Abstract

To explore the emergence of power laws in social and economic phenomena, the authors discuss the mechanism whereby reversal quasi-symmetry and Gibrat’s law lead to power laws with different powerlaw exponents. Reversal quasi-symmetry is invariance under the exchange of variables in the joint PDF (probability density function). Gibrat’s law means that the conditional PDF of the exchange rate of variables does not depend on the initial value. By employing empirical worldwide data for firm size, from categories such as plant assets K, the number of employees L, and sales Y in the same year, reversal quasi-symmetry, Gibrat’s laws, and power-law distributions were observed. We note that relations between power-law exponents and the parameter of reversal quasi-symmetry in the same year were first confirmed. Reversal quasi-symmetry not only of two variables but also of three variables was considered. The authors claim the following. There is a plane in 3-dimensional space (log K, log L, log Y ) with respect to which the joint PDF P_J (K, L, Y ) is invariant under the exchange of variables. The plane accurately fits empirical data (K, L, Y ) that follow power-law distributions. This plane is known as the Cobb-Douglas production function, Y = AK^αL^β which is frequently hypothesized in economics.

Introduction

In various phase transitions, it has been universally observed that physical quantities near critical points obey power laws. For instance, in magnetic substances, the specific heat, magnetic dipole density, and magnetic susceptibility follow power laws of heat or magnetic flux. We also know that the cluster-size distribution of the spin follows power laws. Using renormalization group methods realizes these conformations to power law as critical phenomena of phase transitions [1].

2011.08

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Abstract

This paper demonstrates that fat-tailed distributions of trade volume and stock returns emerge in a simultaneous-move herding model of rational traders who infer other traders’ private information on the value of assets by observing aggregate actions. Without parametric assumptions on the private information, I analytically show that the traders’ aggregate actions follow a power-law distribution with exponential truncation. Numerical simulations show that the model is able to generate the fat-tailed distributions of returns as observed empirically. I argue that the learning among a large number of traders leads to a criticality condition for the power-law clustering of actions.

Introduction

Since Mandelbrot [27] and Fama [14], it has been well established that the short-term stock returns exhibit a fat-tailed, leptokurtic distribution. Jansen and de Vries [20], for example, estimated the exponent of the power-law tail to be in the range 3 to 5, which warrants a finite variance and yet deviates greatly from the normal distribution in the fourth moment. This anomaly in the tail and kurtosis has been considered as a reason for the excess volatility of stock returns.

2011.08

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Abstract

We propose a new method for estimating the power-law exponents of firm size variables. Our focus is on how to empirically identify a range in which a firm size variable follows a power-law distribution. As is well known, a firm size variable follows a power-law distribution only beyond some threshold. On the other hand, in almost all empirical exercises, the right end part of a distribution deviates from a power-law due to finite size effect. We modify the method proposed by Malevergne et al. (2011) so that we can identify both of the lower and the upper thresholds and then estimate the power-law exponent using observations only in the range defined by the two thresholds. We apply this new method to various firm size variables, including annual sales, the number of workers, and tangible fixed assets for firms in more than thirty countries.

Introduction

Power-law distributions are frequently observed in social phenomena (e.g., Pareto
(1897); Newman (2005); Clauset et al. (2009)). One of the most famous examples
in Economics is the fact that personal income follows a power-law, which was
first found by Pareto (1897) about a century ago, and thus referred to as Pareto
distribution. Specifically, the probability that personal income x is above x₀ is
given by

P>(x) ∝ x ^−µ  　for x > x₀

where µ is referred to as a Pareto exponent or a power-law exponent.

2011.07

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Abstract

We examine the downward rigidity of nominal wage in Japan between 1993 and 2006 by constructing a quasi-panel data set of individual worker from the microfile of Basic Survey on Wage Structure. The results are as follows: although the downward rigidity of nominal hourly wage of fulltime regular workers is weak in Japan, it has increased since around 2000s. The flexibility of hourly wage comes from the changeable scheduled hour worked. During the economic downturn, many establishments reduce the hourly wage by increasing scheduled hour worked while keeping the amount of payment constant.

Introduction

賃金は、労働市場で決定される重要な価格変数である。マクロ経済を考察するうえでは、賃金決定の様相が財政政策や金融政策の効果を左右するとされることが少なくない。労働市場においても、需要や供給の変化に対する賃金、すなわち均衡価格の振る舞いは、市場の機能そのものを表象する要素として、いまもって研究者に重要な手がかりを与え続けている。

2011.06

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Abstract

Central banks react even to intraday changes in the exchange rate; however, in most cases, intervention data is available only at a daily frequency. This temporal aggregation makes it difficult to identify the effects of interventions on the exchange rate. We apply the Bayesian MCMC approach to this endogeneity problem. We use “data augmentation” to obtain intraday intervention amounts and estimate the efficacy of interventions using the augmented data. Applying this new method to Japanese data, we find that an intervention of one trillion yen moves the yen/dollar rate by 1.7 percent, which is more than twice as much as the magnitude reported in previous studies applying OLS to daily observations. This shows the quantitative importance of the endogeneity problem due to temporal aggregation.

