‘Entrepreneurial-Choice’ models feature infinitely-lived households who decide whether to be an Entrepreneur or a Worker based on their relative productivity in each of the two, as well as their assets. Entrepreneurs face collateral constraints that can prevent them from investing as much in their firm as they would like (which generates misallocation). Two important benchmark examples are Kitao (2008) and Bruggemann (2021), the former has exogenous labor supply and the later extends this to endogenous labor supply. Both also feature a ‘corporate’ sector (alongside the non-corporate entrepreneurs) with a Cobb-Douglas production fn, and general eqm in perfectly competitive labor and capital markets.
Here is an example code for Kitao (2008) – Entrepreneurship, Taxation and Capital Investment
Here is an example code for Bruggemann (2021) – Higher Taxes at the Top: The Role of Entrepreneurs
Both examples just solve a stationary general equilibrium.
There are also codes implementing a full replication for both papers, the links go to github repos that also contain pdfs that give a brief outline of the model and compare the original and replication tables and figures.
Replication of Bruggemann (2021)
Both papers replicate cleanly, at most minor quantitative variation.
There is one important difference between entrepreneurship in the two models that is worth mentioning. Kitao (2008) has “ Each agent enters a period with an occupation that he chose in the previous period.” (second sentence of Section 2). Bruggemann (2021) has “A young household starts the period knowing its assets, labor ability, and entrepreneurial ability. Based on these endowments, it makes its occupational choice between becoming an entrepreneur or a worker”. In the models this means that in Kitao (2008) entrepreneur-worker is an endogenous state, while in Bruggemann (2021) entrepreneur-worker is not part of the state space (although to make the codes easier to read/write, I include it as a decision variable). This timing in Bruggemann (2021) is made clear in her eqn (7).
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Someone is going to ask, ‘why not replicate Cagetti & De Nardi (2006)?’, so figure I will get in early 
CDN2006 is substantially different at a mathematical details level from the entrepreneurial-choice models here, in a way that makes solving the model much more complicated but has little impact on the final results. Hence the literature nowadays always uses the modelling approach seen in both Kitao (2008) and Bruggemann (2021). Specifically, nowadays everyone uses a ‘collateral constraint’ —k \leq (1+d)a in K2008 and k \leq \lambda a in B2021— that imposes that the entrepreneur cannot always borrow as much capital (k) as they might like, and are required to have assets (a) as collateral for any borrowing. In CDN2006 there is no ‘collateral constraint’, instead they impose an ‘incentive-compatible borrowing constraint’, that imposes that the entrepreneurs borrowing for capital k is limited to be such that they would never choose to default. As CDN2006 put it in their conclusion “entrepreneurs face an endogenous borrowing constraint that limits the amount that they can borrow. The entrepreneur’s wealth acts as collateral, so the richer the entrepreneur, the higher the amount that he can borrow.” This substantially changes the computation, as now within the value function problem we have to check that the incentive compatibility constraint is satisfied. The model based on ‘incentive-compatible borrowing constraint’ gives much the same outcomes for all the aggregate and cross-sectional stats as the model based on ‘collateral constraint’, but the former is much more difficult to compute. As a result the literature nowadays just all uses the later.
Two other papers warrant a mention on the grounds of historical interest. Quadrini (2000) looks for the most part like Kitao (2008), but the capital used in entrepreneurship is not something that can be chosen, instead entrepreneurs get ‘projects’ that arrive i.i.d. and come with a fixed value for the k that must be invested in them. Meh (2005) also uses this ‘projects’ approach. None of Quadrini (2000), Meh (2005), nor Cagetti & De Nardi (2006) are solving transition paths. Quadrini (2000) has entrepreneurship as an endogenous state, like Kitao (2008), while Cagetti & De Nardi (2009) has entrepreneurship as something you decide each period like Bruggemann (2021).
In Kitao (2008) labor supply is exogenous. In Bruggemann (2021) labor supply is endogenous for workers, but fixed for entrepreneurs. It is possible to further endogenize the labor supply of the entrepreneurs and you can find this setup in Wellschmeid & Yurdagul (2021); helps capture that there are a lot of low-productivity self-employed working few hours, and means collateral constraints not binding for as many entrepreneurs. Both Kitao (2008) and Bruggemann (2021) are about taxation, and we might also consider tax avoidance by entrepreneurs as in Di Nola, Kocharkov, Scholl, Thkir & Wang (2025). Both of these two other papers, WY2021 and DKSTW2025 could be solved in VFI Toolkit.
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How much easier is solving with VFI Toolkit? Under 1/3th the lines of code and solves on 2/3 the hardware in 1/3 the runtime!
Bruggemann (2021) in the replication materials says “Computation of the transition path for one [top marginal tax rate] on 5 32-core nodes takes at least 2 hours.”, and a quick check by me says that a single 32-core cpu today costs ~US$2500 for a total of $12500. By contrast, VFI Toolkit solved it on a NVIDIA A100 worth around ~US$8000. So VFI toolkit solves the model on hardware costing less than 2/3 the price! Replication is higher accuracy and the 12 transition paths average 1/2 hour each.
B2021 code to solve the baseline model is 3000 lines of fortran (benchmark.f90), plus another 2800 for the final eqm (experiment.f90) and 3000 for the transition (Transition.f90). There are some other f90 files, so the total is well over 10,000 lines of fortran code (7000ish if you don’t count the copy-paste chunks; but there are another 2700 lines of stata analysing model output). By contrast the full replication with toolkit is around 2800 lines of matlab code (1600 of which are blank or comments), most of which creates graphs and tables. Plus Matlab is easier to code than Fortran.
This paragraph just collects info on how many grid points most papers are using. B2021 uses 300 points on labor and 480 on assets, and appears to do pure discretization so next period assets are on the grid. K2008, the original used 3000 points on assets and does pure discretization so next period assets are on the grid. WY2021 uses 10 points on labor and 245 on assets but with 2197 points on next period assets. CDN2009 appears to use 260 on assets, and appears to do pure discretization so next periods assets are on the grid. Both replications here use higher levels of accuracy than this.