What is the difference between these time series AR(1) regression models (lead in the dependent vs lag in the dependent variable)?
$$\begin{align}y_t = constant + \alpha y_{t-1} + error \tag{1}\label{eq1}\\ y_{t+1} = constant + \alpha y_{t} + error \tag{2}\label{eq2}\end{align}$$
Will they have different coefficients?