You are interested in estimating the following model: Y₁ Bo + B₁Y21 + B₂X11 + B3X21 + ni but are worried about the endogeneity of Y₂, you have 2 potential instruments, denoted Z₁, and Z₂. You have n = 100 observations and estimate the following models by OLS: Dep. Variable Y Y₁ Y₁ Y₁ Y₂ Y₂ Y₂ 2.251 2.114 0.457 constant Y₂ X₁ X₂ Y₂ û 17 ĥ 0.119 2.889 1.765 -1.004 -0.883-1.269 0.249 0.086 0.221 0.294 1.221 1.001 0.992 0.823 0.445 0.557 0.678 0.125 0.064 0.178 -0.665 1.229 0.886 1.005 -0.216 -0.042 -0.142 -0.707-0.882-0.802 0.221 Y₁ Z₁ Z₂ RSS 0.446 14.20 14.85 13.76 0.233 -0.112 0.345 0.445 0.141 0.345 -0.292 -0.118 -0.097 14.06 10.02 11.59 9.85 6.99 7.33 0.114 -0.162 6.62 where û are the residuals and Y₂ are the fitted values from the appropriate 1st stage regression. The test for instrument relevance is (2 decimal places):

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You are interested in estimating the following model:
Y₁ Bo + B₁Y21 + B₂X11 + B3X21 + ni
but are worried about the endogeneity of Y₂, you have 2 potential instruments, denoted Z₁, and Z₂. You have n = 100
observations and estimate the following models by OLS:
Dep. Variable Y Y₁ Y₁ Y₁ Y₂ Y₂ Y₂
2.251 2.114
0.457
constant
Y₂
X₁
X₂
Y₂
û
Y₁
Z₁
Z₂
RSS
Answer:
17
2.889 1.765 -1.004 -0.883-1.269 0.249 0.086
0.119
0.221
0.294
1.221 1.001 0.992 0.823 0.445 0.557 0.678 0.125 0.064 0.178
0.886 1.005 -0.216 -0.042 -0.142
-0.707-0.882-0.802
-0.665 1.229
0.221
0.446
ĥ
0.233
-0.112 0.345
0.445 0.141
0.345 -0.292
-0.118 -0.097
14.20 14.85 13.76 14.06 10.02 11.59 9.85 6.99 7.33
0.114
-0.162
6.62
where û are the residuals and Y₂ are the fitted values from the appropriate 1st stage regression. The test for instrument
relevance is (2 decimal places):
Transcribed Image Text:You are interested in estimating the following model: Y₁ Bo + B₁Y21 + B₂X11 + B3X21 + ni but are worried about the endogeneity of Y₂, you have 2 potential instruments, denoted Z₁, and Z₂. You have n = 100 observations and estimate the following models by OLS: Dep. Variable Y Y₁ Y₁ Y₁ Y₂ Y₂ Y₂ 2.251 2.114 0.457 constant Y₂ X₁ X₂ Y₂ û Y₁ Z₁ Z₂ RSS Answer: 17 2.889 1.765 -1.004 -0.883-1.269 0.249 0.086 0.119 0.221 0.294 1.221 1.001 0.992 0.823 0.445 0.557 0.678 0.125 0.064 0.178 0.886 1.005 -0.216 -0.042 -0.142 -0.707-0.882-0.802 -0.665 1.229 0.221 0.446 ĥ 0.233 -0.112 0.345 0.445 0.141 0.345 -0.292 -0.118 -0.097 14.20 14.85 13.76 14.06 10.02 11.59 9.85 6.99 7.33 0.114 -0.162 6.62 where û are the residuals and Y₂ are the fitted values from the appropriate 1st stage regression. The test for instrument relevance is (2 decimal places):
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