It's important to note that the choice of the appropriate model or test depends on the research question and the characteristics of the data.

There are several non-linear causality tests and models that can be used in panel data analysis.

1. Granger causality test: The Granger causality test is a common way to test for causality between two time series data. It can be extended to panel data by using panel Granger causality test.

2. Nonlinear causality test: Nonlinear causality tests can be used to test for causality between two variables when the relationship between them is nonlinear.

3. Nonlinear panel data models: Nonlinear panel data models can be used to estimate nonlinear relationships between variables in panel data.

4. Nonlinear dynamic panel data models: Nonlinear dynamic panel data models can be used to estimate the effects of lagged dependent variables on the current dependent variable.

Therefore, it is recommended to consult with a statistician or econometrician to determine the most appropriate model or test based on your specific research question.

Yes, there are non-linear causality tests and models that can be used in panel data analysis.

One commonly used non-linear causality test is the Granger causality test, which tests whether one variable can predict another variable better than random chance. This test can be extended to non-linear models by using techniques such as the threshold autoregressive (TAR) model, the smooth transition autoregressive (STAR) model, and the Markov switching autoregressive (MSAR) model. These models can capture non-linear relationships between variables and help to identify the presence of non-linear causality.

Another non-linear causality model that can be used in panel data analysis is the panel threshold model, which extends the TAR model to a panel data context. This model allows for the presence of different thresholds across individuals or groups, and can help to identify non-linear causality between variables in a panel setting.

Overall, there are several non-linear causality tests and models that can be used in panel data analysis to capture the complex relationships between variables and identify non-linear causality.

@Bayan Alshaib

Article A new test of multivariate nonlinear causality

Yes, there are non-linear causality tests and models that can be utilized to analyze panel data. These tests and models are designed to identify non-linear relationships between variables, where the relationship between two variables may differ depending on the value of a threshold variable.

One example of a non-linear causality test is the Granger causality test, which is based on the threshold autoregressive (TAR) model. The TAR model is capable of detecting non-linear relationships between variables, and can be applied to panel data by estimating a separate TAR model for each cross-section.

Another non-linear model that can be used to test for causality in panel data is the panel smooth transition regression (PSTR) model. This model estimates the parameters of a linear regression model separately for different regimes, based on the value of a threshold variable. By examining whether the inclusion of lagged values of the potential causal variable improves the prediction of the dependent variable, the PSTR model can be used to test for non-linear causality between two variables.

In addition to the Granger causality test and the PSTR model, there are other non-linear models and tests that can be applied to panel data. These include the Markov-switching model and the threshold vector autoregressive (TVAR) model. These models and tests can be valuable tools for capturing non-linear relationships and testing for non-linear causality in panel data.

In principle, it is impossible to find out causality only with statistical methods. Statistics can only tell you, if there is a more or less good relation between variables. It is on you to assume causality between variables, this is part of the identification of the model. Luckily, it is mostly quite clear in which direction causality runs (using logics, theories or merely common sense). If you formulate a linear equation for a (assumed) causal relation and you get bad statistical results, you can be sure that the relation is either non-linear or does not exist. That is why I think, that one should think about how the relation (function) may be already in the process of identification.

As, in general, causality needs time (i.e. the "caused" variable reacts with some time lag and the data of a sample are for the same period, one cannot find out the "timing", which might be necessary for testing causality (But this is also true for e.g. annual time series, when the reaction lag is short).

Yes, there are non-linear causality tests and models that can be applied to panel data to examine non-linear relationships and causality among variables. Here are a few commonly used approaches:

When working with non-linear causality tests and models in panel data, it's essential to consider the following:

• Data Stationarity: Ensure that your panel data is appropriately pre-processed, and tests or models are applied to stationary or co-integrated data, as non-linear models may require this assumption.
• Model Selection: Choose the non-linear model or test that best fits your research question and data characteristics. Model selection may involve testing for the presence of non-linearity and selecting an appropriate model specification.
• Interpretation: Interpretation of non-linear models can be more challenging than linear models. It may involve identifying threshold values or regime switches and understanding the implications of non-linear relationships.
• Robustness: Assess the robustness of your results and consider sensitivity analyses to account for potential model misspecification.

Applying non-linear causality tests and models to panel data can be a powerful tool for uncovering complex relationships and dependencies among variables, especially when linear models are insufficient to capture the underlying dynamics. However, it also requires careful consideration of model assumptions and interpretation of results.