Table 1.
Summary: Univariate case.
Fig 1.
Comparison ratio IV/OLS vs treatment effect/OLS.
Notes: This figure plots the ratio between the IV and OLS estimates on the vertical axis and the ratio between the Treatment effect and OLS estimates on the horizontal axis. The red line is the function given by the equality of the two axis. Data are distributed on this line for any value of the ratios suggesting there is no difference between high and low values of the IV/OLS ratio.
Table 2.
Comparison of delta: True (i.e. simulated) versus estimated.
Table 3.
Comparison of delta: Estimated versus true (i.e. simulated).
Table 4.
Frequency.
Fig 2.
Distribution of the treatment effect and estimators.
Notes: This figure plots the distribution of the treatment effect and the three estimators considered in this paper: OLS, IV and Oster for the samples in which the sign of the coefficient of proportionality δ is correctly estimated (i.e. 9,668 samples out of 10,000). Given the structure of the samples the OLS and Oster estimators are respectively a lower- and upper- bound of the Treatment effect. This figure indicates that, in this setting, the Oster estimator is more accurate than the OLS estimator. In particular, this is the case for 90% of the samples.
Fig 3.
Decision tree for estimating and interpreting δ.
Table 5.
Checklist for interpreting the coefficient of proportionality δ.
Table 6.
Comparison of OLS and IV estimates.
Table 7.
Comparison of OLS and IV estimates.
Table 8.
Comparison of OLS and IV estimates.
Table 9.
Comparison of OLS and IV estimates.