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Difference-in-Differences Brady Neal causalcourse.com Motivation and Preliminaries Difference-in-Differences Overview Assumptions and Proof Problems with Difference-in-Differences Brady Neal 2 / 25 Motivation and Preliminaries

  1. Difference-in-Differences Brady Neal causalcourse.com

  2. Motivation and Preliminaries Difference-in-Differences Overview Assumptions and Proof Problems with Difference-in-Differences Brady Neal 2 / 25

  3. Motivation and Preliminaries Difference-in-Differences Overview Assumptions and Proof Problems with Difference-in-Differences Brady Neal Motivation and Preliminaries 3 / 25

  4. Motivation Context: Treatment and control group both before and after treatment administered Advantage: Use time dimension to help with identification Treatment administered p u o r g t outcome n e m t a e r t control group time Brady Neal Motivation and Preliminaries 4 / 25

  5. Example from Card & Krueger (1994) Minimum wage increase in New Jersey New Jersey employment Pennsylvania time Brady Neal Motivation and Preliminaries 5 / 25

  6. Average Treatment Effect on the Treated (ATT) Brady Neal Motivation and Preliminaries 6 / 25

  7. Average Treatment Effect on the Treated (ATT) ATE: <latexit sha1_base64="vFl/7vZyIfYMc4akmWOEzBEsI7E=">AUu3icrVjbtGEN2kt8S9Oanf+sJGKeAsiq5KZwXAQFsp0XRA7ga2PDkCjKZs1bScquI+iT2p/pU4H2X3rm7FIUdaMUWILI1ezMmdm5LZftyHOTtF7/5979Dz786ONPHjxc+fSz7/4cvXR48Mk7MW2c2CHXhgft1uJ47mBc5C6qecR7HT8tuec9S+2pb5o2snTtw2E9vI+fMb10Ebte1WylI56s/nu6+PVlvPLM2rJP1+rMzq2kJxTr13Y51mgIq9Z0gBblxBp4Zc/Wz89VKvVbnx5ocNMygosxnL3z08C91qjoqVLbqKV85KlApxp5qQTft6qh6ioC7Uz1QYsxcjnvqIFagWwPXA4WqBe4XqBf28NcB/wUwobUOLh18MSUt9a3g6GHdJ1XfRb43wztLRJ7bYeIt72D6oKbqEtQyuYxzcbk2vn7JqlOs4QVX62IlESniB7uw5i7uHv6nWKFcb8HpYNSBVIyRDZoHqaIjh37XnxzSUj0SKfg5FYPc/ueVbLfIjvFbBaGCe0VGy1CsTl4CaHdoqPB5jOhvxD6xQ2zcPqztcg8u461UI7z4oV+odRkXkeTpHs2s2V2qQB1N0CX9KjgDcCSghM9+F/1xwFHPVBqboaDGSF1xLxAyqGeSfOZ9lc4R4btCehFGzmG8u9USmsnK7Mzs93NvEjiHfx9wl9YgvqrDHIXbM7M28WCV3jH83/GfTRnuMXmNlSjyrWJNkVxW4IWbcIZb2hPZnZpG2rg+aZb4b6hfqdxD3Kr0ieV2FbEgLdRYn1BWY2DfRV8QvPq5CFc9mlCp1+LTjktlyBVquTyOJvu+wioT14xnUPu4evRYRpUrt4p8bjn2uSLao+4bjDvUI9IWel1NbRk7BgWt4huX3WlSq8X8k9rVnXFcq8gFrFTLZGWTmurquVmxREDsHvWabqh7skJVzcYs6pN+/OuITlatE+k8vgUY9VhNl5SqogrXpy+zmlr2WSdVBlL8f0FOJqU6hp6wtqMjKaVkfrbNlUSMh427JCV3vou1mbKYPum85YFP17nsSTLzOzBbzKlTem90fh7irpHPdgPp+H1S58sdsrKsjFG/eHMfHmXI4f+0SOJuMaL6OuIa/lm+LNGZhbFvhu8YAJRMjY1SIuid5gb01e+ryroBRVkVdGfEmhxHw6iTB+OuR8ClzhvaKWABSp8P5wflAagx1QBsZjXc5ldZjb4Lzdch5ajJPc+iKSsc4pKrna5W8nJY3mj5ftjPM96Ksps+XFco1c9M1/SAh1nGJXMo4iIQ/kqX7JVIh9wRN1zafLGBfwL2Z/IiNhYelUj67DF6VaGpytel9qXsgrHxicj8+h4evGb/G/AJaFk/5rLpUt7M5W7fy6e5/M2Sns0l/SX9m0u+K5F0uDe4Q5rIvCmtKeHaK+XS+VS2JzjYTbLnF1tV7b8KLs2R3TmSyz30hW6N2xyR5QXag/T+47UsmN0jrusfu2Ydiau7MqZ2DO0PLI9hbYH0J8z0/Xy5SX9PkFs+bcZhWnfMZvQTSP4Ukp0ekpH9ySV+frLo8ynwxuxk2fPgBjNAx/An9MLXeMYaUNP3eL5r4PqsOstirnrJ7pl6O4m0Dewn61w31tedzInIY2Cmemo5daMh+A3O6zLk9cwaYhbSM3unIOus6E2eRcU36afMSXPoEdluCmOfxdLz58Z2OrN+UhDwB5Oewu0AePWMuhpfnzOw3AmXvKWafniPcu7h67OiJ4d1h1ns7A56jD7h6en7Yl3FZK/m6gKyd3+k8dj+or46fC5e+DIefQpJqW0po0izjpHR5RJzdNiwjNnfrKuFU7KGm/ctmQkr3yD1zT9yDG7xcr5aqUx/vZtcnC4Wv8UKu/eV5+cK8mXugvlZP1Dr8tKVeojL34Fdb/an+Vv+q/9a/bab2ueZr1/z8h8pQqftd7/QaAK1w=</latexit> E [ Y (1) − Y (0)] Brady Neal Motivation and Preliminaries 6 / 25

  8. Average Treatment Effect on the Treated (ATT) Unconfoundedness: ATE: <latexit sha1_base64="D5f7B1rjye1XD6q4mhbO9Bf8J+Y=">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</latexit> ( Y (0) , Y (1)) ⊥ <latexit sha1_base64="vFl/7vZyIfYMc4akmWOEzBEsI7E=">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</latexit> E [ Y (1) − Y (0)] ⊥ T Brady Neal Motivation and Preliminaries 6 / 25

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