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A change in the price of a good______.
Select one:
a. does not shift the good's demand curve but does cause a movement along it.
b. shifts the good's demand curve and also causes a movement along it.
c. neither shifts the good's demand curve nor causes a movement along it.
d. shifts the good's demand curve but does not cause a movement along it.
Discuss the type of price control that a government would implement if it wishes
to impose a national minimum wage. Include in your answer the economic effects
of such a price control. Motivate your answer with the aid of a diagram
Show that the test taking the overall significance of regression model using ANOVA table to be expressed as:
𝑹𝟐⁄𝒌−𝟏
𝑭=(𝟏−𝑹𝟐)⁄𝒏−𝒌
Where, R be a level of determination and k is the number of parameters in the n sampled regression model.
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
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. (3 points)
b). Given that ∑ n Y i = 25 , ∑n Yi2 = 50 , n = 50 calculate the maximum likelihood
estimate of β.
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
Let X 1 , X 2 , ⋯,Xn be a random sample from a normal distribution with mean µ
and variance σ2. Consider e X as an estimator of e µ where X is the sample
µ mean. Show that e X is consistent estimator of e .
A. Does identification state have any implication on the estimation of the econometric parameters? How? (1 point)
B. What is the difference between autocorrelation and multicollinearity? (1 point)
C. State briefly the four stages in econometric researches? (1 point)
D. Discuss the difference between structural models and reduced form models? (2 point) E. Why do you study econometrics in your field of study? (2 point)
Log (earnings) = 4.016 + 0.092 . educi + 0.079 .expei + 0.002 . experi 2
( 0.222) ( 0.008) ( 0.025) (0.001)
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?
a). What do you think the sign of the correlation between ability and years of education?
b). If we estimate the regression function with ability included, do you think that the
estimated value of β 2 will be greater or less than what it was in the regression without ability? Explain.
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.
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). (3 points)
