One Lag Too Many

Using a long history of daily closes for a liquid stock, you fit $S_{t+1} = \beta_1 S_t + \beta_2 S_{t-1} + \varepsilon_t$. (a) What signs and rough magnitudes should you expect for $\beta_1$ and $\beta_2$? (b) If you instead run two separate one-variable regressions — $S_{t+1}$ on $S_t$ alone, and $S_{t+1}$ on $S_{t-1}$ alone — what coefficients should each produce? (c) Which estimate of the coefficient on $S_t$ carries the smaller standard error: the joint fit or the univariate one?