This paper presents a toolkit to solve for equilibrium in a computationally efficient way in economies facing the effective lower bound on the nominal interest rate under a special assumption about the underlying shock process, a two-state Markov process with an absorbing state. We illustrate the algorithm in the canonical New Keynesian model by replicating the optimal monetary policy in Eggertsson and Woodford (2003), and we show how the toolkit can be used to analyse the medium-scale dynamic stochastic general equilibrium model developed by the Federal Reserve Bank of New York. As an application, we show how various policy rules perform relative to the optimal commitment equilibrium. A key conclusion is that previously suggested strategies – such as price level targeting and nominal GDP targeting – do not perform well when there is a small drop in the price level, as observed during the Great Recession, because they do not imply a sufficiently strong commitment to low future interest rates (“make-up strategy”). We propose two new policy rules – the cumulative nominal GDP targeting rule and the symmetric dual-objective targeting rule – that are more robust. Had these policies been in place in 2008, they would have reduced the output contraction by approximately 80 percent. If the Federal Reserve had followed average inflation targeting – which arguably approximates the policy framework announced in August 2020 – the output contraction would have been roughly 25 percent smaller.