We propose a novel approximate fixed effects (AFE) estimator that employs interpolation in the computation of its criterion function. This feature greatly reduces the number of times the underlying economic model needs to be solved. In the case of dynamic programming models this can reduce the estimation time from days to minutes. We study the asymptotic behavior of the AFE estimator and derive the leading additional biases due to approximations under mild regularity conditions. We demonstrate that the Jackknife removes both the usual incidental parameter bias and biases due to approximations. Monte Carlo results highlights the attractive features of the AFE which is much faster than the exact FE estimator and with only small additional estimation errors. We apply the AFE to fit the buffer-stock consumption-saving model with unrestricted heterogeneity in the discount factor on Danish register data.