Trying to estimate rational expectations does not usually minimise forecast error when forecasting macroeconomic or financial variables in reality. This is because, with samples of realistic length, optimal feasible forecasts contain conditional biases that reduce forecast variance. I demonstrate this by using penalised factor models to show that statistically simple inflation forecasts, primarily based on past inflation, are optimal even when other relevant financial and economic variables are available. I also show that US household inflation forecasts display many similarities to these simple optimal forecasts, but also contain mistakes that increase forecast error. Therefore a combination of `optimal feasible expectations' and behavioural errors explain US household inflation forecasts. This suggests that optimal feasible expectations, with additional behavioural errors in some cases, could explain forecast formation across economics and finance.