Instrumental variables I & II April 8, 2020 PMAP 8521: Program Evaluation for Public Service Andrew Young School of Policy Studies Spring 2020
Plan for today Endogeneity & exogeneity Instruments Using instruments IV with R Treatment effects & compliance
Endogeneity & exogeneity
<latexit sha1_base64="f2d68HvCsNx8Z8Bq9QBfTKlYx3E=">ACLnicbVBNSwMxFMzW7/pV9eglWARBKLtV0ItQFMGjglWhuyzZ9LUGs9kleSuWpb/Ii39FD4KePVnmLZ70NaBwDAzL8mbKJXCoOu+OaWp6ZnZufmF8uLS8spqZW39yiSZ5tDkiUz0TcQMSKGgiQIl3KQaWBxJuI7uTgb+9T1oIxJ1ib0Ugph1legIztBKYeXUR3jA/JRpJVTX9ENBj6gfAbLQpbsF82iRamejuUHMmpAaIe0tIqxU3Zo7BJ0kXkGqpMB5WHnx2wnPYlDIJTOm5bkpBjnTKLiEftnPDKSM37EutCxVLAYT5MN1+3TbKm3aSbQ9CulQ/T2Rs9iYXhzZMzw1ox7A/E/r5Vh5zDIhUozBMVHD3UySTGhg+5oW2jgKHuWMK6F/Svlt0wzjrbhsi3BG195klzVa95erX6xX20cF3XMk02yRXaIRw5Ig5yRc9IknDySZ/JOPpwn59X5dL5G0ZJTzGyQP3C+fwAfJaiW</latexit> Does education cause higher earnings? Earnings Education Earnings i = � 0 + � 1 Education i + ✏ i Outcome variable Policy/program variable
<latexit sha1_base64="f2d68HvCsNx8Z8Bq9QBfTKlYx3E=">AAACLnicbVBNSwMxFMzW7/pV9eglWARBKLtV0ItQFMGjglWhuyzZ9LUGs9kleSuWpb/Ii39FD4KKePVnmLZ70NaBwDAzL8mbKJXCoOu+OaWp6ZnZufmF8uLS8spqZW39yiSZ5tDkiUz0TcQMSKGgiQIl3KQaWBxJuI7uTgb+9T1oIxJ1ib0Ugph1legIztBKYeXUR3jA/JRpJVTX9ENBj6gfAbLQpbsF82iRamejuUHMmpAaIe0tIqxU3Zo7BJ0kXkGqpMB5WHnx2wnPYlDIJTOm5bkpBjnTKLiEftnPDKSM37EutCxVLAYT5MN1+3TbKm3aSbQ9CulQ/T2Rs9iYXhzZZMzw1ox7A/E/r5Vh5zDIhUozBMVHD3UySTGhg+5oW2jgKHuWMK6F/Svlt0wzjrbhsi3BG195klzVa95erX6xX20cF3XMk02yRXaIRw5Ig5yRc9IknDySZ/JOPpwn59X5dL5G0ZJTzGyQP3C+fwAfJaiW</latexit> If we ran this regression, would β 1 give us the causal effect of education? Earnings i = � 0 + � 1 Education i + ✏ i No! Omitted variable bias! Unclosed backdoors! Endogeneity!
Exogeneity and endogeneity Exogenous variables Value is not determined by In a DAG, a node that doesn’t anything else in the model have arrows coming into it Earnings Education is exogenous here Education
Exogeneity and endogeneity Endogenous variables Value is determined by In a DAG, a node that has something else in the model arrows coming into it Ability Education is endogenous now Earnings Education
<latexit sha1_base64="f2d68HvCsNx8Z8Bq9QBfTKlYx3E=">AAACLnicbVBNSwMxFMzW7/pV9eglWARBKLtV0ItQFMGjglWhuyzZ9LUGs9kleSuWpb/Ii39FD4KKePVnmLZ70NaBwDAzL8mbKJXCoOu+OaWp6ZnZufmF8uLS8spqZW39yiSZ5tDkiUz0TcQMSKGgiQIl3KQaWBxJuI7uTgb+9T1oIxJ1ib0Ugph1legIztBKYeXUR3jA/JRpJVTX9ENBj6gfAbLQpbsF82iRamejuUHMmpAaIe0tIqxU3Zo7BJ0kXkGqpMB5WHnx2wnPYlDIJTOm5bkpBjnTKLiEftnPDKSM37EutCxVLAYT5MN1+3TbKm3aSbQ9CulQ/T2Rs9iYXhzZZMzw1ox7A/E/r5Vh5zDIhUozBMVHD3UySTGhg+5oW2jgKHuWMK6F/Svlt0wzjrbhsi3BG195klzVa95erX6xX20cF3XMk02yRXaIRw5Ig5yRc9IknDySZ/JOPpwn59X5dL5G0ZJTzGyQP3C+fwAfJaiW</latexit> Exogeneity and endogeneity Endogeneity The error term ( ϵ ) is related to the explanatory variables Earnings i = � 0 + � 1 Education i + ✏ i Education is related to some part of this this unobserved stuff ϵ
