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The Eisner Puzzle, the Unemployment Threshold and the Range of Equilibria


Using a two-regime model of the inflation-unemployment process for US data 1960:2 to 2000:2, this paper finds strong evidence to support the Eisner puzzle, which occurs when the short-run Phillips curve (SRPC) is flatter at low rates of unemployment than at higher rates. The puzzling aspect of this pattern is the expectation of excess demand to become apparent at very low rates of unemployment causing the SRPC to be steep rather than fairly flat. We show the puzzle can be resolved by estimating a three-regime model which reveals a steep SRPC at very low rates of unemployment. The estimates of the three regime model also reveal a horizontal SRPC at intermediate rates of unemployment, implying the existence of a range of equilibrium rates of unemployment at those intermediate rates.

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  1. 1.

    In natural rate models, the reliance solely on expectational error to explain business cycle fluctuations in unemployment, deviations of unemployment from the natural rate, was thought to be implausible by many, including Tobin (1972).

  2. 2.

    Throughout this paper, our definition of supply factors does not include supply shocks, such as dramatic increases in food and energy prices. Supply shocks are usually found to have a significant impact on inflation in the US and we include them in our estimation. However, the theoretical basis for their impact is not standard in microeconomic analysis of markets and the analysis that underlines Friedman’s natural rate definition, but instead rests on a presumption of short run price stickiness. Because short run price stickiness is suggestive of a weak demand effect, the interpretation of supply shocks is clouded. Their existence may tell us more about the size of the demand effect, in particular that it is small, rather than about supply factors. For example, in a flexible price economy, the effect on the price of a supply shock is ambiguous, due to the classical dichotomy.

  3. 3.

    Whilst the term NAIRU is often used, we take the view that this is simply an alternative term for the natural rate.

  4. 4.

    Staiger et al. (1997, p. 228) conclude that “the labor market variables…fail to provide estimates of the [non-accelerating inflation rate of unemployment] NAIRU any more precise than do the statistical models.” Gordon (1998, p. 299) aimed to take “the next step” to try and explain changes in the TV NAIRU but only used supply shock variables and not supply factors. Katz and Krueger (1999) focused on the impact on the NAIRU of labor market variables but only for temporary help industry did they use the inflation-unemployment relation. They used shift-share analysis or qualitative appraisals for the other labor market variables: demographic age structure, prison population, union power, worker insecurity and competitive pressure.

  5. 5.

    Solow (1990) showed that a Phillips curve model with a “wandering equilibrium” unemployment rate does at least as well on US data as a model with a fixed natural rate of unemployment. He argued for the natural rate to be “a meaningful doctrine, it is important that the critical unemployment rate should be a slowly changing ‘structural’ characteristic of the labor market and not some casual or erratic will o’the wisp” (Solow 1990, p. 64).

  6. 6.

    Friedman goes on to discuss some troubling implications of this uneasy acceptance and concludes that “the economies of monetary policy is hardly a closed field” (Solow and Taylor 1998, p. 58).

  7. 7.

    In Coen et al. (1999), Eisner and his collaborators found evidence supporting a concave SRPC in local labor markets.

  8. 8.

    From similar evidence, Stiglitz (1997) did not dismiss the natural rate concept. Solow was also skeptical about the inferences drawn from Eisner’s piecewise SRPC, suggesting that it showed the SRPC “just becomes mushy” at low rates of unemployment (Solow and Taylor 1998, p. 15). Our argument is a three-piecewise linear SRPC based on the theory of the range of equilibria can eradicate this mushiness.

  9. 9.

    This minimum rate in Laxton et al. (1999), denoted φ, follows a filter and is anchored from below by a 4% rate of unemployment. They do not use supply factors to determine this minimum rate of unemployment.

  10. 10.

    These convex SRPCs also imply a virtual absence of excess supply pressures and, thus, at high rates of unemployment, a flat SRPC. Thus, they are inconsistent with the Eisner two-piecewise linear estimates at both ends of the SRPC.

