Final Exam ECO321 Summer 2016

  1. The following estimated equation was obtained by OLS regression using quarterly data for 1958 to 1976 inclusive:

Yt = 2.20 + 0.104X1t − 3.48X2t + 0.34X3t.

(3.4) (0.005) (2.2) (0.15)

Standard errors are in parentheses. The explained sum of squares is 80 and the residual sum of squares 40.

a. Test the hypothesis that the coefficient on X2t equals −4.

b. when three seasonal dummy variables are added and the equation re-estimated, the explained sum of squares rose to 90. Define the seasonal dummy variables and write down the regression equation (using β’s for coefficients). Test the null hypothesis of no seasonality.

  1. ExplainCLT and LLN in details.
  1. What is the different between interpretation of coefficient in SLRM and MLRM? How does it relate to omitted variable bias? How about a linear versus nonlinear multiple regression model coefficients? (Quadratic). What is the role of controls?
  1. How do you choose between log-linear model and log-log model? How about linear log-linear? And how about linear-log and log-log? Why? How do you interpret coefficients of a A) log-linear B) log-log and C) linear-log model?
  1. The following equation represents a regression model for the number of children in a family:

Children = β0 + β1motherseduc + β2fatherseduc + β3familyincome + u,

Where children is the number of children, motherseduc and fatherseduc are the years of education of the mother and father respectively and familyincome is the income of the family. We expect β1 < 0, β2 < 0 and β3 < 0.

a. What is the effect of omitting family income from the regression model on β1 andβ2 if each parent’s education is positively correlated with family income?

b. Write the null hypothesis, restricted regression, test statistic and degrees of freedom for a test of the hypothesis that the effect of mother’s education equals the effect of father’s education.

  1. TheStata fileairlinecosts.dta containsdataon indexes ofvariablecosts (variablecost),output(seatmiles)and pricesoflabor (pricelabor),materials(pricematerials)and fuel(pricefuel)for23airlines (name)foramaximumperiod of 13years(years)from1971-1986. Thedatasetcontains268 observations. Iftheproduction function isCobb-Douglas, onecan showthatthevariablecostfunction is of theform

Wherecdenotesvariablecost,ydenotesoutputandPjdenotesthe priceof inputj.

a)EstimatetheCobb-Douglascostfunction. Interpretyourcoefficients(discuss thesign,significance and magnitudeofeach slopecoefficient).

b)Writedownthenull hypothesis corresponding tothestatementthatinputpriceshaveno effect on costs.Testthishypothesisusing an appropriaterestricted regression.

c)Write down the null hypothesis corresponding to thestatementthattheeffectof labor pricesisequal to theeffectof fuelprices.Testthishypothesisusing an appropriaterestricted regression.

d)Thereturnstoscaleof theassociatedproduction function is1/βy.EstimatetheCobb-Douglas cost function. Testtheappropriatehypothesistodeterminewhether thisproduction function displays increasing,decreasing or constantreturnstoscale. Notethatincreasing,decreasing and constant returnstoscaleareassociated with 1/βy1, 1/βy1and 1/βy=1respectively.

e)Often weassumethatthecostfunction isa quadraticfunction,

Can yourejectthehypothesisthatthecostfunction islinear?Whatistheshape of theestimatedquadraticfunction?