In the regression analysis，Explanation of the endogenousness of the variable may lead to non -consistency of estimation quantity。Many documents take endogenous treatment as an important content of empirical research。This article is from the source、Impact、Treatment and other aspects of the basic ideas of endogenous problems combed，I hope to provide some slight reference for economic empirical analysis。

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Endogenity in the Analysis of Return，In general，refers to the interpretation variable and error items in the regression equation。The impact from the error item will cause the explanatory variable to change，But we cannot directly observe the impact of error items，You can only see the change of the interpretation variable and the interpretation variable。So，When estimating parameters，Estimation measurement may attribute the change of the interpreted variable to the explanation variable related to error items，Although this change is caused by error items rather than explaining variables。So，The coefficient of the explanation variable will be systematically overestimated or underestimated，Estimation errors。

When the interpretation variable endogenous，that is, when the error item of the current (or individual itself) is related to，The probability limit of the ordinary minimum daily estimation (OLS) is not equal to the authentic value，So that the real parameters are irregular，This is the unanimous estimate。When the explanation variable is weak，is irrelevant to the error item of the current (or individual itself)，Instead, it is related to the error items of other time (or other individuals)，OLS estimation although there are errors in limited samples，But its probability limit is equal to the authentic value，This is consistent estimation。

Bet365 app download So，endogenous interpretation Variables have an impact on the coefficient of interpretation variables in the model? at this time，Unless the exogenous interpretation variable is not related to the endogenous explanation variable，Otherwise，OLS estimation of its coefficient is also the same。and，Empirical analysis，Explanation variables are strict exogenous (it is not related to any individual error items at any time). It is difficult to satisfy，So，Limited sample error is common。

　　Endogenous source analysis

The source of endogenousness is mainly four types: the connection of variables、Model error setting、Sample intercept、Measurement error。

First，joint。The connection of variables refers to，Multiple variables are mutually dependent、Decided at the same time。If the price and transaction volume、Salary and employment level、Interest rate and currency liquidity, etc.。In a regression equation，If one of the variables is explained variable，Other variables connected to it must be an explanation variable，These explanations must be endogenous。What needs to be explained here is，Link and feedback are two different mechanisms。The difference is，Lianqin variable is determined at the same time，and feedback is not necessarily，It is likely that the feedback variable is in the next period instead of the current period。The feedback mechanism between variables may not necessarily lead to endogenous，But the connected variable will definitely cause endogenous。

2，Model Mistake。The endogenousness caused by the mistake of the model is mainly derived from the leakage variable，It is the necessary explanation variable that the variable is intentionally or unintentionally ignored。At this time，The impact of the omissions on the explained variable can only be reflected by the error item，Error items are no longer pure random errors。Because there is usually a certain correlation between social and economic Bet365 lotto review variables，Error items containing omitted variables may be related to the interpretation variable in the model，thus leading its endogenous。Obviously，Because there are usually certain correlation between variables in the same period，The necessary interpretation variables that omitted the omissions usually cause all the interpretation variables in the model to be endogenous。In addition to omitting the necessary explanation variable，Error setting error in the form of regression square function can also cause error items to contain the omitted systemic information，thus leading to endogenous。The autocorrelation of the error items in the self -regression model，If the sequence related to the dynamic model and the cross -section related to the space regression model，It will inevitably lead to the endogenousness of the self -regression item。

third，Sample intercept。Sample interception refers to an observation threshold for the existence of the explanatory variable，Only greater than (or less) this threshold can be observed。Sample interception is divided into two cases: First, the intercepted individual or sample point is known，Although the explained variables of the sample point point are irresistible，But the explanation variable is observed，This sample is called TOBIT sample。Second, the intercepted individual or sample point is unknown，Any information of the sample point that is not intercepted in the sample，Such samples are called Truncated samples。Whether it is TOBIT samples or truncated samples，The lower tail (or upper tail) of the error item is cut off，If the average value of sub -samples with complete information is returned，Then the average value of the error items is not 0，and will change with the changes of the explanation variable。At this time，The condition of the explanatory variable expects to be two parts: First, explain the product of the variable and its coefficient，Second is the conditional average of the error term，This bet365 Play online games average is the function of the explanation variable。Obviously，The consequences of intercepting the sample are similar to the omissions variable，The conditional average of the error item is omitted here，It is related to the interpretation variable。So，A mean return on the average value of sub -samples with complete information，Explanation variables have endogenous，will lead to non -consistent estimates。

Fourth，Explanation variables have measurement errors。When the explanation variable has measurement errors，Measurement error needs to be offset by the model error item，So the explanation variable and error items contain the measurement error with the opposite symbol，This causes the interpretation variables and error items，Its influence is similar to omitted the necessary explanation variables。

