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Valuation 4: Econometrics

Valuation 4: Econometrics. Why econometrics? What are the tasks? Specification and estimation Hypotheses testing Example study. Last week we looked at. What is so special about environmental goods? Theory of consumer demand for market goods

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Valuation 4: Econometrics

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  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 a and b 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 – R2

  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 • R2 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. 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? Results: The estimated coefficients ------------------------------------------------------------------------------ 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. 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 Results: Analysis of variance 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 Expected value: Homoskedasticity:

  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 ------------------------------------------------------------------------------

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