1 – Introduction
1On page 213 of his Business Cycles, Joseph Schumpeter  provided a famous illustration of the superposition of different “waves” or economic cycles, varying in duration and amplitude. Along a linear, horizontal trend, Schumpeter drew three kinds of sinusoidal waves: long, intermediate, and short ones, with their amplitudes somewhat proportional to the respective wavelengths. Although each type of wave was pictured as a sine function, the result of adding up the three different curves onto one another—i.e. the superposition—results in a, although still symmetric, more complicated image. In accordance with Schumpeter’s general argument, it was thus shown that even such movements as the “Kondratiev”, “Juglar” and “Kitchin” cycles, postulated to be regular in their frequency, could be combined to form the more complicated time lines of economic variables that can be observed in reality.
2However, in addition to conveying this message, the graph has also influenced later discussions in other ways. As virtually the only graphical representation of some of his theoretical ideas in Schumpeter’s own work, the superposition figure may be found referenced in discussions of Schumpeter’s theory of economic development in general, not just specifically the idea of superposition (see e.g. Hanusch and Pyka [2007b: 23]). In this paper, though, it will be argued that the idea of drawing a business cycle around a steady linear, especially horizontal, trend as the economy’s gravitational centre (i.e. its equilibrium) is insufficient when referring to and trying to depict Schumpeter’s core ideas about discontinuous economic development. While it is true that the superposition figure provides the reader with some idea of Schumpeter’s thought on economic development, particularly regarding the central role cyclical fluctuations play in capitalist economies, it does not contain the whole theoretical argument. This applies especially to the relations between cycles, underlying growth trends, and growth on the whole, as well as to the question of the development of the equilibrium level of production. While Schumpeter’s superposition graph does illustrate the theoretical idea of observable “complications” as a consequence of concurrent waves, used as an explanation to such phenomena as the Great Depression of the 1930s, it should not be interpreted as representing the theoretical movements and components of every constituent cycle at the same time.
3The discussion in this paper will start by summarizing core theoretical remarks by Schumpeter and then, after a short account of Schumpeter’s business cycle theory, demonstrate why the idea of linking Schumpeter’s superposition figure directly to his central ideas concerning economic development meets with some problems. In Schumpeter’s theory, if any cycle does occur, it is always accompanied by a marked shift in the equilibrium level of production, since this is the primary effect of innovation, the core driver initiating the cycle. Thus, in the absence of exogenous shocks, what is observed ex post as the general picture of economic growth or development, is really a combination of those cyclical shifts, the accompanying fluctuations around the respective equilibrium levels, and underlying trend factors which induce gradual growth. In order to contribute to the discussion on this issue, a graphical interpretation of Schumpeter’s ideas on discontinuous economic development in general, deeply rooted within his theoretical considerations, will be provided in what follows.
2 – Schumpeter on the underlying trend, cyclical movements, and the observed trend
2.1 – The three factors constituting movements in economic variables
4One of the core theoretical ideas in Schumpeter’s writings on the business cycle and economic development in general is the strict distinction between cyclical movements and an underlying trend in economic variables. Even more separate from these two are those influences which fall into the category of exogenous shocks. The importance of this differentiation becomes evident from the repeated and meticulous mentioning of the issue, most notably in Schumpeter’s papers on “The Explanation of the Business Cycle”  and “The Analysis of Economic Change” ,  but also in many other publications, e.g., in an extensive review of Mitchell’s  Business Cycles [Schumpeter, 1930] and in Schumpeter’s own Business Cycles [1939, 6-13, 72-87]. In fact, one may go back even further, for already in his earlier German writings, in accordance with the fundamental distinction between statics and dynamics, Schumpeter drew a clear demarcation line between those factors driving economic development and disturbing the static equilibrium which originated from within the economy on the one hand, and those stabilizing influences which lead back to the static equilibrium on the other hand (see e.g. Schumpeter [1910: 324-5]). 
5The theoretical identification and separation of the elements that constitute movements in economic variables over time was thus at the heart of Schumpeter’s analysis of economic change in modern capitalist economies, within which the explanation of the business cycle was regarded as essential to a complete understanding of the whole process [Schumpeter, 1939: v]. Following Schumpeter, observed time lines in economic variables, especially aggregate production, are the result of three different factors driving the movement in various ways. The following list is a summary of Schumpeter’s remarks on this topic [see especially 1935: 2-5; also 1927: 288]:
- “Outside factors”: to this category belong possible influences which have no immediate link to economic considerations, e.g. season- or “sunspot”-specific variations in agricultural production, natural disasters, or political events such as revolutions, wars, shifts in trade or exchange rate regimes, etc. In general, they may be referred to as exogenous shocks. They contribute to the historical uniqueness of every economic fluctuation, but do not originate directly from within the economy.
