Structural Economics for Beginners
Manski and McFadden's book on structural economics was intended as an introduction to graduate students. It is no longer in print but it exists in its entirety online here. It's sort of a root-canal to read, however. A better first post to go to is Kenneth Train's book which can be found free online here. Its conversational, almost colloquial, so it's my preferred introduction to acolytes. (Start at Sampling Enumeration in the second link)
More useful, and the text for structural economics that Heckman uses with his students at Chicago are his handbook chapters on structural policy evaluation found (part 1, part 2, part 3). Also, Keane, Todd, and Wolpin have a useful handbook chapter initiating students to (static and dynamic) discrete choice models, normally called Discrete Choice Dynamic Programming methods (DCDP).
Increasingly, structural models are wanted for publication and the job market. The question becomes, to some economists, if it's a program evaluation...why do economists need to do it? What makes it economics other than it's doer is trained in an economics department. I can see the line of this point.
The most vocal structural advocates can be a bit condescending to their reduced-form colleagues: For instance,
They claim that reduced-form parameters are not "reduced-form" at all (make a face of suspense and wonder as they tell you this; this will make the interaction truly satisfying for the other). In this they mean to say that the original language all originates from early Cowles Foundation work in which a reduced-form model is derived from a fully-specified structural model. I wonder if they've read Shakespeare. In the modern sense, reduced-form mirrors that original language in that the object of both reduced-form as a way to structural and reduced-form as it's own end rely on modeling an endogenous variable on exogenous variation. I don't see the inconsistency.
Instead, they verbally differentiate "economics" literature (referring to structural work) from "treatment effects" literature (referring to reduced-form work).
Finally, and surprisingly, structuralists claim that the marginal distributions from reduced-form studies are not economics but "statistics" while the joint distribution estimation from structural work is "real economics". In reality, a joint distribution is as much statistics as the marginal distribution; and, of course, marginal distributions have economic content.
Notwithstanding, structural models are extremely valuable. Developed Roy models can estimate distributional effects, counterfactual analysis, welfare effects, switching costs, and can recover policy invariant parameters to simulate the effects of never-before implemented policies. They have a lot of power.
A great start for students interested in public economics and labor economics is the Roy Model. The big picture is that you model individual's decision as individually rational, choosing the sector, education, or treatment which maximizes his utility.
In an idealized research world we would like to observe an single individual existing in two alternate realities. One in which she is "treated" (broadly defined) and in a parallel realm where she has not been treated. We could then compare those two realities to identify the impact of treatment on each individual in the population. This research design has alluded us.
In the most simple case where we can observe outcomes, costs, and choices, we can directly infer the joint distribution of Y0 and Y1--generating an estimate of the counterfactual outcome!
A very careful introduction for structural labor exists in Cunha and Heckman's "A New Framework for the Analysis of Inequality", which can be found here or, if that doesn't work, here.
In the simplest (non working) structural models, it requires some policy change to identify the effect to extrapolate to new policies "never before experienced." But in this case, you are simply extrapolating the reduced-form effect.
The real flexible power is estimating the utility function of individuals and then simulating these individuals in different policy environments in which the agent optimizes among choice sets. With this you can try on different experimental policies and estimate some of the outcomes. If the utility function is correctly specified, the structural model should simulate correctly the effect of the policy.
Key Words: Structural estimation, policy evaluation, structural economics, Andrew Johnston, Andrew, Johnston, economics, applied economics, economist, microeconomics, empirics, empirical economics, Wharton