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The following contents are all my understanding.

1 What is an econometric model?

It is a way to test a certainly aspect of an economic theory or the effect of a policy. Because of the complicated situation in real life, it is necessary to use an error term. If we want to measure all the relationship (the direct and the indirect) b/w the explanatory variable and the explained variable, we must let E (ut|xt) =constant, in another words, let f(x) =E (yt|xt)-constant. If we let constant=0, this kind of regression is called mean regression or least squares regression (this is not the exact relationship, but include a constant term. This constant term stems from other cause included in the error item). A well specified model is a model that will generate data if given the value of the parameter and the value of explanatory variable (in order to do this, you need to put restrictions or called assumptions on the relationship), and the real DGP should be included in the model.

In fact, I can't tell the exact meaning of econometric model before looking at the whole picture of this subject.

2 What is the simple regression model?

With the form: y=β0+β1x+u   and five assumptions

1) Linearity, it is shown in the form already

2) Identification, rank(X) =2

3) Strict exogeneity, E (u|X) =0

4) Homoskedasticity and Non-autocorrelation, var (u|x) =σ²I_n

5) Normality, u|X~N (0, σ²I_n)

3 What is the relationship b/w model and estimation method?

Basically, they are just different things, or rather two stages in figuring out the real DGP. First, we have a model either from economic theory or from common knowledge. Even if the model is well specified, we still don't know the real DGP, because we don't know the value of the parameter. Second, we use the data to estimate the value of the parameter with certain method. So we can see that only with well specified model and good estimation method, can we get close to the real DGP.

So, remember, all the method works well only when the model is well specified, and all the method is adopted to estimate the value of the parameter in the model. (In the estimation stage, technically, it is the parameter that is the variable, not the explanatory)

 4 What are two kinds of property of the parameter in estimation procedure?

One is the basic property which only depends on the estimation method, that is to say it holds no matter whether the model is well specified or not, the other is property which holds only when the model itself is well specified. The latter is the most important one, because it tells us about the statistical property of the parameter (unbiased, var, MSE, consistent, the whole distribution?).

 5 From the discussion above, we can see that with a fundamental restriction E (ut|xt) =constant, we can measure the relationship b/w variables. But only with that restriction, we can't tell more about the relationship from the given data, so we should guess! With some other more detailed assumptions; we have a whole model to estimate the real DGP with certain method. The key point is the assumption we can adopt. It should be as close to the DGP as possible. So as far as I can understand, an econometric model is in fact a series of assumptions in order to guess the real relationship. After this stage, we then choose a method to get good estimation (good statistical property) with regard to the model.

PS: whether is E (ut|xt) =constant an assumption of the model (equal to the other assumptions)? I doubt it. I think it is better to consider it as the restriction put on the form of DGP. As a consequence, it is also a restriction of the model which cannot be taken away because we create the model to estimate DGP.

 6 Then another important question arises: how do we know whether the model is well specified or not? The other form of the question is: how do we know whether the assumption is reasonable or not?

 Residual analysis? I do not know completely.

      This semester, I should say, is the longest period of time I spend in studying ever since the university entrance examination. With too many things to learn, I finally find there is no way to learn all of them well(not in terms of examination). Advanced-Macro, micro, econometrics, the first three basic economic courses had worn me out. Not that I am not smart enough, but it seems that I know nothing about math. I start to understand what math means to so-called economics. Though I still don't think people can explain economics with complicated math more deeply than with natural language nowadays, it is still important in some way to know something about math. I can't tell exactly why, but I can feel it in terms of real situation and the development of the subject. Math never takes place of imagination; on the contrary, math develops from experience and imagination itself. So I totally agree with what Steven Cheung said: think with common knowledge and basic logic, and then write using advanced technique.

      In the history of science, most important discoveries were made within the limit of age. Great minds think alike. Not that they can figure out news things, but they can see the most important thing among the other thinkers’ thoughts and in the mean time keep out the less important ones. I don’t think it’s time for economists to summarize and make great improvement like Keynes. So maybe we are doomed to be ordinary economists at most. But in some specific fields like finance, there is a whole world waiting for us.

       Next semester, I think I will master math I need and learn some more basic knowledge of finance. With good foundation, next steps will be easier and I will increase my pace.