As described earlier, the allocation of individuals across occupations is represented through a multinomial logit model (McFadden 1974a, 1974b), specified as follows: where is a vector of characteristics specific to individual i and household h, are vectors of coefficients, for the following activities j={salaried, self-employed, not employed}, and are random variables identically and independently distributed across individuals and activities according to the law of extreme values. Separate models are estimated for household heads, spouses and other members. The vector of characteristics is given by a set of individual and household characteristics such as age, or a range of ages, education level, dependency rates, region and area, among others. Within a discrete utility-maximizing framework, is interpreted as the utility associated with activity s, with being the unobserved utility determinants of activity s and utility of inactivity being arbitrarily set to 0. In order to calculate the utility of activity s and therefore allow for people to change occupations in the simulation exercise when either or change, we must estimate the residual terms of occupational choice model, which are unobserved. They must be drawn from extreme values distributions in a way that is consistent with observed occupational choices. Train and Wilson (2008) define the distribution functions of extreme value errors alternative. In particular, assume that the alternative zero is chosen conditional on the chosen () and denote for. Define and where is the logit choice probability. Then the cdf for the alternative chosen is: Calculating the inverse of this distribution: (a) where is a draw from a uniform distribution between 0 and 1. Error terms for other alternatives must be calculated conditioned on the error terms of the alternative chosen (). The distribution for these errors is: The inverse of this distribution is: (b) where is a draw from a uniform distribution between 0 and 1. We repeat this same method when alternative other than zero are chosen and using expressions (a) and (b). 2—Earning Equations: Nonfarm and Farm workers Turning to the labor market determination of earnings, we separate the sample into two different groups attending to the kind of activities that these individuals perform: non-farm and farm workers. Individual earnings equations for the first group are estimated separately for household heads, spouses and other members if they are performing as self-employed or
As described earlier, the allocation of individuals across occupations is represented through a multinomial logit model (McFadden 1974a, 1974b), specified as follows: where is a vector of characteristics specific to individual i and household h, are vectors of coefficients, for the following activities j={salaried, self-employed, not employed}, and are random variables identically and independently distributed across individuals and activities according to the law of extreme values. Separate models are estimated for household heads, spouses and other members. The vector of characteristics is given by a set of individual and household characteristics such as age, or a range of ages, education level, dependency rates, region and area, among others. Within a discrete utility-maximizing framework, is interpreted as the utility associated with activity s, with being the unobserved utility determinants of activity s and utility of inactivity being arbitrarily set to 0. In order to calculate the utility of activity s and therefore allow for people to change occupations in the simulation exercise when either or change, we must estimate the residual terms of occupational choice model, which are unobserved. They must be drawn from extreme values distributions in a way that is consistent with observed occupational choices. Train and Wilson (2008) define the distribution functions of extreme value errors conditional on the chosen alternative. In particular, assume that the alternative zero is chosen () and denote for. Define and where is the logit choice probability. Then the cdf for the alternative chosen is: Calculating the inverse of this distribution: (a) where is a draw from a uniform distribution between 0 and 1. Error terms for other alternatives must be calculated conditioned on the error terms of the alternative chosen (). The distribution for these errors is: The inverse of this distribution is: (b) where is a draw from a uniform distribution between 0 and 1. We repeat this same method when alternative other than zero are chosen and using expressions (a) and (b). 2—Earning Equations: Nonfarm and Farm workers Turning to the labor market determination of earnings, we separate the sample into two different groups attending to the kind of activities that these individuals perform: non-farm and farm workers. Individual earnings equations for the first group are estimated separately for household heads, spouses and other members if they are performing as self-employed or
862480NWP0Worl0Changes0in0Pakistan.docx