There is not really a general endogeneity test that can be applied in all situations.

If there is one right-hand-side variable that you are particularly interested in Emily Oster has developed a widely used method for testing for endogeneity arising from selection:

https://emilyoster.net/wp-content/uploads/UnobservableSelectionandCoefficientStabilityTheoryandEvidence.pdf

Dear Chetna,

A few useful links are as follows:-

https://www.hbs.edu/research-computing-services/Shared%20Documents/Training/intro_endogeneity.pdf

Testing endogeneity with high dimensional covariates -

https://www.stat.rutgers.edu/home/zijguo/Guo-Kang-Cai-Small-Endogeneity-Test-HighDim.pdf

Without knowing what you want to analyse and what data you use, it is impossible to give advice. You should first think about the specification of your model. I do not think, that endogeneity is caused by omitted variables, but rather, that independent variables are dependent on other independent ones. If use absolute values for a test, it will likely show much endogeneity, even endogeneity does not exist, in fact. Maybe you can follow Obiajulus proposal with differences.

Dear Chetna,

Endogenity can surely exist in cross-sectional data.

Therefore an OLS regression based on a theoretical model is important.

Furthermore, you can use Hausman test and verify with Kennefy's test.

All the best

Endogeneity occurs in an OLS equation if the residuals are correlated with an explanatory variable. In such a case the OLS estimates of the coefficients are biased. In some circumstances the boss can extend to explanatory variables which are not correlated with the residuals. Endogeneity can arise in three circumstances

1. Missing explanatory variables

2. Errors in variables

3. Simultaneity. One of the explanatory variables is impacted by the dependent variable. E.g. Consumption might be determined by income while income is determined by consumption.

You first evaluation of Endogeneity should have regard to the theory of the topic. E.g. in a study of student performance you may not have a good measure of student ability. Even if You have a measure is it subject to serious error.

If you consider that there is a problem you might ask why the collector of the data did not take this into account. If you have instrumental variables that are correlated with the residuals you can use Instrumental variable estimation to derive unbiased coefficient estimates. Note that these are also unbiased when there is no Endogeneity. One can test it there is a significant difference between the two sets of coefficient estimates. The bulls is that OLS is valid and a significant difference allows one to reject the null.

Endogeneity is more a problem with the basic model rather than a statistical problem.

In addition to @John C Frain, endogeneity can also be caused by the inclusion of lags of dependent variable in a dynamic model as the dependent variable can easily corelate with the pre-determined lag of dependent variable..

Hamid, you are right, but the problem is that one cannot find-out lagged effects from cross-sectional data. I think, endogeneity tests, in general, do not make sense for cross-sectional data. It is also difficult (maybe: impossible) to statistically test a highly dynamic (theoretical) model.

Hamid Muili The question was about cross-sectional data. The requirements of exogeneity in time series analysis are more restrictive than you have set out. In time series strict exogeneity requires that the disturbance at time t be uncorrelated with all future and past values of the explanatory variables even when there are no lags in the model. For example, see page 7 of Hayashi (2000), Econometrics, Princeton.

Consider the case that you have two estimation methods 1 and 2. Method 1 is consistent when condition A holds (e.g. A - causal explanatory variable uncorrelated with disturbance term) Method 2 is valid when A or B hold (A - causal explanatory variable uncorrelated with disturbance term and B - causal explanatory variable correlated with disturbance term)

In the example, the Instrumental Variables methodology produces consistent estimates when conditions A or B holds. OLS produces consistent results when A holds. Now the null test is that the estimates produced by method 1 and method 2 are the same. Failure to accept the difference may be due to factors such as weak instruments or small data sets etc. I regard the test as an simply looking at the appropriateness of the two methodologies. (This is a similar methodology as that used in testing for "fixed effects" in panel analysis.)

Note that exogeneity/endogeneity has a wider meaning in econometric theory than in economic theory where it largely arises due to simultaneity.

1. to check the endogeneity run a regression and find residuals.

2. then check the correlation between endogenous variable(s) and residuals.

3. if there is a high correlation endogeneity is present otherwise not.

Alternet method usge ivreg and ivendog with Instrumental Variables

@Kishor Mehra Sorry, this is a common mistake. By definition, OLS residuals are orthogonal (uncorrelated )with the explanatory variables. This is a direct consequence of the least squares optimization routine. Thus, you can not detect endogeneity in this way

Testing for endogeneity in cross-sectional data can be challenging because cross-sectional data typically lacks the time dimension necessary to establish the temporal order of events. Nevertheless, there are several techniques and approaches that can be used to detect and address endogeneity concerns in cross-sectional data. Here are a few commonly employed methods:

1. Instrumental Variables (IV) Analysis: IV analysis is a technique commonly used to address endogeneity. It involves identifying instrumental variables that are correlated with the potentially endogenous explanatory variable but are not directly related to the dependent variable. By using these instruments, you can obtain consistent estimates of the coefficients while addressing endogeneity concerns.

2. Difference-in-Differences (DID) Approach: The DID approach utilizes panel or longitudinal data, but it can be adapted to cross-sectional data in some cases. By comparing changes over time between treatment and control groups, you can identify the causal effect of the treatment variable of interest while mitigating endogeneity concerns.

3. Natural Experiments and Regression Discontinuity Design: In cross-sectional data, natural experiments or regression discontinuity designs can sometimes be leveraged to identify causal effects. These designs rely on the presence of a quasi-random assignment mechanism or a cutoff point that determines treatment or exposure. By exploiting these sources of exogenous variation, you can mitigate endogeneity concerns.

4. Control Variables and Robustness Checks: Including appropriate control variables in the regression model is essential to reduce the potential for omitted variable bias. By including relevant covariates that are correlated with the dependent variable, you can help address endogeneity concerns. Additionally, conducting robustness checks, such as using alternative control variables or specifications, can provide further insights into the robustness of the results.

5. Qualitative Tests: While not definitive, qualitative tests such as expert opinion, literature review, and plausibility checks can provide indications of potential endogeneity. These tests involve examining the theoretical and logical relationships between variables to assess the likelihood of endogeneity.