Archive for the 'DSGE models' Category

What’s Wrong with DSGE Models Is Not Representative Agency

The basic DSGE macroeconomic model taught to students is based on a representative agent. Many critics of modern macroeconomics and DSGE models have therefore latched on to the representative agent as the key – and disqualifying — feature in DSGE models, and by extension, with modern macroeconomics. Criticism of representative-agent models is certainly appropriate, because, as Alan Kirman admirably explained some 25 years ago, the simplification inherent in a macoreconomic model based on a representative agent, renders the model entirely inappropriate and unsuitable for most of the problems that a macroeconomic model might be expected to address, like explaining why economies might suffer from aggregate fluctuations in output and employment and the price level.

While altogether fitting and proper, criticism of the representative agent model in macroeconomics had an unfortunate unintended consequence, which was to focus attention on representative agency rather than on the deeper problem with DSGE models, problems that cannot be solved by just throwing the Representative Agent under the bus.

Before explaining why representative agency is not the root problem with DSGE models, let’s take a moment or two to talk about where the idea of representative agency comes from. The idea can be traced back to F. Y. Edgeworth who, in his exposition of the ideas of W. S. Jevons – one of the three marginal revolutionaries of the 1870s – introduced two “representative particulars” to illustrate how trade could maximize the utility of each particular subject to the benchmark utility of the counterparty. That analysis of two different representative particulars, reflected in what is now called the Edgeworth Box, remains one of the outstanding achievements and pedagogical tools of economics. (See a superb account of the historical development of the Box and the many contributions to economic theory that it facilitated by Thomas Humphrey). But Edgeworth’s analysis and its derivatives always focused on the incentives of two representative agents rather than a single isolated representative agent.

Only a few years later, Alfred Marshall in his Principles of Economics, offered an analysis of how the equilibrium price for the product of a competitive industry is determined by the demand for (derived from the marginal utility accruing to consumers from increments of the product) and the supply of that product (derived from the cost of production). The concepts of the marginal cost of an individual firm as a function of quantity produced and the supply of an individual firm as a function of price not yet having been formulated, Marshall, in a kind of hand-waving exercise, introduced a hypothetical representative firm as a stand-in for the entire industry.

The completely ad hoc and artificial concept of a representative firm was not well-received by Marshall’s contemporaries, and the young Lionel Robbins, starting his long career at the London School of Economics, subjected the idea to withering criticism in a 1928 article. Even without Robbins’s criticism, the development of the basic theory of a profit-maximizing firm quickly led to the disappearance of Marshall’s concept from subsequent economics textbooks. James Hartley wrote about the short and unhappy life of Marshall’s Representative Firm in the Journal of Economic Perspectives.

One might have thought that the inauspicious career of Marshall’s Representative Firm would have discouraged modern macroeconomists from resurrecting the Representative Firm in the barely disguised form of a Representative Agent in their DSGE models, but the convenience and relative simplicity of solving a DSGE model for a single agent was too enticing to be resisted.

Therein lies the difference between the theory of the firm and a macroeconomic theory. The gain in convenience from adopting the Representative Firm was radically reduced by Marshall’s Cambridge students and successors who, without the representative firm, provided a more rigorous, more satisfying and more flexible exposition of the industry supply curve and the corresponding partial-equilibrium analysis than Marshall had with it. Providing no advantages of realism, logical coherence, analytical versatility or heuristic intuition, the Representative Firm was unceremoniously expelled from the polite company of economists.

However, as a heuristic device for portraying certain properties of an equilibrium state — whose existence is assumed not derived — even a single representative individual or agent proved to be a serviceable device with which to display the defining first-order conditions, the simultaneous equality of marginal rates of substitution in consumption and production with the marginal rate of substitution at market prices. Unlike the Edgeworth Box populated by two representative agents whose different endowments or preference maps result in mutually beneficial trade, the representative agent, even if afforded the opportunity to trade, can find no gain from engaging in it.

An excellent example of this heuristic was provided by Jack Hirshleifer in his 1970 textbook Investment, Interest, and Capital, wherein he adapted the basic Fisherian model of intertemporal consumption, production and exchange opportunities, representing the canonical Fisherian exposition in a single basic diagram. But the representative agent necessarily represents a state of no trade, because, for a single isolated agent, production and consumption must coincide, and the equilibrium price vector must have the property that the representative agent chooses not to trade at that price vector. I reproduce Hirshleifer’s diagram (Figure 4-6) in the attached chart.

