This paper is the basis for the talk given at the URPE sessions of the Allied Social Sciences Associations convention in New Orleans on January 7, 2000. All footnotes were lost in the translation to HTML. 

Work in progress: Do not quote, unless favorably. Comments welcome. 
The Rise and Fall of Stagflation: Toward Empirical Tests of Alternative Theories
By
James Devine
Economics Department
4227 University Hall
Loyola Marymount University
Los Angeles, CA 900468410
310/3382948; 310/3381950 FAX
http://bellarmine.lmu.edu/~JDevine
January 3, 2001
click here to see the handout or here to see the bibliography.
This paper aims to set the stage for testing two distinct approaches to understanding and explaining the phenomenon of stagflation  and thus its rise and fall for the United States after the 1950s as seen in Chart I discussed below. These are the dominant neoclassical (NC) school and the dissident Political Economy (PE) school, which correspond roughly to the natural rate hypothesis (NRH) and the conflict theory of inflation (CTI), respectively, for the topic of the unemploymentinflation nexus. My version of the CTI builds on the work of Carlin & Soskice (C&S, 1990) and Burdekin & Burkett (B&B, 1996). (See also Palley, 1996.) However, unlike in those authors' work, this paper emphasizes a single factor in causing stagflation, i.e., low profit rates corrected for variations in capacity utilization. That is, low profitability encourages stagflation in a society utilizing fiat money: capitalists are able to punish society for its persistence  with high inflation and/or unemployment (Devine, 1980, ch. 6). While it is possible that a wellorganized and militant labor movement might also cause stagflation, I do not see that case as relevant to the U.S. during the historical period in question (cf. Brenner, 1998). While "supply shocks" such as the 1970s oil crises are important, I interpret them as being transitory phenomena that hardly explain the decade of stagflation during the 1970s. That is, though they have an effect on the rate of stagflation, they are not central to my theory  nor do they contradict it. For a preview of my results, see the empirical relationship between fullcapacity profitability and stagflation in Charts II and tables I through III below.
Because of my long conviction about the role of low profitability in causing stagflation, I have a prior bias that can easily distort my econometric research, simply reinforcing my own prejudices. To deal with this problem, the framework of generaltospecific modeling (cf. Charemza and Deadman, 1992, ch. 4) will be used for econometric estimation. In this methodology, the goal is to state a regression equation that involves and tests major competing hypotheses, embedded in the same functional form. Though the present paper does present some empirical data, the emphasis below is on specifying the key equations and is thus rather theoretical. The actual estimation, however, is the topic for a future version of this paper.
Not surprisingly, the CTI and the NRH have different methodological bases. The original or "hardcore" NRH (Friedman, 1968) followed the NC tradition: it was idealist, deductivist, and marketoriented, seeing the empirical world of capitalism as an imperfect reflection (as if on the wall of Plato's cave) of the ideal form of Walrasian general equilibrium. As B&B (ch. 1) make clear, the CTI involves a distinct analytical approach to inflation, what might be called the method of political economy: this approach is more materialist, inductive, and institutionalist, starting with a complex and heterogeneous empirical reality and trying to attain theoretical generalizations from it, with no presumptions of either the real world having a high degree of perfection or the applicability of the same model to all countries and all time periods.^{ }
Despite these methodological differences, there has been convergence between these views, with many practitioners of the NRH moving in the direction of the CTI, probably due to their aim of understanding the empirical world in an era when economic data keep on indicating that previous estimates of the natural rate of unemployment were too high. It is not only that the highlyideological phrase "natural rate of unemployment" seems to be replaced more often by the more scientificsounding "NonAccelerating Inflation Rate of Unemployment" (NAIRU). More crucially, as Pollin (1998) notes, recent confrontations of the NRH against empirical data have encouraged the use of CTI concepts (cf. Stiglitz, 1997: 7; R.J. Gordon, 1997, 1998: 30; Blanchard and Katz, 1997). For example, perhaps based on work by Diamond (1982), Blanchard and Katz (hereafter called "B&K") use a model first developed by Soskice (1983; cf. C&S, 1990) as part of an institutionalist conflictoriented model of inflation. For lack of a better name, this move toward a NRH/CTI synthesis will be called the "softcore NRH."
Despite convergence, fundamental differences remain. Instead of dwelling on highlevel methodological issues, however, this paper tries to get the two visions to face off in the empirical realm. The careful specification of regression equations is required so that this battle is on a methodologically level playing field. Below, section I presents the basic theory of, and some evidence for, the profitabilitydriven version of the CTI, developed by comparing it to the hard and softcore NRH. Then, section II [not in current ms.] analyzes empirical reasons for rising and then falling stagflation. All of this involves some contrast of the PE and NC methodologies and, more importantly, the development of a complete politicaleconomic story of that rise and fall.
I. Theories of Stagflationary Potential.
This section starts with a summary of the history we are trying to understand and the definition of central concepts, and then moves to a presentation of both my version of the CTI and the main orthodox views. Critiques of the NRH and some other ways that NC economists approach these questions (such as analysis of the Beveridge curve) plus clarification of the different types of unemployment then set the stage for a move to understanding the political economy of stagflation in the United States since the 1950s.
