Long Term Risk: An Operator Approach

We create an analytical structure that reveals the long run risk-return relationship for nonlinear continuous time Markov environments. We do so by studying an eigenvalue problem associated with a positive eigenfunction for a conveniently chosen family of valuation operators. This family forms a semigroup whose members are indexed by the elapsed time between payoff and valuation dates. We represent the semigroup using a positive process with three components: an exponential term constructed from the eigenvalue, a martingale and a transient eigenfunction term. The eigenvalue encodes the risk adjustment, the martingale alters the probability measure to capture long run approximation, and the eigenfunction gives the long run dependence on the Markov state. We establish existence and uniqueness of the relevant eigenvalue and eigenfunction. By showing how changes in the stochastic growth components of cash flows induce changes in the corresponding eigenvalues and eigenfunctions, we reveal a long-run risk return tradeoff.

“Value Added Taxes, Chain Effects and Informality”, Second Version

This paper investigates determinants of informal economic activity. We present an equilibrium model of informality and test its implications using a survey of 48,000+ small firms in Brazil. We define informality as tax avoidance; firms in the informal sector avoid tax payments but suffer other limitations. A novel theoretical contribution in this model is the role of value added taxes in transmitting informality. It predicts that the informality of a firm is correlated to the informality of firms from which it buys or sells. The model also implies that higher tolerance for informal firms in one production stage increases tax avoidance in downstream and upstream stages. Empirical analysis shows that, in fact, various measures of formality of suppliers and purchasers (and its enforcement) are correlated with the formality of a firm. Even more interestingly, when we look at sectors where Brazilian firms are not subject to the credit system of value added tax, but instead the value added tax is applied at some stage of production at a rate that is estimated by the tax authorities, this chain effect vanishes.Informal Sector, VAT, Tax Avoidance

The Informal Sector: An Equilibrium Model and Some Empirical Evidence from Brazil, Second Version

We test implications of a simple equilibrium model of informality using a survey of 48,000+ small firms in Brazil. In the model, agent's ability to manage production differ and informal firms face a higher cost of capital and limitation on size, although these informal firms avoid tax payments. As a result, informal firms are managed by less able entrepreneurs, are smaller, and employ a lower capital-labor ratio. The model predicts that the interaction of an index of observable inputs to entrepreneurial ability and formality is positively correlated with firm size, which we verify in the data. Using the model, we estimate that informal firms in our dataset faced at least 1.3 times the cost of capital of formal firms.Informal Sector, Tax Avoidance, Brazil

The Informal Sector

This paper investigates the determinants of informal economic activity. We present two equilibrium models of informality and test their implications using a survey of 48,000+ small firms in Brazil. We define informality as tax avoidance; firms in the informal sector avoid tax payments but suffer other limitations. In the first model there is a single industry and informal firms face a higher cost of capital and a limitation on size. As a result informal firms are smaller and have a lower capital labor ratio. When education is an imperfect proxy for ability, we show that the interaction of the manager’s education and formality has a positive correlation with firm size. These implications are supported by our empirical analysis. A novel theoretical contribution in this paper is a model that highlights the role of value added taxes in transmitting informality. It predicts that the informality of a firm is correlated to the informality of firms from which it buys or sells. The model also implies that higher tolerance for informal firms in one production stage increases tax avoidance in downstream and upstream sectors. Empirical analysis shows that, in fact, various measures of formality of suppliers and purchasers (and its enforcement) are correlated with the formality of a firm. Even more interestingly, when we look at sectors where Brazilian firms are not subject to the credit system of value added tax, but instead the value added tax is applied at some stage of production at a rate that is estimated by the State, this chain effect vanishes.Informal Sector, VAT, Tax Avoidance

Non-Market Interactions

A large body of recent research argues that social, or non-market, interactions can explain a wide range of puzzling phenomena from fashion cycles to stock market crashes. This paper attempts to connect the range of these papers with a general model and a broad empirical overview. We establish conditions for existence and uniqueness of equilibria in social interactions models. The existence of multiple equilibria requires sufficient non-linearity in social interactions and only moderate heterogeneity across agents--strategic complementarities are neither necessary nor sufficient for multiple equilibria. We establish conditions for the existence of a social multiplier, which is the ratio of the aggregate outcome-input relationship to the individual outcome-input relationship. Models with multiple equilibria are empirically indistinguishable from models with significant social multipliers. Finally, we show the formal relationship between three known methods of empirically estimating social interactions, and suggests the plusses and minuses of these three approaches.