Introduction

Are foreign exchange interventions effective? This issue has been debated extensively since the 1980s, but no conclusive consensus has emerged. A key difficulty faced by researchers in answering this question is the endogeneity problem: the exchange rate responds “within the period” to foreign exchange interventions and the central bank reacts “within the period” to fluctuations in the exchange rate. This difficulty would not arise if the central bank responded only slowly to fluctuations in the exchange rate, or if the data sampling interval were sufficiently fine.

2011.05

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Abstract

In constructing a housing price index, one has to make at least two important choices. The first is the choice among alternative estimation methods. The second is the choice among different data sources of house prices. The choice of the dataset has been regarded as critically important from a practical viewpoint, but has not been discussed much in the literature. This study seeks to fill this gap by comparing the distributions of prices collected at different stages of the house buying/selling process, including (1) asking prices at which properties are initially listed in a magazine, (2) asking prices when an offer for a property is eventually made and the listing is removed from the magazine, (3) contract prices reported by realtors after mortgage approval, and (4) registry prices. These four prices are collected by different parties and recorded in different datasets. We find that there exist substantial differences between the distributions of the four prices, as well as between the distributions of house attributes. However, once quality differences are controlled for, only small differences remain between the different house price distributions. This suggests that prices collected at different stages of the house buying/selling process are still comparable, and therefore useful in constructing a house price index, as long as they are quality adjusted in an appropriate manner.

Introduction

In constructing a housing price index, one has to make several nontrivial choices. One of them is the choice among alternative estimation methods, such as repeatsales regression, hedonic regression, and so on. There are numerous papers on this issue, both theoretical and empirical. Shimizu et al. (2010), for example, conduct a statistical comparison of several alternative estimation methods using Japanese data. However, there is another important issue which has not been discussed much in the literature, but has been regarded as critically important from a practical viewpoint: the choice among different data sources for housing prices. There are several types of datasets for housing prices: datasets collected by real estate agencies and associations; datasets provided by mortgage lenders; datasets provided by government departments or institutions; and datasets gathered and provided by newspapers, magazines, and websites. Needless to say, different datasets contain different types of prices, including sellers’ asking prices, transactions prices, valuation prices, and so on.

2011.04

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Abstract

本稿では生産関数の形状を選択する手法を提案する。世の中には数人の従業員で営まれる零細企業から数十万人の従業員を擁する超巨大企業まで様々な規模の企業が存在する。どの規模の企業が何社存在するかを表したものが企業の規模分布であり，企業の規模を示す変数である Y （生産）と K（資本）と L（労働）のそれぞれはベキ分布とよばれる分布に従うことが知られている。本稿では，企業規模の分布 関数 と生産 関数 という 2 つの関数の間に存在する関係に注目し，それを手がかりとして生産関数の形状を特定するという手法を提案する。具体的には，K と L についてデータから観察された分布の関数形をもとにして，仮に生産関数がある形状をとる場合に得られるであろう Y の分布関数を導出し，データから観察される Y の分布関数と比較する。日本を含む 25 カ国にこの手法を適用した結果，大半の国や産業において，Y ，K，L の分布と整合的なのはコブダグラス型であることがわかった。また，Y の分布の裾を形成する企業，つまり巨大企業では，K や L の投入量が突出して大きいために Y も突出して大きい傾向がある。一方，全要素生産性が突出して高くそれが原因で Y が突出して大きいという傾向は認められない。

Introduction

企業の生産関数の形状としてはコブダグラス型やレオンチェフ型など様々な形状がこれまで提案されており，ミクロやマクロの研究者によって広く用いられている。例えば，マクロの生産性に関する研究では，コブダグラス生産関数が広く用いられており，そこから全要素生産性を推計することが行われている。しかし，生産 Y と資本 K と雇用 L の関係をコブダグラス型という特定の関数形で表現できるのはなぜか。どういう場合にそれが適切なのか。そうした点にまで踏み込んで検討する研究は限られている。多くの実証研究では，いくつかの生産関数の形状を試してみて，回帰の当てはまりの良さを基準に選択するという便宜的な取り扱いがなされている。

2011.04

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Abstract

This paper investigates price rigidity arise out of the specific market structures, such as degree of market concentration and pricing decisions of retailers and manufacturers. Using Japanese scanner data that contains transaction prices and sales for more than 1,600 commodity groups from 1988 to 2008, we find statistically significant negative correlation between the degree of market concentration and the frequency of price changes, including both bargain price changes and regular price changes. The results of two-way analysis of variance suggests that the variation of the frequency of price changes depends on the dierences among manufacturers as well as those among retailers.

Introduction

The relationship between price rigidity and market structure has been discussed since the American economist, Gardinar C. Means suggested that the downward rigidity of price during the Great Depression had a relationship to industrial concentration in a Senate Document in 1935. The implication of Means' findings is that the prices of less competitive markets tend to be sticky. This is referred to as the "administered prices" hypothesis (Domberger, 1979) and still attracts considerable attention. This is partly because empirical literature in this field found strong heterogeneity in price stickiness across commodity items and is interested in the determinants of item-levels variation in the frequency of price changes.

2011.04

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