Econometri cs April – 2002 60 Marks Note: (1) Section I is compulsory. (2) Attempt any three questions from Section II. (3) Figures to the right indicate full marks to a question or a subquestion. (4) Answers to both the sections should be written in the-same answerbooks. (5)Use of calculator is allowed Section — I (1) Explain the following: (a) Econometrics. (b) Closed input-Output Model. (c) Endogenous variable. (d) Critical region. (e) Explanatory variable. (10 ) (2) (a) Evaluate the following model: Ĉ = 300.29 + 7.42 Y + 8.044 T t table = 2.179 SE → (78.32) (0.0475) (2.9835) F table = 3.89 C = Consumption Expenditure R 2 = 0.9976 Y. = Disposable income n = 15 T = Time (b) Evaluate the following model: Y t = 7.1933 -- 13925 X 2t + 1.4700 X 3t Se = (1.5948) (0.3050) (0.1758) R 2 = 0.8766 N = 13 Y = actual rate of inflation X 3 = expected rate of inflation X 2 = Unemployment rate t 0. 05 = 2. 16 F 0. 05 fo r (2 ,1 0) df = 4. 10
Transcript
EconometricsApril – 2002
60 Marks
Note:(1) Section I is compulsory.(2) Attempt any three questions from Section II.(3) Figures to the right indicate full marks to a question or a subquestion.(4) Answers to both the sections should be written in the-same answerbooks.(5)Use of calculator is allowed
(a) Derive the coefficient of determination of goodness of fit for a Bivariate
regression model.
(b) Estimate the demand function by using the following data:
Demand 50 32 42 62 35 29
Price 10 7 9 11 8 5
(a) State the assumptions of a Multiple Regression Model.
(b) Data on 89 firms gives the following sum of squares and the cross-products in
the deviation form.
(5)
(5)
(3)
(7)
y x1 x2
y 114 37 100
x1 50 -66
x2 967
ȳ =5.8X1 =2.9X2 = 3.9
(i) Fit the regression equation of Y on X1 and X2.
(j) Prepare ANOVA and test the overall significance of the estimated model.
F0.05 for 2.86 degrees of freedom is 3.10.
F0.05 for 1.87 degrees of freedom is 3.95.
(5)
(6)
(a) What is meant by Auto correlation? Why is it experienced in econometric
models?
(b) What are causes of Heteroscedasticity?
(c) What are the solutions to the problem of multicollinearity?
(a) Why do simultaneous equation models require a different treatment?
(b) Write briefly on:
(i) ILS method
(ii) 2SLS method.
(4)
(3)(3)
(4)(6)
TY BMS – Sem VI Page 2 of 3 Econometrics
(7)
EconometricsApril – 2002
(a) Explain the following with respect to input output model:
(i) Assumptions of the Open Leontief model.
(ii) Backward and Forward Linkages.
60 Marks
(5)
(b) Obtain the technology matrix and find gross outputs of the two sectors if the
final demands change to 200 &800 respectively.
Ag, Industry F.D.
Ag, 300 600 100
Industry 400 1200 400
(5)
TY BMS – Sem VI Page 3 of 3Econometrics
EconometricsApril – 2003
60 Marks
Note:(1) Section us compulsory.(2) Attempt any three questions from Section II.(3) Figures to the right indicate full marks to a question or a subquestiou.(4) Use of calculator is allowed.(5) Answers to both the sections should he written in the same answerbooks.
Section — I
(1) Explain the following: (a)
Econometric model.(b) Unbiasedness.(c) A priori assumption.(d) Endogenous variable.(e) Type I Error.
(10)
(2)
(a) Coffee demand function is estimated by using 10 observations.
Evaluate the model.
Ŷ = 2.6911 - 0.4795X
SE (0.1262) (0.1140)
R2 = 0.6628 ¯R2 = 0.6253
D-w = 0.727
coffee demand in terms of cups per person per
(10)
=Yday
X = Average retail price
t05 = 2.306
F05 = 5.32
dL = 0.763
dU = 1.332
(b) Evaluate the following model:
Y = 24.77 + 0.94x1— 0.142x2
t: (3.69) (1.444) (0.526)
R2 = 0.956n = 10
t.05(7) = 2.365 ; F.05(2,7) = 4.74
Y = Consumption expenditure
X1 = Disposable Income
X2 = Wealth
(10)
TY BMS – Sem VI Page 1 of 3 Econometrics
EconometricsApril – 2003
60 Marks
Section — II
(3)
(4)
(a) Derive the following Bivariate Regression model.
