EEP 118 / IAS 118 Elisabeth Sadoulet ad Daley Kutzma Uiversity of Califoria at Berkeley Fall 013 Itroductory Applied Ecoometrics Midterm examiatio Scores add up to 50 (5 poits for each sub-questio) Your ame: SID: 1. (5 poits) Usig data o birth weights, we estimated the followig two models: bwght = 119.8 0.5cigs R =0.03 =1388 (0.6) (0.09) bwght = 116.9 0.46cigs + 0.09 famic (1.0) (0.09) (0.03) R =0.03 =1388 where bwght is birth weight (i ouces), cigs is the umber of cigarettes smoked daily durig pregacy ad famic is 1988 family icome, i $1000. How does the itroductio of the variable famic affect the estimated parameter o cigs? What ca you ifer about the correlatio betwee famic ad cigs? Justify your respose.
. (5 poits) Below are summary statistics for the GPAs of a sample of 101 studets from Michiga State Uiversity. The dea of MSU, Lou Aa Simo, firmly believes that the true average GPA of her uiversity is 3.1 ad your sample below is a iaccurate represetatio. Should you be skeptical of Lou Aa s claim? Support your opiio with a hypothesis test at the 5% sigificace level. Variable Obs Mea Std. Dev. Mi Max -------------+-------------------------------------------------------- colgpa 101.984.373103. 4 3. (10 poits) Usig a small sample of households from Nicaragua, we estimate the relatioship betwee the log of eergy expediture (leergyexp) ad the log of household total expediture per capita (ltotexppc), household size (hhsize), ad whether the household ows a stove (stove).. regress leergyexp ltotexppc lhhsize stove Source SS df MS Number of obs = 174 -------------+------------------------------ F( 3, 170) = 30.10 Model 8.586459 3 7.588176 Prob > F = 0.0000 Residual 155.493187 170.914665804 R-squared = -------------+------------------------------ Adj R-squared = 0.3354 Total 38.07964 173 1.3761889 Root MSE =.95638 leergyexp Coef. Std. Err. t P> t [95% Cof. Iterval] ltotexppc.7763713.101408 7.66 0.000.5761897.976558 lhhsize.490481.1654038.97 0.003.163973.81699 stove.358545.40303 _cos -.7896446 1.09109-0.7 0.470 -.943354 1.364064 a. What is the p-value for the test that havig a stove has o effect o the cosumptio of eergy? Iterpret your results. b. Calculate ad iterpret the R-squared for this estimatio.
4. (15 poits) You have = 40 quarterly observatios o the imports M of a coutry, a idex of import prices P M, ad real aggregate icome GDP. Addig dummy variables Q,Q3, ad Q4 for the d, 3 rd, ad 4 th quarters of the year, you estimate the model: log M = β 0 + β 1 log P M + β loggdp + β 3 Q + β 4 Q3+ β 5 Q4 + u ad fid the followig results: log M = 4.30 0.58log PM +1.45logGDP +.15Q +.10Q3+.40Q4 (0.13) (0.1) (.10) (.05) (.1) (a) Costruct a 95% cofidece iterval for β 1. Iterpret. R = 0.53, = 40 (b) Test the hypothesis β = 1 agaist β 1 at the 5% sigificace level. Iterpret this result i ecoomic terms. (c) Why is a first quarter Q1 dummy variable ot icluded i the model? Iterpret the estimated parameters o Q,Q3, ad Q4.
5. (15 poits) Usig data for the US gasolie market betwee 1960 ad 1999, we estimated the followig model:. regress lg lic lpriceg lprewcar lprusedcar Source SS df MS Number of obs = 40 -------------+------------------------------ F( 4, 35) = 440.79 Model.14671037 4.3066791 Prob > F = 0.0000 Residual.019480675 35.000695738 R-squared = 0.9910 -------------+------------------------------ Adj R-squared = 0.9888 Total.16619104 39.061891173 Root MSE =.0638 lg Coef. Std. Err. t P> t [95% Cof. Iterval] lic 1.69181.154954 7.85 0.000 1.50759.133604 lpriceg -.35466.0595617-3.90 0.001 -.354553 -.1105399 lprewcar -.33414.1795357-1.30 0.04 -.6011761.134348 lprusedcar -.059739.0693655-0.86 0.396 -.01816.083558 _cos -3.957868.581538-1.53 0.136-9.4591 1.330174 where: lg=log(total US gasolie cosumptio per capita), lic = log(icome per capita), lpriceg = log(gasolie price), lprewcar = log(price of ew cars), ad lprusedcar = log(price of old cars) a. Suppose the govermet imposes a tax o gasolie that iduces a price icrease of 15%. What would be the effect o gasolie cosumptio? b. Is the cosumptio of gasolie iflueced by the price of ew cars ad the price of used cars, whe you cosider them oe at a time? Justify your respose. c. We ow estimate the model without the prices of ew ad used cars (See table o the last page). Comparig the two estimated models, would you say that the cosumptio of gasolie is iflueced by the prices of cars, ew or used, cosidered together? (Do a joit test of sigificace o the two parameters).
Statistics Formulae Covariace betwee two variables i a populatio: cov x, y cov( a 1 x + b 1, a y + b ) = a 1 a cov( x, y) ( ) = a var x + b var y + abcov(x, y) var ax + by Variace for the differece i meas of two idepedet samples: var ( x 1 x ) = var ( x 1 ) + var ( x ) ( ) = 1 ( x i x )( y i y ) Whe y is a biary variable with probability prob(y = 1) = p, its variace is p (1 p) OLS estimator ˆβ 1 = cov ( x, y ) var x with var ( ˆβ1 ) = σ SST x For multiple regressio: var ( ˆβ j ) = ( ) σ ( ) SST j 1 R j SST = y i y, SSE = ŷ i y, ad SSR = û i Test statistics: ( ) F statistic for q restrictios i a regressio doe with observatios ad k exogeous variables: R ( UR R R ) q ~ F q, k 1 ( 1 R UR ) ( k 1) ( ) i Table for questio 5c. regress lg lic lpriceg Source SS df MS Number of obs = 40 -------------+------------------------------ F(, 37) = 69.99 Model.13986669.534966673 Prob > F = 0.0000 Residual.0634354 37.000849173 R-squared = 0.9878 -------------+------------------------------ Adj R-squared = 0.9863 Total.16619104 39.061891173 Root MSE =.0914 lg Coef. Std. Err. t P> t [95% Cof. Iterval] lic.13019.148784 14.3 0.000 1.86743.433637 lpriceg -.158558.0535811 -.85 0.008 -.6135 -.0435763 _cos -5.605895.165544 -.59 0.015-10.055-1.1894