  11. 11.

    The resolution of the Eisner puzzle through two sections of the SRPC does not require a horizontal SRPC at intermediate rates of unemployment, only one shallower than the SRPC at low rates of unemployment. The estimation of Barnes and Olivei (2003), Driscoll and Holden (2004), and our estimates do return a horizontal section of the SRPC.

  12. 12.

    The regime-switching model with endogenously determined switching points, used in this paper, has been previously applied to Australia (Lye et al. 2001). In that application, two regimes were found, a peak and a range, with no evidence to support the existence over the data period 1965:3 to 1997:4, of a third, or trough, regime.

  13. 13.

    Barnes and Olivei (2003) report results using other exogenous NAIRUs such as a two-sided moving average of actual unemployment and a NAIRU based on a time-varying intercept.

  14. 14.

    Driscoll and Holden (2004) ignore supply factors altogether and instead choose bounds on the range that are constant over time. They use a grid search method to estimate these bounds.

  15. 15.

    The corollary of Barnes and Olivei’s point is also reason to investigate the determination of the natural rate. The existence of a horizontal section to the SRPC may be obscured by specifications of the natural rate that respond simply to changes in the actual rate of unemployment, such as the time varying NAIRU.

  16. 16.

    With in the range of discontinuity, the marginal valuations of the payoffs to the bargaining parties, due to asymmetric information or loss aversion, imply the equilibrium will not be changed by changes in these factors.

  17. 17.

    A description of the theory of the range of equilibria that underpins the estimates of the three regime model in this paper and a list of various models of the range of equilibria can be found in a longer version of this paper (Lye and McDonald 2007).

  18. 18.

    Following the well-known convention, specifying the dependent variable as the change in inflation captures the idea that the lagged rate of inflation proxies for the expected rate of inflation. Thus, regression I is an expectations augmented Phillips curve with a coefficient on expected inflation assumed equal to one.

  19. 19.

    For the similar form to regression I and using quarterly data, Staiger et al. (1997, Table 5.1) estimate the constant NAIRU as 6.2%. Our specification differs in sample period, 1960:2 to 2000:2 compared with 1955:1 to 1994:4, and in dropping the Nixon price controls dummy. The latter tended to be insignificant, when included in the specifications reported.

  20. 20.

    To save space, the estimates of the four unemployment level effects are not reported. It is notable that they alternate in sign.

  21. 21.

    We do not include the unemployment exit hazard in our estimates of supply factors because this variable is not exogenous to the actual rate of unemployment. Indeed, it is strongly influenced by the actual rate of unemployment. For example, in a world with a fixed natural rate of unemployment, an increase in the actual unemployment caused by a demand shock would cause the unemployment exit hazard to decrease even though the natural rate was constant. Thus, a significant negative estimate of the link from the unemployment exit hazard to the natural rate may result even with no change in the natural rate of unemployment. It would not be correct to infer from such an estimate that a decrease in search efficiency was being reflected in an increase in the natural rate of unemployment.

  22. 22.

    The model is estimated by maximum likelihood. Standard errors are calculated according to the delta method, see Rao (1973, pp.385–89).

  23. 23.

    We experimented with the supply factors listed above considered by Staiger et al. (1997). The variable for the fractions of the civilian labor force that is female and non-white are highly correlated, R squared = 0.88, so these two variables were combined using a principle components analysis. Adding the principle components variable for non-white and female and the fraction of the civilian labor force that is teen yielded insignificant coefficients on both these variables, with p values of 0.598 and 0.617. The unemployment-benefit replacement ratio retained its significance, p value = 0.019, with a slightly lower coefficient value, 0.77 compared with 0.89. The implied series for the natural rate is hardly affected. The estimates of the other coefficients are virtually unchanged. In sum, adding non-whites, females and teens to the natural rate equation is not justified. Adding the fraction of the civilian labor force that is unionised yields a significant coefficient but with an incorrect negative sign.

  24. 24.

