If a firm's costs of installing capital are not quadratic, then its optimal investment is not a linear function of fundamentals, such as the returns and costs of capital. This study specifies a model in which a firm may face fixed, linear, and convex costs of investing, and estimates the resulting investment function using firm-level data from 11 countries. The evidence suggests important nonlinearities, consistent with the presence of fixed or other non-quadratic costs, in the relationship between investment and fundamentals for most countries. These findings are statistically signficant at the level of the firm, and economically significant when aggregated by country.