9.两阶段最小二乘：目的：针对过度识别的联立方程组，选定有效的工具变量

9. Two-stage least squares: <br>Purpose: To select effective instrument variable <br>operations for overidentified simultaneous equations : first use parsimony to obtain an estimate of an endogenous variable for an equation OLS, and then use it as a tool Variables are brought into other equations for OLS (use instrumental variables to estimate endogenous variables, and then use the estimated endogenous variables as new explanatory variables for OLS regression) <br><br>10. Dynamic: <br>refers to a previous explanatory variable will The influence of dependent variables <br>11. Time series <br>(1) When the error series is correlated: Dubin-H statistics <br>(2) Granger Causal Relation Test: test the causality, combine the constrained and unconstrained residuals and the difference/constrained residual , If it is close to 0, there is no causality. Constraint: The coefficients of X and its lag items as explanatory variables are both 0. <br>(3) Unit root test: test whether it is stable, which can be integrated/differentiated by Xth order <br>(4) cointegration: for unstable data , but it may be a linear combination of smooth, so the residual stationarity test sequence, if stable, the cointegration established, OK also unstable <br><br>fixed panel 12. the effects regression data <br>for different individuals (cross section data), regression Different solutions for the intercept term (βi0) of the equation <br>: LSDVE: least squares dummy variable estimation, that is, each intercept introduces a dummy variable

9. Two-stage minimum-difference:<br>Purpose: Select effective tool variables for over-recognized intermodal systems<br>Operation: First use the simple method to obtain an estimate of an endogenous variable for an equation OLS, and then take it as a tool variable into other equations, to make OLS (to estimate endogenous variables with tool variables, and then to estimate endogenous variables as new explanatory variables for OLS regression)<br><br>10.Dynamic:<br>A previous explanatory variable has an effect on the dependent variable<br>11.Time series<br>(1) When the error sequence is related: Dubin-H statistics<br>(2) Granger Causal Relation Test: Test causality, will constrain and non-constraint residuals and do difference/constraint residuals and, if close to 0, no causality. Constraint: X as an explanatory variable and its lag term have a coefficient of 0<br>(3) Unit root inspection: check whether it is smooth, through the difference / X whole (integrated of Xth order)<br>(4) co-integration: for uneven data, but the linear combination may be stable, so will test the stability of the residual sequence, if stable, then co-integration is established, not smooth also OK<br><br>12. Fixed effect regression of panel data<br>For different individuals (cross section data), the intercept term of the regression equation (intercept term, betai0) is different<br>Solution: LSDVE: Least-squares virtual variable estimation, i.e. one Dummy variable per intercept introduced

9. Two stage least squares<br>Objective: to select effective instrumental variables for over identified simultaneous equations<br>Operation: firstly, get the estimator of an endogenous variable for an equation OLS, and then use it as a tool variable to carry out OLS (estimate the endogenous variable with instrumental variable, and then use the estimated endogenous variable as a new explanatory variable for OLS regression)<br>10. Dynamic:<br>It refers to the influence of an explanatory variable in the earlier period on the dependent variable<br>11. Time series<br>(1) Correlation of error sequences: dubin-h statistics<br>(2) Granger causal relation test: Test causality. Sum the constrained and unconstrained residuals and the error / constraint residuals. If it is close to 0, there is no causality. Constraint: the coefficients of X and its lag term as explanatory variables are 0<br>(3) Unit root test: to test whether it is stable, it can pass the integration of Xth order<br>(4) Cointegration: for non-stationary data, it may be stable after linear combination, so the stationarity of residual sequence will be tested. If it is stable, cointegration will be established, and unstable will be OK<br>12. Fixed effect regression of panel data<br>For different individuals (cross section data), the intercept term (β I0) of regression equation is different<br>Solution: lsdve: least squares virtual variable estimation, that is, each intercept introduces a dummy variable