# A note on GHH preferences

Today I want to talk a little bit about a family of prefernces which are famous in macro economics, the GHH preferences. Their origins go back to 1988 to a paper by Jeremy Greenwood, Zvi Hercowitz, and Gregory Huffman. The main idea of the function is to achieve some sort of separability of the labor with consumption, without explicitly making it a linear term, like

$u(c,l) = \frac{ c^{1-\phi} } { \phi}+\frac{ l^{1-\theta} }{1- \theta}$

They engineered then this:

$u(c,l) = \frac{1}{1-\gamma} ( c – \psi \frac{ l^{1+\theta} }{1+\theta} )^{1-\gamma}$

The beauty of such a functional form is twofold. First of all, it looks like a plausible utility function. If the parameters are not crazy, one can have in a way similar results to that of a typical CES utility. More importantly, when solving for the Lagrangian, the consumption term will disappear for the labor derivative. That means that labor will be determined only by the wage, eliminating the wealth effect for the consumption, meaning that intertemporal consumption and saving choices don’t affect labor. This is a reasonable assumption if one believes that people work independently of how the economy is doing.

By doing so, the volatility of consumption is reduced, or in other words, as shown in this paper, there will be comovements of consumption, labor and labor productivity. More recently, there is a paper which explores the consequences of large multipliers in a Neo Keynesian framework.

As always, I share a picture, now it is from the Luray Caverns. Worth exploring.