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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Physica A: Statistical Mechanics and its Applications, Volume 329, Issues 1–2, 1 November 2003, Pages 249–263
In the aftermath of the burst of the “new economy” bubble in 2000, the Federal Reserve aggressively reduced short-term rates yields in less than 2 years from 61/2 to 11/4% in an attempt to coax forth a stronger recovery of the US economy. But, there is growing apprehension that this is creating a new bubble in real estate, as strong housing demand is fuelled by historically low mortgage rates. Are we going from Charybdis to Scylla? This question is all the more excruciating at a time when many other indicators suggest a significant deflationary risk. Using economic data, Federal Reserve Chairman A. Greenspan and Governor D.L. Kohn dismissed recently this possibility. Using the theory of critical phenomena resulting from positive feedbacks in markets, we confirm this view point for the US but find that mayhem may be in store for the UK: we unearth the unmistakable signatures (log-periodicity and power law super-exponential acceleration) of a strong unsustainable bubble there, which could burst around the end of the year 2003.
While the US economy has generally been contracting in the last 2 years, real estate has been growing: house prices have been rising at a rate of about 2% a year faster than income gains. Real consumer outlays and spending on residential construction each rose about 3% during 2001. Meanwhile, the gross domestic product (GDP) fell about one-half percent, a drop that would have been far worse without a strong real estate sector. While stock market losses have destroyed maybe as much as $US 5 trillion in investor wealth since the market's peak, there has been an offsetting effect in the real estate market. Home equity has gained about $US 1.7 trillion in the same period, according to the chief economist at the biggest US mortgage firm, Fannie Mae. Since, according to the Federal Reserve, home values have double the impact on consumer spending that stock values have via the “richness effect,” the housing boom has offset almost two-third of the stock market losses on the economy. Such offsets have triggered talks about a real estate bubble in the US. Investment weekly Barron's claimed to spot a “bubble mentality” last April 2002 and analysts are increasingly scrutinizing the possible evidence. A managing director of Pacific Investment Management Co. (PIMCO), the largest America bond fund, agrees there is “potential for a bubble in the US residential property market” as a result of the lowest mortgage rates since the 1960s. The statistics released every month continue to confirm that “the housing sector continues to defy all odds,” in the words of the chief economist for the National Association of Realtors, David Lereah. Sales of existing housing have been and are continuing to run at a robust if not enthusiastic pace. Total mortgage debt outstanding has risen sharply during the last decade. While the total was about $US 2.7 trillion in the first quarter of 1990, by the fourth quarter of 1999, it had almost doubled, to $US 5.2 trillion. As a comparison, the total amount of cumulative borrowing by the Federal Treasury (the national debt) was about $US 5.7 trillion in August 2000. American mortgages are on the path of becoming the single largest class of fixed income securities on the planet. Add to these elements that the demand for mortgage borrowing outstrips aggregate domestic saving (which is currently negative and has reached in the last months the lowest level since record keeping began in 1959). This negative saving rate combined with the continuing rapid growth of mortgage borrowing implies that there must be a reduction in non-mortgage lending or an increase in fund flows from abroad or both . This may lead to an increased instability through globalization, resulting from the behavior of international investors . To make things look even worse, the real estate bubble is part of a general huge credit “bubble” that has developed steadily over the last decades, which includes the various US federal money supply, the personal, municipal, corporate debt and federal debts (estimated by some to add up to as much as several tens of trillion US dollars), which may not only drag down the recovery of the economy but also lead to vulnerability to exogenous crises. But is there really a real estate bubble? The science of complexity, which studies the emergence of organization in systems as diverse as the human body (biology), the earth (geology) or the cosmos (astrophysics), suggests novel insights in this troubling question. The science of complexity explains the spontaneous occurrence of coherent large-scale collective behavior, such as well-functioning capitalistic markets but also financial crashes and depressions, from the repeated non-linear interactions between the constituents of economies. This bottom-up mechanism explains the robustness and strength of modern developed economies as well as their vulnerability to endogenous instabilities. The theory of complex systems thus explains the origin of Adam Smith's invisible hand in society according to which a collection of selfish self-centered individuals coldly maximizing their individual “utility functions” achieve an optimal aggregate social welfare. This theory explains capitalism and free trade. However, it also explains and predicts the occurrence of instabilities and of far-from-optimal equilibria, which are inherent in the bottom-up self-organization . Recent academic research in the field of complex systems suggest that the economy as well as stock markets self-organize under the competing influences of positive and negative feedback mechanisms ( and references therein). Positive feedbacks, i.e., self-reinforcement, refer