Abstract
This paper elaborates a simple model of growth with a Taylor-like monetary policy rule that includes inflation-targeting as a special case. When the inflation process originates in the product market, inflation-targeting locks in the unemployment rate prevailing at the time the policy matures. Although there is an apparent NAIRU and Phillips curve, this long-run position depends on initial conditions; in the presence of stochastic shocks, it would be path dependent. Even with an employment target in the Taylor Rule, the monetary authority will generally achieve a steady state that misses both its targets since there are multiple equilibria. With only one policy instrument, Tinbergen's Rule dictates that policy can only achieve one goal, which can take the form of a linear combination of the two targets.
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Notes
1. Two recent works that limn out the contours of heterodox macroeconomic theory in a non-polemical spirit are Taylor [2004] and Foley and Michl [1999]. The former puts somewhat more emphasis on the Keynes–Kalecki tradition, the latter on the classical tradition. For other attempts to substantiate the misgivings that heterodox economists have about monetary policy rules, see Freedman et al. [2004], Palacio-Vera [2005], Dutt [2006], Setterfield [2004], or Lavoie [2006]. The latter three develop post-Keynesian models that share some properties with the current effort. One interesting difference is that they attribute to monetary policy the ability to change the long-run growth rate of output, while we will find below that the monetary authorities can influence the level of output but not its rate of growth.
2. In the most famous classical model of the labor market and accumulation, the Goodwin [1967] model, the unemployment rate and the wage share cycle around a “center.” Formally, this means that wherever in the phase space the system begins, it will come right back around to the same point. Any displacement, in other words, would be permanent.
3. Lavoie and Kriesler [2007] argue that Duménil's and Lévy's results depend on their assumption of a zero inflation target, and that efforts to recover the Keynesian-classical duality require embracing the conventional New Consensus model. The current paper questions this interpretation because the model developed here does not gravitate toward a natural rate of unemployment, although it does achieve normal capacity utilization.
4. We will refer to this as the Phillips curve, even though Phillips [1958] himself was concerned with the relationship between wage inflation and unemployment. It seems that general usage has expanded the term to include the relationship between price inflation and unemployment.
5. As mentioned above, Fair [2004] supports this ordering, the reverse of the usual textbook treatment of the Phillips curve in which inflation originates in the labor market. However, his model emphasizes the price level, rather than its rate of change, and is not accelerationist.
6. For a lucid exposition of a reaction function that targets the real interest rate, and full discussion of its relationship to the Taylor Rule, see Carlin and Soskice [2006].
7. For a very clear presentation of recent debates about how to interpret this investment equation, consult Lavoie et al. [2004].
8. Leaving profitability out of the investment equation, as we have done, makes the paradox of costs a foregone conclusion. Including a term for the profit share produces a richer array of outcomes. For a lucid survey of what is known about the paradox of costs, see Blecker [2002].
9. It may, however, be an oversimplification to describe this model as “short-run Keynesian, long-run classical” because monetary policy does affect the level of output in the long run, even though it does not affect the steady state growth rate. We will see that this is also true in the exogenous model below.
10. Again, Lavoie et al. [2004] provides a succinct overview. Their resolution, more in the Keynesian spirit, is to allow managers to form expectations adaptively about what level of utilization is normal, so that in a conflict situation, the normal level of utilization adjusts toward the actual level.
11. This set-up has some resemblance to an approach used in the development literature, for example, by Lewis [1954] and Harris and Todaro [1970]. As one anonymous reviewer pointed out, our treatment makes the unrealistic assumption that formerly employed and unemployed workers are equally likely to secure employment in each period.
12. Alternatively, we might hypothesize that the natural rate adjusts to the warranted rate, putting us back in an endogenous growth setting. This causal structure is often proposed by post-Keynesians [Lavoie 2006].
13. The classic Layard et al. [1991] is a good source. More recently, the essays in Howell [2005] should undermine any misplaced enthusiasm for the empirical foundations of the orthodox, or any, theory of the natural rate of unemployment. Stanley [2004, p. 605] concludes that the results of his meta-analysis of studies of hysteresis “reinstate the viability of unemployment hysteresis as a ‘first approximation.’” Stanley also provides some support for the existence of publication bias.
14. The premise here is that workers and the poor are generally not hurt much by inflation, but bear the brunt of unemployment, so a central bank that identified with those groups might adopt a pure employment target, or at least deemphasize inflation.
15. It has always struck me that the Federal Reserve Board, perhaps the largest employer of Ph.D. economists in the USA, has produced no prominent corpus of research on the real costs of unemployment (including, e.g., their health effects), and very little balanced work on the costs of inflation. Would it be unreasonable to suggest that resources directed toward these questions could have a salubrious effect, especially if they incorporated the full spectrum of viewpoints?
16. If the authorities choose the wrong value for the neutral rate of interest (call it R̄), the system will still converge on full utilization because the model is premised on equality between the warranted and natural rates of growth. The actual rate of interest (as opposed to the perceived neutral rate in the reaction function) would gravitate toward the true neutral rate (i.e., giving u=1). The inflation rate will miss the target by an amount given by p*−p̄=(R n −R̄)/h1.
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Appendix
Appendix
The Jacobian of equation (4), evaluated at the equilibrium employment rate, interest rate, and rate of utilization, is:
The characteristic equation for the Jacobian is:
where the coefficients take the somewhat barbarous forms:
Gandolfo [1997, pp. 90–91] points out that recent work on cubic equations has whittled the number of necessary and sufficient conditions for the roots of the characteristic equation to lie within the unit circle down to three, basically working out the implications of the Schur–Cohn criterion. These are:
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i)
1+a1+a2+a3>0. This condition reduces to:
which will always be satisfied (see text ruling out pure employment-targeting, or h1=0).
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ii)
1−a1+a2−a3>0. This condition reduces to a linear inequality of the form h0<b0−b1h1, with b0 and b1 functions of the parameters.
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iii)
1−a2+a1a3−a32>0. This condition reduces to a polynomial inequality in the form h(h0, h1)<0.
The intersection of the sets defined by conditions (ii) and (iii) form the stable set of reaction function parameters. The stable set is illustrated in Figure 4 for the parameter values used in the simulations reported in the paper.
The stable space (shaded area) formed by conditions (ii) and (iii) of the Schur–Cohn criterion is illustrated for the parameter values: n=0.05, s=0.8, ρ=1, d0=0.1, d1=0.1, d2=0.04, and a=0.5, e*=0.945.
The condition for real roots to the characteristic equation makes use of Cardano's Formula and the polynomial discriminant defined by
where Q=(a12−3a2)/9 and P=(2a13+27a3−9a1a2)/54. These formulas, complete with historical background, were obtained from the World of Mathematics website (http://mathworld.wolfram.com) maintained by Wolfram Research and authored by Eric Weisstein. I have taken the liberty of reversing the signs given there, in order to maintain the convention associated with the quadratic equation that a negative discriminant gives complex roots.
The necessary and sufficient condition for all three roots to be real is that D⩾0. This reduces to a polynomial inequality in the form D(h0, h1)⩾0. Examination of its properties for the parameter values used in numerical simulations supports the statements about the threshold values of h0 and h1 reported in the text.
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Michl, T. Tinbergen Rules the Taylor Rule. Eastern Econ J 34, 293–309 (2008). https://doi.org/10.1057/palgrave.eej.9050037
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DOI: https://doi.org/10.1057/palgrave.eej.9050037