### 1. Introduction to microsimulation

Microsimulation models have become common tools for governments to study the distributional consequences of policy changes. For instance, so-called tax-benefit models are computer programs that have the tax- and benefit rules of a country coded. This code is then applied to a sample of individuals which has all the information of incomes and other circumstances needed to compute the taxes and benefits that apply to each individual. A tax benefit model thus gives the taxes, benefits and disposable incomes of every individual (household) in the sample. These results can then be used to compute various distributions such as the distribution of disposable income, and the share of poor people in various population subgroups. $ ^{2} $ If the purpose of the analysis is to study the consequences of a new policy, for instance a new tax scale, the tax code of the tax-benefit model is changed according to the new scale and the sample of individuals is run through the new code. The results from the new run can be compared to the old in order to evaluate the effect of the new policy compared to the old.

However, a new policy is usually introduced to influence the behavior of people. The tax-benefit model uses the same sample in both runs, i.e., the same income distribution, the same demographic distributions, etc. There is thus no accounting for any adjustments to the new policy. For this reason, the tax-benefit model is said to give only the first order effects of the policy change. To include behavioral adjustment people have added behavioral models to the tax-benefit model, for instance, a labor supply model. Usually this model is estimated from cross-sectional data and thought to capture some kind of steady state. The policy experiment is then considered to be a comparison between two steady states – a view which is at least debatable – while there is no information as to the time span needed to reach a steady state.

A different approach is to build a so-called dynamic microsimulation model. It is a model which ages its population endogenously, i.e., it includes demographic models of births, marriages, deaths, and possibly also migration – events which may or may not be influenced by policy. Typically it also includes submodels which capture transitions from one state to another, for instance from schooling to employment, from employment to unemployment, and from employment to retirement, etc. These transitions may directly or indirectly be influenced by changes in policy. A dynamic microsimulation model thus tries to trace out the many different paths people follow through time. To the extent the model is realistic in this respect, it is a better tool for policy evaluation than the tax-benefit model with or without behavioral equations, because it tries to mirror what actually happens in the economy through time. There is no need to think in terms of hypothetical steady states. Policy makers are usually interested in what will happen in the next few years or in the upcoming mandate period.

Microsimulation models are primarily designed to analyze distributional issues. One is not only interested in simulating the conditional mean of a distribution but the whole distribution.