Here is how Hirshleifer explained what was going on.

Figure 4-6 illustrates a technique that will be used often from now on: the representative-individual device. If one makes the assumption that all individuals have identical tastes and are identically situated with respect to endowments and productive opportunities, it follows that the individual optimum must be a microcosm of the social equilibrium. In this model the productive and consumptive solutions coincide, as in the Robinson Crusoe case. Nevertheless, market opportunities exist, as indicated by the market line M’M’ through the tangency point P* = C*. But the price reflected in the slope of M’M’ is a sustaining price, such that each individual prefers to hold the combination attained by productive transformations rather than engage in market transactions. The representative-individual device is helpful in suggesting how the equilibrium will respond to changes in exogenous data—the proviso being that such changes od not modify the distribution of wealth among individuals.

While not spelling out the limitations of the representative-individual device, Hirshleifer makes it clear that the representative-agent device is being used as an expository technique to describe, not as an analytical tool to determine, intertemporal equilibrium. The existence of intertemporal equilibrium does not depend on the assumptions necessary to allow a representative individual to serve as a stand-in for all other agents. The representative-individual is portrayed only to provide the student with a special case serving as a visual aid with which to gain an intuitive grasp of the necessary conditions characterizing an intertemporal equilibrium in production and consumption.

But the role of the representative agent in the DSGE model is very different from the representative individual in Hirshleifer’s exposition of the canonical Fisherian theory. In Hirshleifer’s exposition, the representative individual is just a special case and a visual aid with no independent analytical importance. In contrast to Hirshleifer’s deployment of the representative-individual, representative-agent in the DSGE model is used as an assumption whereby an analytical solution to the DSGE model can be derived, allowing the modeler to generate quantitative results to be compared with existing time-series data, to generate forecasts of future economic conditions, and to evaluate the effects of alternative policy rules.

The prominent and dubious role of the representative agent in DSGE models provided a convenient target for critics of DSGE models to direct their criticisms. In Congressional testimony, Robert Solow famously attacked DSGE models and used their reliance on the representative-agents to make them seem, well, simply ridiculous.

Most economists are willing to believe that most individual “agents” – consumers investors, borrowers, lenders, workers, employers – make their decisions so as to do the best that they can for themselves, given their possibilities and their information. Clearly they do not always behave in this rational way, and systematic deviations are well worth studying. But this is not a bad first approximation in many cases. The DSGE school populates its simplified economy – remember that all economics is about simplified economies just as biology is about simplified cells – with exactly one single combination worker-owner-consumer-everything-else who plans ahead carefully and lives forever. One important consequence of this “representative agent” assumption is that there are no conflicts of interest, no incompatible expectations, no deceptions.

This all-purpose decision-maker essentially runs the economy according to its own preferences. Not directly, of course: the economy has to operate through generally well-behaved markets and prices. Under pressure from skeptics and from the need to deal with actual data, DSGE modellers have worked hard to allow for various market frictions and imperfections like rigid prices and wages, asymmetries of information, time lags, and so on. This is all to the good. But the basic story always treats the whole economy as if it were like a person, trying consciously and rationally to do the best it can on behalf of the representative agent, given its circumstances. This cannot be an adequate description of a national economy, which is pretty conspicuously not pursuing a consistent goal. A thoughtful person, faced with the thought that economic policy was being pursued on this basis, might reasonably wonder what planet he or she is on.

An obvious example is that the DSGE story has no real room for unemployment of the kind we see most of the time, and especially now: unemployment that is pure waste. There are competent workers, willing to work at the prevailing wage or even a bit less, but the potential job is stymied by a market failure. The economy is unable to organize a win-win situation that is apparently there for the taking. This sort of outcome is incompatible with the notion that the economy is in rational pursuit of an intelligible goal. The only way that DSGE and related models can cope with unemployment is to make it somehow voluntary, a choice of current leisure or a desire to retain some kind of flexibility for the future or something like that. But this is exactly the sort of explanation that does not pass the smell test.