　　Coordinated to solve endogenous problems

Solve endogenous problems，A commonly used method is to use tool variables (IV)。You need to meet two conditions: First, exogenous，At least weak exogenous，That is, it is not related to the random impact of the model or the individual itself。Actually，The tool variables we can usually find are weak exogenous，Strict exterior tool variables are difficult to find。Second is to be related to the explanation variable。Under the premise of satisfying the exogenous，The higher the correlation, the better。

If the tool variable is weak，For example，Internal explanation of the lagging item of the variable as a tool variable，Although we can get the consistent estimation result，but，Under a limited sample，The estimated quantity is still wrong。and，IV estimation is the reduction of the difference at the cost of increasing the square。That is to say，Compared with OLS estimates，IV estimation has a larger variance。The weaker the correlation between the tool variable and endogenous interpretation variable，The greater the variance of the estimated square，This is the so -called weak tool variable problem。Obviously，IV estimation is to weigh between errors and variances。

Bet365 app download Except for the difference in variance，When using IV estimation measurement disposal effect，There are also local recognition questions。When the IV -based estimation measurement disposal effect，The selected IV is generally virtual variables。In the sample，There may be some individual selection behaviors not affected by this virtual variable，The so -called "not follower"。For this part of "No follower"，We cannot recognize its identity，It is even impossible to identify its disposal effect。

Obviously，Tool variable is not a "universal key" for processing endogenous "。So，Except for tool variables，What can I do?

One，Complete model。Obviously，Endogenity caused by omitted variables，It should be avoided by the complete settings of the model。Because the omission variable usually causes all the interpretation variables in the model to be endogenous，to add difficulty to the choice of tool variable set。The setting of the model must have economic theory、The conduction mechanism or prior information is based，Not a simple data experiment，Otherwise，The completeness of the model settings cannot be judged。In the measurement of the disposal effect，If the disposal variable is endogenous，The condition of the output variable expects to explain the product of the interpretation variable and its coefficient，The difference between the two is the ratio of two Mills (Mills)。So，Based on Popularity Assumption，Two inverse Mills ratio ratio as an explanation variable through the HECKMAN two -step method is added to the model，You can use linear regression to identify and deal with the effect。

Its two，error correction。Dynamic panel models have inherent endogenous，There is a sequence -related error item due to individual effects，This leads to lagging variables that are explained as endogenous。but but，LSDV estimation of the dynamic panel model, although it is consistent，But compared with IV estimation，but has the smallest variance。Bet365 lotto review Existing literature gives the extreme error of LSDV estimation quantity。So，You can use iterative algorithm，Mistake correction of lsdv estimation，This retains the variance advantage of LSDV，reduced estimation error。So，For dynamic panel models，IV estimation or broad torque method (GMM) is not an inevitable choice。

Its three，ML Estimation。Wish to know，Selection model of endogenous，Except heckman two -step method，We can also perform ML estimation。and，For many models that exist in endogenous，If the space self -regression model，ML estimation can be performed，Including the quasi great like graive (qmle)、Conditions Extremely graive (CMLE), etc.。

Its four，How to avoid endogenousness? In empirical analysis，DID method is widely used to measure the disposal effect。The reason why I use DID，It must be the condition that the independent assumption is not established，It is impossible to identify the disposal effect by the comparison of individuals and non -disposal individuals on the cross section。DID based on non -disposal individuals control the irreplaceable time effect，Then use the comparison of the individual to identify the disposal effect。Obviously，If the disposal of the individual and the non -disposal individual have different time effects，Part of the time effect of handling individuals will be missed in error items，The estimation of the disposal effect is not consistent，This is similar to omitting the necessary interpretation variables in the model。So how to judge the same time effect between the disposal individual and the non -disposal of the individual? In the regression equation，The same time effect means，The grade difference coefficient of all time points before the processing group and the reference group are 0。This is a multi -constrained test，f Statistics、Statistical quantity of like grant ratio (LR)、Wald (WALD) statistics、Ragram's multiplication (LM) statistics are applicable。It needs to be noted: bet365 Play online games the inspection conclusion of "the same time degeneration" comes from "No Refusal of the Assumption"，At this time，The lower the significant level (the larger the α)，Test the conclusion, the more credible。

Finally, explain a bit，Even if the interpretation variable endogenous，OLS or FMOLS of the co -consolidation equation、DOLS estimation is still super consistent，Generally does not require tool variables。In short，Endogenous treatment The specific problems should be analyzed，No universal paradigm。

　　(Author Unit: School of Economics, Huazhong University of Science and Technology)