- “Growth factors”: these amount to gradual increases in economic output, driven by population growth, savings and consequent capital accumulation related to well-established methods of production, and continuous, small but steady, technical progress, such as gradual increases in labour productivity as a result of learning by doing. In general, thus, “growth factors” are such changes in the data which can be absorbed by the economic system in (gradually changing) equilibrium without notable disturbance. They constitute an economy’s underlying trend, a path of equilibrium points along which the system would move in the absence of other influences.
- “Cyclical factors”: these refer to economic development through innovation, i.e. changes in the production function which cannot be decomposed into a continuum of infinitesimally small gradual improvements (such as those determining the underlying trend), and the thus ensuing creative-destruction part of a business cycle.
6To sum up, Schumpeter [1935: 4] may be quoted for stating that “[i]ndustrial change is due to the effect of outside factors, to the non-cyclical element of growth, and to innovation.” There is thus no conflict in the sense of cycles and underlying growth opposed to one another in Schumpeter’s theory, but, as will be shown more clearly in the discussion in subsection 2.3, they still need to be regarded and treated as separate influences on the whole of economic development—hence this paper’s title. Nonetheless, it should be noted that economic growth as a whole, i.e. the whole general upward movement of an economy over a long period of time, is not captured by those gradual “growth factors” alone (a point Schumpeter [1947b: 7–8] criticized classical growth theory for), as the further discussion will demonstrate in more detail as well.
7To Schumpeter [1935: 3; 1939: 72], exogenous influences are of lesser importance for the explanation not only of the business cycle, but economic movements in general, because they do not originate from the economy itself and lack common elements or regularity. While they played an important role in pre-capitalist societies, owing to the lower level of the division of labour and the high production share of agriculture, more modern economies with a sophisticated division of labour and trade networks as well as per capita production that substantially exceeds mere subsistence levels become increasingly independent especially of natural factors, such as the classic “sunspots”. Even if political factors, such as wars or specific trade policies, still exert significant influence on modern economies, they are only of secondary importance for Schumpeter’s pure analysis of economic development as a consequence of the economic process per se.  Exogenous, or “outside” factors, will thus, following Schumpeter, be left out of the further discussion in this paper. Instead, what really matters are the endogenous economic elements: especially cyclical fluctuations, but also the “growth factors”, that, at least to some extent, may be regarded as endogenous to the economy too.
2.2 – Schumpeter’s theory of economic dynamics: a short summary
8To elaborate on the crucial distinction between “cyclical” and “growth” factors, some general remarks about Schumpeter’s theory of economic development are appropriate. Schumpeter’s whole body of theory rests on the fundamental distinction between what he originally called “statics” and “dynamics” and later, due to the specific use Frisch [1929; 1936] made of this distinction, referred to as the “circular flow” and “economic development” respectively (see for example Hagemann [2003: 55-6]). Corresponding to these two categories, Schumpeter [1927: 290 ff.] also describes two modes of behaviour: “static” behaviour consists in adaptively reacting to the environment, usually in small steps, while “dynamic” behaviour (also labelled “creative response”, see Schumpeter [1939: 72; 1947a]) is the act of trying out something new. Whereas the first is always observed in reaction to every influence affecting the economy, the second need not ensue. For example, in Schumpeter’s understanding, people will always react to an exogenous shock, or the outburst of a business cycle (which requires that somebody has already acted “dynamically”), automatically in an adaptive way, trying to reconcile their previous business plans with the new status quo—or they may come up with a new idea to restructure their own enterprise, which, however, occurs far less frequently.
