Academic journal article Review - Federal Reserve Bank of St. Louis

The Aggregate Implications of Size-Dependent Distortions

Academic journal article Review - Federal Reserve Bank of St. Louis

The Aggregate Implications of Size-Dependent Distortions

Article excerpt

(ProQuest: ... denotes formulae omitted.)


In the United States, new firms created 2.9 million jobs per year on average over the period 1980-2010.1 While new firms clearly play an important role in job creation, many fail after a short period of time or do not grow. Are regulations preventing young businesses from expanding? Many regulators seem to think so: In many countries small firms face lighter regulation than large firms. The rationale for exempting small firms from some regulations is that the compliance cost is too high relative to their sales. A necessary consequence, however, is that regulations are phased in as the firm grows, generating an implicit marginal tax. Because regulations are typically phased in at a few finite points, they are sometimes referred to as "threshold effects."

Regulation, broadly defined, takes many forms-from hygiene and safety rules, to mandatory elections of employee representatives, to larger taxes. Under the Affordable Care Act, firms with 50 or more full-time equivalent employees are required to offer health insurance to their full-time employees. This requirement raises concerns that firms cut employment to stay below the threshold or substitute some of their full-time workers with part-time workers. Similarly, regulations that alter the incentives to expand explain the large number of small community banks in the United States.

These distortions have attracted attention in public policy circles. The common wisdom, as reflected in numerous reports by blue-ribbon panels, is that these regulations significantly impede the growth of small firms and should be suppressed or smoothed out. However, there is little work formally modeling these policies to understand and evaluate their effects. This article proposes a simple model and gives a quantitative evaluation of this common wisdom. What are the potential benefits of removing, or smoothing, the regulation thresholds? To answer this question, this article considers a case study of regulations that apply only to firms in France with more than 50 employees. The firm-size distribution is distorted: There are few firms with exactly 50 employees and a large number of firms with 49 employees. Figure 1 plots the firm-size distribution in our French data, illustrating this well-known pattern. The visibly distorted firm distribution suggests that productivity could be increased if firms close to the threshold grow, as labor would be reallocated toward more-productive firms. Because these regulations depend on a precise threshold, the behavior of firms around the threshold is particularly informative on the effects of distortions.

The rest of the article proceeds as follows. Section 2 presents a model to study regulations that limit firm scale. Section 3 presents a case study of labor laws in France that differ depend- ing on the side of the employment threshold firms stand on. Section 4 applies the model of Section 2 to study these distortions. Section 5 proposes a quantitative analysis. Section 6 concludes.


This section introduces a simple model of production and employment, based on Lucas (1978), to evaluate the impact of size-dependent distortions.

2.1 Environment

There is a continuum of firms with production function


where n is employment and ez is a firm's productivity level (e denotes the exponential function). The distribution of productivity in the population is characterized by the density f. Production displays decreasing returns a e (0,1).2 Aggregate output, Y, is defined as the integral of the production of each firm y(z),

(1) ...

where n(z) is the employment of firms with productivity z.

Firms hire labor in a competitive labor market where workers supply labor inelastically. Let total employment be denoted by N. The wage rate, w, taken as given by each firm, is such that the labor market in equilibrium is

(2) ...

Labor costs for the firm are equal to the wage bill multiplied by a size-dependent tax T(n). …

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