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This process can be seen in the above figure where three model parameters exist, and each parameter is represented by a probability distribution. By applying the Monte-Carlo method, model outputs can also be represented by a probability distribution. In the case of a CBA this process would allow us to make statements such as what is the probability that the Net Present Value (NPV) of a regulatory proposal will be above zero (there is a 95% probability that the regulations benefits would exceed its costs), a confidence interval of the NPV (90% of the time the regulations would provide a NPV of between $50 and $90 million), the standard deviation of the NPV, the average NPV, the most likely outcome NPV, and which parameters are likely to have the greatest impact on the NPV.
This process can be seen in the above figure where three model parameters exist, and each parameter is represented by a probability distribution. By applying the Monte-Carlo method, model outputs can also be represented by a probability distribution. In the case of a CBA this process would allow us to make statements such as what is the probability that the Net Present Value (NPV) of a regulatory proposal will be above zero (there is a 95% probability that the regulations benefits would exceed its costs), a confidence interval of the NPV (90% of the time the regulations would provide a NPV of between $50 and $90 million), the standard deviation of the NPV, the average NPV, the most likely outcome NPV, and which parameters are likely to have the greatest impact on the NPV.
Because uncertainty and risk in an outcome can be considered as a cost itself, this information adds important insight towards improving program choice and implementation of a regulation. In many cases costs need to be incurred to decrease uncertainties and thus the regulatory option with the central or expected highest net-present value may not always be the preferred option if it is important to limit our exposure to risk. This can be particularly important for outcomes that are discontinuous due to thresholds or irreversible outcomes that can result in low probability but high impact outcomes.
Because uncertainty and risk in an outcome can be considered as a cost itself, this information adds important insight towards improving program choice and implementation of a regulation. In many cases costs need to be incurred to decrease uncertainties and thus the regulatory option with the central or expected highest net-present value may not always be the preferred option if it is important to limit our exposure to risk. This can be particularly important for outcomes that are discontinuous due to thresholds or irreversible outcomes that can result in low probability but high impact outcomes.
While Monte-Carlo methods have been around for a long time it is only with the increase of computing power that this kind of analysis has become common. Today there are many statistical programs that can perform Monte-Carlo simulations. While these packages are powerful and feature rich, they may not be accessible to all analysts within the Federal Government. They can be expensive and require special knowledge and training. Furthermore, the human resources required to acquire such packages through government acquisition services can become a barrier to the average analyst. It also becomes difficult to share models created with these software packages with other analysts or departments to confirm reported results or adjust parameters for further analysis as they will need to have the necessary software to do so.
While Monte-Carlo methods have been around for a long time it is only with the increase of computing power that this kind of analysis has become common. Today there are many statistical programs that can perform Monte-Carlo simulations. While these packages are powerful and feature rich, they may not be accessible to all analysts within the Federal Government. They can be expensive and require special knowledge and training. Furthermore, the human resources required to acquire such packages through government acquisition services can become a barrier to the average analyst. It also becomes difficult to share models created with these software packages with other analysts or departments to confirm reported results or adjust parameters for further analysis as they will need to have the necessary software to do so.
RRAT includes two sheets that are referred to by macros. These sheets are called “Model Inputs” and “Model Outputs” any number of additional sheets can be added or copied into the RRAT but “Model Inputs” must always be the 1<sup>st</sup> sheet in the tab list and “Model Outputs” must be the second
RRAT includes two sheets that are referred to by macros. These sheets are called “Model Inputs” and “Model Outputs” any number of additional sheets can be added or copied into the RRAT but “Model Inputs” must always be the 1<sup>st</sup> sheet in the tab list and “Model Outputs” must be the second
=== Stage 1: Define Distributions for Independent Outcomes with Uncertainty ===
The first step in setting up the simulation will be to define what variables you are interested in examining the impact of uncertainty on the outcome of the CBA. Enter the description for each of these variables starting in cell '''B9''' on the '''Model Inputs''' sheet. It is important that a description be entered here as a blank entry in the description column is used as a signal to the program that no more entries exist. The area on the sheet to enter descriptions can be seen in '''Figure 2''' in the area labelled as “'''A'''”.
The second step in the setting up the simulation will be to define the probability distributions for the independent variable inputs. While there are numerous probability distributions used in Monte-Carlo, RRAT is currently limited to five, although this limitation can be overcome by combining distributions.
Two of these are discrete distributions and three are continuous. The continuous distributions used are the normal, triangle and the flat (continuous uniform). The discrete distributions are defined (discrete) and fixed (one non-varying constant). The probability distributions need to be selected from a pull-down option from the column under the heading “'''Distribution Type'''” ('''column D''') on the '''Model Inputs''' sheet ('''Figure 2 – Area “B”''').
[[File:Fig 2.png|left|thumb|774x774px|Figure 2: Setting Distribution Details]]
The final stage in defining a distribution is entering in their parameters. These parameters differ depending on the type of distribution selected and are displayed in the table above the columns where they are entered ('''columns E – F – G). ''' When a distribution type is selected areas that do not need to be defined are blacked out. For instance, in '''Figure 2''' the normal distribution has been selected. As a result, in '''area “C”''' where the distribution parameters are entered the first parameter has been blackened out. From the table above you can see that the mean of the distribution needs to be entered in '''column F''' and the variation needs to be entered in '''column G'''.
A more detailed description of the probability distributions and the required parameters to define them follows.
