Stock price equation Nakamura and Steinsson (2018a)
Hi everyone,
I am in the process of deriving all equations in the DSGE model of Nakamura and Steinsson (2018a). So far, everything is derived correctly, but when I had a look into the replication files, especially in the modelINFO.m, a stock price equation shows up which has only be discussed indirectly in the paper but has no formal expression. Footnote 30 in Nakamura and Steinsson (2018a) states that they “[…] model stocks as an unlevered claim to the consumption stream in the economy.” In the Appendix, the usual budget constraint with wage income, consumption payments, etc. is stated. The term $B_t$ usually refers to one asset in a Basic NK Model, but in the paper, $B_t(x)$ is defined as a “random variable that denotes the state contingent payoff of the portfolio of financial securities held by households of type $x$.” Nothing else is mentioned either directly or indirectly about stock prices in the NK model and it is not even a variable in the paper. Stock prices are only defined as $sp$ in the MATLAB code. I got curious and tried to rearrange the last missing piece of information. However, I could not figure out how to properly derive the equation for the stock price, nor did I find a paper that used this exact equation.
The log-linear form of the stock price equation is
The model is a Basic New Keynesian Model with habit formation and inflation inertia. In the modelINFO.m file, the 19th equation is given as the stock price equation.
I am very grateful for any help. Many thanks in advance! I am also happy about paper suggestions that might lead me to the correct derivation. If anyone requires additional information, I will provide everything needed!
Kind regards
Here is what I extracted from the Code:
