I am trying to estimate a linear regression model (in the context of econometrics) using Bayesian approach (Gibbs sampler). The choice of the explanatory variables and model specification can be backed up by the literature and are intuitively reasonable. Simulated samples look like all converged from trace plots (MC iterations 20000+). However, I computed 95% highest posterior density and the results show that all of the estimated coefficients in the model are not significantly different from 0. It is micro level data and the sample size is around 300.
Could anyone help to explain how to understand such situation and how to deal with such "problem" please?
Model estimated is demand system: expenditure share = intercept + log(price) + log(real expenditure) + log(real expenditure)^2 + sociodemographic variables + error
Have tried 5 and 6 groups (5 or 6 equations to be estimated), and each equation contains at least 8 or 9 (where without any sociodemograghic variables added for testing) explanatory variables.
I am kind of lost in experimenting with data (e.g trying out different number of groups and including different sociodem variables). Is there a systematic framework to approach this question please? e.g. From the perspective of the nature of data, the model specification and the sampling method?