Gibrat's law: Meaning, Criticisms & Real-World Uses

What Is Gibrat's Law?

Gibrat's law, also known as the Law of Proportionate Effect, is an economic principle asserting that the proportional rate of growth of a firm is independent of its absolute firm size. This concept falls under the broader category of firm dynamics within economics, challenging the intuitive notion that larger entities might inherently grow faster or slower than smaller ones. Instead, Gibrat's law suggests that growth is largely a stochastic process, where random events, rather than initial scale, dictate a company's expansion. This implies that a small startup has the same likelihood of doubling its size as a multinational corporation. Gibrat's law is foundational for understanding the distribution of firm sizes in an economy and the forces that drive economic growth.

History and Origin

Gibrat's law was first introduced by French engineer and economist Robert Gibrat in his 1931 work, Les Inégalités Économiques. Gi¹⁵brat's observations on the size distribution of French manufacturing establishments led him to propose the rule of proportional growth, suggesting that the proportional rate of expansion for a company does not depend on its initial scale. Th¹⁴is principle was significant because it provided a theoretical underpinning for the observed log-normal distribution of firm sizes within industries. Fo¹³r decades following its introduction, Gibrat's law gained considerable popularity among economists and statisticians, serving as a basis for mathematical modeling of industrial structures.,

¹²#¹¹# Key Takeaways

Gibrat's law posits that a firm's proportional growth rate is unaffected by its current size.
It implies that random events, not initial scale, are the primary drivers of growth.
The law suggests that firm size distributions tend towards a log-normal pattern over time.
Empirical evidence on Gibrat's law is mixed, with some studies supporting it for mature firms and others rejecting it, especially for smaller or younger firms.
The concept has implications for policymakers regarding market structure, competition, and support for small businesses.

Formula and Calculation

Gibrat's law can be expressed mathematically by considering the size of a firm over time. If ( S_t ) represents the size of a firm at time ( t ), and ( g_t ) is its growth rate during period ( t ), the law implies that ( g_t ) is independent of ( S_{t-1} ).

The growth rate can be defined as:

g_t = \frac{S_t - S_{t-1}}{S_{t-1}}

Rearranging this, we get:

S_t = S_{t-1}(1 + g_t)

Taking the logarithm of both sides, assuming a constant growth rate over discrete periods and random shocks:

\ln(S_t) = \ln(S_{t-1}) + \ln(1 + g_t)

If ( \ln(1 + g_t) ) is a random variable with a constant mean and variance, independent of ( S_{t-1} ), then repeated application of this process leads to ( \ln(S_t) ) following a normal distribution, implying that ( S_t ) itself follows a log-normal distribution. This formulation emphasizes that the proportional change (or the change in the logarithm of size) is random and not correlated with the initial size.

Interpreting Gibrat's Law

Interpreting Gibrat's law means understanding that, under its premise, all firms, regardless of their current scale, face the same probabilities of proportional expansion or contraction. This doesn't mean that a small firm will add the same absolute number of employees as a large firm in a given period, but rather that it has the same chance of, say, growing by 10%. For example, a firm with 100 employees has the same chance of growing to 110 employees (10% growth) as a firm with 1,000 employees has of growing to 1,100 employees (also 10% growth). This perspective suggests a level playing field in terms of growth opportunities, where factors external to a firm's size, such as changes in market demand or industry-wide shifts, play a more significant role. The law influences how analysts perceive industry dynamics and the long-term equilibrium distribution of firm sizes.

Hypothetical Example

Consider two hypothetical companies in the software industry: "Startup Solutions," a small firm with 50 employees, and "Global Tech," a large corporation with 5,000 employees. According to Gibrat's law, both companies have an equal probability of achieving a 20% proportional growth in a given year.

Startup Solutions: If it experiences 20% growth, its employee count would increase by ( 50 \times 0.20 = 10 ) employees, bringing its new total to 60 employees.
Global Tech: If it also experiences 20% growth, its employee count would increase by ( 5,000 \times 0.20 = 1,000 ) employees, resulting in a new total of 6,000 employees.

In this scenario, while Global Tech adds a much larger absolute number of employees, the proportional growth rate for both firms is identical, aligning with the core tenet of Gibrat's law. This highlights how random events, such as successfully launching a new product or a sudden surge in sector demand, could impact companies of any firm size equally in percentage terms.