It is first necessary to define the main theory being criticized and (hopefully) replaced and then to more clearly define the issue being discussed, stagflation.
A. The HardCore NRH vs. Structural Inflation.
A description of what used to be the only NC way to understand stagflation helps frame the discussion. Robert J. Gordon (1997) examines inflationary behavior at different unemployment rates, hoping to discover the value of the NAIRU. Before bringing in such complications as the "TimeVarying NAIRU" (discussed below), he employed what he calls the "triangle model" of the Phillips Curve (PC), which had been developed in a less of a NRH mode by Eckstein (1981). For the purposes of this paper, the model is summarized by an equation of the following sort for a given year:
p = b (U  N) + shock + l p^{e} 
[1] 
where p refers to the inflation rate, while b and l are positive constants. The first term on the righthand side represents demand inflation or shortterm PC inflation, which rises as the unemployment rate (U) falls relative to the NAIRU (N). The second term refers to transitory supplyshock inflation. The variable in the third term, p^{e}, is expectations of future inflation. The coefficient l refers to the degree to which expectational inflation passes through to cause actual inflation, which allows the possibility of positive feedback and inflationary acceleration.
i) Following the canonical NRH assumptions that l = 1 and shock = 0 gives a vertical longrun PC at U = N with p = p^{e}. In the NRH literature, N is typically assumed to be independent of the current U, even if the gap between unemployment and N persists (i.e. there is no hysteresis). In the hardcore NRH though not in the softcore version, N is assumed to be unique and equal to the structuralfrictional unemployment rate, U_{SF}, representing "supplyside" inefficiencies in laborpower markets that cannot be abolished via demand expansion without inducing accelerating inflation. That is, U_{SF} is the unemployment rate associated with Friedman's famous definition of the "natural" rate of unemployment as
"the level which would be ground out by the Walrasian system of general equilibrium equations, provided that there is imbedded in them the actual structural characteristics of the labor and commodity markets, including market imperfections, stochastic variability in demands and supplies, the cost of gathering information about job vacancies and labor availabilities, the costs of mobility, and so on" (1968: 8).
This formulation implies that if U = U_{SF}, there are no problems of inadequate aggregate demand, so the economy has attained its potential, given resources, technology, and institutional "imperfections" of the sort that Friedman mentions.
Despite his Walrasian presumptions, we need not embrace that unrealistic framework to acknowledge the existence of frictional and structural unemployment, i.e., workers temporarily between jobs (due to turnover or job search) and, more importantly, those with the wrong skills or living in the wrong location for the available jobs (mismatch unemployment). That is, even if we do not accept the hardcore NRH, we cannot automatically reject the existence of some (unknown) supplyside barrier due to inefficiencies in laborpower markets that implies that inflationary acceleration can arise from excessive demand growth (cf. Malinvaud, 1994: ch. 4). To my mind, the existence of these barriers is the part of the hardcore NRH that makes the most sense.
ii) In the canonical NRH theory, if U < N for long, the actual p > p^{e}, so that, following a partial adjustment or "adaptive expectations" mechanism, p^{e} rises. If l > 0, this feeds back to cause higher actual inflation (inflationary acceleration). Similarly, when U > N for a significant length of time, p < p^{e}, the latter falls. If l > 0, the actual inflation rate also falls (disinflation). Finally, when U = N, p^{e} = p, so expectational inflation does not change (equilibrium). Assuming that l =1, N has the desired property of uniqueness. In the simplest possible terms, this implies that, N can be estimated by looking for that value of U where the inflation rate neither rises nor falls (cf. Staiger, Stock, and Watson, 1997: 345). It is common to estimate the NAIRU by looking at the average U over a few years, presuming that the economy automatically tends toward labormarket equilibrium due to wage adjustment (which seems the basis for the TimeVarying NAIRU in Gordon's recent work) or by adjusting a posited N for a single period using demographic weights, presuming that it is determined totally by demographic variables (as in his earlier work, e.g., Gordon, 1982). That these methods are far from a direct examination of laborpower markets and thus do not look to find out the extent of U_{SF}, but rather simply assume it equal to N, is a source of theoretical problems with the hardcore NRH discussed below. But at this point, it is important to discuss an important alternative view and its implications for Phillips Curve theory.
iii) Using the above framework, the rise and fall of stagflation should be described by changes in the factor that shifts the shortrun PC to the northeast and then later to the southwest. For believers in the NRH, the only relevant shift factor is N, except in the short run, during which transitory shocks play a role. But there is at least one alternative perspective. Many economists break with the Walrasian framework of universal pricetaking, instead emphasizing the institutional nature of the U.S. economy (what Friedman might call "imperfections"), including the existence of corporations with pricesetting power, unions and informal worker groups with some wagesetting power, and thus the wageprice spiral. Some emphasize a different "main shifter" to explain stagflation. They point to structural inflation, built into the normal workings of the economy, with the clear policy implications that recessions are a very expensive  and inefficient  way to fight inflation. This phenomenon might be represented by a PC that is horizontal until unemployment is very low (cf. Piore, ed., 1979; Bowles and Edwards, 1993: 4002). In the absence of supply shocks, structural inflation^{ }would be the vertical distance under the PC.
