Greenwood–Hercowitz–Huffman preferences

GHH preferences (short for Greenwood-Hercowitz-Huffman preferences), refer to an economic formula developed by Jeremy Greenwood, Zvi Hercowitz, and Gregory Huffman, in their 1988 paper Investment, Capacity Utilization, and the Real Business Cycle. It describes the macroeconomic impact of technological changes that affect productivity.

GHH preferences have Gorman form.

Often macroeconomic models assume that agents' utility is additively separable in consumption and labor. I.e., frequently the period utility function is something like $u(c,l)={\frac {c^{1-\gamma }}{1-\gamma }}-\psi {\frac {l^{1+\theta }}{1+\theta }}$

Where $c$ is consumption, $l$ is labor (e.g., hours worked). Note that this is separable in that the utility (loss) from working does not directly effect the utility (gain or loss) from consumption.

GHH preferences might instead have a form like:

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

Where now consumption and labor are not additively separable in the same way. With this utility function, the amount you work will actually effect the amount of utility received from consumption.

More generally, the preferences are of the form

$u(c,l)=U\left(c-G(l)\right),U'>0,U''<0,G'>0,G''>0.$

The first order condition of $u(c,l)$ with respect $l$ is given by

$U'\left(c-G(l)\right)\left({\frac {dc}{dl}}-G'(l)\right)=0$

which implies

${\frac {dc}{dl}}=G'(l).$

As $dc/dl$ is typically just a wage $w$, this means the labor choice $l$ is a function of only the wage and has a closed form with $l=G'^{-1}(w)$. As a result, the preferences are exceptionally convenient to work with. Moreover, as the marginal rate of substitution is independent of consumption and only depends on the real wage, there is no wealth effect on the labour supply. Using preference without a wealth effect on the labour supply might help to explain the aggregate economic behaviour following news shocks, government spending shocks.. Their use is also very common in open macro studies.

Generalization: Jaimovich-Rebelo Preferences

GHH preferences are not consistent with a balanced growth path. Jaimovich/Rebelo proposed a preference specification that allows scaling the short-run wealth effect on the labor supply. The two polar cases are the standard King-Plosser-Rebelo preferences and the GHH-preferences.

References

• Investment, Capacity Utilization, and the Real Business Cycle (Jeremy Greenwood's website)