I'm starting to study econometrics from the Wooldrige's book. But some doubts arise regarding the structural model, its definition and its comprehension in general. Let's look at the author's opinion. It begins with this equation:

$$y = \beta_0 + \beta_1x_1 + ... \beta_k x_k + u$$

"The error form of the model in equation is useful for presenting a unified treatment of the statistical properties of various econometric procedures. Nevertheless, the steps one uses for getting to equation are just as important. Goldberger (1972) defines a structural model as one representing a causal relationship, as opposed to a relationship that simply captures statistical associations. A structural equation can be obtained from an economic model, or it can be obtained through informal reasoning."

Then arise some doubts that I am going to list here:

1. What is the definitive definition of a structural model (equation)? If it were just that derived from a theoretical model, that would be fine, but he also says that it can be obtained through informal reasoning. What really means causal relationship? Examples?
2. In what sense the error is useful for presenting a unified treatment of the statistical properties of various econometric procedures? Examples?
3. Once well-known the definition of a structural model, what is the meaning of "relationship that simply captures statistical associations" What is a statistical association e how it is opposed to the structural model?

thanks

I'm starting to study econometrics from the Wooldrige's book. But some doubts arise regarding the structural model, its definition and its comprehension in general. Let's look at the author's opinion. It begins with this equation: $$y = \beta_0 + \beta_1x_1 + \dotsm \beta_k x_k + u$$ "The error form of the model in equation is useful for presenting a unified treatment of the statistical properties of various econometric procedures. Nevertheless, the steps one uses for getting to equation are just as important. Goldberger (1972) defines a structural model as one representing a causal relationship, as opposed to a relationship that simply captures statistical associations. A structural equation can be obtained from an economic model, or it can be obtained through informal reasoning."

Then arise some doubts that I am going to list here:

1. What is the definitive definition of a structural model (equation)? If it were just that derived from a theoretical model, that would be fine, but he also says that it can be obtained through informal reasoning. What really means causal relationship? Examples?
2. In what sense the error is useful for presenting a unified treatment of the statistical properties of various econometric procedures? Examples?
3. Once well-known the definition of a structural model, what is the meaning of "relationship that simply captures statistical associations" What is a statistical association e how it is opposed to the structural model?