Identification in Synthetic Control
The Role of the Factor Model
The identifying assumption in synthetic control that was presented in Abadie, Diamond and Hainmueller (2010) was that of a “factor model”. I don’t know the history of the factor models, so I won’t even attempt, but they look like this.
\(Y(0)_{it} = \alpha + \beta_{t}X_i + \omega_{t} \mu_i + \varepsilon_{it}\)
where Y(0) is the untreated potential outcome (e.g., earnings without some intervention), \alpha is a constant, \beta i…