Practical Applications

Gibrat's law, while a theoretical construct, has informed discussions in various areas of finance and economics. For entrepreneurs and venture capitalists, the law suggests that smaller businesses inherently possess the same potential for rapid proportional growth as larger, more established companies. This perspective encourages investment in early-stage firms, emphasizing the role of random factors like successful innovation or favorable market conditions over initial scale.

In the realm of business strategy, the law implies that firms should focus on adapting to market shifts and leveraging new opportunities, rather than relying on size advantages for growth. For government policymakers, Gibrat's law underscores the importance of fostering an environment conducive to fair market entry and growth for all firms, regardless of their existing scale, to promote a diversified and competitive economy. The International Monetary Fund (IMF), for instance, studies firm dynamics to understand aggregate productivity growth, noting how factors like access to finance and product market reforms can impact the ability of firms to scale up.

#¹⁰# Limitations and Criticisms

Despite its theoretical elegance, Gibrat's law faces significant limitations and criticisms in empirical studies. A common finding that often contradicts Gibrat's law is that smaller firms tend to exhibit higher, albeit more volatile, growth rates than larger firms., T⁹h⁸is observation suggests that initial firm size does influence growth, particularly for young companies that need to expand rapidly to reach a minimum efficient scale or simply to survive.

S⁷ome researchers argue that Gibrat's law may hold true only for a subset of firms, such as large, mature companies that have overcome initial growth hurdles and market selection processes., F⁶o⁵r instance, studies have found that financial constraints can disproportionately affect smaller firms, leading to deviations from the law. Th⁴e assumption of growth being solely a stochastic process, uninfluenced by strategic decisions, managerial talent, or external factors beyond random shocks (e.g., specific technological advancements that favor large players), also presents a challenge to its universal applicability. While the law predicts a log-normal distribution of firm sizes, empirical evidence often points to distributions that are skewed in ways not fully explained by Gibrat's original formulation.

Gibrat's Law vs. Zipf's Law

Gibrat's law and Zipf's law are two distinct, though sometimes related, concepts concerning the size distribution of entities, primarily firms or cities. Gibrat's law, or the Law of Proportionate Effect, specifically states that the proportional growth rate of an entity (like a firm) is independent of its size. This implies that if growth is a purely random multiplicative process, the sizes will tend towards a log-normal distribution over time.

In contrast, Zipf's law describes a regularity in the distribution of sizes itself. It postulates that for many types of data sets, the frequency of an item is inversely proportional to its rank in the frequency table. When applied to city sizes, Zipf's law suggests that the second-largest city will be half the size of the largest, the third-largest one-third the size, and so on. While Gibrat's law is a process-based model for growth that can lead to certain size distributions (often log-normal), Zipf's law is an empirical observation about the resulting distribution, typically a power-law distribution. Some research suggests that while Gibrat's law may explain the log-normal distribution for the entire range of city or firm sizes, Zipf's law often holds more strictly for the upper tail or largest entities within a distribution., Th³e confusion often arises because both laws attempt to describe patterns in size distributions, but they do so from different perspectives—one focusing on the growth mechanism and the other on the resulting static distribution.

FAQs

What does "proportionate effect" mean in Gibrat's law?

The "proportionate effect" means that a firm's growth is a random percentage of its current size, rather than a fixed absolute amount. For instance, a 10% growth rate is equally likely for a small firm as for a large one, meaning the increase in size is proportional to the starting size.

Is Gibrat's law consistently observed in the real world?

Empirical evidence on Gibrat's law is mixed. While some studies, particularly those focusing on large and mature firms, have found support for the law, many others, especially those including smaller and younger firms, tend to reject it, showing that smaller firms often grow faster.,

##²#¹ What are the implications of Gibrat's law for investment decisions?
Gibrat's law implies that superior growth is not necessarily tied to a firm's initial scale. This perspective suggests that investors seeking high-growth opportunities might find them in smaller, nimble companies as readily as in large corporations, as proportional growth is equally probable for all.

How does Gibrat's law relate to market structure?

If Gibrat's law held universally, it would imply that competitive markets could sustain a wide range of firm size without inherent advantages for larger players in terms of growth. This contributes to the understanding of how competition and market entry can lead to diverse industry structures over time.