9Within this theoretical framework, Schumpeter [1927: 290] notes that static conditions, i.e. those that characterize the circular flow of an economy in, or in close proximity of, an equilibrium, are compatible with “growth factors”. The changes are so gradual that they can be absorbed by adaptive routine behaviour without affecting the economy’s reference equilibrium in a drastic, non-gradual way, or even causing the economy to temporarily leave the neighbourhood of equilibrium. If the economy was only moved by growth factors, it would continuously transition smoothly from one equilibrium to a nearby other. The business cycle, in contrast, cannot spring from these conditions themselves, it is an inherently dynamic, not static, process [Schumpeter, 1927: 289]. Thus, it becomes clear why Schumpeter would draw such a clear line between “growth” and “cyclical” factors and why he would separate them theoretically: one is compatible with the circular flow and does not require any kind of behaviour different from that in the circular flow, and the other demands economic agents to act differently, namely in a “dynamic” way.
10To further illustrate this point, it is helpful to look a bit closer at Schumpeter’s theoretical understanding of the business cycle. Central to this theory is the idea of innovation: an innovation occurs when a pioneering entrepreneur  picks up an invention (the mere technical capability to do something) and transforms it into something marketable. This usually requires a bank loan (or other form of borrowed capital), because most entrepreneurs do not command the means to fund their business entirely on their own, see Schumpeter [1934: 102]. Here, Schumpeter differs especially from most of his classical predecessors not only by separating the roles of “entrepreneur” and “capitalist” (see, for example, [Schumpeter 1928a;1928b]), but also by pointing out that banks are not merely traders, but creators of purchasing power, because they can virtually create credit out of nothing, see Schumpeter [1934: 98]. It is, however, important to note that credit taken out for the sake of innovation is used in a productive manner, hence, even though it may not be “backed” by current savings, it will ultimately be backed by future savings when the credit is paid back from the revenues generated from the innovation [Schumpeter, 1934: 115 fn]. It is also important to add that, while Schumpeter basically sees banks playing a passive role, simply serving pioneering entrepreneurs’ credit demand, he nevertheless acknowledges that, if they so will, they may influence the amplitude of a cycle by their credit policy, e.g. if they set off or intensify a second, speculative wave through easy credit [Schumpeter 1927: 307]. Such a speculative wave may turn a recession into a depression during the downswing [Schumpeter, 1939: 148 ff.]. 
11Once an entrepreneur is in command of the additional purchasing power bestowed upon him through credit creation, he may bid away resources from other firms (especially those acting in a “static” manner) to pursue his innovation, e.g. manufacture a new product or produce in a wholly new manner. The innovation (in a way, successful by definition) will increase the entrepreneur’s profit. It is these rents, plus the fact that it is easier to follow in somebody else’s footsteps, which draw imitators into the market, following the innovator in “crowds” or “swarms”, (e.g. Schumpeter [1927: 297 f.]). Imitators are still acting in a dynamic manner, but somewhat less so than the first pioneer did. This will lead to increased economic activity as the economy explores the potentials of the innovation, and competition increases not just between “dynamically” acting firms and “static” ones, but also between the innovator and imitators. Through this, the extra rents available from the innovation slowly disappear at the margin, which diminishes the core propagator of the cyclical upswing [Dal-Pont Legrand and Hagemann, 2007: 11].
12Schumpeter then follows Clément Juglar in describing the crisis as a necessary outcome of the upswing, and as the “turning point” leading to the downswing [Schumpeter, 1931: 6]. The crisis sets in when more and more of the consequences of the innovation actually reach the market, extra profits diminish, and entrepreneurs start paying back their loans. The recession in particular is the necessary adjustment to the results of the innovation [Schumpeter, 1934: 231 ff.]. Just as the upswing saw credit inflation, the downswing sees credit deflation, when the pioneering entrepreneur and the imitators pay back their loans with revenue generated from the innovation. Whether or not the economy overshoots its equilibrium during the downswing, the adaptive forces will ensure that sooner or later, the economy reaches its equilibrium level, which had been originally determined by the new combinations introduced through the innovation, i.e. at the outset of the cycle. In any way, up until this new equilibrium level is reached, all the processes leading towards it through the cycle are out-of-equilibrium movements. To sum up, it is suitable to refer to Stolper [1982: 239] and describe innovations as changes in the economy’s production function, which, fuelled by credit, draw the economy out of its old equilibrium level and cause cyclical movements—because it takes some time to introduce new processes, and for everybody to adjust to them [Schumpeter, 1934: 232 ff.].
