The simultaneity problem is a central issue in econometrics, and therefore by extension in empirical economic analysis. It falls within a broader class of problems known as endogeneity, and is the basis for misidentification of the coefficient linking two variables in a model.
Suppose we want to study the relationship between the crime rate and the number of police officers in a city. If we translate this into an equation, we get:
Y = a x1 + B X2 + c
where x1 is the number of police officers (X2 representing other variables that are important for explaining Y, such as income level, for example).
The problem is that the number of police officers cannot be considered an exogenous variable here, i.e., a variable that influences the model without itself being influenced by it. In fact, the number of police officers is often a function of the crime rate in a city: it is common practice to increase the number of police officers when insecurity rises.
The relationship to be measured here cannot be measured correctly: in a standard OLS model, the coefficient represents the impact of a change in x on y, with all other variables being fixed; here, the problem is that x also varies in response to y. It is therefore not possible to vary only x and measure its impact on y, as the data collected is by nature non-experimental (see this other insight for the definition of this term). This will pose a problem of endogeneity. In econometric terms, our estimator will be biased and non-convergent, in other words, the relationship will be incorrectly measured.
Julien P.
