Selection and the Evolution of Industry

Recent evidence shows that within an industry, smaller firms grow faster and are more likely to fail than large firms. This paper provides a theory of selection with incomplete information that is consistent with these and other findings. Firms learn about their efficiency as they operate in the industry. The efficient grow and survive; the inefficient decline and fail. A perfect foresight equilibrium is proved by means of showing that it is a unique maximum to discounted net surplus. The maximization problem is not standard, and some mathematical results might be of independent interest. 1. THEORY AND EVIDENCE ON THE GROWTH AND SURVIVAL OF FIRMS Do SMALL FIRMS grow faster than large firms? Are they less likely to survive? Early studies found no relation between the size of firms and their growth rates [8, 14, 16]. The growth of firms seemed to be proportional to their size. In later work, adjustment costs with constant returns to scale were shown to imply that firms should grow in proportion to their size [10, 11]. Recent evidence from larger samples tells a different story. Mansfield [13] finds that smaller firms have higher and more variable growth rates. Du Rietz [6], in a sample of Swedish firms, again finds that smaller firms grow faster, and that they are less likely to survive [6,8,13]. These findings conflict with the adjustment costs theory in which all firms grow at the same rate, and in which failure does not happen. To explain these deviations from the proportional growth law, I propose a theory of noisy selection. Efficient firms grow and survive; inefficient firms decline and fail. Firms differ in size not because of the fixity of capital, but because some discover that they are more efficient than others. The model gives rise to entry, growth, and exit behavior that agrees, broadly, with the evidence. The model also agrees with some more tentative findings. First, firm size and concentration seem to be positively related to rates of return.2 Second, the correlation over time of rates of return is higher for larger firms and in the concentrated industries [15, 17]. Third, the variability of rates of return at a point in time is higher in the concentrated industries [17]. Finally, higher concentration is associated with higher profits for the larger firms, but not for the smaller firms