2.3 – Economic development as the product of different influences
13Schumpeter’s primary concern had always been cyclical fluctuations. Nevertheless, in the following discussion, as mentioned before, “growth factors” will also be considered, since they do not complicate the picture much, but enrich the argument. These growth factors manifest themselves in some kind of trend, which in the absence of cyclical fluctuations caused by innovations determines the continuous path of the economy’s stationary equilibria through time. This underlying trend has to be clearly distinguished from the observed trend, which is a result of all of the three components listed in subsection 2.2 which drive the movement in observed variables, e.g. production. Therefore, the underlying trend is made up of these “growth factors”, while the observed trend is what would be regarded as growth in a more general discussion, i.e. the “averaged” or “trend” movement of the economy over some longer period of time, and therefore a result not merely of the underlying “growth factor” trend, but also of the impulses coming from cyclical fluctuations (Schumpeter [1939, 206–7] uses the term “Result Trend”). To be sure, Schumpeter was well aware of this difference and the implications it bears for interpreting statistically determined trend lines. Thus, as he rightly notes [1928a: 374]:
We could, of course,… fit trend lines through the facts succeeding one another historically; but they would merely be expressions of whatever has happened, not of distinct forces or mechanisms; they would be statistical, not theoretical; they would have to be interpreted in terms of particular historic events,… and not in terms of the working of an economic mechanism sui generis.
15Schumpeter was, of course, not the only one to discuss this general argument, even in his time. To name just one noteworthy example, Frickey  submitted five theoretical and methodological problems in determining a trend for an economic time series. Schumpeter [1930: 166-7] may be quoted again here, this time from his review of Mitchell’s  Business Cycles, a vast empirical work which thus obviously made use of trend analysis:
… if trend-analysis is to have any meaning, it can derive it only from previous theoretical considerations, which must not only guide us in interpreting results, but also in choosing the method. Failing this, a trend is no more than a descriptive device summing up past history with which nothing can be done. It lacks economic connotation. It is, in fact, merely formal. We can apply the familiar methods just as well to e.g. a few successive years of a prosperity-phase, as to the whole of the material we may happen to have (as, again, to a period of political commotion). The result has the same claim in every case to be called a trend in the statistical sense, and may in each case be decomposed into component elements in an indefinite number of ways which have no rational connection to each other—unless it be supplied by the theory of the subject under research.
17Now, however, nowhere in Schumpeter’s published writings can a graphical representation of these theoretical ideas be found sketched into a figure. Nonetheless, there is one famous illustration which Schumpeter provided on page 213 of his Business Cycles  and which is replicated in Figure 1 here. This “superposition” graph shows how adding up three highly symmetric movements—in Schumpeter’s example, long “Kondratiev” waves, medium-run “Juglar” cycles (the “ordinary” business cycle), and short-run “Kitchin” cycles, with their respective amplitudes roughly scaling in proportion to their wavelengths—can result in a complicated overall picture.  Even if all of those constituent waves have the shape of sine curves, and even if every Kondratiev cycle is made up of six Juglar cycles, each of which in turn is made up of three Kitchin cycles, a symmetric, but highly volatile picture emerges. Within this framework, Schumpeter [2000: 184; in a letter to Arthur Spiethoff from 1931] argued that extreme events, such as the Great Depression of the 1930s, could be explained by the joint occurrence of simultaneous troughs in the Kondratiev, Juglar, and Kitchin cycles.
Replication of Schumpeter’s original superposition graph from Business Cycles . The continuous black line displays the sum of the three dashed cyclical movements added up onto one another
Replication of Schumpeter’s original superposition graph from Business Cycles . The continuous black line displays the sum of the three dashed cyclical movements added up onto one another
18There is, however, one major problem when trying to link Schumpeter’s superposition figure to his core theoretical ideas about economic development as a process driven by cyclical movements. All cyclical movements in Schumpeter’s graph basically evolve around an unchanged steady trend and end on that very same trend again as they complete. While this suffices to demonstrate the complications caused by different waves superimposed upon one another—for sure, it does not matter whether or not the trend is flat, or rising, to demonstrate this—it certainly does not incorporate the core idea of economic development through innovation which shifts the equilibrium point, and consequently the path, of the economy upwards in a discontinuous manner, which is sharply different from underlying trend movements. If, in Schumpeter’s theory, any of the cycles does occur, it occurs because some pioneering entrepreneur innovates (see especially Schumpeter [1939: 166-7, 171-2] on this monocausality argument). This, however, introduces new combinations into the economy. New combinations imply a different equilibrium level of production—usually higher—than before. Any underlying trend may continue, even at the same rate, but it will do so from a higher level.
