# Metoda uparivanja po vjerojatnosti sklonosti

Kovačević, Sanja (2014) Metoda uparivanja po vjerojatnosti sklonosti. Diploma thesis, Faculty of Science > Department of Mathematics.

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Language: Croatian

In this paper focus was on estimating average treatment effects. We used different assumptions and different methods- regression methods, methods based on the propensity score and instrumental variables methods. Variable $y_1$ denoted the outcome with treatment and $y_0$ without the treatment, while $\textbf{x}$ denoted a vector of observed covariates and w denoted receiving the treatment. To estimate the difference $y_1-y_0$, we observed average treatment effect (ATE) defined as $AT E \equiv E( y_1-y_0 )$ and average treatment effect on the treated ($AT E_1$ ) defined as $AT E_1 \equiv E( y_1-y_0 | w = 1)$. Key assumption was assumption called ignorability of treatment (given observed covariates $\textbf{x}$): ATE.1: Conditional on $\textbf{x}$, $w$ and ( $y_0, y_1$) are independent. ATE.1’: (a) $E(y_0 | \textbf{x}, w) = E(y_0 | \textbf{x}$); (b) $E(y_1 | \textbf{x}, w) = E(y_1 | \textbf{x})$. Propensity score $p(\textbf{x})$ is the probability of receiving the treatment given the covariates. For using methods based on the propensity score we needed strong ignorability of a treatment assumption. We described matching algorithm based on the propensity score. For estimating the local average treatment effect (LATE), we used the instrumental variables method in the simplest scenario- when an instrumental variable $z$ is binary. Finally, we showed how to use the propensity score matching in practice. We estimated the impact of IWT subsidies on firms’ R$\And$D intensity and employment in the Flemish region.