Working Paper: NBER ID: w13430
Authors: Xavier Gabaix
Abstract: This methodological paper presents a class of stochastic processes with appealing properties for theoretical or empirical work in finance and macroeconomics, the "linearity-generating" class. Its key property is that it yields simple exact closed-form expressions for stocks and bonds, with an arbitrary number of factors. It operates in discrete and continuous time. It has a number of economic modeling applications. These include macroeconomic situations with changing trend growth rates, or stochastic probability of disaster, asset pricing with stochastic risk premia or stochastic dividend growth rates, and yield curve analysis that allows flexibility and transparency. Many research questions may be addressed more simply and in closed form by using the linearity-generating class.
Keywords: Linearity-Generating Processes; Asset Pricing; Stochastic Processes
JEL Codes: E43; G12; G13
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| LG processes (L68) | closed-form expressions for stock and bond prices (G12) |
| expected growth rate of the stochastic discount factor multiplied by dividends (G35) | linear in the factors (C29) |
| expected growth rate of the stochastic discount factor times the vector of factors next period (O40) | linear in the factors (C29) |
| LG processes (L68) | pricing of stocks and bonds (G12) |
| higher-order moments (C69) | not influence pricing outcomes significantly (D49) |
| LG framework (L68) | applicable to various economic scenarios (E17) |
| LG processes (L68) | model long-term risks (D15) |
| LG processes (L68) | maintain a closed form for stock prices (G17) |