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I N ST R U M E N TA L VA R I A B L E S I PMAP 8521: Program Evaluation for Public Service November 11, 2019 Fill out your reading report on iCollege! P L A N F O R T O D A Y Endogeneity and exogeneity Instruments Using instruments IV

  1. I N ST R U M E N TA L VA R I A B L E S I PMAP 8521: Program Evaluation for Public Service November 11, 2019 Fill out your reading report on iCollege!

  2. P L A N F O R T O D A Y Endogeneity and exogeneity Instruments Using instruments IV regression with R

  3. E N D O G E N E I T Y & E XO G E N E I T Y

  4. <latexit sha1_base64="f2d68HvCsNx8Z8Bq9QBfTKlYx3E=">ACLnicbVBNSwMxFMzW7/pV9eglWARBKLtV0ItQFMGjglWhuyzZ9LUGs9kleSuWpb/Ii39FD4KePVnmLZ70NaBwDAzL8mbKJXCoOu+OaWp6ZnZufmF8uLS8spqZW39yiSZ5tDkiUz0TcQMSKGgiQIl3KQaWBxJuI7uTgb+9T1oIxJ1ib0Ugph1legIztBKYeXUR3jA/JRpJVTX9ENBj6gfAbLQpbsF82iRamejuUHMmpAaIe0tIqxU3Zo7BJ0kXkGqpMB5WHnx2wnPYlDIJTOm5bkpBjnTKLiEftnPDKSM37EutCxVLAYT5MN1+3TbKm3aSbQ9CulQ/T2Rs9iYXhzZMzw1ox7A/E/r5Vh5zDIhUozBMVHD3UySTGhg+5oW2jgKHuWMK6F/Svlt0wzjrbhsi3BG195klzVa95erX6xX20cF3XMk02yRXaIRw5Ig5yRc9IknDySZ/JOPpwn59X5dL5G0ZJTzGyQP3C+fwAfJaiW</latexit> O U R F A V O R I T E Q U E S T I O N Does education cause higher earnings? Earnings i = � 0 + � 1 Education i + ✏ i Outcome variable Policy/program variable

  5. <latexit sha1_base64="f2d68HvCsNx8Z8Bq9QBfTKlYx3E=">ACLnicbVBNSwMxFMzW7/pV9eglWARBKLtV0ItQFMGjglWhuyzZ9LUGs9kleSuWpb/Ii39FD4KePVnmLZ70NaBwDAzL8mbKJXCoOu+OaWp6ZnZufmF8uLS8spqZW39yiSZ5tDkiUz0TcQMSKGgiQIl3KQaWBxJuI7uTgb+9T1oIxJ1ib0Ugph1legIztBKYeXUR3jA/JRpJVTX9ENBj6gfAbLQpbsF82iRamejuUHMmpAaIe0tIqxU3Zo7BJ0kXkGqpMB5WHnx2wnPYlDIJTOm5bkpBjnTKLiEftnPDKSM37EutCxVLAYT5MN1+3TbKm3aSbQ9CulQ/T2Rs9iYXhzZMzw1ox7A/E/r5Vh5zDIhUozBMVHD3UySTGhg+5oW2jgKHuWMK6F/Svlt0wzjrbhsi3BG195klzVa95erX6xX20cF3XMk02yRXaIRw5Ig5yRc9IknDySZ/JOPpwn59X5dL5G0ZJTzGyQP3C+fwAfJaiW</latexit> Would β 1 in this regression give us the causal effect of the program? Earnings i = � 0 + � 1 Education i + ✏ i Omitted variable bias! Selection bias! Endogeneity!

  6. T Y P E S O F V A R I A T O N Exogenous variables Value is not determined by anything else in the model In a DAG, a node that doesn’t have arrows coming into it

  7. T Y P E S O F V A R I A T O N Endogenous variables Value is determined by something else in the model In a DAG, a node that has arrows coming into it

  8. We’d like education to be exogenous (an outside decision or intervention) , but it’s not! Part of it is exogenous, but part of it is caused by ability, which is in the model

  9. How can we fix the endogeneity? Close back door and adjust for ability Filters out the endogenous part of education and leaves us with just the exogenous part

  11. <latexit sha1_base64="f2d68HvCsNx8Z8Bq9QBfTKlYx3E=">ACLnicbVBNSwMxFMzW7/pV9eglWARBKLtV0ItQFMGjglWhuyzZ9LUGs9kleSuWpb/Ii39FD4KePVnmLZ70NaBwDAzL8mbKJXCoOu+OaWp6ZnZufmF8uLS8spqZW39yiSZ5tDkiUz0TcQMSKGgiQIl3KQaWBxJuI7uTgb+9T1oIxJ1ib0Ugph1legIztBKYeXUR3jA/JRpJVTX9ENBj6gfAbLQpbsF82iRamejuUHMmpAaIe0tIqxU3Zo7BJ0kXkGqpMB5WHnx2wnPYlDIJTOm5bkpBjnTKLiEftnPDKSM37EutCxVLAYT5MN1+3TbKm3aSbQ9CulQ/T2Rs9iYXhzZMzw1ox7A/E/r5Vh5zDIhUozBMVHD3UySTGhg+5oW2jgKHuWMK6F/Svlt0wzjrbhsi3BG195klzVa95erX6xX20cF3XMk02yRXaIRw5Ig5yRc9IknDySZ/JOPpwn59X5dL5G0ZJTzGyQP3C+fwAfJaiW</latexit> <latexit sha1_base64="L5L3hnZliv7KHVqvDVDaHuU4+Yc=">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</latexit> But what if we can’t measure ability? Unmeasurable! Earnings i = � 0 + � 1 Education i + � 2 Ability + ✏ i Earnings i = � 0 + � 1 Education i + ✏ i Ability is in here

  12. What would exogenous variation in education look like? Choices to get more education that are essentially random (or at least uncorrelated with omitted variables)

  13. <latexit sha1_base64="hL+s4WFObzyFUfM5D+8dsiUhF5k=">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</latexit> <latexit sha1_base64="hL+s4WFObzyFUfM5D+8dsiUhF5k=">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</latexit> <latexit sha1_base64="hL+s4WFObzyFUfM5D+8dsiUhF5k=">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</latexit> <latexit sha1_base64="hL+s4WFObzyFUfM5D+8dsiUhF5k=">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</latexit> What if we could split education into exogenous and endogenous parts? Earnings i = � 0 + � 1 Education i + ✏ i � 0 + � 1 (Education exog. + Education endog. ) + ✏ i i i � 0 + � 1 Education exog. + � 1 Education endog. + ✏ i i i | | {z {z } } w i � 0 + � 1 Education exog. + w i i

  14. <latexit sha1_base64="K6dOq/rSKEGX4M7Cfs1toN2V28=">ACNHicbVDLSgMxFM34tr6qLt0EiyAIZaYKuhGKIghuKtgqtHXIpLdtaCYzJHfUMvSj3PghbkRwoYhbv8G0nYWvA4HDOedyc08QS2HQdZ+dicmp6ZnZufncwuLS8kp+da1mokRzqPJIRvoqYAakUFBFgRKuYg0sDCRcBr3joX95A9qISF1gP4ZmyDpKtAVnaCU/f9ZAuMP0hGklVMcMfEPaSMAZL5LdzLm0SzVSsZzNnY9luAu6hQHNnrCz9fcIvuCPQv8TJSIBkqfv6x0Yp4EoJCLpkxdc+NsZkyjYJLGOQaiYGY8R7rQN1SxUIwzXR09IBuWaVF25G2TyEdqd8nUhYa0w8DmwZds1vbyj+59UTbB80U6HiBEHx8aJ2IilGdNgbQkNHGXfEsa1sH+lvMs042h7ztkSvN8n/yW1UtHbLZbO9wrlo6yObJBNsk28cg+KZNTUiFVwsk9eSKv5M15cF6cd+djHJ1wspl18gPO5xdoqtL</latexit> How do we isolate the exogenous part of education? Earnings i = β 0 + β 1 Education exog. + w i i Use an instrument!

  15. I N S T R U M E N T S

  16. W H A T I S A N I N S T R U M E N T ? Something that is correlated Relevance with the policy variable Testable with stats! Something that does not Exclusion directly cause the outcome (“only through”) Not testable! Something that is not correlated Exogenous with the omitted variables

  18. R E L E V A N C Y Instrument causes changes in policy Probably not relevant Social security number Uncorrelated with education Potentially relevant 3rd grade test scores Early grades cause more education Relevant Father’s education Educated parents cause more education

  19. E X C L U S I O N Instrument doesn’t directly cause outcome (“only through”) Exclusive Social security number SSN isn’t correlated with hourly wage Potentially exclusive 3rd grade test scores Early grades probably don’t cause wages Exclusive Father’s education Parent’s education doesn’t correlate with your hourly wage

  20. E X O G E N E I T Y Instrument independent of all other factors; is randomly assigned Exogenous Social security number Unrelated to anything related to education Not exogenous 3rd grade test scores Grades correlated with other education factors Exogenous Father’s education Birth to parents is random

  21. Relevant Exclusive Exogenous

  22. T H E H U H ? F A C T O R “A necessary but not a sufficient condition for having an instrument that can satisfy the exclusion restriction is if people are confused when you tell them about the instrument’s relationship to the outcome .” Scott Cunningham, Causal Inference: The Mixtape , p. 213

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