While Solow’s criticism of the representative agent was correct, he left himself open to an effective rejoinder by defenders of DSGE models who could point out that the representative agent was adopted by DSGE modelers not because it was an essential feature of the DSGE model but because it enabled DSGE modelers to simplify the task of analytically solving for an equilibrium solution. With enough time and computing power, however, DSGE modelers were able to write down models with a few heterogeneous agents (themselves representative of particular kinds of agents in the model) and then crank out an equilibrium solution for those models.

Unfortunately for Solow, V. V. Chari also testified at the same hearing, and he responded directly to Solow, denying that DSGE models necessarily entail the assumption of a representative agent and identifying numerous examples even in 2010 of DSGE models with heterogeneous agents.

What progress have we made in modern macro? State of the art models in, say, 1982, had a representative agent, no role for unemployment, no role for Financial factors, no sticky prices or sticky wages, no role for crises and no role for government. What do modern macroeconomic models look like? The models have all kinds of heterogeneity in behavior and decisions. This heterogeneity arises because people’s objectives dier, they differ by age, by information, by the history of their past experiences. Please look at the seminal work by Rao Aiyagari, Per Krusell and Tony Smith, Tim Kehoe and David Levine, Victor Rios Rull, Nobu Kiyotaki and John Moore. All of them . . . prominent macroeconomists at leading departments . . . much of their work is explicitly about models without representative agents. Any claim that modern macro is dominated by representative-agent models is wrong.

So on the narrow question of whether DSGE models are necessarily members of the representative-agent family, Solow was debunked by Chari. But debunking the claim that DSGE models must be representative-agent models doesn’t mean that DSGE models have the basic property that some of us at least seek in a macro-model: the capacity to explain how and why an economy may deviate from a potential full-employment time path.

Chari actually addressed the charge that DSGE models cannot explain lapses from full employment (to use Pigou’s rather anodyne terminology for depressions). Here is Chari’s response:

In terms of unemployment, the baseline model used in the analysis of labor markets in modern macroeconomics is the Mortensen-Pissarides model. The main point of this model is to focus on the dynamics of unemployment. It is specifically a model in which labor markets are beset with frictions.

Chari’s response was thus to treat lapses from full employment as “frictions.” To treat unemployment as the result of one or more frictions is to take a very narrow view of the potential causes of unemployment. The argument that Keynes made in the General Theory was that unemployment is a systemic failure of a market economy, which lacks an error-correction mechanism that is capable of returning the economy to a full-employment state, at least not within a reasonable period of time.

The basic approach of DSGE is to treat the solution of the model as an optimal solution of a problem. In the representative-agent version of a DSGE model, the optimal solution is optimal solution for a single agent, so optimality is already baked into the model. With heterogeneous agents, the solution of the model is a set of mutually consistent optimal plans, and optimality is baked into that heterogenous-agent DSGE model as well. Sophisticated heterogeneous-agent models can incorporate various frictions and constraints that cause the solution to deviate from a hypothetical frictionless, unconstrained first-best optimum.

The policy message emerging from this modeling approach is that unemployment is attributable to frictions and other distortions that don’t permit a first-best optimum that would be achieved automatically in their absence from being reached. The possibility that the optimal plans of individuals might be incompatible resulting in a systemic breakdown — that there could be a failure to coordinate — does not even come up for discussion.

One needn’t accept Keynes’s own theoretical explanation of unemployment to find the attribution of cyclical unemployment to frictions deeply problematic. But, as I have asserted in many previous posts (e.g., here and here) a modeling approach that excludes a priori any systemic explanation of cyclical unemployment, attributing instead all cyclical unemployment to frictions or inefficient constraints on market pricing, cannot be regarded as anything but an exercise in question begging.



The Standard Narrative on the History of Macroeconomics: An Exercise in Self-Serving Apologetics

During my recent hiatus from blogging, I have been pondering an important paper presented in June at the History of Economics Society meeting in Toronto, “The Standard Narrative on History of Macroeconomics: Central Banks and DSGE Models” by Francesco Sergi of the University of Bristol, which was selected by the History of Economics Society as the best conference paper by a young scholar in 2017.

Here is the abstract of Sergi’s paper:

How do macroeconomists write the history of their own discipline? This article provides a careful reconstruction of the history of macroeconomics told by the practitioners working today in the dynamic stochastic general equilibrium (DSGE) approach.