Y1 = β0 + β1 Xi +ui
(b) The following results have been obtained from a sample of 11 observations on
values of sales (Y) on corresponding prices (X) of a product.
(i) Estimate the regression of Y on x(ii) What is the part of variation in sales which is not explained by the
regression line?(iii) What is the average elasticity of Y on X?
(a) Write briefly on R2 and ¯R
2
(b) Intermediate data on quantity demanded, price and income (in deviation form)
are given below—
n = 10 ¯Y = 80 ¯X1 = 06 X2 = 800
Variable y x1 x2
y 3450 -300 65,000
x1 30 5900
x2 1,58,000
(i) Fit a regression equation of Y on X1
(ii) Fit a regression equation of Y on X1 and X2.
(iii) Test the incremental contribution of ‘X2’ to the model (Use ANOVA)
F.05(1,7) = 5.59 F.05(1,8) = 5.32
(4)
(6)
(3)
(7)
(5) Attempt any two of the following
(a) What is Auto correlation? Why is it experienced in econometric models?
(b) Discuss the solutions to the problem of ‘Multicollinearity’.
(c) Estimate the following model by using ‘weighted least square method’.
Yi 2 4 6 7 11
Xi 1 2 3 4 5
(10)
V(ui) 1 2 4 2 1
TY BMS – Sem VI Page 2 of 3 Econometrics
(6)
EconometricsApril – 2003
60 Marks
(a) Distinguish between single equation and simultaneous equation models.
(b) Write briefly on identification problem in the context of simultaneous equation
model.
(c) What is 2 stage least square method?
(3)
(3)
(4)
(7)
(a) Write briefly on:
(i) Open Input-out models.
(ii) Hawkins-Simon conditions.
(b) Given the Technology matrix, find the new output levels if final demand for two
sectors is 110 and 120 units respectively
(4)
(6)
A = [ ]0.20 0.16
0.50 0.26
TY BMS – Sem VI Page 3 of 3Econometrics
EconometricsApril – 2004
60 Marks
Note:(1) Section I is compulsory.(2) Attempt any three questions from Section II.(3) Figures to the right indicate full marks to a question or a subquestiou.(4) Use of calculator is allowed.(5) Answers to both the sections should he written in the same answerbooks.
Section — I
(1) Solve the following:
(a) If Σxy = 19, Σx2 = 10 where x and y are deviations from x and y.
(b) If R2 =0.5 and F value if n=10, k=3.
(c) Write ANNOVA TABLE for single equation with one explanatory variable.
(d)
Writ
e
form
ula
for (10)
(10)
2 2 = 5,37,192 where et is
(e) If Σet = 5,73,069 and Σ(et - = et-1 ) residual. Find Durbin-Watson (d) statistic.
(2)
(a) Evaluate the following model.
(b) Evaluate the following model.
TY BMS – Sem VI Page 1 of 3 Econometrics
EconometricsApril – 2004
Section — II60 Marks
(3)
(4)
(5)
(6)
(a) Prepare ANNOVA TABLE for both the equations
(b) Verify that the value of average price elastically of the following estimated
demand function
(a) State stepwise procedure (Methodology) of conducting econometric study.
(b) Examine whether following model is significant or not
x1 2 1 5 8 7 2 3 3 0 9
x2 6 5 5 7 3 1 8 2 6 7
y 13 9 15 16 21 9 15 10 12 30
(a) Define (i) Homoscadasticity (ii) Heteroscadasticity
(b) For the following data series to check whether there is autocorrelation
(a) Distinguish between structural form and reduced form of simultaneous
equations Models.
(b) Examine the identifiability of the following model. [Use rank and order method]
Where L: amount of labour
W: Wage Rate
S: Sales
P: Productivity of Labour
(5)
(5)
(3)
(7)
(5)
(5)
(3)
(7)
TY BMS – Sem VI Page 2 of 3 Econometrics
EconometricsApril – 2004
60 Marks
(7)
(a) Write briefly on:
(i) Input - Output Model
(ii) Assumptions of Input-Output Model.
(b) Given the Technology matrix find the new output levels if final demand for two
sectors is 150 and 180 units respectively and labour requirements
**********
(5)
(5)
TY BMS – Sem VI Page 3 of 3Econometrics
EconometricsApril – 2005
60 Marks
Note:(1) Section I is compulsory.(2) Attempt any three questions from Section II.(3) Figures to the right indicate full marks to a question or a subquestiou.(4) Use of calculator is allowed.(5) Answers to both the sections should he written in the same answerbooks.