What would exogenous variation in education look like? Choices to get more education that are essentially random (or at least uncorrelated with omitted variables)
We’d like education to be exogenous (an outside decision or intervention) , but it’s not! Ability Earnings Education Part of it is exogenous, but part of it is caused by ability, which is in the DAG
<latexit sha1_base64="L5L3hnZliv7KHVqvDVDaHuU4+Yc=">ACR3icbVDLSgMxFM3Ud31VXboJFkEQykwVdCP4QHBZwVahrUMmva2hmcyQ3BHL0L9z49adv+DGhSIuzbQj+DoQOJxz7k1yglgKg675BQmJqemZ2bnivMLi0vLpZXVhokSzaHOIxnpq4AZkEJBHQVKuIo1sDCQcBn0TzL/8ha0EZG6wEM7ZD1lOgKztBKfum6hXCH6SnTSqieGfqCHtBWAMh8l27nzKN5qpOM57LYl1nNzaNASIGDYWZAbIS064VfKrsVdwT6l3g5KZMcNb/02OpEPAlBIZfMmKbnxthOmUbBJQyLrcRAzHif9aBpqWIhmHY6mFIN63Sod1I26OQjtTvEykLjRmEgU2GDG/Mby8T/OaCXb326lQcYKg+PibiIpRjQrlXaEBo5yYAnjWti3Un7DNONoqy/aErzfX/5LGtWKt1Opnu+WD4/zOmbJOtkgW8Qje+SQnJEaqRNO7skzeSVvzoPz4rw7H+Nowcln1sgPFJxPQTexjA=</latexit> Fixing endogeneity with DAGs Ability Earnings Education Close back door and adjust for ability Filters out the endogenous part of education and leaves us with just the exogenous part Earnings i = � 0 + � 1 Education i + � 2 Ability + ✏ i
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<latexit sha1_base64="f2d68HvCsNx8Z8Bq9QBfTKlYx3E=">ACLnicbVBNSwMxFMzW7/pV9eglWARBKLtV0ItQFMGjglWhuyzZ9LUGs9kleSuWpb/Ii39FD4KePVnmLZ70NaBwDAzL8mbKJXCoOu+OaWp6ZnZufmF8uLS8spqZW39yiSZ5tDkiUz0TcQMSKGgiQIl3KQaWBxJuI7uTgb+9T1oIxJ1ib0Ugph1legIztBKYeXUR3jA/JRpJVTX9ENBj6gfAbLQpbsF82iRamejuUHMmpAaIe0tIqxU3Zo7BJ0kXkGqpMB5WHnx2wnPYlDIJTOm5bkpBjnTKLiEftnPDKSM37EutCxVLAYT5MN1+3TbKm3aSbQ9CulQ/T2Rs9iYXhzZMzw1ox7A/E/r5Vh5zDIhUozBMVHD3UySTGhg+5oW2jgKHuWMK6F/Svlt0wzjrbhsi3BG195klzVa95erX6xX20cF3XMk02yRXaIRw5Ig5yRc9IknDySZ/JOPpwn59X5dL5G0ZJTzGyQP3C+fwAfJaiW</latexit> <latexit sha1_base64="L5L3hnZliv7KHVqvDVDaHuU4+Yc=">ACR3icbVDLSgMxFM3Ud31VXboJFkEQykwVdCP4QHBZwVahrUMmva2hmcyQ3BHL0L9z49adv+DGhSIuzbQj+DoQOJxz7k1yglgKg675BQmJqemZ2bnivMLi0vLpZXVhokSzaHOIxnpq4AZkEJBHQVKuIo1sDCQcBn0TzL/8ha0EZG6wEM7ZD1lOgKztBKfum6hXCH6SnTSqieGfqCHtBWAMh8l27nzKN5qpOM57LYl1nNzaNASIGDYWZAbIS064VfKrsVdwT6l3g5KZMcNb/02OpEPAlBIZfMmKbnxthOmUbBJQyLrcRAzHif9aBpqWIhmHY6mFIN63Sod1I26OQjtTvEykLjRmEgU2GDG/Mby8T/OaCXb326lQcYKg+PibiIpRjQrlXaEBo5yYAnjWti3Un7DNONoqy/aErzfX/5LGtWKt1Opnu+WD4/zOmbJOtkgW8Qje+SQnJEaqRNO7skzeSVvzoPz4rw7H+Nowcln1sgPFJxPQTexjA=</latexit> But we can’t measure ability! Ability Earnings Education Unmeasurable! Earnings i = � 0 + � 1 Education i + � 2 Ability + ✏ i Ability is in here Earnings i = � 0 + � 1 Education i + ✏ i
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