19This, now, is the core idea of the interpretation of Schumpeter’s remarks this paper wishes to propose. Both “growth” and “cyclical” factors move an economy’s equilibrium level upward, but they do so in a different manner. Growth factors appear in a gradual, steady way, and if they were the only one among the three factors responsible for economic fluctuations which were listed in subsection 2.1, one could think of both an economy’s equilibrium and actual level of output as moving along the same line through time. An innovation, on the other hand, shifts the economy’s equilibrium level in a notable way by altering its production function  far more than gradually (if it did not, then it would not be an innovation, but simply part of the underlying growth trend). In an economy affected only by this pure innovation effect, its output level through time would follow a flat line, except for every time an innovation occurred, where it would jump upwards. Adding an underlying growth trend to this, each of the fragment lines between points of innovations would be tilted upwards, with the shifts, too, appearing at higher levels.
20So much about the movement of the equilibrium level. The actual, observed movement of this theoretical economy is more complicated though, because, as has already been pointed out, the business cycle arises as the effect of the dynamic innovation process. An innovation may shift the economy’s equilibrium or reference level, but that, of course, does not mean that the economy will automatically reach this new level in an instant. Instead, when the innovation happens and the economy’s equilibrium level shifts, the actually realized level of production at this point in time will in all likelihood be below the new, and close to the old equilibrium level. The new equilibrium level at this specific point will be more of a production “potential” provided by the innovation. For example in the case of a product innovation, the innovator may have already begun producing the new commodity, through which formerly latent demands for it have been activated. However, the full potential of the innovation could not be put to use so quickly, if only because the innovator would have needed a correspondingly higher amount of funding capital right at the outset—and, of course, the technical capability to bring it into being within a logical second.
21The pioneering entrepreneur, however, will soon notice and reap the fruits of his success in terms of extra rents on his innovation. This will not only lead him to expand his production further and therefore bring the economy closer to its new equilibrium level, but also attract imitators. In any way, this will cause the actual level of output to rise further, and most likely faster than just before. The general story of Schumpeter’s description of the cycle, as outlined in the previous subsection, ensues. It is only at the end of the cycle that the economy reaches its new equilibrium level on the shifted path (where, in the absence of exogenous shocks, it remains until the next innovation occurs), while until that point, there is overshooting both in the upswing and possibly in the downswing, the extent of which depends on banks’ lending policies and the strength of the “secondary waves” of reaction to the original impulse and speculation they may provoke [Schumpeter, 1935: 5-6; 1939: 145 ff.].
22Figure 2 displays the graphical version of these theoretical considerations. The bold black line depicts the time path of an economic variable’s natural log level as it is actually observed—i.e. the overall course of economic development. To minimize on possible complications while still sticking to the spirit of both Schumpeter’s ideas, and to what can actually be observed in empirical business cycle research, it can be thought of as an economy’s production level. The blue line shows the economy’s equilibrium path of production which follows an upward sloped trend (due to gradual expansions or improvements in production, namely the “growth factors”). This underlying trend, in turn, shifts (dashed blue line), or in Schumpeter’s [1927: 297] own term leaps, every time a pioneering entrepreneur innovates. As already pointed out earlier, exogenous shocks are abstracted from. Finally, the dashed green line shows the observed trend, which as the result of the combination of both “cyclical” and “growth” factors, is different from the underlying growth trend.
Graphical interpretation of Schumpeter’s theoretical understanding of trend, cyclical elements, and resulting fluctuations forming a business cycle and economic development
Graphical interpretation of Schumpeter’s theoretical understanding of trend, cyclical elements, and resulting fluctuations forming a business cycle and economic developmentOwn figure. The variable displayed is most apt to represent economic variables growing over time, and fluctuating during the cycle, such as gross domestic product. The numbers in the graph refer to a new cycle starting off (1) right after the previous cycle has completed (i.e. equilibrium is reached), (2) some time after the new equilibrium has been reached, (3) after the previous cycle has completed even before the new static equilibrium is restored, or at least without a depression having set in.
