Obtain the ols estimates the standard errors and complete

Question

Question 1:

The following table is output for a regression of the growth rate Y (%) on the investment rate X(%) for a group of industrial countries. You will notice that the table is missing information on various rate various statistics as indicated by the question mark?

.....NOTE..SAMPLE RANGE SET TO:     1,     35

R-SQUARE = ?    R-SQUARE ADJUSTED = 0.1452

                                                               ANALYSIS OF VARIANCE - FROM MEAN

                                                       SS                        DF                     MS                    F

REGRESSION                                     77.444                    ?                      77.444                ?

ERROR                                                    ?                     ?                      11.434             P - VALUE

TOTAL                                              454.75                   34                    13.375               0.014  

VARIABLE NAME	ESTIMATED COFFICIENT	STANDARD ERROR	T-RATIO 33DF	PARTIAL STANDARD ELEASTICITY
				P - VALUE  CORR.	COEFFICIENT	AT MEANS
X	?	0.1548	2.603	0.014 -0.413	0.4127	2.9834
CONSTANT	?	?	-1.701	0.098-0.284	0	-1.9834

You are additionally given X' = 19.68% and V' = 2.66%

1. Obtain the OLS estimates, the standard errors, and r².

2. Complete the ANOVA table.

3. Obtain a 95 percent confidence interval for the slope coefficient.

Question 2:

We looked at the following model of wage inflation in class, in which the rate of growth of nominal wages (WAGE, %) is regressed on the rate of growth of worker productivity (PROD, %), and the rate of price inflation (INF, %).

WAGE = 0.50 + 0.40PROD + 0.56INF                   N = 35, R-squared = 0.83

s.e                   (0.16)       (0.18)

(i) Construct a 95% confidence interval for (β₂ + β₃), assuming that b₂ and b₃ have a zero covariance.

(ii) What does the restriction β₂ + β₃ = 1 mean? Conduct a two tail-test of this restriction using your answer to (i) above.

Question 3:

The following model of gas consumption was estimated from quarterly US data.

GAS^ = 5856.1 -5.435PRICE + 0.330INC + 60.3CARS N=296, R-squared = 0.766

  s.e                 (1.238)         (0.0113)     (20.24)

Sample means: GAS = 7430.8, CARS=9.24, INC = 4974.3, PRICE= 114.88

GAS = quantity of gas consumed (thousands of gallons), PRICE = the price of gas (cents per gallon), INC = personal income (5 billion), and CARS = car sales (millions).

A. Explain whether the slope coefficients have the sins expected on prior grounds.

B. Test whether the PRICE and INC coefficients are each zero at the 1 percent level. Make sure you incorporate prior expectations about the signs of the coefficients in stating your alternative hypotheses.  

C. Is the demand for gas inelastic with respect to (i) price and (ii) income? Demonstrate.

Question 4:

Theory suggests that a country's net exports are inversely related to output and to the value of its currency (the exchange rate). This relationship was estimated for the US.

NXA = 165.3 -0.0276GDP - 0.8372ERATE         N = 29, R-Squared = 0.54

se       (50.9)     (0.005)        (0.425)

NX = real net exports ($ billion), GDP = real GDP ($ billion), and ERATE= index of the US real exchange rate -100).

Note: an increase in ERATE means an appreciation of the US currency.

1. Interpret the slope coefficients.

2. If the ERATE =130, what is the predicted change in net exports of a 10 percent depreciation of the US currency, other things remaining constant?

By how much would GDP have to change to prevent net exports from changing in response to the 10 percent depreciation of the US currency?

3. Test whether the exchange rate has an impact on net exports. Specify the alternative according to theory. Use the 5 percent significance level.

Question 5:

It has been argued by many that economies that are more open to trade (that is, trade a lot) grow faster than those that are less open, other things being equal. Consider the following simple model for examining this issue.

GGDP= β₁ + β₂TRADE + β₃GKAP + β₄GLAB + u

GGDP=growth rate of real GDP (%), TRADE= total trade to GDP ratio (%), GKAP growth rate of capital, measured by the investment to GDP ratio (%), and GLAB=growth rate of employment (%).

An economy's openness here is being measured by the ratio of total trade (exports plus imports) to GDP. This is the variable TRADE.

The higher the ratio, the more open the economy. The file trade.txt on P drive contains data on these variables for a cross-section of industrial countries in 2005. The variables appear in the following order: GGDP TRADE GKAP GLAB.

A. Estimate the model, present your results as shown in class (or see Questions 3 & 4 above). Interpret the slope coefficients.

B. Does openness promote growth? Test this proposition using the 5% level of significance.

C. Is the regression as a whole statistically significant? Conduct the appropriate test at the 5% level.

D. Test the hypothesis that the impact of the growth in employment (β₃) is equal to the impact of the growth in capital (β₄) using a t test at the 5 percent level of significance. (You can use any of the two methods shown in class).