What are supply shocks?
Dave raises a question that I, along with much of the new Keynesian literature, have struggled with in recent years: What is the distinction between a shock to potential output (aka the natural level of output) and a shock to the Phillips curve?
Thanks for this, it's the clearest exposition I've seen. It's my problem, not yours, but I'm still confused about NK models, despite bothering Gertler and Gali regularly with questions. The main issue is supply. Wouldn't most things that shift DAS also shift the long-run value Ybar? One way to put this is the contrast between your Figs 14-5 and 14-6. Why wouldn't an increase in (imported) oil prices work like a drop in TFP? Isn't that the mistake the Fed made in the1970s, trying to resist a shift left in Ybar? Or think of Greenspan's question in the late 1990s about whether the increase in output was also an increase in Ybar-- probably not, looking back, but it was a good question. I may have missed something obvious, but despite your usually lucid exposition, it's not clear why v might shift DAS but not affect Ybar. Is this totally clueless?
Under some sets of assumptions, there is no such distinction. In this case, the Phillips curve equation relates inflation to expected inflation and the output gap (the deviation of output from potential) without any error term. Monetary policy is particularly easy in this situation. Stabilizing inflation will also stabilize output at its natural level. The central bank does not face any tradeoff between stability in inflation and stability in the output gap. Olivier Blanchard and Jordi Gali have called this situation the "divine coincidence."
Many economists, including Blanchard and Gali, doubt that this simple case describes the world. So what is one to do? It is common to tack an additional shock onto the Phillips curve equation, which automatically makes the divine coincidence disappear. But one might wonder where, at a deeper microeconomic level, this shock comes from.
Some new Keynesian modelers build in this shock as a "markup shock." That is, with monopolistic competition, price is a markup over marginal cost. Rather than assuming this markup is constant, it could be time-varying. (Formally, you could have a stochastic elasticity of substitution among the various goods.) In this case, the natural level of output could be defined as the level of output when the markup is at its average level; it would be influenced by productivity, for example, but not the current markup. Inflation would be a function of expected inflation, the output gap, and the markup shock. In this case, because of the markup shock, the central bank faces a tradeoff between stabilizing inflation and stabilizing output at its natural (and welfare-appropriate) level, which does not change in response to the markup. Examples of papers incorporating stochastic markups include Steinsson and my article with Ball and Reis, although there are many others as well.
You might wonder whether the idea of a markup shock makes sense empirically. The fact that OPEC was an oil cartel exercising monopoly power with varying degrees of success is perhaps a good example of time-varying markups. But I would not push this argument too hard.
I suspect that the real answer is that these markup shocks are proxying for something funny going on within the price-adjustment process. I have a couple of things in mind. Blanchard and Gali have tried to build in real wage rigidities and get a kind of endogenous markup shock from that feature of wage adjustment. Alternatively, some years ago Larry Ball and I suggested that shocks to the Phillips curve might result from the interaction between the distribution of relative-price shocks and the price adjustment decision in a menu-cost environment. The result is a kind of transistory markup shock.
The bottom line: Great question. The literature is only beginning to figure out what the answer might be.