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

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.

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)  Indicator 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 squares

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

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 ).

Estimates and Tests

Estimates and Tests - Results

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)

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)

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)

Specification Tests Conducted on Models - III

Ordinary Least Squares with Robust Standard Errors

Model 1 – OLS with Robust Standard Errors - I

Jarque-Bera Test White’s Test

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 study

Weighted Least Squares – Model 2 – w i = 1/s 2 {d i }

Model 2 – Specification Tests

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 =  F obs = , P =.0234 While for Model 2:  R 2 =  F obs = , P =.0020