Such a tale is a “standard narrative”: a widespread and “standardizing” view of macroeconomics as a field evolving toward “scientific progress”. The standard narrative explains scientific progress as resulting from two factors: “consensus” about theory and “technical change” in econometric tools and computational power. This interpretation is a distinctive feature of central banks’ technical reports about their DSGE models.

Furthermore, such a view on “consensus” and “technical change” is a significantly different view with respect to similar tales told by macroeconomists in the past — which rather emphasized the role of “scientific revolutions” and struggles among competing “schools of thought”. Thus, this difference raises some new questions for historians of macroeconomics.

Sergi’s paper is too long and too rich in content to easily summarize in this post, so what I will do is reproduce and comment on some of the many quotations provided by Sergi, taken mostly from central-bank reports, but also from some leading macroeconomic textbooks and historical survey papers, about the “progress” of modern macroeconomics, and especially about the critical role played by “microfoundations” in achieving that progress. The general tenor of the standard narrative is captured well by the following quotations from V. V. Chari

[A]ny interesting model must be a dynamic stochastic general equilibrium model. From this perspective, there is no other game in town. […] A useful aphorism in macroeconomics is: “If you have an interesting and coherent story to tell, you can tell it in a DSGE model.  (Chari 2010, 2)

I could elaborate on this quotation at length, but I will just leave it out there for readers to ponder with a link to an earlier post of mine about methodological arrogance. Instead I will focus on two other sections of Sergi’s paper “the five steps of theoretical progress” and “microfoundations as theoretical progress.” Here is how Sergi explains the role of the five steps:

The standard narrative provides a detailed account of the progressive evolution toward the synthesis. Following a teleological perspective, each step of this evolution is an incremental, linear improvement of the theoretical tool box for model building. The standard narrative identifies five steps . . . .  Each step corresponds to the emergence of a school of thought. Therefore, in the standard narrative, there are not such things as competing schools of thought and revolutions. Firstly, because schools of thought are represented as a sequence; one school (one step) is always leading to another school (the following step), hence different schools are not coexisting for a long period of time. Secondly, there are no revolutions because, while emerging, new schools of thought [do] not overthrow the previous ones; instead, they suggest improvements and amendments, that are accepted as an improvement by pre-existing schools therefore, accumulation of knowledge takes place thanks to consensus. (pp. 17-18)

The first step in the standard narrative is the family of Keynesian macroeconometric models of the 1950s and 1960s, the primitive ancestors of the modern DSGE models. The second step was the emergence of New Classical macroeconomics which introduced the ideas of rational expectations and dynamic optimization into theoretical macroeconomic discourse in the 1970s. The third step was the development, inspired by New Classical ideas, of Real-Business-Cycle models of the 1980s, and the fourth step was introduction of New Keynesian models in the late 1980s and 1990s that tweaked the Real-Business-Cycle models in ways that rationalized the use of counter-cyclical macroeconomic policy within the theoretical framework of the Real-Business-Cycle approach. The final step, the DSGE model, emerged more or less naturally as a synthesis of the converging Real-Business-Cycle and New Keynesian approaches.

After detailing the five steps of theoretical progress, Sergi focuses attention on “the crucial improvement” that allowed the tool box of macroeconomic modelling to be extended in such a theoretically fruitful way: the insistence on providing explicit microfoundations for macroeconomic models. He writes:

Abiding [by] the Lucasian microfoundational program is put forward by DSGE modellers as the very fundamental essence of theoretical progress allowed by [the] consensus. As Sanajay K. Chugh (University of Pennsylvania) explains in the historical chapter of his textbook, microfoundations is all what modern macroeconomics is about: (p. 20)

Modern macroeconomics begin by explicitly studying the microeconomic principles of utility maximization, profit maximization and market-clearing. [. . . ] This modern macroeconomics quickly captured the attention of the profession through the 1980s [because] it actually begins with microeconomic principles, which was a rather attractive idea. Rather than building a framework of economy-wide events from the top down [. . .] one could build this framework using microeconomic discipline from the bottom up. (Chugh 2015, 170)

Chugh’s rationale for microfoundations is a naïve expression of reductionist bias dressed up as simple homespun common-sense. Everyone knows that you should build from the bottom up, not from the top down, right? But things are not always quite as simple as they seem. Here is an attempt to present microfoundations as being cutting-edge and sophisticated offered in a 2009 technical report written by Cuche-Curti et al. for the Swiss National Bank.