Some empirical basis for the role of structural inflation can be found in recent empirical work in the NRH tradition, as when Brayton, Roberts, and Williams (1999: 3) find that "estimates of the NAIRU are much more precise in longlag equations than in shortlag equations." Similarly, Gordon (1998) finds past inflation from the previous 6 years to determine current inflation rates. Staiger, Stock, and Watson (1997b) also find long lags. However, these lags are hardly infinite in length, while most economists would see the Fed's antiinflation campaign of the early 1980s as successful (if very costly). So the idea of structural inflation should be modified, not by rejecting the institutional framework (and accepting Walrasian theory) but instead by allowing its adjustment over time, following a rough partialadjustment model. Thus, the concept is here renamed the inflationary hangover, p^{H}.
This is the inflation left over from the past. It fits the typical econometric practice, which tries to measure p^{e} by a weighted average of lagged inflation rates. As in most treatments of p^{e}, this variable follows partial adjustment over time. The concept of inflationary hangover is less restrictive than p^{e}, because it allows for objective inertial inflationary processes, such as the pricewage spiral, to play a role. The theory in which hangover inflation is totally expectational is only a special case.
B. Measuring Stagflation
This paper avoids  and aims to transcend  the debate between the NRH and structuralist visions by assuming that a downwardsloping shortterm PC exists in (p, U) space during any given year (b > 0). Then the Stagflation Potential Factor (SPF) is used to measure the shifts of this curve. It measures the increase in inflation that occurs over time at any given unemployment rate or the increase in unemployment that occurs at a given inflation rate.
The preliminary SPF used is a version of the famous "Misery Index" (MI), the sum of the official inflation and unemployment rates (p + U). The usual MI has no real scientific basis but instead is a shortterm political index used in journalism, indicating the possibility of incumbent politicians being thrown out of office and the like. The SPF, on the other hand, is not meant to be normative or political but simply a way of measuring changes in the NAIRU and/or structural inflation. Using the p + U to measure its location assumes that the PC for a year can be approximated by a line with a slope of 1. Given b = 1, plus the canonical NRH assumptions, equation [1] implies that MI equals the sum of the two most common shift factors, p^{H} + N.
Other formulas for the SPF can be used to measures shifts of other possible forms of the PC. The one I tried was using Gordon's estimate of the Phillips curve (1998: 3145) to assign weights to p and U for a year's period of time. Gordon's estimated b = 0.6, so that p + 0.6∙U is the weighted sum of the two shift factors for the shortterm (oneyear) PC under canonical NRH assumptions. This will be called the "weighted SPF." As seen below, this weighting does not change the results significantly.
{Chart I goes about here.}
A broadstrokes history shows rising (unweighted or weighted) SPF from the 1950s and the 1960s to the 1970s, followed by a fall in the 1980s to the 1990s. Chart I shows four measures of the unweighted SPF based on the CPIUX1, an alternative to the usual CPIU that is calculated in a more consistent way over time; the CPIURS (research series); the average price of total personal consumption expenditure (PCE) prices; and finally, the average price for the nonfinancial corporate business (NFCB) sector. While the SPFs differ, they generally move together.
Unlike the standard MI, an ideal SPF would exclude the direct effects of transitory supply shocks. It would thus use a measures of persistent inflation such as the core inflation rate, which is calculated using a price level stripped of volatile energy and food prices. However, this does not seem to matter very much, as seen in the yearly data table I below, since using the "core CPI" does not imply radically different results from the noncore versions of the CPIUX1 and the CPIRS.
The ideal SPF might also exclude those kinds of inflation and unemployment which do not change as the result of the effort by capitalists to attain a target profit rate (and are thus not explained by the theory developed below). These would include changes in the amount of structural unemployment that occur due to demographic changes (assuming that such a theory is valid), and changes in the measurement of either unemployment or inflation that lower the MI. Similarly, changes in the importance of "demandshift inflation" (cf. Schultze, 1959) due to changes in the degree of overall downward price and wage stickiness would not be part of the SPF because they do not arise from profitseeking changes. However, this exclusion of nonprofitdriven factors is mathematically equivalent to avoiding the calculation of an ideal SPF and then bringing in other variables to reflect other causes of a changing MI. This latter strategy is pursued, initially assuming that these other variables are assumed constant.
Turn now to the main theory of this paper, the profitdriven version of the CTI.
C. Profitability's Role.
1. Theory
Because of the aforementioned convergence of theoretical schools in empirical research, this paper's story of the rise and fall of stagflation can be understood by translating one statement of the softcore NRH theory. B&K (1997: 57) and Stiglitz (1997: 7) posit the "wageaspiration effect," i.e., "excessive" claims by workers relative to productivity growth (a _{W}), which they see as raising the NAIRU relative to the structuralfrictional unemployment rate. If one rejects the vertical longrun PC of the NRH, this view can be extended to say that a rising wageaspiration gap ("excess real wage push") encourages the SPF to grow, while the lowering of this gap encourages it to fall. Recent pleasant experience with falling SPF can then be linked to a falling wage aspiration gap or even a negative one (i.e., workers only being capable of aspiring to attain real wages that fall relative to labor productivity).
