08_Computer-Assisted Mass Valuation Flashcards
Computer-Assisted Mass Appraisal
- to identify relationship between property attributes (age, size, location) and prices that have been paid for them
- Application: Residential Properties
- Reliability: large quantity of data
Steps in Computer-Assited Mass Appraisal
1. Definition of Problem
2. Preliminiary Analysis + Data Collection
3. Demand and supply data, property characteristics: location, neighbourhood and structure
4. Model building and calibration
5. Model testing and quality control
6. Assesment
Hedonic Valuation
identifies price factors according to price that is determined both by internal characteristics of good and external environmental characteristics
1. Consider characteristics of a house
- # of floors, presence of garden, # of bedrooms, # of bathrooms, sqm of house, type of house, age garage, etc.
2. Consider external environmental characteristics
- accessibility to schools, shopping, sport facilities, public transport, etc.
Composite goods has a price, how about implicit price for each characteristic?
Hedonic Valuation
Constraints in Maximization problem
- income
- price of house
- level of taxes
-> housing market gives us information on buyers preferences for housing e.g. structure and environmental characteristics
Hedonic Pricing
Definition
- method applies simple concept to characteristics of property (land) price
- Willingness to pay (WTP) determined b y price difference between houses that have different levels of structural and locational quality
-> assess value of environmental quality according to market prices of residential properties
-> variation in environmental quality affects price of housing
Hedonic Price
Formula
- derivative function with respect to one of characteristics (k) is implicit price of k, or consumer is willing to pay p(k) for a marginal change of characteristics of k
implicit Price = d(p) / d(x(k))
p = f(x1, x2, …, xk)
e.g. housing price and # of bedrooms p(i) = 500 + 100n(i)
Regression Model
Formula
y(i) = b(1) + b(2) * x(i) + e(i)
e(i) = error term, difference between observed y(i) and estimated y(i) (noise)
Y(i) = dependent or endogenous variable or variable to be explained at observation time i
x(i) = independent or exogenous or explaining variable (regressor)at time i
beta = regression coefficient
Linear Regression model
Definition
- modeling a linear relationship between a dependent variable to be explained and one or several explaining (independent) variables
- simple linear regression when single explaining variable
- multiple linear regression otherwise
Function Form of Linear Regression Model
- linear means that parameters are included linearly in the model
- doesn
- t imply there has to be a linear relationship between variables
- if no linear relationship between variables linear regressin model can nevertheless be applied in certain cases by transforming one or several explanatroy variabels or the entire model
Additional examples for models which are linear in the parameters
Linear Regression Model
− Yt=β1+β2Xt+ut
− Yt=β1+β2ln(Xt)+ut
− ln(Yt)=β1+β2Xt+ut
− ln(Yt)=β1+ β2ln(Xt)+ut
− Yt=β1+β2Xt2+ut
We observe 10 transactions:
Interpretation:
ln( yˆi) = 2.51 + 0.66 ln(x1i) + 0.67x2i
- Keeping the presence of park in the nearby area constant, 1% increase in no. of bedrooms will increase the house price by 0.66% on average.
- Keeping the number of bedroom constant, the presence of park in the nearby area will increase the house price by 67% on average.
Pros and Cons of Log-Transformation
Pros
- decrease heteroskedasticity in data
- model the non-loinear relationship using linear regression: diminishing marginal utility
- simplify a model e.g. sometimes log can simplify number and complexity of interaction terms
- interpret the implicit price in % changes
Cons
- can destroy normal distribution of data sometimes
natural logarithm is probably most widespread transformation
- Implications
linear regression
- interpretation of slope parameter must be adjusted accordingly
1. Level- log
Y and ln(X)
∆Y= (β1 / 100) %∆X
2. Log-Level
ln(Y) and X
%∆Y = (100 * β1 ∆x
3. Log-log
ln(Y) and ln(X)
%∆Y = %β1∆X
Model Evaluation
Dimensions
2 items
Global Evaluation
- can model explain data generating process of dependent variables as a whole?
Global Criteria
- coefficient of determination
- adjusted coefficient ofdetermination
Coefficient of Determination
Model Evaluation (Global Criteria)
R-squared
- proportion of variance explained by regression model (variance of estimated Y) with respect to total variance of observations of Y
- frequently indicated in %
R^2= ssy(expected)ˆ2 / ssy(total variance)^2
