Bayesian estimation for parameters of varying coefficient models

[Linh Trang Nguyen]

Hi guys,

I'm conducting my thesis and I'm getting trouble with the ways to conduct Bayesian estimation for the equation (pic 2). Can anyone help me to figure out what commands can I use to estimate this varying coefficient equation
Thanks a lot.

[Stephen Jenkins]

The model appears to refer to panel data (firms by year) in which there is a random intercept (mu_i) and one random slope (beta_1). It is unclear why one needs Bayesian methods to fit this model: see e.g. mixed. But you can use Bayesian methods: have you looked already at help bayesian estimation ? If not, why not? [Please see the Forum FAQ about how to post good questions.] As the help file shows, mixed models can fitted using Bayesian methods in Stata.

[Linh Trang Nguyen]

First of all, thanks a lot for helping Mr.Jenkins.

Regarding the reasons why I want to use bayesian to estimate firm-varying coefficient (beta_1_i), it is because the number of parameters to be estimated is large when using other methods like OLS and other techniques also involve many normality assumptions as well. As a result, bayesian estimation method is a more appropriate method for a full probabilistic inference of all parameters (including the firm varying ones).

I have tried the mixed command, however, I still have some questions regarding this topic, so can you help me to solve these problems ^^:
1. The picture below is my draft running, so can you check whether I have conducted the right estimation or not?
(as you can see in the table 3 above, there is a line said that dependent variable is (deltaCH_i_t) / (TA_i_t-1) while the dependent variable in equation 2 is (deltaCH_i_t) / (TA_i_t), so do I need to change the data of dependent variable)

2. I need to include the time dummies for the estimation to compare with no time dummies, so how can I do it?

3. As you can see in the table 3 (the picture above), I need to display the information regarding firm-varying coefficient like (minimum, maximum, % > 0, % <0,...) but the results seem to have some figures only, how can I display the remaining. And I want to confirm whether the coefficient that I want to estimate is {U1:firm1}

4. The density graph when I display the graph of parameters is kernel density graph right?

Once again, thank you for assisting me with stata.

Best regards,