The alternative profitaspiration thesis, turns this view on its head  without totally contradicting it. Our ability to do so arises because, as the CTI indicates, it is not a single group's "excessive" claim on the product that encourages inflation but rather the sum of the claims of all groups contending in the battle over the production and distribution of the product that can be "excessive" and thus encourage inflation. That is, what's important in the inflationary process is total excess claims on the product, a , which for a simple twoclass model equals:
a = a _{R }+ a _{W} 
[2] 
where a _{R} is the claim by capital on the total product. Following Brenner's (1998) research, there is good reason to assume that workers' aspirations were either constant or falling during the period after 1950 or so. For simplicity, assume that a _{W} is constant. Given this, we can summarize the profitaspiration thesis by rewriting two sentences by B&K (1997: 57), changing the name of the active force. This conception can be broken into [i] shortrun and [ii] longrun components:
Suppose, for example, that the rate of productivity growth decreases. If, at a given unemployment rate, [i] capitalists keep asking for profit rates corresponding to the previous higher rate of productivity growth, lower productivity growth will lead to a higher NAIRU until [ii] aspirations have adjusted to the new realities.
For the presumed fall in productivity growth, we can substitute the complex of politicaleconomic changes occurring in the transition from the socalled "Golden Age" of 1950s and 1960s to the 1970s (described in section II), including slower productivity growth and a rising degree of international competition (Brenner's emphasis). These changes are summarized by a fall in the cyclicallycorrected rate of profit (r*), as after 1965 as seen, for example, in Liebling (1980).
i) The falling profit rate implied that in the short run, capitalists "aspired" to a higher rate of profit (the target profit rate, r^{T}) than they could receive, given slow productivity growth, the resistance of other societal forces, and the like. Therefore, they strove to attain the profit rate to which they had become accustomed  by depressing the real claims of other classes and groups on the total product. Continuing the logical chain, this raised the NAIRU and thus the SPF even if structural conditions in laborpower markets (such as the demographic mix or its effects) and U_{SF} are held constant.
To understand how the impact of this profitseeking works in greater depth, first consider the shortrun situation, with a given unemployment rate, for example, equal to U_{SF}. Also assume initially that p^{H} is constant. Other nominal claims on the total product cannot be reduced immediately, so the capitalists can strive to restore profits only by raising prices. Having a low aggregate average r* compared to r^{T} means that these conditions affect enough capitalists that it causes a general rise in prices rather than mere changes in relative prices. But these individual efforts to find a solution do not work for the class as a whole to raise the profit rate: pricehikes do not automatically solve the shortrun problem of other groups having the ability to claim part of the product at any given U as those groups fight to preserve real standards of living by raising nominal incomes. As long as these other groups can successfully resist real cuts in their incomes, capitalists must raise prices, so that a continuous process of inflation results, on top of any preexisting inflationary hangover. Further, to a large extent, the hike of one capitalist's prices represents an increase in another's costs, so that the conflict over the distribution of income is not only between classes but within the capitalist class.
Going beyond the usual presentation of the CTI, a low profit rate discourages real investment, which in turn encourages productivity stagnation to continue (as emphasized by Liebling, 1980), though it is hardly the whole explanation of that phenomena. Efforts to make the best of a bad situation by raising prices replaces more "progressive" efforts to improve technology and thus profitability via investment. The encouragement of existing tendencies toward productivity stagnation intensifies the capitalists' predicament. Thus, stagflation, as during the 1970s, is a response to what Liebling terms the "disequilibrium" of the rate of return on capital ownership.
Following B&B's framework, this discussion implies that an extra profitaspiration term a would be added to equation [1], where given [2] and the constancy of a _{W},
a = g (r^{T}  r*); 
g (0) = 0; g ' > 0 
[3] 
Add [3] to equation [1], while assuming that we can replace the N in [1] with U_{SF} following the hardcore NRH assumption. Also making the canonical NRH assumptions, this gives us:
p = a  b (U  U_{SF}) + p^{H} 
[4] 
If r^{T}  r* > 0 so that a > 0, then p > p^{H} even when U = U_{SF}. If we now allow for partialadjustment determination of p^{H}, this in turn implies inflationary acceleration even at U_{SF}.
This result implies that both the softcore NRH and my interpretation of the CTI eliminate the hardcore identification of the NAIRU with the structuralfrictional unemployment rate: dropping the assumption of a constant U rate while making the canonical NRH assumptions, constantinflation equilibrium is defined as the unemployment rate where p = p^{H}, so that equation [4] implies an equilibrium unemployment rate or NAIRU of:
N = U_{SF} + U_{B} = U_{SF} + a /b 
[5] 
The first kind, structuralfrictional unemployment, was discussed above. The second is bargainingpower unemployment, equal to a /b . Equation [5] implies that we can present a conflict theory of the PC without adding an explicit a term to equation [1], but by simply distinguishing between N and U_{SF}.
What is the economics behind this distinction? Intuitively, if a > 0, to prevent accelerating inflation at U_{SF} when the r* is low compared to r^{T}, the economy needs extra unemployment to undermine the bargaining power of workers in order to reduce workers' wage aspirations to force them in line with profit goals. This kind of unemployment is akin to Marx's "floating" reserve army of the unemployed (1867: ch. 25 § 4), Lerner's (1951: 195) "economic friction," and C&S's "involuntary" unemployment. It cannot exist in the unvarnished Walrasian general equilibrium model that dominates hardcore conceptions of the NRH. In the Marxian tradition, it is not a form of labormarket "inefficiency" in the sense that structural or frictional unemployment is (i.e., due to barriers to the movement of laborpower between firms, industries, and geographical areas). Rather, it is a normal component of a capitalist economy needed to motivate work under often authoritarian, boring, and/or demeaning conditions and to preserve profitability. Note that this reserve army need not be of the same size in all timeperiods, since laborpower market institutions change. Nor need the economy supply enough unemployment to match the notional reserve army at all times. Rather, if it does not do so, accelerating inflation is encouraged, absent incomes policies and similar institutional changes.
