I. Two Empirical Research Approaches
There are mainly two factions within the econometricians: reduced form and structural approaches. The biggest difference between them lays in the impacts they have on the economic theories in the empirical research. The reduced form approach insists to let data speak for itself. The status, purpose and tradition of the researchers permeate their theory, which leads an incompletely objective perspective when they are dealing with the data. If and only if their theory is true, the conclusion from the data imposed with their concepts is true. The issue here is that the researcher will never know which models are true.
The structural approach thinks data can never reveal its own data generating process. Understanding the true DGP cannot be fulfilled without the economic models. A priori economic theory is the starting point. Testing and correcting the theory are the main tasks. Even the economic models are possibly wrong, as D. Hendry (1995, page 22) defended, researchers can keep returning to revise their ideas until the process achieves internal consistency. The structural approach is very similar to the research method of physicist. To understand the motion of matters, physicists propose a model and then test by experiments. Structuralists pay much attention to estimate the primitive (‘deep’) parameters which are invariant to the policy inventions. Ideally, the policy forecast deduced from structural approach can pass through the Lucas critique, where reduced form approach has difficulties.
II. Structure
What is structure? Is there really something called ‘structure’? Yes, there exists, that is the reason why our simulation method is not meaningless, but it is not interpretable. One of the appealing examples is the dynamic factor models. The models catch certain ‘structure’ of the economic system, but the factors are always uninterpretable. With the application of DFMs, it is possible for modelers to remain agnostic about the structure of the economy and not rely on different assumptions and economic theories, which is often the case in structural estimations.
Structure is rule. Suppose we are playing chess, and one of the pieces is missing, we can still use any substitution such as a coin instead. The game still continues because the rule remains unchanged. Like a language game, the meaning of a word is not rooted in the content itself but the rules and language system (for example grammars). The rule in an economic system is a structure.
Suppose there are two primitive tribes on islands which are extremely far from each other. However, they share similar totems like eagle, music or myth. There probably exist communications between them. But to under all the appearances, the more important thing is the common way of thinking which is a structure.
In the context of econometrics, structure is defined as the set of basic and permanent features of the economic mechanism. It requires the invariance of an extension of the sample period, regime shifts and adding variables to analysis (D Hendry, 1995, page 34). A structure can be just the data generating process, economic relations, population parameters 
However, in a complex system of human society, it is not required to put extra explanations on structures. Especially, a ‘deep’ enough structure in the sense of economic structuralist is unknowable and uninterpretable. It is rooted in the collective unconsciousness of human beings. Any structures which I can imagine so far are not `deep’ enough in the sense of invariance.
III. The Limitation of Structural Models in the Context of Econometrics
Firstly, Economic theory tends to simplify the economic phenomena in a complex system. The restoration of the simplicity offers an easier way to underlying problems. However, there probably no simple laws or expressions in a complex system. Theory tends to underestimate the complexity of the economic system.
In contrast, the reduced form approach views the economic phenomena as a black box. The decision not to use any theories of human behaviors, even some hypotheses, reduces the fun of learning economics. And it cannot provide us with a further explanation about how the economic system evolves.
Ideally, the prediction of a structural model is testable and falsifiable. In a very complex system, even a very general prediction is valuable, because the prediction based on the theories helps us explain the general patterns and how they are spontaneously created in an economic system. However, an economic theory is to describe the possible patterns which may appear restricted to that certain conditions that are satisfied. Forecasting for a specific phenomenon is unrealistic.
Secondly, the empirical data are extremely hard to satisfy the stability requirements of the structural parameters. If the stability cannot be ensured, the structural models lose their essential advantage. For the time and regime invariance, as Lucas pointed out, it is hardly satisfied in reality. For the sample invariance, the data have to be homogenous with DGP, that is, the high quality of the data is required.
However, in DFMs, we only require that the instability of the factor loadings is sufficiently independent across series. Then even the factor loadings are unstable, the instability can be averaged out when we pool many series to estimate the common factors. The forecast is more robust than structural models. The assumptions of the structure are not necessary.
Thirdly, the empirical models are difficult to represent the DGP structurally. It is partially because of the complexity and agnosticity of the DGP. The extreme of a structuralist is to describe the observable part of the DGP by imposing the economic restrictions.
Last but not least, the structural parameters are unchangeable even in the unlimited time, which suggests that the space of the structural parameters is closed. Structuralists try to find the universal laws in economic system paralleling to the physical world. The possibilities of discovering such rules in human society are questionable. The structure exists but probably with self-evolution. This is the reason that I find very difficult to understand the concept of ‘deep’ parameters.