1. Empirical Estimation Review EconS 451: Lecture # 8 Describe in general terms what we are attempting to solve with empirical estimation. Understand why Ordinary Least Squares has been a very popular estimation technique. Understand the five assumptions of the Classical Linear Regression Model. Understand how to choose the appropriate functional form. Understand the applications associated with Indicator (Dummy) Variables. Estimation Examples.

2. What is our goal ? Our economic understanding about how certain variables interact…….leads us to develop a functional specification. Dependent Variable = F (Explanatory Variables)

3. How would we define a relationship ?

4. We can be more specific! Ordinary Least Squares: Minimizes the sum of the squared errors to produce a line that best fits the data.

5. How would we define a relationship ?

6. Assumptions of Classical Linear Regression Model Assumption: 1 Dependent variable is a linear function of a specific set of independent variables, plus a disturbance. Violations Wrong regressors. Nonlinearity. Changing parameters.

7. Assumptions of Classical Linear Regression Model Assumption: 2 Expected value of disturbance term is zero. Violations Biased intercept.

8. Assumptions of Classical Linear Regression Model Assumption: 3 Disturbances (error term) have uniform variances and are uncorrelated. Violations Heteroskedasticity. Autocorrelated errors.

9. Assumptions of Classical Linear Regression Model Assumption: 4 Observations on independent variables can be considered fixed in repeated samples. Violation Autoregression.

10. Assumptions of Classical Linear Regression Model Assumption: 5 No exact linear relationship between independent variables. Violation Multicollinearity.

11. Interpreting Results Regression Statistics Multiple R0.562956 R Square0.316919 Adjusted R Square0.298943 Standard Error37.80161 Observations40 ANOVA dfSSMSFSignificance F Regression125193.03 17.63030.000155854 Residual3854300.561428.962 Total3979493.58

12. Interpreting Results Variable Coefficients Standard Errort StatP-value Intercept40.8222.131.8420.072962 Income0.1280.0304.1950.000156

13. Choosing a Functional Form Linear Quadratic Hyperbola Semi-Log Double Log Log-Inverse

14. Choosing a Functional Form Use economic theory. Plot the independent variable against the dependent variable to discern pattern. First without any transformation. Then make the different transformations that you may be interested to see and plot them against the dependent variable.

15. Using Indicator Variables (Dummies) Capture Structural Change Some unusual occurrence that isn’t capture elsewhere in the other variables ExpenditureIncome Structural Dummy 52.50258.300 58.32343.100 81.79425.000 119.90467.500 125.80482.900 100.46487.701 121.51496.501 100.08519.401 127.75543.301 104.94548.701

16. ! Estimation Demo Using Excel ! See Example

17. 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?