Crucially, U_{B} corresponds to a chronic kind of deficientdemand unemployment (a.k.a. cyclical unemployment), with the number of unemployed workers usually exceeding the number of vacancies (job openings). Some of potential output is forgone, in order to sap workers' bargaining power. In the tradition of J. M. Keynes, C&S label it "involuntary unemployment." In contrast, U_{SF} corresponds to types of unemployment which would exist even if the number of available jobs equaled the number of unemployed workers (at "Beveridge full employment," discussed below).
In sum, the existence of a positive U_{B} implies that the NAIRU and the "natural" rate of unemployment (U_{SF}) are distinct concepts. That means that the hardcore NRH is a special case, one that assumes that U_{B} equals zero. However, both B&K's softcore NRH and my own profitdriven theory are special cases of the more general CTI. B&K in effect admits the existence of bargainingpower unemployment as necessary to force workers' aspirations in line. As far as I know, they do not acknowledge the need to keep the supply of vacancies scarce as part of this picture. The big difference is that B&K blame changes in a _{W}, while I blame changes in a _{R} for the specific period being studied.
ii) In the longer run, my profitdriven version of the CTI presents a clear alternative vision of causation to that of B&K: unlike workers, the capitalists did not need to adjust to the new "reality" during the last 25 years. Instead, starting in the 1970s they used their political and economic power to launch a broadbased offensive, changing "reality" to make it more to their liking, so that "adequate" profit rates could be attained once again. In this, they were joined by economists such as Liebling (1980: ch. 7), who proposed policies to boost profit rates  and of course by politicians, who are always responsive to the lure of campaign contributions and lobbyists' influence. Eventually, the fullcapacity profit rate enjoyed substantial (though not as yet complete) recovery, so that both the bargainingpower unemployment needed to protect profits and the SPF fell during the 1990s. In other words, the persistence of low inflation in the face of low unemployment during recent years (possible because of a falling NAIRU or SPF) is intimately tied to growing differences in power and income between classes, as the CTI emphasizes (especially that presented by B&B). This story is central to the political economy developed in section II.
The interpretations of the softcore NRH and the CTI may be "observationally equivalent" (having exactly the same empirical implications), in both the short and long runs. This equivalence suggests not only that my theory (as presented so far) does not automatically add new understanding but also that most or all evidence in favor of the softcore NRH also endorses the CTI. Crucially, however, the theory presented here differs by (1) emphasizing the importance of the rate of profit and (2) positing determinants of capitalists' aspirations or "reservation" profit rates. Turn to these issues next.
2. Clarifications.
The theory presented here is quite appropriate to an economic system driven by aggressive profitseeking (i.e., capitalism). The anarchy of production is presumed to prevail, so that capitalists pursue price hikes on the microlevel even when they do not solve macro problems of low profitability. Further, there are two separate but complementary microeconomic perspectives behind the causal link between profitability and inflation, which help us state the theory more clearly. At this level, we must also consider the role of the actual profit rate in the story and also the historical context of this paper.
i) The first presumes product market imperfection, firms desire to apply shortrun markup pricing (where the size of the markup is determined by a longterm profitmaximization strategy, given each firm's competitive environment). The magnitude of the desired markup on fullcapacity unit production ("prime") labor costs is determined by a target rate of profit (r^{T}). A falling r* relative to the target rate of profit means that a higher price/cost markup is needed. This implies more stagflationary potential. In this model, r^{T} would likely be the average of past profit rates, so that firms are seeking to return to the "good old days" of profitability. Of course, since they do not attain their goals immediately, this encourages stagflation.
The second "microfoundation" assumes competition between industries: in the longer run, if an industry's profit rate is below that available in other sectors, exit of capital will occur, driving supplies down and prices up. For an economy as a whole, the "reservation profit rate" (the alternative profit rate, r^{A}) that would be relevant to encouraging inflation would be the rate on investment overseas.
For simplicity, r^{T} and r^{A} are merged in the discussion below, with their roles left implicit until needed. But note one implication: all else constant, it is possible that the United States might suffer from increased SPF if the rate of profit realized on foreign investment rises, encouraging higher capitalist aspirations in real production at home. This implication separates the present theory from that of B&K.
