# Is there any identification assumption for IV?

I am asking this because I know there are IA's for cross sectional estimators and D-in-D estimators, but am unsure if there are any for IV estimation. Does anyone know if there is or isn't, and if there is - what would it be?

-

## 1 Answer

The instrumental variable $Z$ must be:

1. Uncorrelated with the error term (IV exogeneity)
2. Correlated with the regressor $X$ for which it is to serve as instrument (IV relevance).

There is also a third assumption that has to do with what parameter you are trying to estimate. It only applies if there's heterogeneity in the effect of X on Y. Simply put, IV measures the average effect of X on Y caused by wiggling X through Z. If there are 2 types of people who respond differently when X changes, and our instrument only wiggles X for the first type, IV will give you the effect of X on Y for only those folks. OLS would give you a weighted average of the two (assuming you solved the endogeneity problem somehow). If everyone is the same (no heterogeneity), you don't need to worry about this.

-
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9567875266075134, "perplexity_flag": "middle"}