Alignat wrong spacing

Question

I want the \Leftrightarrow to be directely above the \kappa from the last line. If this is not possible i would be ok if one can put the \Leftrightarrow directely above the equals sign (from the last line).

\documentclass[]{article}
\usepackage{amsmath}
\begin{document}

\begin{alignat*}{3}
\hat \pi_t & = \kappa \Tilde{y_t} + \beta E_t[\hat \pi_{t+1}] \quad &\Leftrightarrow \qquad \qquad \gamma_\pi a_t &= \kappa \gamma_y a_t + \beta \gamma_\pi a_{t+1} \\
\gamma_\pi a_t &= \kappa \gamma_y a_t + \beta \gamma_\pi \rho_a a_t   \quad &\Leftrightarrow \quad \gamma_\pi - \beta \gamma_\pi \rho_a &= \kappa \gamma_y \\
&&\gamma_\pi = \frac{\kappa}{(1-\beta \rho_a)} \gamma_y
\end{alignat*}
\end{document}

Answer 1

Here is a solution with eqparbox , to have the = of the last equation centred w.r.t. \Leftrightarrow and mathtools:

\documentclass[]{article}
\usepackage{mathtools}
\usepackage{eqparbox}
\newcommand*{\eqmathbox}[2][M]{\eqmakebox[#1]{$\displaystyle#2$}}

\begin{document}

\begin{alignat*}{3}
\hat \pi_t & = \kappa \Tilde{y_t} + \beta E_t[\hat \pi_{t+1}] & &\Leftrightarrow &\gamma_\pi a_t &= \kappa \gamma_y a_t + \beta \gamma_\pi a_{t+1} \\
\gamma_\pi a_t &= \kappa \gamma_y a_t + \beta \gamma_\pi \rho_a a_t & &\eqmathbox{{}\Leftrightarrow{}} &\gamma_\pi - \beta \gamma_\pi \rho_a &= \kappa \gamma_y \\
&& \mathllap{\gamma_\pi} &\eqmathbox{=} \mathrlap{\frac{\kappa}{(1-\beta \rho_a)} \gamma_y}
\end{alignat*}

\end{document}