Is there a long-run tradeoff between inflation and unemployment?

Question

In most first-year undergrad macroeconomics courses, students are taught about the Phillips curve and how whilst there may exist a tradeoff between inflation and unemployment in the short-run, there is no such thing in the long-run as a result of agents adjusting inflation expectations. Is this result valid or could it be the case that the natural rate of unemployment changes with the output gap, in which case there could exist a long-run trade-off between inflation and unemployment?

Answer 1

could exist a long-run trade-off between inflation and unemployment?

This depends on the long-run shape of Philips curve. Well done and highly cited empirical studies generally cannot reject the long run Philips curve is flat implying there is no long run inflation unemployment trade-off, although alternative explanation is that current studies are simply not powered enough to detect (very) small slope of long run Phillips curve.

Following Benati 2015:

Both cointegration methods, and non-cointegrated structural VARs identified based on either long-run restrictions, or a combination of long-run and sign restrictions, are used in order to explore the long-run trade-off between inflation and the unemployment rate in the post-WWII U.S., U.K., Euro area, Canada, and Australia. Overall, neither approach produces clear evidence of a non-vertical trade-off. The extent of uncertainty surrounding the estimates is however substantial, thus implying that a researcher holding alternative priors about what a reasonable slope of the long-run trade-off might be will likely not see her views falsified.

....

Overall, the evidence discussed in this paper provides essentially no support to the notion of a non-vertical long-run Phillips trade-off—in particular of a trade-off which can be actively exploited by a policymaker in order to permanently reduced the unemployment rate.

In addition you can also see from data that there does not seem to be any long-run relationship (see ibid pp 258).

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PS: One should not confuse hysteresis effect (situation where temporary shocks have permanent effect), with Phillips curve inflation-unemployment trade-off where increase in inflation can decrease unemployment and vice versa.

Let me illustrate the difference.

Inflation Unemployment Trade-off

Suppose that the Phillips curve is given by following equation (see Romer Advanced Macroeconomics pp 259):

$$\pi = \pi^* + \beta (y_A- \bar{y}_A) + e$$

where $\pi$ is inflation $\pi^*$ expected inflation and $y$ is a log of actual output and $\bar{y}$ log of natural level output so the expression in brackets is output gap. Output gap in turn determines the level of employment in the economy.

Now in short run there will be a inflation/unemployment trade-off (non-flat Phillips curve) as long as $\pi \neq \pi^*$ (since $\pi \neq \pi^*$ implies inflation can affect output and thus employment which correlates with output). However, suppose that in long run $\pi = \pi^*$. In that case we will have no inflation employment trade-off.

Hysteresis

Now suppose we have not just one equation but 2

$$\pi = \pi^* + \beta (y_A- \bar{y}_A) + e \tag{1}$$

and

$$\pi = \pi^* + \beta (y_B- \bar{y}_B) + e \tag{2}$$

where $(y_B- \bar{y}_B)< (y_A- \bar{y}_A)$, with a switching rule that we move from equation (1) to (2), whenever output gap $(y_A- \bar{y}_A)$ passes some threshold for triggering hysteresis $k$.

Clearly as long as we assume that $\pi= \pi^*$ in long run Philips curve is flat (no employment inflation trade-off) in spite of the hysteresis effect.

Answer 2

Opinions differ (as always in economics) but there is some evidence that there also a long-run tradeoff due to hysteresis. Long periods of unemployment may cause the natural rate of unemployment to move up as well, e.g. due to the loss of human capital or insider-outsider dynamics in labor markets. One of the earliest papers is the Blanchard/Summers (1986) paper. But already Phelps (1972) in his book outlined that hysteresis may cause the long-run Phillips curve not to be vertical. See for example Cross (1987)

Studies like Di Bella et al. (2018) suggest this to also be an empirical issue. Hysteresis implies that for example fully stabilizing inflation at a low level vie monetary policy after temporary supply shocks may result in permanently higher unemployment. This contrasts with typical Phillips curve models where the natural rate of unemployment is independent of such demand factors like monetary policy.