INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 136 It is simple to compute the nonstochastic component in observation i because Y can take only two values. It is 1 with probability and 0 with probability (1 –
): ( ) ( )
…[5.11] The expected value in observation i is therefore
…[5.12] Probability function is thus also the nonstochastic component of the relationship between Y and X. It follows that, for the outcome variable to be equal to 1, as represented by the point A in Figure 5.2, the disturbance term must be equal to (
) Thus the distribution of the disturbance term consists of just two specific values. Figure 5.2. Linear Probability Model Which means that the standard errors and the usual test statistics are invalidated. For good measure, the two possible values of the disturbance term change with X, so the distribution is heteroscedastic as well. It can be shown that the population variance of is (
