About the dynamic panel threshold model:
used to study the intertemporal relationship of economic variables.
Use the dynamic panel threshold model to study the relationship between finance and economic growth. The key formula is:
(Equation 1)
where ui is the fixed effect of a country; FINit is the threshold variable used to divide the sample into different regions or groups; λ is the unknown threshold parameter ; I(·) is an indicator function. If the parameters in parentheses are valid, the value is 1, otherwise 0.
This type of modeling strategy allows different levels of FIN (that is, whether it is higher or lower than λ) , The role of finance is different;
Xit represents an explanatory regression vector, including the lag value of the dependent variable and other endogenous variables, as well as exogenous variables, in which the slope coefficients are assumed to be region-independent. The vector of explanatory variables is divided into a subset X1it of exogenous (or predetermined) variables that are not related to εit, and a subset of endogenous variables X2it that are related to εit. For countries with a low (high) level of financial development, the impact of finance on growth will be β1 (β2);
δ represents the difference between countries;
initial income is regarded as an endogenous variable, that is, X2it = GDP per capita in the previous period, and X1it contains the remaining control variables.
The β
parameter estimation cannot be obtained by the first difference method, etc., but can only be obtained by the forward orthogonal deviation transformation (for details, see the explanation below, no details, too troublesome)
According to Caner and Hansen (2004), there are three steps to estimate the specification coefficient. First, estimate the reduced form regression of the endogenous variable X2it, and use ordinary least squares (OLS) to fit Zit to obtain the fitted value of X2it.
Then, the predicted value of X2it is substituted into equation (1), and the threshold parameter λ is estimated by the OLS method.
Let S(λ) denote the resulting sum of squared residuals.
Repeat this step for the strict subset supported by the threshold variable FIN.
Finally, the smallest residual sum of squares is selected as the estimator of the threshold λ.
According to Hansen (2000) and Caner and Hansen (2004), the critical value of the 95% confidence interval of the threshold is determined as follows:
where C(α) is the likelihood The ratio statistic LR(λ) is 95% of the asymptotic distribution.
The basic likelihood ratio has been adjusted to account for the number of time periods used for each cross section (Hansen, 1999).
Once the estimated value of the threshold λ is determined, the generalized method of moments (GMM) can be used to estimate the slope coefficient.
Following Arellano and Bover (1995), Bick (2010) and Kremer et al. (2013), we use GROWTHit as a tool.
Experimental data:
Attached, explanation of terms:
panel data observation data of two or more observation objects at multiple time points (or time intervals).
Time series data: time series data
Cross section data: cross section data
Panel data: panel data
Panel data, namely Panel Data, is a data type that combines cross-sectional data and time series data.
It has two dimensions: time series and cross-section. When this type of data is arranged in two dimensions, it is arranged on a plane, which is obviously different from data with only one dimension arranged on a line. The entire table is like a panel , So translate panel data as "panel data". However, in terms of its internal meaning, translating panel data as "time series-cross-sectional data" can better reveal the essential characteristics of this type of data. It is also translated as "parallel data" or "TS-CS data (Time Series-Cross Section)".
1 For example
: City names: The GDPs of Beijing, Shanghai, Chongqing, and Tianjin are 10, 11, 9, 8 (units of 100 million yuan). This is the cross-sectional data, cut at a point in time to see the difference in each city is the cross-sectional data.
For example, the GDP of Beijing in 2000, 2001, 2002, 2003, and 2004 was 8, 9, 10, 11, and 12 (in 100 million yuan). This is the time series. Choose a city and look at the difference in time of each sample is the time series.
2 For example, in
2000, 2001, 2002, 2003, and 2004, the GDPs of all municipalities directly under the central government in China are:
Beijing's 8,
9, 10, 11, and 12; Shanghai's 9, 10, 11, 12, and 13;
Tianjin The cities are 5, 6, 7, 8, and 9;
Chongqing is 7, 8, 9, 10, and 11 (units of 100 million yuan).
