IGNOU MECE 101 SOLVED ASSIGNMENT

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MECE 101 (July 2024 - January 2025) - ENGLISH

MECE-101: INTRODUCTORY ECONOMETRIC METHODS

Tutor Marked Assignment

Course Code: MECE-101

Asst. Code: MECE-101/AST/2024-25

Maximum Marks: 100

Note: Answer all the questions. While questions in Section A carry 20 marks each, those in Section B carry 12 marks each.

Section A

1. What is meant by heteroscedasticity? What are its consequences? How do you detect the presence of heteroscedasticity in a data set?

2. Explain why an error term is added to the regression model. What assumptions are made about the error term? What are the implications of such assumptions? What will happen to the estimators of the parameters of the regression model, if these assumptions are violated?

Section B

3. Consider the regression equation  where u is a stochastic error term.

a) Explain how estimators of a and ẞ can be obtained.

b) What algebraic properties do the estimators fulfil?

4. What is meant by identification in a simultaneous equation model? Check the identification status of the equations in the following model:

Demand function: 

Supply function: 

5. What is meant by multicollinearity? What are its consequences on estimates? What remedial measures do you suggest for the problem?

6. While estimating a regression model you found that the explanatory variable is measured with certain error. Specify the model. What are its consequences on the parameters?

7. Write short notes on the following:

a) Dummy variable trap

b) Coefficient of Determination

MECE 101 2025 2026 - English

MECE-101: INTRODUCTORY ECONOMETRIC METHODS

Assignment

Course Code: MECE-101
Asst. Code: MECE-101/AST/2025-26
Maximum Marks: 100

Note: Answer all the questions. While questions in Section A carry 20 marks each, those in Section B carry 12 marks each.

Section A

1. In the case of a two-variable regression model show that TSS = ESS + RSS. Use appropriate diagram to explain your result. In this context, define the concept of R-squared and interpret it.

2. The relationship between Y and X is given by where u_i follows classical assumptions. Consider the following set of data and answer the questions.

| Y | 11 | 12 | 13 | 14 | 15 ||---|----|----|----|----|----|| X | 18 | 16 | 19 | 22 | 20 |

a) Estimate parameters of the model from the following data by using OLS method.

b) What is the estimate of error variance in the above case?

c) Find the value of R2 for the above data.

Section B

3. Explain the concept of identification in a simultaneous equations model. Why is it called the paradox of identification?

4. How do you express the multiple regression model in matrix form? Derive OLS estimator for the parameters of the model. Show that the OLS estimators are Best Linear Unbiased Estimators (BLUE).

5. What is meant by multicollinearity? What are its consequences on estimates? What remedial measures do you suggest for the problem?

6. Why is the OLS method inappropriate when a dataset is having heteroscedasticity problem? Explain the White's Test to detect heteroscedasticity in a data set.

7. Write short notes on the following:

a) Lagrange-Multiplier (LM) Test

MECE 101 2025 2026 - Hindi

एमईसीई-101: परिचयात्मक अर्थमितीय विधियाँ

(सत्रीय कार्य)

पाठ्यक्रम कोड: एमईसीई-101

सत्रीय कार्य कोड: एमईसीई-101/एएसटी/2025-26

अधिकतम अंकः 100

नोटः सभी प्रश्नों के उत्तर दें। खंड क के प्रत्येक प्रश्न के लिए 20 अंक हैं, जबकि खंड ख के प्रत्येक प्रश्न के लिए 12 अंक हैं।

खंड क

1. किसी द्वि-चर समाश्रयण मॉडल के मामले में, दर्शाइए कि TSS = ESS + RSS होता है। अपने परिणाम की व्याख्या करने के लिए उपयुक्त आरेख का प्रयोग करें। इस संदर्भ में, R-वर्ग की अवधारणा को परिभाषित करें और उसकी व्याख्या करें।

2. चर Y और X के बीच संबंध y₁ = x + βx₁ + u₁ से दर्शाया जाता है, जहाँ u₁ क्लासिकी अवधारणाओं का अनुसरण करता है। निम्नलिखित आँकड़ों के निकाय पर विचार करें और प्रश्नों के उत्तर दें -

Y	11	12	13	14	15
X	18	16	19	22	20

a) साधारण न्यूनतम वर्ग (OLS) विधि का प्रयोग करके उपर्युक्त आँकड़ों से मॉडल के प्राचलों का आकलन करें।

b) उपर्युक्त स्थिति में त्रुटि प्रसरण का आकल क्या होगा?

c )उपर्युक्त आँकड़ों के लिए R2 का मान ज्ञात करें।

खंड ख

3. युगपत समीकरण मॉडल अभिनिर्धारण की संकल्पना स्पष्ट करें। इसे अभिनिर्धारण का विरोधाभास (paradox of identification) क्यों कहा जाता है?

4. आप बहु समाश्रयण मॉडल को आव्यूह रूप में कैसे व्यक्त करते हैं? मॉडल के प्राचलों के लिए OLS आकलक अवकलित कीजिए। दर्शाइए कि OLS आकलक ही सर्वोत्तम रैखिक अनभिनत आकलक (BLUE) होते हैं।

5. बहुसंरेखता का क्या अर्थ है? आकलों पर इसके क्या परिणाम होते हैं? इस समस्या के लिए आप क्या उपचारात्मक उपाय सुझाएँगे?

6. जब किसी डेटासेट में विषमविसारिता समस्या हो, तो OLS विधि अनुपयुक्त क्यों होती है? डेटासेट में विषमविसारिता का पता लगाने के लिए व्हाइट के परीक्षण की व्याख्या करें।

7. निम्नलिखित पर संक्षिप्त टिप्पणियाँ लिखें

क लैग्रेज-गुणक (LM) परीक्षण

ख संभाव्यता अनुपात परीक्षण

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