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Throughout his paper, Krugman argues about the troubles behind mathematical modeling. He often claims that it produces inaccurate results, citing evidence from mapping Africa in the 16th century. I feel that this is a flawed concept, as mathematical modeling has advanced quickly from those days. Also, I do not believe that mathematical modeling is flawed, merely the assumptions made in mathematical models are flawed.
The dish-pan model that is represented in the article is also overly simplistic, as it rules out many possible outcomes. Some of these outcomes could even be beneficial to the high development firms from a game theoretic (utility-maximizing) perspective. For example, the high production firms may choose to lower prices to knock out low production firms from the market, then take advantage of the oligopolistic powers they have attained and raise prices significantly. Krugman does not consider this concept, which would likely have dramatically altered his theory.
Krugman does bring up an interesting argument, but there are certainly flaws in it. As another student previously noted, he spends paragraphs on the beginning criticizing modeling for being incorrect due to being overly simplistic. However, when he presents his version of the "Big Push" theory, he presents it in an overly simplistic model that overlooks concepts that I mentioned earlier. His ideas about self-reinforcing growth are particularly interesting. Should these comments be deemed correct, many developing countries could put them into action to catapult themselves forward form an economic standpoint, and drastically increase the well-being of their citizens.

Lauren Howard

Like many of the students before me, I did not read this paper as a critique of Hirschman (which Krugman himself acknowledges in his first sentence) or even a discussion of "high development theory." Rather, the paper focuses on explaining and justifying economics' (the discipline's) infatuation with rigorous modeling -- graphical, mathematical, or narrative -- of its concepts. In short, Krugman is using the "high development theory" as a (narrative) model to clearly and simply illustrate the need for models within economics.

As I read this paper, I was struck by its overlapping themes with one of the theories my developmental psychology class recently discussed. In that class, we talked extensively about Piaget's "Cognitive Development Theory," which postulates that in the last stage of development, the "formal operational" stage (which was theorized to begin at age 11 and continue until death), people are constantly creating "schemas." These "schemas" serve as scripts for what is and is not appropriate in certain contexts, and they allow us to not have to actively think about and assess options when we encounter familiar situations. One example "schema" pertinent to W&L is to ask someone what Greek organization they are a part of. Depending upon the answer, we (tend to) draw conclusions or make assumptions about many things: how often the person goes out, whether or not he or she plays a sport, etc. When asked, however, we would of course acknowledge that individuals within a certain Greek organization are all different from one another. Yet it is easier for our brains to deal with the categorizations, "schemas," or, equivalently, models, to which we are accustomed.

Krugman states that "the problem is that there is no alternative to models. We all think in simplified models, all the time." Krugman's emphasis in his illustrative examples of mapping Africa and observing weather patterns in a dish-pan, as well as in economics (and in life), is that we must be aware that we are drawing but initial, tentative conclusions from these models. In being "self-conscious" and recognizing that we are "not telling an entirely true story," we can use models to better understand economics without losing sight of the complexity of the real world.

Rachael Wright

As a student who initially struggled immensely with preliminary Econ classes, I was pleased to finally (after 3 years) begin to understand why I wasn't catching on. When I first started learning the basics of economics I was confused by the perfect models. It seemed to me that, at times, the very processes that models explained and predicted were too intricate to be explained through a single model. This is not to belittle the importance or utility of models. In fact, I am hopeful that models will continue to adapt and eventually manage to encompass all of the factors at hand. After reading Krugman's article, however, I was particularly taken by the idea that despite the advances in economics between the 1940s and 1970s, a linear progression of economics was not visible. Krugman states that, "A rise in the standards of rigor and logic led to a much improved level of understanding of some things, but also led for a time to an unwillingness to confront those areas the new technical rigor could not yet reach. Areas of inquiry that had been filled in, however imperfectly, became blanks." This explanation, along with his example of African mapping across centuries, highlighted the reasons why the expected linear progression was not seen. I now wonder, in comparison to the journey from where African mapping began to its current state, where we are in terms of the advancement of modern economics.

Genny Francis

Krugman discusses the losses to the economic community and possible policy implications from the high development theory not being accepted sooner, but he does not address what the policy implications have been from the discovery of formal models to illustrate the high development theory. When I was reading this, I also though about the behavioral development economics article we read on Tuesday, and how a lack of formal models has prevented that knowledge from being included in policy decisions until recently. Krugman’s idea that models are important, but theories without formal models should still be taken into account is interesting to consider in terms of future policy decisions, because knowledge that may not have formal models could have a large influence on the direction of policy in different areas if it is taken into account.

Alex Fox

Krugman's paper deals partly with the discussion of the evolution of thought and methodology, and the ability of science and mathematics to evolve in step with this thought. The proof, in the case of high development theory, was a step behind. Going back to our discussion on Tuesday on "The Science of Compassion" and the work of Dr. James Doty in cognitive neuroscience I think brings up an interesting point to this discussion. As economic thought continues to evolve and establish connections in developing areas such as neuroscience, how is it being received? Is this just a recycling of intellectual understanding of economics, another step in the cycle in which accurate theory precedes concrete proof? Or will it be different, as different science is used to explain our thoughts and actions, concepts may once again prove difficult to validate using models. Will economic theory always be tied to the substantive proof of modeling, even as we delve into areas of science that might seem more abstract?

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