The key property of DSGE models is that they rely on explicit micro-foundations and a rational treatment of expectations in a general equilibrium context. They thus provide a coherent and compelling theoretical framework for macroeconomic analysis. (Cuche-Curti et al. 2009, 6)

A similar statement is made by Gomes et al in a 2010 technical report for the European Central Bank:

The microfoundations of the model together with its rich structure allow [us] to conduct a quantitative analysis in a theoretically coherent and fully consistent model setup, clearly spelling out all the policy implications. (Gomes et al. 2010, 5)

These laudatory descriptions of the DSGE model stress its “coherence” as a primary virtue. What is meant by “coherence” is spelled out more explicitly in a 2006 technical report describing NEMO, a macromodel of the Norwegian economy, by Brubakk et al. for the Norges Bank.

Various agents’ behavior is modelled explicitly in NEMO, based on microeconomic theory. A consistent theoretical framework makes it easier to interpret relationships and mechanisms in the model in the light of economic theory. One advantage is that we can analyse the economic effects of changes of a more structural nature […] [making it] possible to provide a consistent and detailed economic rationale for Norges Bank’s projections for the Norwegian economy. This distinguishes NEMO from purely statistical models, which to a limited extent provide scope for economic interpretations. (Brubakk and Sveen 2009, 39)

By creating microfounded models, in which all agents are optimizers making choices consistent with the postulates of microeconomic theory, DSGE model-builders, in effect, create “laboratories” from which to predict the consequences of alternative monetary policies, enabling policy makers to make informed policy choices. I pause merely to note and draw attention to the tendentious and misleading misappropriation of the language of empirical science by these characteristically self-aggrandizing references to DSGE models as “laboratories” as if what was going on in such models was determined by an actual physical process, as is routinely the case in the laboratories of physical and natural scientists, rather than speculative exercises in high-level calculations derived from the manipulation of DSGE models.

As a result of recent advances in macroeconomic theory and computational techniques, it has become feasible to construct richly structured dynamic stochastic general equilibrium models and use them as laboratories for the study of business cycles and for the formulation and analysis of monetary policy. (Cuche-Curri et al. 2009, 39)

Policy makers can be confident that the conditional predictions corresponding to the policy alternative under consideration, which are derived from their “laboratory” DSGE models, because those models, having been constructed on the basis of the postulates of economic theory, are therefore microfounded, embodying deep structural parameters that are invariant to policy changes. Microfounded models are thus immune to the Lucas Critique of macroeconomic policy evaluation, under which the empirically estimated coefficients of traditional Keynesian macroeconometric models cannot be assumed to remain constant under policy changes, because those coefficient estimates are themselves conditional to policy choices.

Here is how the point is made in three different central bank technical reports: by Argov et al. in a 2012 technical report about MOISE, a DSGE model for the Israeli economy, by Cuche-Curti et al. and by Medina and Soto in a 2006 technical report about a new DSGE model for the Chilean economy for the Central Bank of Chile.

Being micro-founded, the model enables the central bank to assess the effect of its alternative policy choices on the future paths of the economy’s endogenous variables, in a way that is immune to the Lucas critique. (Argov et al. 2012, 5)

[The DSGE] approach has three distinct advantages in comparison to other modelling strategies. First and foremost, its microfoundations should allow it to escape the Lucas critique. (Cuche-Curti et al. 2009, 6)

The main advantage of this type of model, over more traditional reduce-form macro models, is that the structural interpretation of their parameters allows [it] to overcome the Lucas Critique. This is clearly an advantage for policy analysis. (Medina and Soto, 2006, 2)

These quotations show clearly that escaping, immunizing, or overcoming the Lucas Critique is viewed by DSGE modelers as the holy grail of macroeconomic model building and macroeconomic policy analysis. If the Lucas Critique cannot be neutralized, the coefficient estimates derived from reduced-form macroeconometric models cannot be treated as invariant to policy and therefore cannot provide a secure basis for predicting the effects of alternative policies. But DSGE models allow deep structural relationships, reflecting the axioms underlying microeconomic theory, to be estimated. Because they reflect the deep, and presumably stable, microeconomic structure of the economy, estimates of deep parameters derived from DSGE models, DSGE modelers claim that these estimates provide policy makers with a reliable basis for conditional forecasting of the effects of macroeconomic policy.