23With the help of the picture, it becomes clearer once more why Schumpeter had been so eager to emphasize the difference between “cyclical” and “growth” factors (the underlying trend), and where his theoretical concerns with statistically determined trend lines from empirical data came from. Following Schumpeter [1928a: 374; 1930: 166–7], quoted earlier in this subsection, it is important not merely to estimate a statistical trend, but to embed this analysis in a theoretical framework—which then unveils possible problems, e.g. the difference between the underlying and observed trend. For example, one could, as is quite the frequent practice in theoretical and empirical work, take a time line, plot a trend curve, and use this as a reference point for determining at which points in time the economy realized activity levels above (positive deviation) and below (negative deviation) its presumed equilibrium level.  However, even in absence of asymmetric shocks, this is only valid if cyclical components do not shift the economy’s centre of attraction, that is, the equilibrium level, as in a highly stylised steady state growth model without Schumpeterian innovation. Otherwise, as in Schumpeter’s case, which is illustrated in Figure 2, some serious misinterpretations are possible, especially when innovations are also accompanied by business cycles. For example, it can easily be seen from Figure 2 that, even though there are some obvious intersections, different intervals would be obtained for above or below equilibrium levels of activity respectively (and correspondingly for the timing of “turning points”), if these levels are taken to be reflected either relative to the observed trend, or the underlying trend. Since such estimates, e.g. of an “output gap” in economic activity, are central to much macroeconomic policy advice, it is evident that a different theoretical underpinning could lead to distorted economic policy.
24The statistically determined, observed trend provides an account of average growth, but it does not distinguish between the cyclical and the underlying growth components. Thus, it cannot be used as an unproblematic reference point for economic policy, and it does not represent the movement which would be observed in the absence of exogenous shocks and cycles. If movements in economic variables are the result of both underlying growth and the cyclical component in Schumpeter’s sense, then an observed trend which does not take their combination into account measures neither of the two factors accurately—indeed, it cannot. Therefore, the two have to be strictly separated theoretically for a precise analysis—exactly because the resulting, observed trend, is intimately linked with the movements connected to business cycles. Whereas the underlying trend and the business cycle are separate theoretical entities, the observed trend and the cycle are not. Unfortunately, while these arguments point to the necessity of careful analysis and the possible pitfalls when not following this theoretical road, they do not, by themselves, help with the practical problem of actually determining and disentangling the different components in the data.
25On an additional note and for the sake of completeness, Figure 2 displays three ways in which two cycles can follow one another. This is of interest for one reason especially: while Schumpeter [1927: 294] emphasized the necessary connection between upswing and recession through the crisis, he did not seek to establish another causal link between recovery and boom. Indeed, Schumpeter [1927: 292] remarked that dynamic behaviour, i.e. exactly the kind of behaviour which produces cyclical movements, “cannot, with any certainty, be relied on to happen,” and that it can only be expected to originate in a stable situation, i.e. in proximity of an equilibrium [Stolper 1951: 175; Böhm, 2008: 151]. This argument can also be found in Oskar Lange’s [1941: 191] review of Business Cycles, where Lange points to the lower risk of innovating which economic agents face in an economy in the neighbourhood of equilibrium (further see Schumpeter [1934: 235–6; 1939: 135]. In Figure 2, situation (1) depicts somewhat of an ideal case, where a new cycle begins right after the previous one has been completed, i.e. when the new equilibrium which had been established through the innovation is finally reached. As Kuznets [1940: 263] argued, Schumpeter never provided a comprehensive theoretical argument for this case, except for the small remarks mentioned just before. Nevertheless, this course of events may be regarded as a reference case. Case (2) depicts a cycle which only begins after the economy had remained in equilibrium for a while. Case (3) subsequently represents the situation which may occur if the downward movement does not shoot over into a depression, either because a new cycle starts early, or because the first cycle ends in equilibrium after the recession, whereupon a consecutive cycle may begin. 
26The “observed trend” depicted in Figure 2 as the dashed green line is, of course, only one possible way of constructing and portraying the trend. But whether this trend is determined by linking the first point of the series to the last one, by calculating moving averages, by applying a Hodrick-Prescott-filter or by linear regression, one independent but important conclusion arises: the observed trend is different from the underlying “growth” trend. To solve this problem and measure the underlying trend, it will most likely be necessary to combine a trend analysis which allows for structural breaks with spectral analysis, but how exactly to calibrate these methods is, once again, a difficult theoretical question. Additionally, there have been some further simplifications made in drawing the graph which, however, are not a theoretical necessity and not explicitly described by Schumpeter—they were merely chosen for the sake of simplicity, but not making them does not change the core argument, it merely alters and further complicates the graph: (a) the growth rate behind the underlying trend is assumed to be constant, (b) which also applies to the discontinuous, “jumpy” growth resulting from innovations during cyclical processes, (c) only one “kind” of wave has been drawn, no superposition, (d) pictured waves have a fairly simple, sinusoidal shape, and (e) depressions do not alter the equilibrium level (see footnote 10).
