1. Valuation 4: Econometrics Why econometrics? What are the tasks? Specification and estimation Hypotheses testing Example study

2. Last week we looked at What is so special about environmental goods? Theory of consumer demand for market goods Welfare effects of a price change: Equivalent variation versus compensating variation Consumer demand for environmental goods Welfare effects of a quantity change: Equivalent surplus versus compensating surplus Theory and practise

3. Why econometrics? Analysis –To test the validity of economic theories Policy making –To test the outcome of different government economic policy moves Forecasting or prediction –To predict the value of other variables

4. What are the tasks? Specification –From an economic model to an econometric model Estimation Testing hypotheses Predictions

5. Specification – the function Include all relevant exogenous variables Functional form: linear relationship? Estimates parameters for  and  are constant for all observations

6. Specification – disturbance (1) Expected value is zero

7. Specification – disturbance (2) Variance is constant –Homoscedasticity vs. heteroscedasticity

8. Specification – disturbance (3) disturbances are not autocorrelated disturbances are normally distributed

9. Specification – disturbance (4)

10. OLS - Point estimates disturbance vs. residual

11. OLS – R 2

12. OLS – hypotheses testing T-test F-Test P values

13. Data and variables Data –Cross-section –Time-series –Panel data Variables –Continuous –Discrete including dummy variables –Proxy variables

14. Functional forms FunctionImplicit Price –Linear –Quadratic –Semi-log –Logarithm –Inverse

15. Functional forms - Diagnostics RESET test R 2 is of limited use Box-Cox test

16. Example using the SOEP data The German Socio-Economic Panel Study (SOEP) offers micro data for research in the social and economic sciences The SOEP is a wide-ranging representative longitudinal study of Germany‘s private households in Germany and provides information on all household members Some of the many topics include household composition, occupational biographies, employment, earnings, health and satisfaction indicators The Panel was started in 1984; in 2005, there were nearly 12,000 households, and more than 21,000 persons sampled We use data on the level of a household for the year 1997 and perform an OLS regression with one explanatory variable We try to explain differences in square meter by differences in household income

17. Example results. use "C:\data\kdd\data1.dta", clear (SOEP'97 (Kohler/Kreuter)). regress sqm hhinc Source | SS df MS Number of obs = 3126 -------------+------------------------------ F( 1, 3124) = 694.26 Model | 986537.128 1 986537.128 Prob > F = 0.0000 Residual | 4439145.82 3124 1420.98138 R-squared = 0.1818 -------------+------------------------------ Adj R-squared = 0.1816 Total | 5425682.95 3125 1736.21854 Root MSE = 37.696 ------------------------------------------------------------------------------ sqm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hhinc |.0165935.0006298 26.35 0.000.0153588.0178283 _cons | 55.76675 1.38561 40.25 0.000 53.04995 58.48355 ------------------------------------------------------------------------------

18. Results: The estimated coefficients How do square meters occupied change with higher income? What is the estimated size given a certain income? Are the results significant? What does the confidence interval tell us How does the estimated size for a household compare to the observed size? ------------------------------------------------------------------------------ sqm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hhinc |.0165935.0006298 26.35 0.000.0153588.0178283 _cons | 55.76675 1.38561 40.25 0.000 53.04995 58.48355 ------------------------------------------------------------------------------

19. Estimates and observed values

20. Results: Analysis of variance Sum of squares The model is able to explain only little of the TSS (MSS=TSS-RSS) The higher MSS and the smaller the RSS the „better“ is our model Degrees of freedom We have 3125 total degrees of freedom (n-1) of which 1 is consumed by the model, leaving 3124 for the residual Mean square error Defined as the residual sum of squares divided by the corresponding degrees of freedom Source | SS df MS -------------+------------------------------ Model | 986537.13 1 986537.128 Residual | 4439145.82 3124 1420.981 -------------+------------------------------ Total | 5425682.95 3125 1736.219

21. Results: Model fit The F-statistic Tests that all coefficients except the intercept are zero In our example it has 1 numerator and 3124 denominator degrees of freedom The R-squared MSS/TSS=1-RSS/TSS The adjusted R-squared Takes changes in k and n into account The root mean square error Root MSE= Number of obs = 3126 F( 1, 3124) = 694.26 Prob > F = 0.0000 R-squared = 0.1818 Adj R-squared = 0.1816 Root MSE = 37.696

22. Diagnostics Homoskedasticity: Expected value:

23. Diagnostics - 2. hettest Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of sqm chi2(1) = 119.04 Prob > chi2 = 0.0000

24. Multiple regression. regress sqm hhinc hhsize east owner Source | SS df MS Number of obs = 3125 -------------+------------------------------ F( 4, 3120) = 442.09 Model | 1962110.21 4 490527.553 Prob > F = 0.0000 Residual | 3461836.42 3120 1109.56295 R-squared = 0.3617 -------------+------------------------------ Adj R-squared = 0.3609 Total | 5423946.63 3124 1736.21851 Root MSE = 33.31 ------------------------------------------------------------------------------ sqm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hhinc |.0108534.0006002 18.08 0.000.0096766.0120301 hhsize | 3.044151.4817334 6.32 0.000 2.099605 3.988698 east | -9.290054 1.321768 -7.03 0.000 -11.88168 -6.69843 owner | 35.63969 1.290836 27.61 0.000 33.10872 38.17067 _cons | 48.69397 1.612865 30.19 0.000 45.53158 51.85635 ------------------------------------------------------------------------------