Economics of Enterprise Answers

The phase of the business cycle at which almost all available resources in the economy are in use is referred to as

Production possibility curve shows the various

Consider a k-variables linear regression model, i.e., Y = X 1β1 + X 2 β2 + ε,  Where, X1 is (N  k1 ) , X 2 is (N  k2 ) and k = k1 + k2 . As you may recall, adding columns to the X matrix (including additional regressors in the model) gives positive definite increase in R2. The adjusted R2 ( R 2 ) attempts to avoid this phenomenon of ever increase in R2. Show that the additional k2 number of variables (regressors) in this model increases R 2 if the calculated F-statistic in testing the joint statistical significance of coefficients of these additional regressors (β2 ) is larger than one. 

A measure of value of money in an economy is what?

the desire to hold money in liquid form instead of investing it is what?

Problem 1

Consider a k-variables linear regression model, i.e.,

Y = X 1β1 + X 2 β2 + ε,

Where, X1 is (N  k1 ) , X 2 is (N  k2 ) and k = k1 + k2 . As you may recall, adding columns to the X matrix (including additional regressors in the model) gives positive definite increase in R2. The adjusted R2 ( R 2 ) attempts to avoid this phenomenon of ever increase in R2. Show that the additional k2 number of variables (regressors) in this model increases R 2 if the calculated F-statistic in testing the joint statistical significance of coefficients of these additional

regressors (β2 ) is larger than one.

Problem 3

In this question we look at the relation between the logarithm of weakly earnings and years of education. Using data from the national longitudinal study of youth, we find the following results for a regression of log weekly earnings and years of education, experience, experience squared and an intercept:

Log (earnings) = 4.016 + 0.092 . educi + 0.079 .expei + 0.002 . experi 2

( 0.222) ( 0.008) ( 0.025) (0.001)

c). Labour economist studying the relation between education and earnings are often concerned about what they call “ability bias”. Suppose that individuals differ in ability, and that the correct specification of the regression function is one that includes ability:

log ( earnings )I = β1 + β 2 ⋅ educI + β 3 ⋅ experI − β 4 ⋅ experI2 + β5 ⋅ abilityI + εI .

In this regression, what do you expect the sign of β5 (the coefficient on ability) to be?

Problem 2

Let X1 , X2 , ⋯, XN be a random sample of size n from normal distribution with mean μ and variance σ2 .

a). Find the maximum likelihood estimator of σ2  2 . (2 points)

b). Find the asymptotic distribution of the maximum likelihood estimator of σ2  2

obtained in part (a).

Problem 1

Consider a k-variables linear regression model, i.e.,

Y = X 1β1 + X 2 β2 + ε,

Where, X1 is (N  k1 ) , X 2 is (N  k2 ) and k = k1 + k2 . As you may recall, adding columns to the X matrix (including additional regressors in the model) gives positive definite increase in R2. The adjusted R2 ( R 2 ) attempts to avoid this phenomenon of ever increase in R2. Show that the additional k2 number of variables (regressors) in this model increases R 2 if the calculated F-statistic in testing the joint statistical significance of coefficients of these additional

regressors (β2 ) is larger than one.

Problem 4

Suppose the production(Y) is determined as a function of labour input in hours (L) and capital input in machine hours (K). Using the Cobb-Douglas function:

Y= β0 + β1K β1 + ek

Write the procedure to estimate the coefficients of this function

Problem 5

Show that the test taking the overall significance of regression model using ANOVA table to be expressed as:

𝑭=𝑹𝟐𝒌−𝟏⁄(𝟏−𝑹𝟐)𝒏−𝒌⁄

Where, R be a level of determination and k is the number of parameters in the n sampled regression model.

Problem 3

A random sample Y1 , Y 2 , ⋯,Yn is drawn from a distribution whose probability density

function is given by: f (Y ) = βe− βY , Y  0 & β > 0

a). Obtain the maximum likelihood estimator (MLE) of β.

b). Given that Σ n

Y i = 25 ,

Σn

Yi2

= 50 , n = 50 calculate the maximum likelihood

i =1

i =1

estimate of β.

(3 point)

c). Using the same data as in part (b), test the null hypothesis that β =1against the alternative

hypothesis that β ≠1at 5% level of significance.