Dear Statalist,

I'm asking for advice to solve a problem with my meta-regression model based on a WLS regression:
I'm using a dataset of 538 observations from 80 hedonic pricing studies that all report the price discount that houses experience due to the proximity to a negative environmental externality.
In my meta-regression model, I try to explain the variance of effect sizes across studies through 20 study characteristics that are, among others, the location in which the study was conducted, the type of negative externality, quality indicators for the original hedonic regression and most importantly the mean distance of the houses in each respective study. I expect that, when the average house in a given study is located more distant, then the reported effect size should be smaller, c.p. However, my regression results point significantly (p<0.01) to the opposite, indicating that, being closer to a negative externality is beneficial for the house prices, which is certainly counterintuitive.

I'm using
Code:
reg y x1 x2 ... x19 x_distance [aw=precision_sq], cluster(ID_Study)
where precision_sq is the squared precision of each estimate i.e. the inverse of each estimates squared standard error, as advised by
Stanley TD, Doucouliagos H (2012) Meta-regression analysis in economics and business. Routledge (p.69)
to give comparatively more weight to more precise estimates and to correct for heteroscedasticity.

I looked for outlying or influential observations, checked for multicollinearity, thought about omitted variables and used different definitions of the distance variable with no problem detected and robust "wrong" sign and significance.
However, when considering simple partial correlations, using WLS with a different weight (sample size) or using OLS instead, the coefficient on the distance variable takes the expected sign and is significant. Additionally, several other coefficients change sign and significance as well.

Does anyone have an idea why using WLS with precision squared as weight results in remarkably different results at least for some variables? As weighting by precision is the standard approach, it might be hard to abandon this approach.

I highly aprreciate your efforts and thank you in advance.

Kind regards

Marvin Schütt