27To further clarify this paper’s message, a comparison with and distinction from some other graphical representations of Schumpeterian ideas, as well as similar graphs illustrative of different theories, seems appropriate. On the one hand, Figure 2 presented here corresponds to and goes further than the theoretical observation by Rühl [1994: 183]; on the other hand, it catches the essence of neo-Schumpeterian models of growth where innovations cause the income or production path of the economy to jump upwards (see e.g. Aghion and Howitt [1998: 60 or 248; 2009: 201]), but the business cycle is usually abstracted from.  Both components are combined, catching the essence of Schumpeter’s idea that cyclical movements and overall economic growth are intimately entwined with each other. The graph provides a detailed illustration with explicit connections to Schumpeter’s remarks, and especially, its focus is not limited to a gradual growth process, but it combines and integrates cyclical movements with trend components. In doing so, some of the core results in the general discussion on Schumpeter’s theory of economic development are theoretically replicated, e.g. the fact that Schumpeterian growth cannot be understood as simple steady state growth. Figure 2 also bears some resemblance to possible depictions of Duesenberry’s  description of the trade cycle,  although the dynamics in this approach are clearly focused and based on the demand side, i.e. the consumption function, whereas the present paper, following Schumpeter’s considerations, illustrates a supply-side perspective, with cycles driven by innovation and the consequent restructuring of the economy.
3 – Conclusion
28This paper has provided a theoretically grounded graphical interpretation of some of Schumpeter’s core theoretical remarks on economic development. Schumpeter was quite explicit in pointing out that, in the absence of “outside factors”, movements in economic time lines consist of a steady underlying trend element compatible with static economic analysis, and the more jerky ups and downs caused by, as it were, “true” economic development through innovation and creative destruction. The observed trend is then a result of both these movements, and it is thus not what Schumpeter refers to as the gradual, steady, “underlying” trend movement. This can be pointed out in another way as well: Since it is described as compatible with the circular flow, the underlying trend can be seen as the time path of the economy’s equilibrium, or in other words, its gravitational centre. However, it is the very nature of innovation through creative destruction to “lift” the economy’s equilibrium path to a new, usually higher, level. This new state may still be characterized by a gradual upward trend. But the innovation causes this underlying trend line to break and jump at the point of innovation, i.e. when the new combinations are introduced—a shift which cannot be seen in the observed trend determined statistically, e.g. by linear regression, ex post. The figure proposed here bears some resemblance to graphical representations of Schumpeter’s ideas in other works which were referred to as well, but, at least to the author’s knowledge of the literature, it is new in the way it combines both the ideas of “cyclical” and (underlying trend) “growth” movements, incorporates not just the innovation element of cycles, and links the picture directly and intimately to Schumpeter’s meticulous remarks on the matter.
29As a concluding note, it should be remembered that Figure 2 provided in this article and Schumpeter’s original superposition graph (replicated here as Figure 1), which served as the starting point for this discussion, are in no way contradictory. Rather, Schumpeter’s Business Cycles [1939: 213] graph depicts the idea of explaining complex movements by a handful of quite simple underlying processes, while the graph presented in this paper aimed at drawing a single class of these cyclical movements more in accordance with Schumpeter’s own ideas. The two figures can thus be complementary and combined:  obviously, the more one deviates from the simple sinusoidal shape of cyclical movements, and the closer one tries to integrate the three cycles along a respective non-steady underlying trend, the more complicated the resulting picture will become, although the basic ideas are, at least theoretically, still quite simple.
University of Hohenheim, Department of Economics (520h), D 70593 Stuttgart, Germany; Niels.Geiger@uni-hohenheim.de
Paper presented at the 14th International Conference of the Charles Gide Association for the Study of Economic Thought, Nice, 7-9 June 2012: History of Macroeconomics: From the Years of ‘High Theory’ (1926-1939) to Modern Approaches. I thank Johannes Schwarzer for helpful remarks on the original version of this paper, as well as my discussant Iurii Bazhal for his comments. Additional remarks from two anonymous referees were crucial to honing this paper as well, and are also gratefully acknowledged. Of course, responsibility for all remaining errors remains with myself.
