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Empirical Modeling Process

Empirical Modeling Process. 1 - Identify Problem / Question 2 - Conceptualize model 3 - Collect data 4 - Examine and Summarize data 5 - Estimate model 6 - Examine model performance 7 - Revise model as needed. Demand Curve. Price. Quantity. Price: Deflated Constant Dollar Price.

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Empirical Modeling Process

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  1. Empirical Modeling Process 1 - Identify Problem / Question 2 - Conceptualize model 3 - Collect data 4 - Examine and Summarize data 5 - Estimate model 6 - Examine model performance 7 - Revise model as needed

  2. Demand Curve Price Quantity

  3. Price: Deflated Constant Dollar Price Quantity: Per Capita Consumption

  4. Mathematical Conceptual Model: Model 1 TP = b0+ b1TQ + e Where: TP= real quarterly retail turkey price (cents/lb.) TQ=quarterly per capita turkey consumption (lbs./capita) b0, b1 are parameters to be estimated e is an error term

  5. Turkey Demand Curve TP b0 TP = b0+ b1TQ b1 TQ

  6. Objective: To quantify determinants of quarterly retail price of Turkey over 1980-2008 Estimate the demand curve

  7. Empirical Modeling Process 1 - Identify Problem / Question 2 - Conceptualize model 3 - Collect data 4 - Examine and Summarize data 5 - Estimate model 6 - Examine model performance 7 - Revise model as needed

  8. Empirical Modeling Process 1 - Identify Problem / Question 2 - Conceptualize model 3 - Collect data 4 - Examine and Summarize data 5 - Estimate model 6 - Examine model performance 7 - Revise model as needed

  9. Summary Statistics of Quarterly Real Turkey Price and Per Capita Turkey Consumption, 1980-2008

  10. Goodness of Fit Measures

  11. Residual Summary

  12. Parameter Estimates

  13. Model 1 Regression Estimates: TP = 227.48 – 17.81 TQ (0.00) (0.00) p-values Adj. R-Sq.=0.33 RMSE=29.35 cents/lb. Observations=116

  14. Turkey Demand Curve TP 227.48 TP = 227.48 – 17.81 TQ -17.81 TQ

  15. Diagnostic Testing of Regression 1. Predicted vs. Actual Graph 2. Graphical analysis of residuals

  16. Predicted Values & Residuals (Errors) Predicted TP = 227.48 – 17.81 TQ Residual = TP – Predicted TP

  17. Performance Summary Model 1 • Adj. R-square only 0.33 • RMSE = 29.35 cents/lb (std dev TP=35.8) • Sign on coefficient is as expected • TQ is statistically significant • Not predicting well • We suspect we have left out some • relevant important factors • (omitted relevant variable problem)

  18. Empirical Modeling Process 1 - Identify Problem / Question 2 - Conceptualize model 3 - Collect data 4 - Examine and Summarize data 5 - Estimate model 6 - Examine model performance 7 - Revise model as needed

  19. Mathematical Conceptual Model Model 2 TP = b0 + b1TQ + b2BfQ + b3PkQ + b4ChQ + b5INC + e Where: TP and TQ are as defined in model 1, BfQ, PkQ, ChQ quarterly beef, pork and chicken consumption (lbs./capita) INC = real disposable income ($/capita)

  20. Mathematical Conceptual Model Model 2 TP = b0 + b1TQ + b2BfQ + b3PkQ + b4ChQ + b5INC + e Sign Expectations: b1 b2 b3 b4 b5

  21. Summary Statistics of Data Used to Explain Quarterly Real Turkey Price, 1980-2008

  22. Performance Summary of Model 2 • Adj. R-square 0.94 better than twice 1 • RMSE = 8.68 cents/lb less than 1/3 of 1 • BfQ & PkQ unexpected signs • & statistically significant • Appears to be seasonality not • accounted for in other regressors

  23. Mathematical Conceptual Model Model 3Seasonality Adjustment TP = b0 + b1TQ + b2BfQ + b3PkQ + b4ChQ + b5INC + b6Q1Dum + b7Q2Dum + b8Q3Dum+ e Where: Q1Dum = 1 in qtr 1 and 0 otherwise Q2Dum = 1 in qtr 2 and 0 otherwise Q3Dum = 1 in qtr 3 and 0 otherwise

  24. Dummy variables in spreadsheet Year Qtr Q1Dum Q2Dum Q3Dum Q4Dum 1980 1 1 0 0 0 2 0 1 0 0 3 0 0 1 0 4 0 0 0 1 1981 1 1 0 0 0 2 0 1 0 0 3 0 0 1 0 4 0 0 0 1 etc.... Drop one dummy variable column when estimate regression

  25. Performance Summary of model 3 • Adj. R-square 0.94 comparable to 2 • RMSE = 8.46 cents/lb bit less than 2 • Signs on coeff. ok except BfQ & PkQ • See what happens when we drop BfQ

  26. Mathematical Conceptual Model Model 4 TP = b0 + b1TQ + b2BfQ + b3PkQ + b4ChQ + b5INC + b6Q1Dum + b7Q2Dum + b8Q3Dum+e or TP = b0 + b1TQ + b2PkQ + b3ChQ +b4INC + b5Q1Dum + b6Q2Dum + b7Q3Dum+e

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