Hallo everyone

I have a question related to mesurement equation

For example: Based on quarterly data, I have

- y_obs: observable real output growth
- i_obs: observable interest rate
- y: output level is a model variable
- i: interest rate is a model variable

Why the obs. variable should relate to model variables such as

Blockquote

100log(1+y_obs/100) = y-y(-1) + mu_y; % obs. domestic outputlog(1+i_obs/400) = 4*i + mu_i; % obs. domestic interest rate

400

What is the meaning when taking log like the above equations

Thank you so much indeed