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2 Conditional Probability Functions 27 In a conditional probability model, the main quantities of interest are the marginal probability eﬀects (MPE’s). The MPE of the l-th exogenous variable is deﬁned as partial derivative ∂P (yi |xi )/∂xil . For any given probability model, there are always as many MPE’s as there are outcomes of the dependent variable. For example, if we consider a binary response variable, then there are two such MPE’s, namely the marginal change of the probability of a zero, and the marginal change of the probability of a one, as one of the regressors changes and the others are kept constant.

We begin with an example. 1. S. General Social Survey on the number of children among women aged 40 or above. 2 of the previous chapter, we displayed the average number of children by survey year. Each mean can be interpreted as an estimator for the true average in that year, and thus for the expectation conditional on the survey year, denoted by E(yi |yeari ). 36 between 1986 and 2002, and this decline is statistically signiﬁcant. We cannot tell from this mean comparison, however, what changes in the fertility distribution were responsible for the average decline.

How would you specify the parameters in terms of the explanatory variables? d) How would you proceed with the variables? 1 Introduction Consider the problem of estimating the unknown parameter of a population when the population distribution is known (up to the unknown parameter or unknown vector of parameters), and when a random sample of n observations has been drawn from that population. Common examples are sampling from a Bernoulli distribution with unknown parameter π, sampling from a Poisson distribution with unknown parameter λ, or sampling from a normal distribution with unknown parameters µ and σ 2 .