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 coe?cients). Test the null hypothesis of no seasonality.
2. Explain CLT and LLN in details.
3. 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?
4. 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?
5. 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.
6. The Stata file airlinecosts.dta contains data on indexes of variable costs (variablecost), output (seatmiles) and prices of labor (pricelabor), materials (pricematerials) and fuel (pricefuel) for 23 airlines (name) for a maximum period of 13 years (years) from 1971-1986. The dataset contains 268 observations. If the production function is Cobb-Douglas, one can show that the variable cost function is of the form Where c denotes variable cost, y denotes output and Pj denotes the price of input j.
a) Estimate the Cobb-Douglas cost function. Interpret your coe?cients (discuss the sign, significance and magnitude of each slope coefficient).
b) Write down the null hypothesis corresponding to the statement that input prices have no e?ect on costs. Test this hypothesis using an appropriate restricted regression.
c) Write down the null hypothesis corresponding to the statement that the e?ect of labor prices is equal to the e?ect of fuel prices. Test this hypothesis using an appropriate restricted regression.
d) The returns to scale of the associated production function is 1/βy. Estimate the Cobb-Douglas cost function. Test the appropriate hypothesis to determine whether this production function displays increasing, decreasing or constant returns to scale. Note that increasing, decreasing and constant returns to scale are associated with 1/βy > 1, 1/βy < 1 and 1/βy = 1 respectively.
e) Often we assume that the cost function is a quadratic function, Can you reject the hypothesis that the cost function is linear? What is the shape of the estimated quadratic function?
Attachment:- airlinecosts.rar