ii) Note that in my theory the actual, realized, profit rate (r) is not directly relevant to this inflationary process: if the profit rate's depression results from a low rate of capacity utilization, that low demand for the product counteracts the ability of capitalists to raise prices. So the relevant profit rate is cyclically corrected ( r*). This number is supposed to measure the depression of profit rates that arises only due to costs (including wages) and productivity growth, i.e., the other real claims on the product besides profits. The profit rate should be measured over a significant length of time (e.g., a year) to indicate the rigidity of those costs. This restriction meshes well with restrictions on the type of data that is available.
Another view that sees the profit rate as playing a role is that of Phelps (1999), who finds a positive correlation between r and the growth of employment, and thus by his implication, the fall in the NAIRU. Not only do I believe that r* is a better measure, but I found the role of the profit rate in his theory to be ad hoc and hardly consistent with the NC theory he professes. (With constant or steadilyrising rates of capacity utilization (as in recent years), r and r* should be closely connected, so that Phelps' evidence is a backhanded endorsement of my hypothesis.) See also the criticism of his "structural slumps" approach to inflation by van Ees and Garretson (1996).
iii) In general, I follow Brenner's (1998) explanation of the falling rate of profit in the United States as not being due to the rise in the working class' institutional bargaining power (and a _{W}) but instead being due to the rising degree of international competition, as other advanced capitalist powers recovered from World War II, along with the defensive ability of workers to resist wage cuts. Similarly, partial recovery of profitability in the 1990s is seen as occurring not only due to the generally successful onesided class struggle against workers but due to U.S. victories in competition with its economic competitors like Germany and Japan. Nonetheless, this paper's thesis is consistent with any theory of profitrate fluctuations that does not stress aggregate demand (capacity utilization) fluctuations alone. For the latter, the key variable r* does not change over time (except due to measurement error) and therefore cannot explain changes in stagflation within my theory.
Finally, international issues must be addressed. Even though for issues of inflation, most macroeconomists until 1970 or so treated the United States as being in effect a "closed economy" subject to some external shocks, the role of exchangerate regimes should be considered (cf. B&B, 3436). In the fixed exchangerate system of Bretton Woods, the fixed dollar exchange rate with major trading partners meant that any U.S. inflation hurt domestic businesses competing with imports or vying to export. A fixed exchange rate system encourages inflation rates to be "in sync," potentially constraining U.S. inflation. On the other hand, under the post1973 managed floating regime, domestic inflation relative to that of trading partners eventually leads to currency depreciation. This in turn helps U.S. exporters and importcompeting companies, allowing U.S. inflation to be out of line with that of other countries. However, the difference between these two regimes may be illusory: because of the U.S. dominance during the classic Bretton Woods period (including its global seigniorage power), the U.S. could determine the rate toward which world inflation rates converged. Nonetheless, some dummy variable can be introduced to test the importance of the two regimes.
3. Some Evidence.
In addition to showing the rise and fall of stagflation, diagram I also show some evidence for the basic theory I am advocating. The righthand scale measures the inverse of the cyclicallycorrected rate of profit, r*. In the diagram and those below, it is measured crudely, by taking the rate of return of domestic nonfinancial corporations and dividing it by the manufacturing rate of capacity utilization. The rough correlation between the fall of the rate of profit (a rise in its inverse) and a rise in the SPF can be seen.
Diagrams IIA, B, C, D, and E more clearly show the negative correlation between the SPF and this r*. This will be called the "profitabilitystagflation curve" (PSC). Not surprisingly, "supply shocks" and the like (e.g., the "looping" seen in most PC studies) lead to deviations between an ideal regression line and actual experience. However, for the first three of these diagrams, we do not see more than one obvious permanent shifts in the PSC  unlike similar scatter plots for the Phillips Curve that litter macroeconomics textbooks  despite all of the monumental institutional and political changes that occurred between 1960 and 1998. So the emphasis can change from trying to explain PSC's shifts, to using it to explain the shifts of the PC and changes in estimates of the NAIRU.
Diagrams IID and E show more obvious shifts than most, suggesting that the PSC may have shifted southeast for the late 1980s and the 1990s. This suggests that the PSC does not present a complete story of PC shifts, perhaps due to the way in which GDP and consumption deflators are calculated compared to that for consumer price indices. However, the possibility of institutional and political changes playing a role was never ruled out (not should it be).
{diagrams II appear near here}[diagram IIa] [diagram IIb] [diagram IIc] [diagram IId] [diagram IIe]
Tables I through III show ordinary leastsquares regressions for the PSC, using three measures of the SPF, using logs of annual data for both the independent and dependent variables. In these simple tests, the regression coefficient for the relationship between a falling r* and rising SPF (and viceversa) is statistically significant by usual standards. In the regressions that introduce time trends (in table II) have significant negative coefficients on the time trend, but without knocking out the role of profits: in fact, the coefficients on r* become more significant. The same can be seen in most of table III, which introduces a dummy variable for the period after 1986. The exceptions are for the "core" versions of the SPFs based on the various CPIs. Not surprisingly, bringing in the dummy variable lowers the significance of the time trend (with one exception). All of this suggests that the role of the dummy reflects raw material price declines, including the "oil uncrisis" of the late 1980s. Nonetheless, the tstats on our key variable r* stays significant in all three specifications.
Table 1: Different SPFs versus r*, 196098 

