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Meta-Analysis and Meta-Regression Meta-Analysis and Meta-Regression

Meta-Analysis and Meta-Regression - PowerPoint Presentation

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Meta-Analysis and Meta-Regression - PPT Presentation

Airport Noise and Home Values JP Nelson 2004 MetaAnalysis of Airport Noise and Hedonic Property Values Problems and Prospects Journal of Transport Economics and Policy Vol 38 Part 1 pp 128 ID: 384701

squares model standard test model squares test standard models meta ndi errors airport noise weighted fit tests regression robust values predictors specification

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Slide1

Meta-Analysis and Meta-Regression

Airport Noise and Home Values

J.P. Nelson (2004). “Meta-Analysis of Airport Noise and Hedonic Property Values: Problems and Prospects,”

Journal of Transport Economics and Policy

, Vol. 38, Part 1, pp. 1-28.Slide2

Data Description

Results from 20 Studies (containing 33 separate estimates), relating home prices to airport noise. All studies in US and Canada, from 1967 to present

Regressions control for other factors including: structural variables (e.g. size), locational variables, local taxes, government services, and environmental quality.

Primary Variable: Noise Depreciation Index (NDI) and its Regression coefficient (effect of increasing airport noise by 1 decibel on house cost). Positive coefficient implies that as noise increases, home value decreases. The units are percent depreciation.Slide3

Study Specific Variables / Models

For each study (with several exceptions), there are:

Noise Depreciation Index (NDI) and its estimated standard error

Mean Real Property Value (Year 2000, US $1000s)

An indicator of whether accessibility (to airport) adjustment was made (1 if No Adjustment, 0 if Adjustment was made)

Sample Size (log scale)

I

ndicator of whether the response (price) scale was linear (1 if Linear, 0 if Log)

Indicator of whether airport was in Canada (1 if Canada, 0 if US)

Models Considered

Fixed and Random Effects Meta-Analyses with no covariates

Meta-Regressions with predictors: Ordinary Least Squares with robust standard errors and Weighted Least squaresSlide4

Data

Note: Due to missing data, analyses will be based on only 31 or 29 airports.Slide5

Meta-Analysis with No Covariates

Fixed Effects Model – Assumes that each airport has the same true NDI, and that all variation is due to sampling error

Random Effects Model – Allows true NDIs to vary among airports along some assumed Normal Distribution.

Test for Homogeneity (Fixed Effects) can be conducted after estimating the mean (Hedges and

Olkin

, 1985, pp.122-123).Slide6

Estimates and TestsSlide7

Estimates and Tests - ResultsSlide8

Meta-Regressions

Regressions to determine which (if any) factors are associated with NDI

Three Models Fit:

Ordinary Least Squares with robust standard errors (White’s

heteroscedastic

-consistent standard errors)

Weighted Least Squares with weights equal to the inverse variance of the NDI:

w

i = 1/s

2

{d

i

}Weighted Least Squares with weights equal to the inverse

standard error

of the NDI:

w

i

=

1/s{d

i

}Model 1 based on k = 31 airports (2 have no Mean property values)

Models 2 and 3 based on k = 29 airports (2 have no weights)Slide9

Specification Tests Conducted on Models - I

Ramsey’s RESET Test – Used to test whether the model is correctly specified and does not involve any nonlinearities among the

regressors

.

Step 1: Fit the Original Regression with all Predictors

Step 2: Fit Regression with same predictors and squared (and possibly higher order) fitted values from first model.

Conduct F-test or t-test on polynomial fitted value(s)Slide10

Specification Tests Conducted on Models - II

White’s Test for

Heteroscedasticity

Step 1: Fit the Original Regression with all Predictors

Step 2

: Fit Regression relating squared residuals from step 1 to the same predictors and squared values for all numeric predictors (other version includes interactions for general specification test)

Compare nR

2

with Chi-Square(df

= # Predictors in Step 2)Slide11

Specification Tests Conducted on Models - IIISlide12

Ordinary Least Squares with Robust Standard ErrorsSlide13

Model 1 – OLS with Robust Standard Errors - ISlide14

Model 1 – OLS with Robust Standard Errors - I

Jarque-Bera

Test

White’s

TestSlide15

Weighted Least Squares – Models 2 and 3

Clearly Model 1 provides a poor fit (non-significant F-Statistic (p=.0826), R

2

=.3086)

Models 2 and 3 Use Weighted Least Squares with weights equal to the Variances and the Standard Errors, respectively, of the NDI estimates from each studySlide16

Weighted Least Squares – Model 2 – w

i

= 1/s

2

{d

i

}Slide17

Weighted Least Squares – Model 2 – w

i

= 1/s

2

{d

i

}Slide18

Model 2 – Specification TestsSlide19

Model 3 – WLS –

w

i

= 1/s{

d_i

}

This is a more traditional weighting scheme than Model2

The fit however, for this analysis is not as good:R

2 = 0.4131Fobs

= 3.2380, P = .0234

While for Model 2:

R

2 = 0.5389

F

obs

=

5.3756,

P = .

0020