AGEC 317



AGEC 317

Test 1

Spring 2004

Do your own work. You can use a calculator and your 8½ x 11 inch cheat sheet. No other books, papers, notes, etc. can be used. Use the points as a guide for your time. Cheating on this examination will result in the recommendation of an “F” for the class.

A young boy was talking to his mother after bring home a bad report card.

The mother asks the boy, “What do you have to say about your bad grades?”

The boy answers, “At least you know I am not cheating.”

Short Answer - answer as concisely as possible - 5 points - use point totals for time allocation.

1. What criteria discussed in class must be met before the adjusted R2 from two or more equations can be compared?

2. You have estimated a relationship between x and y using OLS in which the t-ratio testing for significance of the parameter associated with x is rejected. Can you conclude that x causes y? Why or why not?

3. In class at least eight reasons were given as reasons for using OLS. Give five of these reasons.

4. When running a regression in Excel, why would you check the “labels” box?

5. Graphically show and explain in words, what is meant by a consistent estimator?

6. In economics “total utility refers to the total satisfaction from consuming some commodity.” According to Paul Samuelson, “As you consume more of the same good, the total (psychological) utility increases. However, . . . with successive new units of the good, your total utility will grow at a slower and slower rate because of a fundamental tendency for your psychological ability to appreciate more of the good to become less keen.”

a) Sketch the total utility function (y-axis) as a function of the number of units of good x consumed (x-axis).

b) In terms of the first and second derivative, what is Samuelson telling us?

7. Why is evoking the central limit theorem less restrictive than as assuming the error term is normally distributed?

Longer Answers - use point totals for time allocation

10 points

8. You have estimated the following equation using OLS, [pic]where 1 and 2 are estimated parameters. Graphically show the notion of a residual. Hint, graph the estimated equation and the residuals associated with the two observations {y = 1, x = 1; y = 7, x = 2}. Label your axis.

9. Write the following system of equations in matrix algebra form. Be sure to define each matrix you use. For each matrix, provide the dimensions of the matrix. Hint; be sure your matrices are conformable for matrix multiplication.

[pic]

15 Points

10. What assumptions are necessary for the OLS estimator to be BUE? Explain what BUE means. What is the importance of BUE?

11. To answer the following questions, use the attached Excel printout. Observations are country level data for the year 2000. The dependent variable is the mortality rate for children under-5 (per 1,000 live births). Independent variables are

Per capita gross income,

Illiteracy rate, adult female (% of females ages 15 and above),

Immunization, measles (% of children under 12 months), and

Aid per capita (current US $).

a) What is the economic interpretation of the parameter associated with immunization independent variable in this model? Does it make intuitive sense?

b) What are the null and alternative hypotheses associated with the t-statistic associated with per capital gross income? Do you reject or fail to reject the null hypothesis at the 0.10% level of significance? Why?

c) Interpret the F-test. Be sure to state the null and alternative hypotheses and if you reject or fail to reject the null hypothesis. What are the degrees of freedom for this test for this regression?

20 Points Use back if necessary.

12. Model to be estimated is [pic]. You have the following two observations on y and x, [pic]

a) Using calculus, calculate the OLS estimates for [pic] and [pic]. To obtain credit, you must show all your work.

At this point, if you cannot calculate the estimates, you can hand in your test and receive the estimates to finish the examination.

b) Calculate SST, SSE, and SSR for the estimated equation. In words, why or why not does SST = SSR?

c) Calculate the R2 for the equation. Intuitively, why does R2 equal the value you calculated (do not give a mathematical answer)?

d) Intuitively, why can’t the [pic]for this equation be calculated?

|SUMMARY OUTPUT | | | | | |

| | | | | | | |

|Regression Statistics | | | | | |

|Multiple R |0.814179 | | | | | |

|R Square |0.662887 | | | | | |

|Adjusted R Square |0.648693 | | | | | |

|Standard Error |0.902978 | | | | | |

|Observations |100 | | | | | |

| | | | | | | |

|ANOVA | | | | | | |

|  |df |SS |MS |F |Significance F | |

|Regression |4 |152.3144763 |38.07862 |46.70111 |1.21E-21 | |

|Residual |95 |77.46002272 |0.815369 | | | |

|Total |99 |229.774499 |  |  |  | |

| | | | | | | |

|  |Coefficients |Standard Error |t Stat |P-value |Lower 95% |Upper 95% |

|Intercept |4.740445 |0.59464077 |7.971947 |3.45E-12 |3.559934 |5.920955 |

|Per capita gross income |-4.3E-05 |2.88775E-05 |-1.48142 |0.141805 |-0.0001 |1.45E-05 |

|Illiteracy rate |0.030903 |0.004576094 |6.753055 |1.15E-09 |0.021818 |0.039987 |

|Immunization rate |-0.02639 |0.006222833 |-4.24097 |5.17E-05 |-0.03874 |-0.01404 |

|Aid |0.005807 |0.002529293 |2.295742 |0.02389 |0.000785 |0.010828 |

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OLS Estimates

[pic]

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