Makoto Nirei

A Two Factor Model of Income Distribution Dynamics

This paper analyzes empirical income distributions and proposes a simple stochastic model to explain the stationary distribution and deviations from it. Using the individual tax returns data in the U.S. and Japan for 40 years, we first summarize the shape of the income distribution by an exponential decay up to about the 90th percentile and a power decay for the top 1 percent. We then propose a minimal stochastic process of labor and asset income to reproduce the empirical characteristics. In particular, the Pareto exponent is derived analytically and matched with empirical statistics.

Threshold behavior and aggregate fluctuation

This paper concerns a propagation mechanism in an economy where many individuals follow a threshold rule and interact with a positive feedback. We derive an asymptotic distribution of the propagation size when the number of the agents tends to infinity. The propagation distribution exhibits a slower convergence to a deterministic value than it would if the agents followed a smooth adjustment policy. This gives rise to significant aggregate fluctuations in a finite lumpy-adjusting economy even when the agents are hit by small independent shocks.

Income Distribution and Stochastic Multiplicative Process with Reset Event

This paper examines a stochastic multiplicative process with reset event to explain the power law in the tail of personal income distribution. The tail part of the income distributions in post-war Japan persistently exhibits a power-law distribution with an exponent around 2. We find that a multiplicative process with reset events can explain this pattern. By using a default rate of corporate fundings as a hazard rate of the reset event, we obtain the correct exponent for the power-law in Japanese income.

Closely Competing Firms and Price Adjustment: Some Findings from an Online Marketplace*

We investigate retailers’ price setting behavior using a unique dataset containing by-the-second records of prices offered by closely competing retailers on a major Japanese price comparison website. First, we find that, when the average price of a product across retailers falls rapidly, the frequency of price adjustments increases, and the size of price adjustments becomes larger. Second, we find positive autocorrelation in the frequency of price adjustments, implying that there tends to be clustering where price adjustments occur in succession. In contrast, there is no such autocorrelation in the size of price adjustments. These two findings indicate that the behavior of competing retailers is characterized by state-dependent pricing rather than time-dependent pricing.

Empirical study and model of personal income

Personal income distributions in Japan are analyzed empirically and a simple stochastic model of the income process is proposed. Based on empirical facts, we propose a minimal two-factor model. Our model of personal income consists of an asset accumulation process and a wage process. We show that these simple processes can successfully reproduce the empirical distribution of income. In particular, the model can reproduce the particular transition of the distribution shape from the middle part to the tail part. This model also allows us to derive the tail exponent of the distribution analytically.

AN INTERACTION-BASED FOUNDATION OF AGGREGATE INVESTMENT FLUCTUATIONS

This study demonstrates that the interactions of firm-level indivisible investments give rise to aggregate fluctuations without aggregate exogenous shocks. When investments are indivisible, aggregate capital is determined by the number of firms that invest. I develop a method to derive the closed-form distribution of the number of investing firms when each firms initial capital level varies stochastically. This method shows that idiosyncratic shocks may lead to non-vanishing aggregate fluctuations when the number of firms tends to infinity. I incorporate this mechanism in a dynamic general equilibrium model with indivisible investment and predetermined goods prices. The model features no aggregate exogenous shocks, and the fluctuation is driven by idiosyncratic productivity shocks. Numerical simulations show that the model generates aggregate fluctuations comparable to the business cycles in magnitude and correlation structure under standard calibration.

Critical fluctuations in a random network model

Individual threshold behaviors generate large endogenous fluctuations in a globally interactive network. In a version of NK models, the bonds are allowed to be allocated randomly across nodes in each period. It is shown that the aggregate output asymptotically follows a branching process with martingale property on a unique globally stable state.

An Empirical Study of Interaction-Based Aggregate Investment Fluctuations

Abstract This paper argues that interactions of firms account for a sizable part of fluctuations in aggregate investments without exogenous aggregate shocks. We first establish empirically that the fraction of firms that engage in a lumpy investment follows a non-normal, two-sided exponential distribution across region-year with a panel data set of Italian firms. We then present a simple sectoral model that generates the two-sided exponential distribution that arises from the complementarity of the firms’ lumpy investments within a region. Calibrated by the firm-level estimate of complementarity, the model is capable of generating the two-sided exponential fluctuations observed at the aggregate level.

Time-Varying Employment Risks, Consumption Composition, and Fiscal Policy

This study examines the response of aggregate consumption to active labor market policies that reduce unemployment. We develop a dynamic general equilibrium model with heterogeneous agents and uninsurable unemployment as well as policy regime shocks to quantify the consumption effects of policy. By implementing numerical experiments using the model, we demonstrate a positive effect on aggregate consumption even when the policy serves as a pure transfer from the employed to the unemployed. The positive effect on consumption results from the reduced precautionary savings of the households who indirectly benefit from the policy by a decreased unemployment hazard in future.

Lumpy investment, sectoral propagation, and business cycles (Invited Paper)

This paper proposes a model of endogenous fluctuations in investment. A monopolistic producer has an incentive to invest when the aggregate demand is high. The investment at the firm level is also known to exhibit a threshold behavior called an (S,s) policy. These two facts lead us to consider that the fluctuation in aggregate investment is generated by the global coupling of the non-linear oscillators. From this perspective, we characterize the probability distribution of the investment clustering in a partial equilibrium of product markets, and show that its variance can be large enough to match the observed investment fluctuations. We then implement this mechanism in a dynamic general equilibrium model to explore an investment-driven business cycle. By calibrating the model with the SIC 4-digit level industry data, we numerically show that the model replicates the basic structure of the business cycles.