for instance to the fact that, conditioned on the observation that the market has recently moved up (respectively down), this makes it more probable to keep it moving up (respectively down), so that a large cumulative move may ensue. “Positive feedback” is the opposite of “negative feedback”, the latter being a concept well-known for instance in population dynamics in the presence of scarce resources. Rational markets and stable economic equilibria derive from the forces of negative feedback. When positive feedback forces dominate, deviations from equilibrium lead to crises. Such instabilities can be seen as intrinsic endogenous progenies of the dynamical organization of the system. Positive feedbacks lead to collective behavior, such as herding in buys during the growth of bubbles and in sells during a crash. This collective behavior does not require the coordination of people to take the same action but results from the convergence of selfish interests together with the impact of interactions between people through the complex network of their acquaintances. The analysis presented below relies on a general theory of financial crashes and of stock market instabilities developed in a series of works. We refer to ,  and  and references therein for all details of our approach. In a nutshell, we are looking for signatures of a faster-than-exponential growth and its decoration by log-periodic oscillations. The faster-than-exponential (super-exponential, hyperbolic or power law) growth means that the growth rate itself grows, signaling an unsustainable regime. We add the important ingredient that the log-periodic oscillations have been found to be reliable indicators of endogenous bubbles signaling a coming instability or change of regime . Using these criteria, we find no evidence whatsoever of a bubble in the US real estate market. However, the same analysis applied to the UK real estate market shows that these two signatures of an unsustainable bubble are unambiguously present. Since these signatures have been found to be reliable predictors of past crashes in financial markets, they point to the end of the UK real estate bubble possible around the end of the year 2003, with either a crash or a change of regime in the UK housing market. We should however caution that the crash is only one possible scenarios according to the theory coupling rational expectation bubbles with collective herding behavior ,  and . Technically, we fit the house price indices to the following versions of the model. In the first version, the logarithm of the price is given by equation(1) View the MathML source where φ is a phase constant, 0<m<1 quantifies the acceleration of the price, A=log[p(tc)] and B and C are two amplitudes. B<0 signals an upward acceleration. This first version (1) amounts to assuming that the potential correction or crash at the end of the bubble is proportional to the total price . In contrast, the second version assumes that the potential correction or crash at the end of the bubble is proportional to the bubble part of the total price, that is to the total price minus the fundamental price . This gives the following price evolution: equation(2) View the MathML source Finally, we shall use expression (3) given below, which incorporates higher-order harmonics beyond the first-order log-periodic cosine of formula (1). Indeed, the spectral Lomb analyses reported in Section 2.3 suggests the presence of a very strong harmonic at the angular log-frequency 2ω. The possible importance of harmonics was also noticed and used in our recent analysis of many stock markets in the anti-bubble regime that started worldwide during the summer of 2000  and . This followed the analyses of log-periodicity in hydrodynamic turbulence data  and  which have demonstrated the important role of higher harmonics in the detection of log-periodicity. In view of the parsimony and quality of the fit with expression (3), we shall use it for our test of robustness of the estimation of the critical time tc
نتیجه گیری انگلیسی
Testifying before the Senate Committee on Banking, Housing and Urban Affairs in July 2002, Federal Reserve Board Chairman Alan Greenspan told lawmakers that rising home prices in the USA are a by-product of “low mortgage rates, immigration, and shortages of buildable land in some areas.” As a result, homeowners have more equity they can use to pay off high-cost consumer debt and for other purposes. This leads to a beneficial effect on the US economy rather than suggesting the possibility of a real estate crash. Based on the science of complexity, our analysis provides a confirmation of this conclusion derived from more standard economic analysis. The situation is the opposite for the UK market. Our same analysis applied to the UK real estate market shows two unambiguous signatures of an unsustainable bubble, which started years even before the end of the stock market bubble in 2000. These signatures have been found to be reliable predictors of past crashes in financial markets. The analysis points to the end of the bubble around the end of the year 2003, with either a crash or a change of direction in the UK housing market. While there are very strong correlations between stock markets in developed countries at present , no such correlation has yet materialized in real estate markets. Investors should however remain watchful for indications of a possible contagions to the US in the longer term. To summarize, what we have learned in this paper is that (i) the USA real estate market is in a state compatible with “rational expectation” regime; (ii) the UK real-estate market exhibits an ultimately unsustainable speculative bubble; (iii) The UK house prices will continue going up during the year 2003; and (iv) The Weierstrass-type function (3) outperforms the simple log-periodic power law formula.