  We investigate the short-time universal behavior of the two dimensional
Ashkin-Teller model at the Baxter line by performing time-dependent Monte Carlo
Simulations. First, as preparatory results, we obtain the critical parameters
by searching the optimal power law decay of the magnetization. Thus, the
dynamic critical exponents $\theta _{m}$ and $\theta _{p}$, related to the
magnetic and electric order parameters, as well as the persistence exponent
$\theta _{g}$, are estimated using heat-bath Monte Carlo simulations. In
addition, we estimate the dynamic exponent $z$ and the static critical
exponents $\beta $ and $\nu $ for both order parameters. We propose a refined
method to estimate the static exponents that considers two different averages:
one that combines an internal average using several seeds with another which is
taken over geographic variations in the power laws. Moreover, we also performed
the bootstrapping method for a complementary analysis. Our results show that
the ratio $\beta /\nu $ exhibits universal behavior along the critical line
corroborating the conjecture for both magnetization and polarization.
