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# Final Exam ECO321 Summer 2016 1. The following estimated equation was obtained by OLS regression using quarterly data for 1958 to 1976 inclusive: Yt...

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Final Exam ECO321 Summer 2016 1. The following estma±ed equaton was ob±ained by OLS regression using quar±erly da±a for 1958 ±o 1976 inclusive: Y± = 2.20 + 0.104X1± − 3.48X2± + 0.34X3±. (3.4) (0.005) (2.2) (0.15) S±andard errors are in paren±heses. The explained sum of squares is 80 and ±he residual sum of squares 40. a. Tes± ±he hypo±hesis ±ha± ±he coeﬃcien± on X2± equals −4. b. when ±hree seasonal dummy variables are added and ±he equaton re-estma±ed, ±he explained sum of squares rose ±o 90. De²ne ±he seasonal dummy variables and wri±e down ±he regression equaton (using β’s for coeﬃcien±s). Tes± ±he null hypo±hesis of no seasonali±y. 2. Explain CLT and LLN in de±ails. 3. Wha± is ±he di³eren± be±ween in±erpre±aton of coeﬃcien± in SLRM and MLRM? How does i± rela±e ±o omi´ed variable bias? How abou± a linear versus nonlinear multple regression model coeﬃcien±s? (Quadratc). Wha± is ±he role of con±rols? 4. How do you choose be±ween log-linear model and log-log model? How abou± linear log-linear? And how abou± linear-log and log-log? Why? How do you in±erpre± coeﬃcien±s of a A) log-linear B) log-log and C) linear-log model? 5. The following equaton represen±s a regression model for ±he number of children in a family: Children = β0 + β1mo±herseduc + β2fa±herseduc + β3familyincome + u, Where children is ±he number of children, mo±herseduc and fa±herseduc are ±he years of educaton of ±he mo±her and fa±her respectvely and familyincome is ±he income of ±he family. We expec± β1 < 0, β2 < 0 and β3 < 0. a. Wha± is ±he e³ec± of omiµng family income from ±he regression model on β1 andβ2 if each paren±’s educaton is positvely correla±ed wi±h family income? b. Wri±e ±he null hypo±hesis, res±ric±ed regression, ±es± s±atstc and degrees of freedom for a ±es± of ±he hypo±hesis ±ha± ±he e³ec± of mo±her’s educaton equals ±he e³ec± of fa±her’s educaton. 6. The S±a±a ²le airlinecos±s.d±a con±ains da±a on indexes of variable cos±s (variablecos±), ou±pu± (sea±miles) and prices of labor (pricelabor), ma±erials (pricema±erials) and fuel (pricefuel) for 23 airlines (name) for a maximum period of 13 years (years) from 1971-1986. The da±ase± con±ains 268 observa±ions. If ±he producton func±ion is Cobb-Douglas, one can show ±ha± ±he variable cos± func±ion is of ±he form log c = α + β y log y + β L log P L + β M log P M + B F log P F Where c deno±es variable cos±, y deno±es ou±pu± and Pj deno±es ±he price of inpu± j. a) Es±ima±e ±he Cobb-Douglas cos± func±ion. In±erpre± your coeﬃcien±s (discuss ±he sign, signi²cance and magni±ude of each slope coeﬃcien±). b) Wri±e down ±he null hypo±hesis corresponding ±o ±he s±a±emen± ±ha± inpu± prices have no e³ec± on cos±s. Tes± ±his hypo±hesis using an appropria±e res±ric±ed regression.
Final Exam ECO321 Summer 2016 c) Write down the null hypothesis corresponding to the statement that the efect o± labor prices is equal to the efect o± ±uel prices. Test this hypothesis using an appropriate restricted regression. d) The returns to scale o± the associated production ±unc²on is 1/βy. Estimate the Cobb- Douglas cost ±unc²on. Test the appropriate hypothesis to determine whether this production ±unc²on 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 respec²vely. e) O±ten we assume that the cost ±unction is a quadratic ±unc²on, log c = α + β y log y + β yy ( logy ) 2 + β L log P L + β M log P M + B F log P F Can you reject the hypothesis that the cost ±unction is linear? What is the shape o± the estimated quadra²c ±unc²on?

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The CLT refines the LLN
The LLN gives conditions under which test minutes join to populace minutes as test size increments
The CLT gives data about the rate at which test minutes...

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