1. Summarizing Empirical Estimation EconS 451: Lecture #9 Transforming Variables to Improve Model Using Dummy / Indicator Variables Issues related to Model Identification. Why Deflate Data? What time series do we use? How to identify: Heteroskedasticity Multicollinearity Autoregression

2. Model Identification Why do we believe that by taking prices and quantities and estimating a statistical relationship that we’ve estimated a Demand or Supply Relationship?

3. Model Identification If the economy were perfectly static……it would be impossible to estimate either demand or supply. but supply and demand functions shift with the passage of time, thus allowing one or both to be estimated. D1D1 Quantity / Unit Time Price Supply D2D2 D3D3

4. Model Identification Quantity S2S2 Demand Price S3S3 S1S1

5. Deflating Price and Income Two Reasons Economic Estimate real price and income relationships instead of nominal. Statistical Reduce correlation between independent variables. Reduce heteroskedasticity.

6. Time Series What time series to include? Generally speaking, the greater number of observations the more confidence in estimated coefficients. Time period should reflect the conditions under which you are attempting to capture. What level (yearly, quarterly, monthly, weekly, daily, hourly, etc.) Depends on the type of analysis and availability of data.

7. How to Identify…. Heteroskedasticity = non-constant error variance Eg cross section of firms, the error term for large firms is consistently greater than the error of small firms. Visual inspection of Residual Plot. Goldfeld-Quandt Test. Set Up and Test Hypothesis

8. How to Identify…. Multicollinearity ? Economic logic. Odd signs for estimated coefficients may be first clue. Correlation Matrix

9. Multicollinearity Quantity of Red Roses (doz.) Price of Red Roses (per/doz.) Quantity of Orchids (doz.) Per Capita Income Quantity of Tulips (doz.) Quantity of Red Roses (doz.)1.00 Price of Red Roses (per/doz.)-0.801.00 Quantity of Orchids (doz.)-0.760.971.00 Per Capita Income-0.710.480.571.00 Quantity of Tulips (doz.)-0.440.810.980.421.00 Correlation matrix

10. How to Identify…. Autoregression = error terms are correlated over time Residuals Plot Test Using Durbin-Watson Statistic

11. Durbin-Watson Test Statistic

12. What to do if you find……. Hetereoskedasticity  Add variable to account for difference between groups Multicollinearity Drop correlated variable (s) from estimation. Autoregression Add variable to account for the missing factor over time

13. Summary Questions What are the five assumptions of the classical linear regression model? Describe in words, how Ordinary Least Squares works. What is measured by the R-Square term? How can you determine if a variable is statistically significant? What steps do you take to determine the appropriate functional form for estimating an equation? When would you ever utilize an indicator (dummy) variable in your estimation…..and how would you do it?

14. Summary Questions Explain the process involved with identifying the appropriate functional form to use when estimating a statistical model. What rules do we use to identify a model from price and quantity relationships ? Why do we deflate data? What issues should we consider when conducting time-series estimations ? What techniques can be used to identify Heteroskedasticity and Multicollinearity? If these are present……how do we correct these problems?