Econometrics CAT 1: Regression and Production Function Assignment Questions

Assessment Requirements

The assessment, CAT 1, focuses on applied econometrics and production/operations management concepts. The main objectives include:

1. Regression Analysis:

   • Estimating production functions using sample data.

   • Testing hypotheses such as constant returns to scale.

   • Determining the significance of slope coefficients and calculating R2R^2R2 and adjusted R2R^2R2.

2. Pooled vs. Separate Regression:

   • Estimating regression equations for individual samples and pooled datasets.

   • Identifying assumptions required for pooled regressions and testing their validity.

3. Time Series & Unemployment Analysis:

   • Examining historical unemployment data to test differences in regression results.

   • Assessing the impact of specific variables like benefit levels on unemployment.

4. Heteroscedasticity Testing:

   • Applying Goldfeld-Quandt test for residual variance differences.

   • Understanding the Breusch-Pagan-Godfrey method for homoscedasticity assessment.

5. Serial Correlation:

   • Using Durbin-Watson test to detect autocorrelation in regression residuals.

The assessment tests the student’s ability to interpret, analyze, and apply econometric techniques in real-world and historical datasets.

Approach Taken by Academic Mentor

The Academic mentor guided the student step by step, using a structured approach for each section:

1. Question One – Regression and Production Function:

   • Explained the formulation of the production function regression.

   • Guided the student in conducting hypothesis testing for constant returns to scale.

   • Showed the method to test slope coefficients for significance using t-tests.

   • Demonstrated calculation of R2R^2R2 and adjusted R2R^2R2 to evaluate model fit.

2. Question Two – Pooled and Separate Regression:

   • Taught the student how to estimate linear regressions for individual samples and pooled data.

   • Discussed assumptions like homogeneity of coefficients and error term independence.

   • Explained testing validity via F-tests and residual analysis.

3. Question Three – Unemployment Analysis:

   • Compared regression results for two periods (1920–1938 vs. 1921–1938).

   • Conducted a significance test to assess differences.

   • Explained the use of Goldfeld-Quandt test for heteroscedasticity, including stating null and alternative hypotheses, decision rules, and interpreting results.

4. Question Four – Homoscedasticity Tests:

   • Introduced Goldfeld-Quandt and Breusch-Pagan-Godfrey tests.

   • Walked through applying these tests to sample datasets to detect unequal variance in residuals.

   • Highlighted the practical implications for regression analysis and model reliability.

5. Question Five – Serial Correlation Test:

   • Explained the Durbin-Watson test for detecting autocorrelation in time-series data.

   • Demonstrated how to interpret the statistic to conclude presence or absence of serial correlation.

Outcome and Learning Achievements

Through this guided approach, the student was able to:

• Develop confidence in formulating and testing econometric models.

• Apply regression analysis techniques to practical and historical datasets.

• Understand assumptions behind pooled regressions, homoscedasticity, and serial correlation.

• Learn stepwise interpretation of statistical tests, including t-tests, F-tests, Goldfeld-Quandt, Breusch-Pagan, and Durbin-Watson.

• Achieve hands-on exposure in analyzing production, unemployment, and land price datasets.

• Strengthen critical thinking to draw conclusions from statistical outcomes.

Final Outcome: The student successfully completed CAT 1, producing a comprehensive regression analysis, testing assumptions, detecting heteroscedasticity and serial correlation, and correctly interpreting all econometric results. The process also reinforced theoretical understanding and practical skills in applied econometrics.

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