Finance - Bottazzi Lecture 2

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Information about Finance - Bottazzi Lecture 2
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Published on May 11, 2008

Author: untellectualism

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On the evolution of the firm size distribution: facts and theory : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION On the evolution of the firm size distribution: facts and theory Luìs M. Cabral and Josè Mata Literature Review : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Literature Review Conventional wisdom: expected firm growth rates are independent of size (Gibrat’s law) and the FSD is stable and approximately lognormal However, recent empirical evidence (Evans, 1987, Hall, 1987), based on more complete datasets than used in the past, shows that the relation between growth and size is not constant, but rather decreasing . This paper : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION This paper Derives some stylized facts concerning the FSD and its evolution over time Propose a theoretical explanation for the observed stylized facts Main results : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Main results The data suggest that the distribution of the logarithms of firm size of a given cohort is very skewed to the right at time of birth, and gradually evolves towards a more symmetric distribution. The total firm size distribution, in turn, is fairly stable over time, and somewhat skewed to the right. Possible explanation : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Possible explanation Selection, especially if we consider that exit rates are higher among smaller firms Financial constraint Stylized facts : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Stylized facts Sample of 587 firms results belonging to the manufacturing sector The second data source is a survey conducted by the Portuguese Ministry of Employment | Quadros de Pessoal (QP). This is a comprehensive survey, covering all firms employing paid labour in the economy. Stylized facts : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Stylized facts Stylized facts : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Stylized facts Stylized facts : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Stylized facts Stylized facts : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Stylized facts The authors use the data in their cross-sectional dimension. They identify cohorts of firms and follow their evolution over time. Specifically, they consider the cohort of firms that entered Portuguese manufacturing in 1984 and follow them until 1991. 3 FSD in next slide: The first one is the distribution of all entrants in 1984; the second one, the distribution of survivors in 1991. The third one is the size distribution in 1984 of those firms that survived until 1991. Stylized facts : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Stylized facts Explaining the stylized facts : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Explaining the stylized facts One can now identify two sources for this evolution: As of 1984 the total sample is more skewed than the sample of those firms that survive until 1991: selection plays a role in the shift of the FSD. Within the sample of survivors, the 1984 distribution is more skewed than the 1991 one: ageing also plays a role in this shift. Financing constaints : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Financing constaints Two-period model of a competitive industry. Each firm’s efficiency, measured by θ, is constant in both periods Each entrepreneur is endowed with initial wealth, w(z), where z is a vector of attributes. w(z) is the maximum capacity (measured in number of employees) that the entrepreneur can build given his or her wealth. The model : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION The model Actual first period size is the minimum between q*(θ) and w(z), where q*(θ) is optimal size In the second period, the firm is no longer subject to financing constraints. Actual size is therefore equal to the optimal size, q*(θ). Suppose that variable cost is The model : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION The model Optimal output is then Choose p and α such that: q*=θ Let F(θ) be the distribution of θ and G(w) be the distribution of w. The size distribution in period 2 is then given by F(θ), whereas the size distribution in the first period is the distribution of min(θ; w). The Model : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION The Model In particular, if θ and w are independent, then the density of first period output is given by In words, a firm has inizial size q if q is the desired level on efficiency grounds and the entrepreneur has the necessary wealth for such investment (first term on the right-hand side); or if the entrepreneur has just enough wealth for an output of q, although desired output on efficiency grounds would be greater than that (second term on the right hand side) Age, education and wealth : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Age, education and wealth In addition to industry dummies, the following two variables: The entrepreneur’s education level The entrepreneur’s age Education is a proxy for human capital: entrepreneurs endowed with better education should have better abilities and thus a greater θ, which translates into a greater output Age has a double effect. After controlling for education, age is a proxy for labor market experience, which should raise efficiency. On the other hand, age is also a proxy for the existence of liquidity constraints. Estimating : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Estimating If age is mostly reflecting liquidity constraints, then its effect should be important at birth, but should vanish over time. If, on the contrary, age measures ability, then its effects should persist. Estimating : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Estimating Estimation results : 8204 ENTREPRENEURSHIP, FINANCE AND INNOVATION Estimation results A firm’s initial size is the minimum of its desired size and and the entrepreneur’s wealth constraint: Mature surviving firms are not financially constrained. This implies that the evolution of the size distribution is determined by firms ceasing to be financially constrained.

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