    The confidence interval on the estimate of the natural rate, when specified as a function of the unemployment-benefit replacement ratio, is smaller than the interval for the constant natural rate version. In 1990:1, for example, the confidence interval was between 5.42% and 6.39%, when the natural rate was 5.90%. The comparable regression in Staiger et al. (1997, Table 5.7) estimates NAIRU in 1990:1 at 5.85% with Gaussian confidence interval ranging from 4.66 to 8.97, a range of 4.31 percentage points. This estimate uses unspecified supply factors and quarterly data.

  25. 25.

    The exact specification of the two-regime model can be found in Lye and McDonald (2007).

  26. 26.

    Assuming a constant value for u eq2 over the cycle does not yield satisfactory estimates. The sums of the demand effects are insignificantly different from zero in both the peak and the range and the estimated value of u eq2 is rather high, at 7.02.

  27. 27.

    The estimates shown by regression III of the sums of the unemployment level reveal a statistically significant negatively sloped short-run Phillips curve both for unemployment rates above and below u eq2. Thus, the estimates imply a natural rate model.

  28. 28.

    The null hypothesis for these three tests are as follows, using the notation found in Lye and McDonald (2007). \(H_1^0 \): \(\beta _1^L + \beta _2^L + \beta _3^L + \beta _4^L = - 0.43\), \(H_2^0 \): \(\beta _1^H + \beta _2^H + \beta _3^H + \beta _4^H = - 0.22\) and \(H_3^0 \):\(\beta _1^L + \beta _2^L + \beta _3^L + \beta _4^L = \beta _1^H + \beta _2^H + \beta _3^H + \beta _4^H \).

  29. 29.

    For the cases of the external NAIRU, we assumed γ = 3 for comparability.

  30. 30.

    The exact specification of the three-regime model can be found in Lye and McDonald (2007).

  31. 31.

    The estimates of regression V in Table 4 are based on γ = 38. This value of γ was chosen by a grid search based on minimising the Schwarz BIC because the regression program was unable to identify γ. The problem is that the likelihood function is not single-peaked with respect to variation in γ. For the three regime model as specified by regression V, the Schwarz BIC values for various values of γ are (values of γs in brackets) 645.24 (5), 665.51 (7), 665.51 (10), 660.49 (15), 659.30 (20), 638.94 (25), 638.30 (30), 638.16 (38) and 643.70 (40).

  32. 32.

    The existence of a range of equilibria is not a necessary condition for resolving the Eisner puzzle. All that is needed is a steep SRPC at low rates of unemployment.

  33. 33.

    This is their estimates based on core Personal consumption expenditures (PCE) deflator and core CPI, the closest variables to our CPI variable.

  34. 34.

    The pattern we find of three slopes for the SRPC for the US is in accord with the estimates in Barnes and Olivei (2003) and Driscoll and Holden (2004), discussed in the text. Their estimates of the size of the range of equilibria are 3.5 and 1.8 percentage points respectively.

  35. 35.

    They support De Long’s belief that there is an important role for gap closing in aggregate demand policy, cited in the introduction.

  36. 36.

    If recent globalization has increased product competition, as argued by Rogoff (2008), then this would reduce to u min, as discussed in Lye and McDonald (2007). It would be a useful exercise to incorporate the role of competition into the range model estimates. In investigating the impact on the inflation process in the US economy of the degree of competition, Duca and VanHoose (2000) show that both the natural rate and the slope of the SRPC are influenced by a measure of the price/marginal cost markup. The link with the natural rate would, in the range model, carry over to a link with u min and u max. This is discussed in Lye and McDonald (2007)


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We thank Joe Hirschberg and Bob Solow for help.

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Correspondence to Ian M. McDonald.

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Lye, J.N., McDonald, I.M. The Eisner Puzzle, the Unemployment Threshold and the Range of Equilibria. Int Adv Econ Res 14, 125–141 (2008).

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  • Eisner puzzle
  • Range of equilibria
  • Inflation
  • Unemployment
  • Natural rate


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