What Is Sensitivity Analysis?

Sensitivity analysis is a way to measure the statistical significance of a quantitative variable based on its mean and standard deviation values. It is an important concept in scientific publishing, but not often taught in graduate programs in industrial or chemical analysis. In this article I will describe the sensitivity analysis and the key methods used to interpret the results.

For those unfamiliar with the concept, sensitivity analysis involves a set of three primary decisions: how to measure the statistical significance of the variables being analyzed; the inclusion of unknowns into the models; and the determination of the parameters that control the outcome estimates. The first two concerns the design of the model, where the model’s inputs and its outputs are selected based on the assumptions about the underlying variables. The third concern is the estimation of the parameters themselves, and the judgments made about these parameters by the decision-makers who evaluate the models.

The key concept in sensitivity analysis is the idea of a simple and transparent function, called an “opaque function”, that can be evaluated by any model that is suitable. For example, let’s use the classic economic scenario for what-if analysis: Assume that the unemployment rate is 5%. Let’s further assume that the level of capital spending by businesses is fixed, i.e., it stays the same. Let’s also assume that the central inflation rate is also set the same at that time.

The “what if” scenario simply lets you explore all the possible outcomes if one of the assumptions about the underlying variables is changed. You can see that sensitivity analysis here consists of selecting a model for which the parameters of interest are evaluated using the actual data that would occur in the real world. Of course, this is only one example of how such scenarios can be evaluated, and in many cases it is not even necessary to use an actual data set; the use of an economic model that allows for multiple possible outcomes can still be useful.

Another type of sensitivity analysis looks at the effect of changes in one or more parameters on the values of other variables. These include the dependent variable(s), which are the factors that actually cause the equilibrium value. For example, suppose the level of capital spending is unchanged, but the interest rate is raised. In this case, the financial analyst wants to know what will happen to the value of the NOC. Specifically, what will happen to the weighted average NOC/Growth, since both investments will have a smaller impact if growth is cut in half?

Sensitivity analysis can also be used in a “free crash course”. In a free course, you analyze the relationship between one or more economic variables and the subsequent behavior of market prices. For example, suppose that the general price level is predicted to fall, but instead the Consumer Price Index rises instead. This would indicate a weakness in consumer spending. One could use a free crash course to identify which economic factors are causing this fluctuation and then calculate the implications of those factors on the behavior of prices. This approach may not be as accurate as more sophisticated methods such as the logistic regression, but it can still help a financial analyst arrive at a reasonable estimate of the probability of an economic shock.

Once a set of inputs have been analyzed using sensitivity analysis, the results are typically displayed in a range drawing or bar chart. One can also plot the results of the analysis on a log scale. Some analysts choose to use a maximum likelihood estimation (MLE), where a 95% confidence interval is calculated as a range of values. Using this method, an analyst can estimate the parameters associated with the main outcome. One can use this information in order to determine which variables most strongly affect the outcome. For example, if the result from the sensitivity analysis shows a relatively strong effect of interest rates, one can consider raising the interest rate temporarily in order to reduce stock market volatility.

The sensitivity analysis looks closely at the main economic inputs, looking for parameters that are sensitive to changes in those inputs. In many cases, this type of analysis looks only at the relationship between one or more economic variables and the outcomes of interest rates. Other types of analysis looks into all of the economic variables simultaneously. This form of analysis looks into the effect of interest rates, output gap, inflation, deflation, unemployment, balance of trade, etc. In order to conduct a sensitivity analysis, one needs to select the right indicator for each input variable.