The stochastic simulation procedure used in the manuscript is discussed here and illustrated with two examples. Both examples study the dynamic properties of the simple New Keynesian model without capital when the zero lower bound (zlb) on the interest rate is binding.
The first example studies the output effect of a negative technology shock that strikes during the zlb. It shows that when the wealth effect associated with the technology shock is small (as when the shock is not very persistent) then output rises. This result has received a lot of attention in the literature. The example also shows that when the wealth effect associated with the technology shock is strong enough (as when the shock is more persistent) then output falls with a negative technology shock. The degree of persistence required for this result is not very great. For example, the degree of persistence typically assumed for technology shocks in the Real Business cycle literature is sufficient for a negative technology shock to produce a fall in employment and consumption in the zlb. The MATLAB code to implement the procedure in the example is contained in this zip file.
The second example shows that the response of welfare and other variables to an increase in government consumption in the zlb is roughly the same whether the taxes that finance shocks to the government’s budget constraint are distorting or lump sum. This complements and extends the findings in Erceg and Linde (Journal of the European Economic Association, 2014). The MATLAB code that generated the results can be found here. Much, much faster code using Dynare that is much, much easier to program and produces identical results can be found here.