Here's my code:
\documentclass{beamer}
\usetheme{Berkeley}
\begin{document}
\section{Formula}
\subsection{Time-varying Coefficients}
\begin{frame}{Time-varying Coefficients}
\setbeamercovered{transparent}
Used to get the degree of ERPT:\\
$$ERPT = \alert<2>{\beta_0} + \alert<3>{\phi_0}\alert<4>{G(s_t;\gamma,c)}$$
\begin{description}
\uncover<2,5>{\item [$\beta_0$] pass-through elasticity}
\uncover<3,5>{\item [$\phi_0$] pass-through coefficient}
\uncover<4,5>{\item [$(s_t;\gamma,c)$] logistic transition function driving the nonlinear dynamic}
\item[]
\end{description}
\end{frame}
\end{document}
if i remove the \item[] the the \item [$(s_t;\gamma,c)$] logistic transition function driving the nonlinear dynamic becomes left-aligned up to the border!


\item[]. By the way, take a look at Why is [ … ] preferable to $$ … $$? – Ignasi Nov 26 '15 at 08:03