Table 1: Finite-sample behavior of ̂ 𝛽 𝛽 𝑦 : mean and standard deviation.

DGP parametersSample size
𝛽 𝑦 𝜇 𝑥 Statistic50100200500700

−0.9−1.5Mean 𝟏 . 𝟓 𝟏 𝟎 𝟐 𝟑 . 𝟏 𝟏 𝟎 𝟑 𝟕 . 𝟖 𝟏 𝟎 𝟒 𝟖 . 𝟔 𝟏 𝟎 𝟓 𝟓 . 𝟔 𝟏 𝟎 𝟓
Stand.dev. ( 1 . 8 1 0 3 ) ( 1 . 7 1 0 4 ) ( 1 . 8 1 0 5 ) ( 1 . 1 1 0 6 ) ( 3 . 9 1 0 7 )
−0.75Mean 𝟏 . 𝟓 𝟏 𝟎 𝟐 𝟑 . 𝟑 𝟏 𝟎 𝟑 𝟕 . 𝟔 𝟏 𝟎 𝟒 𝟏 . 𝟎 𝟏 𝟎 𝟒 𝟓 . 𝟑 𝟏 𝟎 𝟓
Stand.dev. ( 1 . 9 1 0 3 ) ( 1 . 6 1 0 4 ) ( 1 . 8 1 0 5 ) ( 1 . 1 1 0 6 ) ( 3 . 9 1 0 7 )
0.75Mean 𝟏 . 𝟒 𝟏 𝟎 𝟐 𝟑 . 𝟐 𝟏 𝟎 𝟑 𝟖 . 𝟎 𝟏 𝟎 𝟒 𝟏 . 𝟎 𝟏 𝟎 𝟒 𝟓 . 𝟖 𝟏 𝟎 𝟓
Stand.dev. ( 1 . 7 1 0 3 ) ( 1 . 6 1 0 4 ) ( 1 . 8 1 0 5 ) ( 1 . 0 1 0 6 ) ( 3 . 9 1 0 7 )
1.5Mean 𝟏 . 𝟓 𝟏 𝟎 𝟐 𝟑 . 𝟎 𝟏 𝟎 𝟑 𝟕 . 𝟐 𝟏 𝟎 𝟒 𝟏 . 𝟎 𝟏 𝟎 𝟒 𝟓 . 𝟖 𝟏 𝟎 𝟓
Stand.dev. ( 1 . 8 1 0 3 ) ( 1 . 6 1 0 4 ) ( 1 . 8 1 0 5 ) ( 1 . 1 1 0 6 ) ( 3 . 9 1 0 7 )

0.9−1.5Mean 𝟐 . 𝟐 𝟏 𝟎 𝟑 𝟔 . 𝟐 𝟏 𝟎 𝟒 𝟏 . 𝟒 𝟏 𝟎 𝟒 𝟐 . 𝟏 𝟏 𝟎 𝟓 𝟏 . 𝟏 𝟏 𝟎 𝟓
Stand.dev. ( 2 . 4 1 0 4 ) ( 2 . 8 1 0 5 ) ( 3 . 4 1 0 6 ) ( 2 . 1 1 0 7 ) ( 8 . 0 1 0 8 )
−0.75Mean 𝟐 . 𝟒 𝟏 𝟎 𝟑 𝟔 . 𝟎 𝟏 𝟎 𝟒 𝟏 . 𝟓 𝟏 𝟎 𝟒 𝟏 . 𝟗 𝟏 𝟎 𝟓 𝟏 . 𝟕 𝟏 𝟎 𝟓
Stand.dev. ( 2 . 3 1 0 4 ) ( 2 . 8 1 0 5 ) ( 3 . 4 1 0 6 ) ( 2 . 2 1 0 7 ) ( 7 . 9 1 0 8 )
0.75Mean 𝟐 . 𝟒 𝟏 𝟎 𝟑 𝟓 . 𝟖 𝟏 𝟎 𝟒 𝟏 . 𝟑 𝟏 𝟎 𝟒 𝟐 . 𝟐 𝟏 𝟎 𝟓 𝟓 . 𝟒 𝟏 𝟎 𝟔
Stand.dev. ( 2 . 3 1 0 4 ) ( 2 . 9 1 0 5 ) ( 3 . 5 1 0 6 ) ( 2 . 2 1 0 7 ) ( 8 . 0 1 0 8 )
1.5 Mean 𝟐 . 𝟐 𝟏 𝟎 𝟑 𝟓 . 𝟔 𝟏 𝟎 𝟒 𝟏 . 𝟐 𝟏 𝟎 𝟒 𝟐 . 𝟏 𝟏 𝟎 𝟓 𝟏 . 𝟏 𝟏 𝟎 𝟓
Stand.dev. ( 2 . 4 1 0 4 ) ( 2 . 9 1 0 5 ) ( 3 . 4 1 0 6 ) ( 2 . 2 1 0 7 ) ( 7 . 9 1 0 8 )