New example based on model of Hopenhayn & Rogerson (1993) – Job Turnover and Policy Analysis: A General Equilibrium Framework. This example illustrates how to solve (stationary) general equilibrium in models with endogenous entry and endogenous exit. The model itself is about how firing costs can cause factor misallocation, and the macroeconomic implications for consumption, productivity and employment.

Another example based on model of Restuccia & Rogerson (2008) – Policy distortions and aggregate productivity with heterogeneous establishments. This example illustrates how to solve (stationary) general equilibrium in models with endogenous entry and exogenous exit. The model itself is about how firm-level distortions can cause misallocation, and the macroeconomic implications for consumption, productivity and employment.

These example demonstrates new features in VFI Toolkit for solving models with (endogenous or exogenous) entry and exit. These features are simply implemented as an option in standard value function, stationary distribution, and general equilibrium commands (and transition paths in near future). This means that entry & exit, while requiring some additional set up, can then be used just like any other model.

For full details of the Hopenhayn & Rogerson (1993) model see the original paper. Code for example.

For full details of the Restuccia & Rogerson (2008) model see the original paper. Code for example.

Have also uploaded a replication of Hopenhayn & Rogerson (1993). There are some substantial differences because the original paper used rough grids on ‘number of employees’. With the increase in computing power over the past 25+ years it is nowadays easy to use much more accurate grids.

Have also uploaded a replication of Restuccia & Rogerson (2008). There are essentially no differences from the original results for Tables 1 to 9; except Table 7 which I failed to replicate, likely due to me simply not understanding from paper what denominator should be in ‘relative’ numbers. Note that the solution algorithm used is quite different from the original which exploited many things unique to this model that the replication does not attempt to take advantage of.

There is also a (in progress) working paper detailing the framework for models with entry and exit implemented by the VFI Toolkit. Most importantly it provides an exact description of the timing assumptions around entry and exit. It describes the exact modeling framework being solved by the VFI Toolkit commands, as well as pseudocode for the algorithms.

An additional example based on Hopenhayn (1992) – Exit, selection, and the value of firms has also been uploaded. Although the timing in the model does not fit that used by the VFI Toolkit this turns out to be largely irrelevant as the model contains no endogenous states, and so the standard commands can still be used to solve it with minor change to the options. The original paper is here, although this example is based on calibration from lecture notes of Chris Edmond.

Chris Edmond’s lecture notes on Hopenhayn & Rogerson (1993) are also nicely done and provide an alternative calibration of the model. His alternative calibration is implemented in the replication codes.