In-depth analysis of the economic phenomenon to be studied, according to the purpose of the study, select the factors to be included in the model, select appropriate variables to represent these factors according to the availability of data, and establish a mathematical expression describing the relationship between these variables according to the relationship between the economic behavior theory and the variables displayed in the sample data, that is, the theoretical model. It is a theoretical model. The design of theoretical model mainly includes three parts: selecting variables, determining the mathematical relationship between variables, and drawing up the numerical range of parameters to be estimated in the model.
1. Determines the variables contained in the model.
In the single equation model, variables are divided into two categories. As the object of study, the "fruit" in causality, such as the output in the production function, is the explained variable in the model; Variables as "causes", such as capital, labor and technology in the production function, are explanatory variables in the model. Determining the variables contained in the model mainly refers to determining the explanatory variables. There are several variables that can be used as explanatory variables: exogenous economic variables, exogenous conditions variables, exogenous policy variables and lagging explanatory variables. Some of these variables, such as policy variables and conditional variables, often appear in the form of imaginary variables.
Strictly speaking, he said, output, capital, labor and technology in the production function can only be called "elements", and there is a causal relationship between these elements. In order to establish an econometric model, we must choose appropriate variables to represent these factors, and these variables must have data availability. Therefore, we can use the total output value to represent output, the original value of fixed assets to represent capital, the number of employees to represent labor, and time as a variable to represent technology. In this way, the final model is a mathematical expression about the relationship between total output value, original value of fixed assets, number of employees and time variables.
The key is how to choose the explanatory variables correctly after determining the explained variables.
First of all, we should correctly understand and grasp the economic theory and the law of economic behavior implied in the economic phenomenon studied. This is the basis of correctly selecting explanatory variables. For example, in the above production problems, it has been clearly pointed out that the supply is insufficient, so the factors affecting the output should be in the input factors. At present, the general input factors are mainly technology, capital and labor. If the demand is insufficient, then the factors that affect the output should be in the demand side, not in the input factor. At this time, if the research object is the production of consumer goods, we should choose variables such as residents' income as explanatory variables; If the research object is the production of means of production, variables such as total investment in fixed assets should be selected as explanatory variables. It can be seen that the same production model is established, and the choice of variables is different in different economic environments and different industries.
Secondly, the availability of data should be considered when selecting variables. This requires a thorough understanding of economic statistics. Econometrics model is based on the support of sample data, that is, sample observation values of variables, and estimates parameters through certain mathematical methods, thus revealing the quantitative relationship between variables. Therefore, the selected variables must exist in the statistical index system and have reliable data sources. If it is necessary to introduce individual policy variables and conditional variables that have an important influence on the explained variables, the method of selecting the observed values of virtual variables samples is adopted.
Third, when selecting variables, we should consider the relationship between all the selected variables, so that each explanatory variable is independent. This is required by econometric model technology. Of course, it was difficult to do this at first. If relevant variables appear in all selected variables, they can be tested and eliminated during the modeling process.
2. Determine the mathematical form of the model.
After selecting the appropriate variables, we should choose the appropriate mathematical form to describe the relationship between these variables, that is, to establish a theoretical model.
The main basis for choosing the mathematical form of the model is the economic behavior theory. In mathematical economics, the mathematical forms of common models such as production function, demand function, consumption function and investment function have been widely studied, and these research results can be used for reference. It should be pointed out that modern economics pays special attention to empirical research, and any theoretical model based on certain economic theoretical assumptions can't be accepted by people if it can't explain the past well, especially historical statistical data. This requires the establishment of theoretical model to be revised repeatedly in the whole process of parameter estimation and model verification, so as to get a mathematical model that can not only have a good economic explanation, but also better reflect the relationship between variables that have happened in history. It is wrong to ignore any aspect. You can also make a scatter plot according to the sample data of variables to explain the relationship between variables and the explained variables, and the functional relationship between variables shown in the scatter plot is used as the mathematical form of the theoretical model. This is also a method that people often use in modeling.
3. Work out the theoretical expectation of the parameters to be estimated in the theoretical model.
The parameters to be estimated in theoretical models generally have specific economic significance, and their values can only be determined after the model is estimated and tested, that is, after the economic mathematical model is completed. However, their numerical range, that is, theoretical expectation, can be drawn up at the beginning according to their economic significance. This theory is expected to be used to test the estimation results of the model. The key to drawing up the theoretical expectation value of the parameters to be estimated in the theoretical model lies in understanding the economic significance of the parameters to be estimated. For example, there are four parameters to be estimated and α, β, γ and A in the theoretical model of production function. Among them, α is the output elasticity of capital, β is the output elasticity of labor, γ is approximately the speed of technological progress, and A is the efficiency coefficient. According to these economic significance, their numerical range should be:
0 < α < 1, 0 < β < 1, α+β ≈ 1, 0 < γ < 1 and approaching 0, a > 0.