This is the panel data.
Reference: http://blog.sina.com.cn/s/blog_72cca2a50102vaxi.html
Data heterogeneity: https://www.zhihu.com/question/22246294
The explanatory variable (explanatory variable), also known as "explainable variable" and "controllable variable", is the independent variable in the econometric model. Explanatory variables, in accordance with certain laws, have an impact on the economic variables that are the dependent variables in the model, and explain or explain the reasons for the changes in the dependent variables. For example, for an econometric model that describes the relationship between the price of a certain commodity in the market and the quantity supplied, the change in price affects the quantity of goods that producers provide to the market. Therefore, the price variable is the explanatory variable of the model. In the simultaneous equation model, endogenous variables, exogenous variables and lagged variables can all be used as explanatory variables.
The econometric model is a random economic mathematical model composed of specific equations. The equation is:
The formula represents the demand for a certain commodity, and represents the disposable income of residents. The sum is called "economic variable", which is used to describe the quantitative characteristics and value changes of economic activities or economic phenomena. In the formula, the variable is called the "explained variable", and the change of its value is caused by the change of other variables in the model; the variable X is called the "explaining variable", and the change of its value does not depend on the change of other variables in the model. Changes are made independently. The sums in the formula are called "parameters", and they are constant coefficients that represent the quantitative relationship between variables in the model. Parameters connect various variables in the model, and specifically indicate the degree of influence of explanatory variables on the explained variables. The formula is called "random disturbance term", which indicates the influence of various random factors on the model and reflects the influence of various other factors not included in the model.
Reference: https://baike.baidu.com/item/Explanatory variables/10337403?fr=aladdin
For a detailed introduction of the first difference method and the forward orthogonal deviation method, please refer to:
http://www.docin.com/p-1498016296.html
According to Kremer et al. (2013), the dynamic panel eliminates country-specific fixed effects (li The conversion method of) and the standard in the first difference method are not applicable, because these two methods violate the distribution assumptions of Hansen (1999) and Caner and Hansen (2004). Therefore, the forward orthogonal deviation transform proposed by Arellano and Bover (1995) is used to eliminate the fixed effect.
The characteristic of this kind of transformation is to avoid the serial correlation between the transformed error terms and keep the error terms irrelevant. This ensures that the estimation procedure of the cross-sectional model proposed by Caner and Hansen (2004) can be applied to dynamic panel specifications, as shown in equation (1) above.
Endogenous variables and exogenous variables:
In economic models, endogenous variables refer to the variables that the model decides. Endogenous variables can be explained in the model system, and exogenous variables themselves cannot be explained in the model system. In the economic model, endogenous variables refer to the variables to be determined by the model. Exogenous variables (exogenous variables) refer to known variables determined by factors other than the model, which are the external conditions on which the model is built. Endogenous variables can be explained in the model system, and exogenous variables themselves cannot be explained in the model system. Parameters are usually determined by factors outside the model, so they are often regarded as exogenous variables.
Example: P=a+bQ, indicating the relationship between price and quantity, then a and b are parameters, both exogenous variables; P and Q are variables to be determined by the model, so they are endogenous variables. In addition, other variables related to the model, such as the price of related commodities and people's income, are all exogenous variables.
Reduced regression: In statistics, especially in econometrics, the simplified form of the equation system is the result of the endogenous variable solution system. This makes the latter a function of exogenous variables, if any. In econometrics, the equations of the structural form model are estimated in the form given by the theory, and another estimation method is to first solve the theoretical equations of the endogenous variables to obtain the reduced form equations.
Let Y be the vector of variables (endogenous variables) to be explained by the statistical model, and X be the vector of explanatory (exogenous) variables. In addition, let ε be a vector of error terms. Then the general expression of the structural form is
where f is a function, in the case of a multi-equation model, it may be from vector to vector. Then the reduced regression form of this equation is:
where g is a functional equation.