Stagflation Potential Factor based on: 

CPIU 
core CPIU 
CPIUX1 
GDP price 
C deflator 

Constant 
6.2578 
6.2594 
6.1359 
5.6734 
6.0735 

Std Err of Y Est 
0.1922 
0.1787 
0.1788 
0.2053 
0.1903 

adj. RSquared 
0.6419 
0.6743 
0.6625 
0.5370 
0.6291 

ln(r*) coefficient 
1.6789 
1.6756 
1.6338 
1.4480 
1.6180 

tstat 
8.3135 
8.9252 
8.6950 
6.7135 
8.0897 

(a) 
(b) 
(c) 
(d) 
(e) 

Note: Regressions use annual data and are loglinear. Each had 37 df. 

Table 2: SPFs versus r* and time, 196098 

Stagflation Potential Factor based on: 

CPIU 
core CPIU 
CPIUX1 
GDP price 
C deflator 

Constant 
7.4545 
7.1808 
7.1753 
7.0744 
7.4051 

Std Err of Y Est 
0.1670 
0.1638 
0.1590 
0.1718 
0.1574 

adj. RSquared 
0.7295 
0.7261 
0.7333 
0.6757 
0.7463 

Time coefficient 
0.0103 
0.0079 
0.0090 
0.0121 
0.0115 

tstat 
3.6037 
2.8285 
3.2881 
4.1017 
4.2546 

ln(r*) coefficient 
2.1030 
2.0022 
2.0022 
1.9445 
2.0900 

tstat 
9.9518 
9.6589 
9.9540 
8.9467 
10.4940 

(a) 
(b) 
(c) 
(d) 
(e) 

Note: Regressions use annual data and are loglinear. Each had 36 df. 
Table 3: SPFs vs. r*, time, and 198698 dummy 

Stagflation Potential Factor based on: 

CPIU 
core CPIU 
CPIUX1 
GDP price 
C deflator 

Constant 
6.3788 
6.1770 
6.1479 
5.9439 
6.4245 

Std Err of Y Est 
0.1220 
0.1248 
0.1157 
0.1229 
0.1183 

adj. Rsquared 
0.8557 
0.8410 
0.8586 
0.8341 
0.8566 

Time coefficient 
0.0077 
0.0089 
0.0083 
0.0069 
0.0050 

tstat 
2.0368 
2.2911 
2.2981 
1.8020 
1.3496 

Dummy coefficient 
0.4448 
0.4150 
0.4248 
0.4674 
0.4054 

tstat 
5.7010 
5.1986 
5.7379 
5.9485 
5.3558 

ln(r*) coefficient 
1.7295 
1.6536 
1.6455 
1.5520 
1.7495 

tstat 
10.3156 
9.6384 
10.3431 
9.1903 
10.7545 

(a) 
(b) 
(c) 
(d) 
(e) 

Note: Regressions use annual data and are loglinear. Each had 35 df. 
Also fitting with my hypothesis, Federal Reserve economists Brayton, Roberts, and Williams write that:
"Our preferred explanation [of changes in the NAIRU] is based on an augmented Phillips curve that includes the level of the markup of price relative to trend unit labor costs as an error correction term. We find that the level of the markup in the nonfarm business sector is highly significant in equations for al measures of inflation examined, with a high markup estimated to restrain inflation and a low markup putting upward pressure on inflation" (1999: 4).
This "markup relative to trend unit labor costs" is of course the most important determinant of r* (along with the outputcapital ratio and the terms of trade with the rest of the world).
It is notable that both in several of diagrams II and in Brayton, et al (pp. 267), 1998 is an exceptional year, with low SPF despite relatively low r* or markup. One possibility (suggested by Brayton et al.) is that measured profitability is inaccurate and will be reestimated upward with new data on labor productivity. Another is that either the measured or actual SPF will rise in the near future (assuming, of course, that the theory is accurate). Finally, it is possible that changes in measured inflation rates have undermined the apparent validity of the theory (without actually contradicting it).
4. Sensitivity Analysis.
We must analyze these results further, to see if they stand up even with other measures of the profit rate, other methods of correcting for cyclical change, and other sample periods. Also, we need to look at the use of the weighted SPF suggested by Gordon's estimates of b . All the following tests use a standard SPF (based on the CPIUX1), keeping the dependent variable constant while varying the independent one, leaving out the time trend and the dummy. (The tests above suggest that which measure of the SPF is used is relatively unimportant.) The following summary of preliminary results uses the tstat to test the significance of the coefficient of r*. This exercise should not be seen as "proof" of the validity of my theory but instead as an informal simulation of the process that took place in the Phillips Curve literature after 1960 or so, in which economists slowly figured out which specifications, which measures of inflation and unemployment, etc., gave the best "fit" and the specifications that were most stable over time. The ones we see today survived a somewhat Darwinian process, one that was of course constrained by theoretical preconceptions (such as the NRH). Here, the point is to imitate that process to a limited extent, in order to gain some guidance for the headtohead test of my PSC versus the NRH, to level the playing field. The tstatistic on the crucial coefficient on r* is the measure of "fitness" used in my Darwinian simulation.
i) Which profit rate is most effective at explaining changes in the SPF? Do we include or exclude interest income? Do we use a pretax or aftertax profit rate? In the empirical tests using Liebling's (1980) data for 1959 to 1977 for the NFCB sector, the type of profit rate that was best at explaining the SPF using the tstatistic criterion was the before tax and excluding net interest income. On the other hand, the weakest ability to explain was associated with an r* measured after tax and including net interest. Table 5 provides a summary of the ttests using Liebling's data to give a feel for my method here. Reading down the average ttest column (column 8) provides a quick glimpse of which rate of return does best on average. Similar results can be seen using Robert Brenner's profit rate data from 1949 to 1998: the PSC works better using the r* (which includes interest income) before tax better than after tax.
Gérard Duménil and Dominique Lévy's data provide a greater variety of possible profit rate from 1948 to 1997. For the NFCB sector (and correcting for capacity utilization), their beforecorporatetax profit rate is more significant than is their aftertax series, while those that include interest income do worse, as shown in the first row of table 4. Those that include not only corporate tax obligation as profits but also the revenues going to indirect business taxes (columns [4] and [5]) do very well, even better than those which exclude the indirect business tax. Interestingly, the profit rate measure that does the best by this criterion is the one that is not adjusted for inventory valuation and capital consumption (column [1]). The lack of these adjustments in this measure seems to counteract the negative effects of including interest income. Note however, that all of their measures pass the "t test."
These authors also present numbers for total business (which includes the selfemployed sector). The tstats appear in the second row of table 4. Again, the grossest profit rate does best. Interestingly, including interest income helps the significance of the profitrate term for this broader level of aggregation. As before, however, not netting out the indirect business tax improves significance. Again, the grossest measure (not adjusted for inventory valuation or capital consumption) does best. In general, the total business sector does better by the ttest compared to similar measures of r* for the nonfinancial corporate business sector. (The exception is for the gross beforetax profit rate excluding interest, adjusted for capital consumption and inventory valuation.) This makes sense, because the total business sector is a closer to the entire economy in terms of the level of aggregation, while the measures of the SPF are for that aggregation level.
Table 4: Duménil and Lévy data. 194897 

