50.2 Coefficient stability

(Oster 2019)

  • Coefficient stability can be evident against omitted variable bias.

  • But coefficient stability alone can be misleading, but combing with \(R^2\) movement, it can become informative.

Packages

  • mplot: graphical Model stability and Variable Selection

  • robomit: Robustness checks for omitted variable bias (implementation of

library(robomit)

# estimate beta 
o_beta(
  y     = "mpg",       # dependent variable
  x     = "wt",        # independent treatment variable
  con   = "hp + qsec", # related control variables
  delta = 1,           # delta
  R2max = 0.9,         # maximum R-square
  type  = "lm",        # model type
  data  = mtcars       # dataset
) 
#> # A tibble: 10 × 2
#>    Name                           Value
#>    <chr>                          <dbl>
#>  1 beta*                         -2.00 
#>  2 (beta*-beta controlled)^2      5.56 
#>  3 Alternative Solution 1        -7.01 
#>  4 (beta[AS1]-beta controlled)^2  7.05 
#>  5 Uncontrolled Coefficient      -5.34 
#>  6 Controlled Coefficient        -4.36 
#>  7 Uncontrolled R-square          0.753
#>  8 Controlled R-square            0.835
#>  9 Max R-square                   0.9  
#> 10 delta                          1

References

Oster, Emily. 2019. “Unobservable Selection and Coefficient Stability: Theory and Evidence.” Journal of Business & Economic Statistics 37 (2): 187–204.