estimated using data on = 1388births:

= 11977 0514 (a) What is the predicted birth weight when = 0? What about when = 20 (one

pack per day)? Comment on the dierence.(b) Does this simple regression necessarily capture a causal relationship between the childs

birth weight and the mothers smoking habits? Explain.

(c) To predict a birth weight of 125 ounces, what would cigs have to be? Comment.

5. (Computer problem) (C2.4) Use the data in the file WAGE2.DTA to estimate a simpleregression explaining monthly salary (wage) in terms of IQ score (IQ).

(a) Find the average salary and average IQ in the sample. What is the standard deviationof IQ? (IQ scores are standardized so that the average in the population is 100 with astandard deviation equal to 15.)

(b) Estimate a simple regression model where a one-point increase in IQ changes wage bya constant dollar amount. Use this model to find the predicted increase in wage for anincrease in IQ of 15 points. Does IQ explain most of the variation in wage?

(c) Now, estimate a model where each one-point increase in IQ has the same percentageeect on wage. If IQ increases by 15 points, what is the approximate percentage increasein predicted wage?

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