Enrico D. Turri

This paper shows that the optimal monetary policy and exchange rate framework depend critically on the economy’s commodity exposure. We develop a flexible but tractable model economy with commodity exports and imports, in which international financial conditions may vary with the commodity cycle. Stabilizing domestic prices is optimal for commodity exporters, in line with standard open-economy policy prescriptions. But for economies that use commodities as inputs in production, optimal policy largely ‘looks through’ the direct and indirect effects of commodity shocks on domestic prices; this contrasts with some earlier findings and policy practice (which only ‘looks through’ the direct effect). Exchange-rate pegs or strict CPI inflation targeting perform better for commodity importers because they stabilize wages and employment, though neither policy is robustly optimal. In emerging and developing economies, where financial conditions are more tied to the commodity cycle, trade-offs are starker and implementing the optimal policy may be challenging, since it requires enough credibility to keep inflation expectations anchored amidst greater volatility in some nominal variables.

The secular decline in the labor share and the long-run reduction in labor supply suggest that imperfect labor markets can play a role in long-run economic growth. Unlike rising markups, rising wage markdowns are compatible with a balanced growth path featuring declining labor share and constant capital-output ratio. We introduce oligopsony and oligopoly power in a neoclassical growth model with superstar firms and an inferior sector which represents workers’ outside option. Faster TFP growth in the superstar sector with respect to the inferior sector generates an endogenously increasing markdown, the driver of growth misallocation. The model can be calibrated to simultaneously match the joint trends of GDP growth, declining labor share, and hours worked. For the US, the consumption-equivalent loss with respect to the optimal growth path is around 7.5 percent. An extension of the model with hand-to-mouth workers and capitalists delivers balanced growth with increasing inequality. While—in this context— proportional taxation distorts equilibrium labor supply, a rising minimum wage can restore efficient growth.

For a long time, I struggled with log linearisation, which macroeconomists commonly use to approximate model equations. As a mathematician by training, I was never introduced to it before starting my PhD. Instead, I was taught to approximate functions and equations using Taylor expansions, and I instinctively tried to reconcile the two. To make my confusion worse, each macroeconomist seems to follow a different procedure to log linearise, and then, when I started working on a paper involving second-order approximations, the algebra of some of these methods became convoluted and I couldn’t find a clarifying reference. So I decided to add to the long-standing tradition of macroeconomists that describe their favourite recipe to log linearise models. In this pedantic note, I show how I log approximate (“linearise” is correct only for first-order approximations) equations by (1) taking a Taylor expansion and (2) choosing a deviation metric, which amounts to choosing coordinates, providing a unifying framework that can nest different approximation strategies. In doing this, I show that the difference between what economists and mathematicians (and natural scientists and engineers) do is purely representational. My approach separates the order of approximation from the choice of deviation metric, and I derive explicit second-order mappings between log and (what I term) “per-unit” deviations and show that, when handled consistently, they yield equivalent local approximations. This analysis also clarifies that the choice of deviation metric should be made based on the equations that one is approximating. Log approximation is natural for the multiplicative equations that dominate macroeconomic modelling, since they are first-order exact in logs. Instead, for example, additive identities remain exact in per-unit form.