# Monte Carlo simulation and Social Cost Benefit Analysis

Monte Carlo simulation is a method based on repeated random sampling of inputs to a deterministic model or calculation procedure. With Monte Carlo simulation, cumulative uncertainties of nature values can be integrated in a socio-economic cost benefit analysis. In the Netherlands, an uncertainty analysis is mandatory in every socio-economic cost-benefit analysis (SCBA), according to the EMVI-guideline. This also applies to other countries that have SCBA guidelines. The purpose of such an analysis is to determine the influence of uncertain assumptions on the balance (net present value) and ranking of the alternatives. In many SCBA’s, the uncertainty analysis is executed in a rather informal way. With the tool presented here, a more formal probabilistic sensitivity analysis can be carried out, based on the Monte Carlo simulation. The advantage of this method is that it provides insight in the cumulative effect of multiple uncertainties, including possible interactions between them. The cumulative effect is especially important for valuation of nature, because these values tend to have rather large uncertainty margins in the balance sheet. The formal sensitivity analysis yields information on which effects contribute most to total uncertainty. This insight can help decision makers in focusing efforts on issues producing the highest uncertainty.

### Uncertainties in socio-economic cost-benefit analysis

A socio-economic cost-benefit analysis (SCBA) is used to assess the welfare impacts of large infrastructural projects. The welfare effect of a project is usually expressed in terms of net present value (in euro’s, dollars, or other currency). In practice, an SCBA consists of the following eight steps:

1. Problem analysis
2. Describing project alternatives with respect to a baseline
3. Cost calculation of every alternative
4. Identification and assessment of physical impacts for every alternative
5. Identification, quantification and monetisation of welfare impacts for every alternative
6. Discounting and making up the balance
7. Sensitivity analysis
8. Conclusions and recommendations

Here, we focus on step 7: sensitivity analysis. Information about the other steps can be found in text books on cost-benefit analysis (see the references of this tool description). Usually, the estimation of uncertainties of the effects is done in a rather simple way by changing the basic assumptions of one effect at a time. The drawback of this so-called sensitivity analysis is that uncertainties are only investigated in the vicinity of the ‘pivot’ point in parameter space (i.e. the standard setting around which each input is varied) and interactions and cumulative effects of uncertainties are poorly understood. The Monte Carlo simulation provides a method to explore the entire parameter space and to include interactions and cumulative effects of uncertainties in a more formal way.

### Monte Carlo simulation

Monte Carlo simulation is a method based on repeated random sampling of inputs to a deterministic model or calculation procedure. For each simulation all input variables are randomly drawn from predefined probability density functions. For each set of inputs, a deterministic model run or calculation is made. The outputs of a large number of such simulations are analysed statistically, to yield probability density functions of the output variables.

### Relevance for Building with Nature

The Building with Nature strategy aims at including nature value in project design and using natural processes to human benefit. However, it is a strategy with more uncertainties than a traditional design, partly because the natural processes are sometimes poorly understood, partly because they include inherent uncertainties. Building with Nature would therefore benefit from a tool that estimates cumulative uncertainties in a socio-economic cost-benefit analysis, thus enabling to formally incorporate uncertainties in important investment decisions. This tool can be used in any investment project where an SCBA is made and where uncertainties play an important role. The SCBA is usually applied in an early stage (e.g. a feasibility study) of infrastructure developments requiring major investments.