The tstatistics on Misery Index using various sectors and definitions. 

dependent variable: log of the misery index; independent: log of r* = r/cu. 

measure of the profit rate 

sector 
grossest measure of the profit rate 
BeforeTax profit rate, not including interest 
BeforeTax profit rate, including interest 
gross BeforeTax profit rate 
gross BeforeTax profit rate, including interest 
AfterTax profit rate, not including interest 
average tstat, excluding [6] 

NFCB 
6.476 
4.358 
3.676 
5.224 
4.392 
2.927 
4.825 

Total Business 
6.554 
4.575 
4.621 
5.145 
5.265 
n.a. 
5.232 

average tstat 
6.515 
4.467 
4.148 
5.185 
4.829 
2.927 
5.029 

[1] 
[2] 
[3] 
[4] 
[5] 
[6] 
[7] 

49 degrees of freedom. 
ii) Liebling (1980) presents several different methods of correcting measures of profitability for cyclical changes in demand, while his data are mostly for 1949 to 1977. To see which cyclical correction method did the best, I also introduced my correction (r/cu) and one based on regressions between r and cu into the pool ("the Devine2 correction"). As seen in table IV, all seven measures pass the ttest when the SPF is regressed against the r*. The ones that do the best following the ttest are those that use the PerloffWachter gap, my correction, and the "trend" gap. The last needs little introduction, because as Liebling notes, it has little effect of cyclically correcting r. Interestingly, the uncorrected r does as well almost as well as the profit rate corrected using the PW gap. (This may be because during the sample period, the Wachtel/Adelsheim theory that falling capacity utilization encourages stagflation worked relatively well.) In fact, how one does cyclical correction doesn't seem to matter very much. The PW gap, unfortunately, is based on the very weak NC theory about the existence of a wellbehaved aggregate production function, while their data is not available for much of the sample period.
Table 5: Liebling data, 194877 

The tstatistics on Misery Index using various methods of cyclical correction. 

dependent variable: log of the misery index; independent: log of rate of return. 

Method of Cyclical Correction of Rate of Return. 

Type of NFCB Rate of Return. 
actual (uncorrected) 
CEA gap 
STL gap 
PW gap 
"trend" gap 
Devine correction (r/cu) 
Devine2 correction 
average tstat 
Beforetax without Interest 
6.769 
4.719 
5.359 
6.813 
5.977 
6.537 
5.300 
5.925 
Beforetax including Interest 
5.265 
3.322 
4.125 
5.900 
4.703 
5.076 
4.102 
4.642 
Aftertax without Interest 
5.382 
3.868 
4.375 
5.220 
5.009 
5.031 
4.235 
4.732 
Aftertax including Interest 
2.365 
1.089 
1.302 
2.854 
2.154 
1.888 
1.516 
1.881 
average tstat 
4.337 
2.760 
3.267 
4.658 
3.955 
3.998 
3.284 
3.751 
[1] 
[2] 
[3] 
[4] 
[5] 
[6] 
[7] 
[8] 

29 degrees of freedom, except for those using the PW gap, which had 23 d.f. 
It should be stressed that the data only indicate the plausibility of my hypothesis and the PSC. But the econometrics should not go any further at this point, since the methodology of generaltospecific modeling suggests that we must consider the alternative perspective (i.e., the NC/NRH) more carefully.