Proxy variables(continued) Without out assumptions can end up with biased estimates ◆Sayx3*=8o+81x1+62x2+82x3+v e Then really running y=(Bo+ B35)+(B+ B31)x计+(2+B302)x2+B3O3x3+(+B3v3) e Bias will depend on signs of B3 and This bias may still be smaller than omitted variable bias, though Economics 20- Prof anderson 10Economics 20 - Prof. Anderson 10 Proxy Variables (continued) Without out assumptions, can end up with biased estimates Say x3* = d0 + d1 x1 + d2 x2 + d3 x3 + v3 Then really running y = (b0 + b3d0 ) + (b1 + b3d1 ) x1+ (b2 + b3d2 ) x2 + b3d3 x3 + (u + b3 v3 ) Bias will depend on signs of b3 and dj This bias may still be smaller than omitted variable bias, though