Hi,

I would like to ask a few questions:

- Should I apply the one-sided hp filter on the matrix of my data (all my data together) or use it on the time series one by one? Because it seems that the function can get a matrix of time series. And if I have to use it on all my data at once, should I differentiate between aggregate variables like consumption and investment and other variables like inflation, interest rate, and share variables (percentage variables)? If yes, should I again differentiate the second group into interest rate and inflation together and share variables together?
- What is the difference between one-sided hp filter and quadratic detrending? Because I am currently using hp filter but a similar paper to my work has used quadratic detrending. What goes in the mind of someone to choose one? Do they use different methods and choose the one that seemingly estimates easier?
- Is it important and does it make a difference if I use billion dollars or million dollars for y, c, g, i or like 1000 hours or 1 hour for labor for scaling in my time series data?
- When I want to make my time series per capita, should I divide by total population over 16 or by employee count?
- I have two share parameters in my model that I have the data for, and they are calibrated for the model as the mean of their respective time series. I have made those two parameters into endogenous variables and have given them a shock each with steady state of data mean and put the rho and sigma of the shock for the estimation to estimate beside other shocks. I have also given their two real world time series as observables. Is what I am doing ok? And if it is, should I demean it normally or use the hp filter? Because these two are percentage (between 0 and 1) variables I’m not sure how to deal with the data preprocessing.
- In the paper ‘Risk Shocks’, they have just demeaned the log of hours worked per capita as labor data. Why didn’t they detrend it with one-side hp filter or differencing like their aggregate variables? Should I detrend my labor observable data with one-sided hp filter as same as my other observables (excluding inflation, interest rates (and possibly share/percentage variables which I asked)? I thought I should detrend labor data as same as aggregate variables but by reading Risk Shocks I don’t know what is right.
- There is no way I can calibrate the Frisch elasticity of labor supply based on my equations. I just put it as 1. Is it ok? It’s a typical new Keynesian utility function with real estate in it. The equation including the parameter Phi is like L^Phi/W = lambda_1. With lambda_1 being the lagrangian multiplier of one of my constraints which its steady state is coefficient/C. So, I basically have to calibrate C*(L^Phi)/W=(a number based on data if i take average or a time series if I don’t take average), which I can’t, the left side is too complex (I have the right side). The values on the left side are scale relevant so I can’t use a method like a regression on the log of the equation to calculate Phi.

Thank you in advance.