Academic journal article Federal Reserve Bank of Atlanta, Working Paper Series

Accounting for the Cyclical Dynamics of Income Shares

Academic journal article Federal Reserve Bank of Atlanta, Working Paper Series

Accounting for the Cyclical Dynamics of Income Shares

Article excerpt

Working Paper 2011-9 March 2011

Abstract: Over the business cycle, labor's share of output is negatively but weakly correlated with output, and it lags output by about four quarters. Profit's share is strongly procyclical. It neither leads nor lags output, and its volatility is about four times that of output. Despite the importance of understanding the dynamics of income shares for understanding aggregate technology and the degree of competition in factor markets, macroeconomics lacks models that can account for these dynamics. This paper constructs a model that can replicate those facts. We introduce costly entry of firms in a model with frictional labor markets and find a link between the ability of the model to replicate income shares' dynamics and the ability of the model to amplify and propagate shocks. That link is a countercyclical real interest rate, a well-known fact in U.S. data but a feature that models of aggregate fluctuations have had difficulty achieving.

JEL classification: E3, E25, J3, E24

Key words: labor's share, frictional labor market, firm entry

1 Introduction

Most research in aggregate fluctuations has assumed factor income shares to be constant at all frequencies due to particular assumptions about technology and about the degree of competition in markets for goods and factors of production. The assumption of constant shares does not pass a test of casually inspecting the data, let alone analyzing it with sophisticated statistical tools. Understanding the time series behavior of income shares is critical for understanding the structure of aggregate technology and the behavior of factor markets. Despite the importance of income shares' behavior, macroeconomics lacks models that can quantitatively match the time series facts of income shares. This paper makes two contributions. First, it shows that existing models with time-varying income shares cannot account for their dynamics. Second, it constructs a model which can replicate, if not for all, many of the properties that describe the behavior of income shares.

During the post-war period, labor's share correlation with output is negative but weak; it lags output by about four quarters and is smoother than output. On the other hand, the profits' share is strongly pro-cyclical; it neither leads nor lags output; and its volatility is about four times that of output. As labor is arguably the most important factor of production, coupled with the fact that perfect competition in labor markets implies a tight link between wages and output, these facts have prompted previous studies to deviate from a Walrasian labor market. They have done so by specifying contractual arrangements between employers and employees that have broken the link between wages and the marginal product of labor. The goal was to match properties of labor's share over the business cycle. Examples of this line of work include Boldrin and Horvath (1995), Gomme and Greenwood (1995), and Danthine and Donaldson (1992).

Dispensing with a Walrasian framework is a characteristic of literature that features search and matching frictions in labor markets, e.g. Pissarides (1985). Our research falls within this framework. (1) Although this literature has claimed success in matching some labor market business cycle moments, we show that the dynamics of income shares are completely at odds with the data. We link this failure to the typical assumption of free entry of firms, which leads to the asset value of a vacant position to be exactly zero at all frequencies. That free entry implies that the value of a vacant position equals zero can be seen easily from the textbook model of search and matching, for example Pissarides (2000). This model features firms posting vacancies to get matched to workers who are searching for jobs. If entry is free and any firm that wishes to do so can pay a vacancy-posting cost and wait for this position to get filled, the present value of such a vacancy must be zero in equilibrium. …

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