or each of the following research designs, state the identifying assumption and provide one reason for why the assumption might not be valid. a) Regression: To study the effect of school spending on test scores, I run the following regression: = + () + () + where controls for the average family income at school .

b) Fixed Effects: To study the effect of years of schooling on wages, I run a regression while adding family fixed effects. That is, I compare future wages between siblings with different levels of educational attainment (this controls for omitted ability bias because siblings are assumed to have similar levels of innate ability on average). c) Differences-in-differences: To study the effect of teacher pay on achievement within a school district, I analyze a group of 20 school districts that increased teacher pay in 2009. I analyze how district performance trended before and after the pay change in 2009, and compare against the trends of school districts that did not increase teacher pay in 2009.