(a) Describe the numerical and statistical properties of OLS estimators.
(b) Given the following intermediate results on total output X and total cost Y.
(i)
(ii) Comment on the theoretical significance of
(iii) Estimate the total cost for an output level of 95.
(5)
(5)
(4)2 2 (3)
(a) Write a note on R and ¯R
(b) Given the intermediate results in deviation form:
(i) Estimate the function of y on x1
(ii) Estimate the function of y on x1 and x2
(iii) Prepare ANOVA table and test the overall significance of he Multiple
Regression Model.
(7)
(5)
(a) What is Multicollinearity? What are its causes?
(b) What are the consequences of Autocorrelation?
(c) Estimate the following model using WLS method:
Y1 6 7 9 10 11
X1 4 8 6 8 7
V(ui) 4 6 3 5 4
(3)
(2)
(5)
TY BMS – Sem VI Page 2 of 3 Econometrics
(6)
EconometricsApril – 2005
(a) What is Simultaneous Equation Bias?
60 Marks
(2)
(b) State with examples what are endogenous and exogenous variables.
(c) Transform the following model into reduced form: C = a0 + a1Y + a2P +ui
I = b0 + b1Y + b2R + vi
Y = C + I + G + X
C = Consumption Expenditure
I = Investment Expenditure G
= Government Expenditure
Y = National Income
P = Price Index
R = Rate of Interest
X = Net Exports
(3)
(5)
(7)
(a) Write brief notes on:
(i) Technological Viability.
(ii) Forward and Backward Linkages.
(b) Given the transactions table, obtain the technology matrix. Compute the new
output levels and labour requirements if final demands change to 600 and 400
respectively.
(4)
(6)
I II Final Demand
I 240 100 60
II 40 350110
TY BMS – Sem VI Page 3 of 3Econometrics
EconometricsApril – 2006
60 Marks
Note:(1) Section I is compulsory.(2) Attempt any three questions from Section II.(3) Use of calculator is permitted(5) Answers to the sections should he written in the same answer-book.
Section — I
(1) Do as directed:
(a) Differentiate between estimator and estimate.
(b) Let X = Income, Y = Expenditure, Correlation coefficient between X and
Y-rxy = 0.9 Compute the coefficient of determination and interpret its value.
(10)
(c)(regression coefficient) Find and interpret the value of average elasticity of demand with respect to price.
(d) Differentiate between Simple and Composite Hypotheses.
(e) Define Power of a Test.
(2) Evaluate the following models.
(a)
(b) Aggregate consumption was estimated as a function of profits and wages by
considering ten data points.
Evaluate the model on the basis of Statistical and Econometrics criteria.
(10)
(10)
TY BMS – Sem VI Page 1 of 3 Econometrics
EconometricsApril – 2006
60 Marks
Section — II
(3)
(a) State the properties of OLS estimators.
(b) Consider the following data
Demand (D): 10 20 23 25 42
Price (P): 8 7 6 4 3
(i) Estimate the demand model D = β0 + β, P + U.
(ii) Predict the demand for a price level of Rs.10.
(iii) Compute the coefficient of determination
(3)
(3)
(2)
(2)
(4) Intermediate results based on a sample of 30 observations are shown in table below
(Deviational form):
(i) Estimate the multiple regression model of Y on X1 and X2
(ii) Find partial elasticity of Y with respect to X1.
(iii) Test for the overall significance of the regression (F 2, 27, 0.05=3.39).
(5)
(3)
(2)
(5)
(a) “In the presence of perfect multicolinearity, the OLS estimates are
indeterminate and their variances are infinite” — Discuss.
(b) Define Durbin — Watson d —statistic. State the limitations of the D-W d-test.
(6)
(4)
TY BMS – Sem VI Page 2 of 3 Econometrics
EconometricsApril – 2006
(6) In the context of simultaneous equations models, differentiate.
(a) Structural form and reduced form of the model.
(b) Rank conditions and order conditions of identification.
60 Marks
(5)
(5)
(7)
(a) State any four assumptions of open Leontief Input — Output Model.
(b) Obtain the technology matrix and find gross outputs of the two sectors if the
final demand changes to 200 and 800 units respectively.
