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I would like to thank, without implication, Peter Isard, Thomas Krueger, Douglas Laxton, Hamid Faruqee, and David Rose for many helpful discussions.
For research on the U.S. Phillips curve see Laxton, Meredith and Rose (1994), Turner (1995), Clark, Laxton and Rose (1996), and Macklem (1996). Studies involving other developed countries include Debelle and Laxton (1996) and Faruqee (1997). A prominent recent study arguing the case in favor of a linear Phillips curve is Gordon (1997).
For two notable examples see Greenspan (1994) and Blinder (1997). A theoretical model of monetary policy with a linear Phillips curve rationalizing opportunistic disinflation strategies was introduced by Orphanides et al. (1996a, b).
This may be because unemployment deviations from target induce a greater social distortion than corresponding inflation deviations. For example, Blinder (1997) argues that unemployment at 2 percent above the natural rate implies that 2 percent of workers are fully unemployed, rather than all workers being 2 percent unemployed. Alternatively, a political economy rationale could be that the central bank’s vulnerability to political attack makes it more sensitive to positive than to negative deviations of unemployment from its natural rate, as positive deviations could threaten its independence.
A dynamic specification could make the intermediate target a time-varying function of past inflation outcomes, e.g.
This assumption will be relaxed in Section V. In general, U=U* implies that there is no time-inconsistency and thus no expected inflation bias. Assuming that the target unemployment rate is less than U* would simply yield the result of positive equilibrium inflation bias with no expected decline in unemployment. For a survey of relevant issues see Cukierman (1992).
In referring to the Phillips curve, we employ the term convex rather than nonlinear as nonlinearity generally includes concave alternatives. For an example of the latter see Eisner (1996) and Stiglitz (1997). The term asymmetric is reserved for the loss function.
There is also a notional horizontal asymptote corresponding to the value of unanticipated inflation in the limiting case U=1: π-Eπ = γ(U*-l)/(l-φ) < 0.
This result is robust to both continuously differentiable and piecewise linear functional forms for the Phillips curve.
Put differently, unemployment rates above (below) the DNAIRU impose first-order (second-order) welfare costs to the policymaker.
The proof is tedious but straightforward. Details may be provided for the interested reader.
It is implicitly assumed that the inflation distribution is ergodic, so that convergence occurs for finite sample sizes after a finite number of iterations.
Note that computing the last term in (21) involves averaging only those draws whose equilibrium unemployment rates are above U*.