Valuation 4 econometrics
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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
Valuation 4: Econometrics

  • Why econometrics?

  • What are the tasks?

  • Specification and estimation

  • Hypotheses testing

  • Example study


Last week we looked at
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


Why econometrics
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


What are the tasks
What are the tasks?

  • Specification

    • From an economic model

      to an econometric model

  • Estimation

  • Testing hypotheses

  • Predictions


Specification the function
Specification – the function

  • Include all relevant exogenous variables

  • Functional form: linear relationship?

  • Estimates parameters for a and b are constant for all observations


Specification disturbance 1
Specification – disturbance (1)

  • Expected value is zero


Specification disturbance 2
Specification – disturbance (2)

  • Variance is constant

    • Homoscedasticity vs. heteroscedasticity


Specification disturbance 3
Specification – disturbance (3)

  • disturbances are not autocorrelated

  • disturbances are normally distributed



Ols point estimates
OLS - Point estimates

disturbance vs. residual



Ols hypotheses testing
OLS – hypotheses testing

  • T-test

  • F-Test

  • P values


Data and variables
Data and variables

  • Data

    • Cross-section

    • Time-series

    • Panel data

  • Variables

    • Continuous

    • Discrete including dummy variables

    • Proxy variables


Functional forms
Functional forms

FunctionImplicit Price

  • Linear

  • Quadratic

  • Semi-log

  • Logarithm

  • Inverse


Functional forms diagnostics
Functional forms - Diagnostics

  • RESET test

  • R2 is of limited use

  • Box-Cox test


Example using the soep data
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


Example results
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

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


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?

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

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



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

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


Results model fit
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


Diagnostics
Diagnostics

Expected value:

Homoskedasticity:


Diagnostics 2
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


Multiple regression
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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