Both of these articles are reprinted in the volume edited by Clemence .
In Schumpeter’s dynamic theory, the economy is in disequilibrium over the course of a business cycle. However, as Schumpeter [1935: 4; 1939: 69] points out, the notion of a Walrasian general equilibrium, i.e. a situation where every single sector of the economy, and thus also the aggregate, is in equilibrium (see Schumpeter [1939: 42–3] specifically), is still useful for the analysis as a reference point or “theoretical norm” [Schumpeter, 1939: 38 ff.], towards which the economy will usually tend to gravitate. Actual economic states can then be defined relative to this equilibrium, more generally with regard to whether or not they are in a “neighbourhood” of it (since perfect equilibria cannot be expected to ever be realized, see Schumpeter [1935: 4; 1939: 69–71]). Schumpeter [1935: 5, 7; 1939: 138, 20] demarcates a cycle as the movement between two neighbourhoods of equilibrium.
To illustrate this, Schumpeter [1935: 3] draws a distinction between a businessman buying an additional machine, or alternatively lobbying for policies beneficial to him (“rent-seeking” in today’s terminology)—both actions may be motivated by economic considerations, but the act of acquiring a new capital good is clearly closer to the, as it were, “economic core” or “part” within the whole system of society, and thus of generally higher interest for the theoretical economist.
The traits of Schumpeter’s heroic figure will not be discussed in any detail here, because its underlying features are of no immediate relevance for the discussion at hand, while innovation per se and the role of credit is.
Whereas in earlier writings, Schumpeter had regarded the cycle as a sequence of two phases, he expanded this view to a four-phase scheme in Business Cycles [Hagemann, 2008b: 154]. However, Schumpeter [1939: 150] still emphasizes that while a recession (i.e. the return to equilibrium after a boom) is a necessary element of a cycle, the depression (i.e. the overshooting of the new equilibrium in the downward direction) is not: The cycle therefore might end after the recession, and let the economy settle in its new equilibrium, but it is unlikely to do so.
A detailed discussion of this model, its original content and more recent interpretations, is beyond the scope of this paper. The interested reader is referred to Duijn [1983: ch. I] or Hagemann [2008a: 232 ff.].
This focus of looking at the aggregates obviously abstracts from one core element of Schumpeter’s creative destruction process, namely the fact that innovations also imply structural change. However, the argument put forward here is independent of this simplification.
See for example the definition of the business cycle as “deviations… from… long-term trend” in Snowdon and Vane [2002: 64].
Here, too, this need not happen immediately after having reached the equilibrium: compare cases (1) and (2). The distinction between cycles ending after the recession, and those which go through depression and subsequent revival as well, merits another remark, for Schumpeter [1939: 149] notes that a depression causes the underlying trend path to shift (downwards) once again due to “abnormal liquidation”. However, since it does not change this paper’s general message (overall economic development is the result of “growth” and “cyclical” elements combined, and every cycle also initiates a shift in the underlying growth trend), this complication has been abstracted from in Figure 2 for simplicity.
The figure found in Aghion and Howitt  on page 201 is the same as the one that appears several times in their previous textbook of 1998. It displays a horizontal line, the time path of an economy’s output, which shifts upwards whenever an innovation occurs, with the size of the shift depending on the power of the innovation. One of the instances where the figure appears is in the chapter on “Growth and Cycles”, where otherwise, no illustration like Figure 2 here, or a detailed discussion of Schumpeter’s theoretical concerns regarding the matter, appears. In general, though, it is surprisingly hard to find graphical representations of Schumpeterian modelling of the time path of production, especially with regard to the theoretical ideas underlying each model. In a search of volumes collecting different strands of the neo-Schumpeterian literature such as those by Magnusson , Pyka et al.  or the very extensive one by Hanusch and Pyka [2007a], which contains 70 different articles, no comparable sketch putting Schumpeter’s theoretical ideas concerning the time path of production into picture was found.
Also see Smithies , who explicitly builds on both Schumpeter and Duesenberry.
In this context, see e.g. Schumpeter’s [1939: 172–3] remarks on how the equilibrium notion will have to be modified when connecting several types of waves to one another, as in the superposition graph.