Unmatched asset returns

[ArlenChiu]

Hi Professor, I have trying to replicate results in the paper and found your code is extremely helpful, especially for people like me who just start to use Dynare. So I got exact same IRF figures as what's shown in the paper. But for the asset returns data, it doesn't seem like quite right. I don't know if that's because we use second approximation instead of log linear asset pricing here. Here is the results I get based on your code and mod file. Numbers in the parenthesis is the results in the paper while those without parenthesis are from the code.

Another silly problem is, could you tell me or give me some hints on how to do log-linear asset pricing and calculate returns moments as in the paper? I searched a pile of papers and codes. None of them is using this approach and no one is writing it explicitly on how to actually do that. Any answer or recommendation would be helpful!!! I also built another model by substituting variable with exp(x). It produces same IRF. So it should be log-linear type of model, right? Then, how I am supposed to calculate expected risk free rate and so on?

Many thanks!!!!!

[JohannesPfeifer]

@ArlenChiu This is a preliminary version of the mod-file. I was never fully able to replicate the results of the paper. So any comments are welcome.

You also may want to check out https://forum.dynare.org/t/replication-codes-for-papers-with-equity-premia/12438/2

The idea of log-linear asset pricing is using the log-normal distribution. If log(x) is mean 0, then x will have mean exp(0+0.5*sigma^2). Thus, the variance of the series matters. This is what I quickly tried at the bottom of the file. You simulate the log of a variable and then undo the log before taking the mean. Theoretically, that should give you the same result.

[ArlenChiu]

Thanks! In fact, everything is fine except the volatility. I am not sure what's the problem. I checked other versions of code but they all have some other problems. Your code is the best one I can find out.

By the way, I am also trying to build the model with financial leverage shown in the paper. So the definition of dividends must be changed like (4.4) in the paper. Then I added pricing of 20-period discount bond, that is, $lambdaV_1 = betastar^20lambda(+20);$. Is that correct? Also I know the resource constraint must be modified accordingly. My question is, how I am supposed to change the resource constraint and is there any other part I need to change?
Thanks!