Because of the consistently poor track record of DSGE models in actual forecasting (for evidence of that poor track record see the paper by Carlaw and Lipsey and my post about their paper) comparing the predictive performance of DSGE models with more traditional macroeconometric models), the emphasis placed on the Lucas Critique by DSGE modelers has an apologetic character, DSGE modelers having to account for the relatively poor comparative predictive power of DSGE models by relentlessly invoking the Lucas Critique in trying to account for, and explain away, the poor predictive performance of the DSGE models. But if DSGE models really are better than traditional macro models why are their unconditional predictions not at least as good as those of traditional macroeconometric models? Obviously estimates of the deep structural relationships provided by microfounded models are not as reliable as DSGE apologetics tries to suggest.

And the reason that the estimates of deep structural relationships derived from DSGE models are not reliable is that those models, no less than traditional macroeconometric models, are subject to the Lucas Critique, the deep microeconomic structural relationships embodied in DSGE models being conditional on the existence of a unique equilibrium solution that persists long enough for the structural relationships characterizing that equilibrium to be inferred from the data-generating mechanism whereby those models are estimated. (I have made this point previously here.) But if the data-generating mechanism does not conform to the unique general equilibrium upon whose existence the presumed deep structural relationships of microeconomic theory embodied in DSGE models are conditioned, the econometric estimates derived from DSGE models cannot capture the desired deep structural relationships, and the resulting structural estimates are therefore incapable of providing a reliable basis for macroeconomic-policy analysis or for conditional forecasts of the effects of alternative policies, much less unconditional forecasts of endogenous macroeconomic variables.

Of course, the problem is even more intractable than the discussion above implies, because there is no reason why the deep structural relationships corresponding to a particular equilibrium should be invariant to changes in the equilibrium. So any change in economic policy that displaces a pre-existing equilibrium, let alone any other unforeseen technological change or change in tastes or resource endowments that displaces a pre-existing equilibrium will necessarily cause all the deep structural relationships to change correspondingly. So the deep structural parameters upon whose invariance the supposedly unique capacity of DSGE models to provide policy analysis upon which policy makers can rely simply don’t exist. Policy making based on DSGE models is as much an uncertain art requiring the exercise of finely developed judgment and intuition as policy making based on any other kind of economic modeling. DSGE models provide no uniquely reliable basis for making macroeconomic policy.


Argov, E., Barnea, E., Binyamini, A., Borenstein, E., Elkayam, D., and Rozenshtrom, I. (2012). MOISE: A DSGE Model for the Israeli Economy. Technical Report 2012.06, Bank of Israel.
Brubakk, L.,Husebø, T. A., Maih, J., Olsen, K., and Østnor, M. (2006). Finding NEMO: Documentation of the Norwegian economy model. Technical Report 2006/6, Norges Bank, Staff Memo.
Carlaw, K. I., and Lipsey, R. G. (2012). “Does History Matter?: Empirical Analysis of Evolutionary versus Stationary Equilibrium Views of the Economy.” Journal of Evolutionary Economics. 22(4):735-66.
Chari, V. V. (2010). Testimony before the committee on Science and Technology, Subcommittee on Investigations and Oversight, US House of Representatives. In Building a Science of Economics for the Real World.
Chugh, S. K. (2015). Modern Macroeconomics. MIT Press, Cambridge (MA).
Cuche-Curti, N. A., Dellas, H., and Natal, J.-M. (2009). DSGE-CH. A Dynamic Stochastic General Equilibrium Model for Switzerland. Technical Report 5, Swiss National Bank.
Gomes, S., Jacquinot, P., and Pisani, M. (2010). The EAGLE. A Model for Policy Analysis of Macroeconomic Interdependence in the Euro Area. Technical Report 1195, European Central Bank.
Medina, J. P. and Soto, C. (2006). Model for Analysis and Simulations (MAS): A New DSGE Model for the Chilean Economy. Technical report, Central Bank of Chile.

About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.


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