The definitions of standard and reduced form in term of simultaneous systems are fairly standard, but when people use the them in the general context, they seems to mean something different. What does it mean when an empirical study is based off of reduced form/ vice versa?
What's reduced form and what's structural form estimation?

I was always perplexed by this difference as well. My personal test for structural vs. reduced form is whether there is a functional form assumption on a utility or profit function that is explicitly used to generate an estimating equation; if that sort of "structure" is imposed on the model, people now usually call this a structural model. I believe the terms now take on a much different meaning than they did in the 70s.
7f41: "assume some model and derive some relationship under these assumption and your parameter estimates have some meaning now"
This is only partially true. If the assumptions that you have made are correct, then you have a really useful model that can get at some interesting behavioral questions. If these assumptions are way off, however, the parameter estimates are still uninterpretable. I could write down a model where people only derive utility from steak and tires and assume that the two are complementary goods. These assumptions could certainly be used to estimate a model, but the results will be total garbage.

I didn't mean for my post to sound like a knock on structural estimation. Unlike a lot of people out there, I think there is a lot to be learned from both the structural as well as the reduced form approaches. Although I have really only started in on the structural literature over the last year or so, I do like how the structural approach really gets me thinking about the mechanisms that are generating the data. A lot of reduced form papers (some of which I have written) focus on the effects of a few key variables without addressing the behavior that gives rise to the effect.
Unless God decides to tell us exactly how to specify utility functions, the structuralreduced form debate will continue.

Using my definition, it is structural if you specify the utility function that generates the choice probabilities. You could also have a reduced form probit where it is solely a statistical investigation about the determinants of some event occurring (no explicit theory backing the model).

Ah, I see. If you want to sell it as structural, I would think you would just need to be more explicit about the connection between micro theory and the functional form restrictions on the indirect utility function used to estimate the mode. As to how much structure you need? That all depends on the referees...

Reduced form estimation is when you use data to make inference about parameters characterizing the distribution of the data, or some atheoretical transformation of these parameters. Structural estimation is when you take a second step and, using econ theoryimplied restrictions on the distribution of the data, you make inference about parameters with structural interpretation in the context of your theory.
example: beta in OLS is a transformation of moments of X and Y. If there is some theory which tells you that beta = f(theta), where theta are parameters in the model, making the step from the estimate of beta to inference about theta is called structural estimation.