R&D and productivity : estimating production functions when productivity is endogenous

We develop a simple estimator for production functions in the presence of endogenous productivity change that allows us to retrieve productivity and its relationship with R&D at the firm level. By endogenizing the productivity process we build on the recent literature on structural estimation of production functions. Our dynamic investment model can be viewed as a generalization of the knowledge capital model (Griliches 1979) that has remained a cornerstone of the productivity literature for more than 25 years. We relax the assumptions on the R&D process and examine the impact of the investment in knowledge on the productivity of firms. We illustrate our approach on an unbalanced panel of more than 1800 Spanish manufacturing firms in nine industries during the 1990s. Our findings indicate that the link between R&D and productivity is subject to a high degree of uncertainty, nonlinearity, and heterogeneity across firms. By accounting for uncertainty and nonlinearity, we extend the knowledge capital model. Moreover, capturing heterogeneity gives us the ability to assess the role of R&D in determining the differences in productivity across firms and the evolution of firmlevel productivity over time

A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification

This paper studies generic properties of Markov perfect equilibria in dynamic stochastic games. We show that almost all dynamic stochastic games have a finite number of locally isolated Markov perfect equilibria. These equilibria are essential and strongly stable. Moreover, they all admit purification. To establish these results, we introduce a notion of regularity for dynamic stochastic games and exploit a simple connection between normal form and dynamic stochastic games.Dynamic stochastic games, Markov perfect equilibrium, regularity, genericity, finiteness, strong stability, essentiality, purifiability, estimation, computation, repeated games

R&D and productivity: Estimating production functions when productivity is endogenous

We develop a simple estimator for production functions in the presence of endogenous productivity change that allows us to retrieve productivity and its relationship with R&D at the firm level. Our dynamic investment model can be viewed as a generalization of the knowledge capital model (Griliches 1979) that has remained a cornerstone of the productivity literature for more than 25 years. We relax the assumptions on the R&D process and examine the impact of the investment in knowledge on the productivity of firms. We illustrate our approach on an unbalanced panel of more than 1800 Spanish man- ufacturing firms in nine industries during the 1990s. Our ¯ndings indicate that the link between R&D and productivity is subject to a high degree of uncertainty, nonlinearity, and heterogeneity across firms. Abstracting from uncertainty and nonlinearity, as is done in the knowledge capital model, or assuming an exogenous process for productiv- ity, as is done in the recent literature on structural estimation of production functions, overlooks some of its most interesting features.production function; knowledge capital; productivity; R&D;

R&D and productivity : estimating production functions when productivity is endogenous

We develop a simple estimator for production functions in the presence of endogenous productivity change that allows us to retrieve productivity and its relationship with R&D at the firm level. By endogenizing the productivity process we build on the recent literature on structural estimation of production functions. Our dynamic investment model can be viewed as a generalization of the knowledge capital model (Griliches 1979) that has remained a cornerstone of the productivity literature for more than 25 years. We relax the assumptions on the R&D process and examine the impact of the investment in knowledge on the productivity of firms. We illustrate our approach on an unbalanced panel of more than 1800 Spanish manufacturing firms in nine industries during the 1990s. Our findings indicate that the link between R&D and productivity is subject to a high degree of uncertainty, nonlinearity, and heterogeneity across firms. By accounting for uncertainty and nonlinearity, we extend the knowledge capital model. Moreover, capturing heterogeneity gives us the ability to assess the role of R&D in determining the differences in productivity across firms and the evolution of firmlevel productivity over time.

Foundations of Markov-Perfect Industry Dynamics. Existence, Purification, and Multiplicity

In this paper we show that existence of a Markov perfect equilibrium (MPE) in the Ericson & Pakes (1995) model of dynamic competition in an oligopolistic industry with investment, entry, and exit requires admissibility of mixed entry/exit strategies, con- trary to Ericson & Pakes's (1995) assertion. This is problematic because the existing algorithms cannot cope with mixed strategies. To establish a firm basis for computing dynamic industry equilibria, we introduce ¯rm heterogeneity in the form of randomly drawn, privately known scrap values and setup costs into the model. We show that the resulting game of incomplete information always has a MPE in cuto® entry/exit strate- gies and is computationally no more demanding than the original game of complete information. Building on our basic existence result, we first show that a symmetric and anonymous MPE exists under appropriate assumptions on the model's primitives. Sec- ond, we show that, as the distribution of the random scrap values/setup costs becomes degenerate, MPEs in cuto® entry/exit strategies converge to MPEs in mixed entry/exit strategies of the game of complete information. Next, we provide a condition on the model's primitives that ensures the existence of a MPE in pure investment strategies. Finally, we provide the first example of multiple symmetric and anonymous MPEs in this literature.

An R&D Race with Knowledge Accumulation

I develop a model of an R&D race with knowledge accumulation. My model does not inherit the memorylessness property of the exponential distribution that troubles existing models of R&D races. Hence, firms’ knowledge stocks are no longer irrelevant to their behavior during the R&D race, and knowledge accumulation has strategic implications. In this more general setting, I obtain results that stand in marked contrast to the previous literature. In particular, under some conditions, the firm that is behind in the race engages in catch-up behavior. This pattern of strategic interactions (action-reaction) is consistent with empirical research

The Role of Permanent Income and Demographics in Black/White Differences in Wealth

We explore the extent to which the huge race gap in wealth can be explained with properly constructed income and demographic variables. In some instances we explain the entire wealth gap with income and demographics provided that we estimate the wealth model on a sample of whites. However, we typically explain a much smaller fraction when we estimate the wealth model on a black sample. Using sibling comparisons to control for intergenerational transfers and the effects of adverse history, we find that differences in income and demographics are not likely to account for the lower explanatory power of the black wealth models. Our analysis of growth models of wealth suggests that differences in savings behavior and/or rates of return play an important role.Black-White Wealth Gap, Siblings, Savings

Avoiding the Curse of Dimensionality in Dynamic Stochastic Games

Discrete-time stochastic games with a finite number of states have been widely ap- plied to study the strategic interactions among forward-looking players in dynamic en- vironments. However, these games suffer from a "curse of dimensionality" since the cost of computing players' expectations over all possible future states increases exponentially in the number of state variables. We explore the alternative of continuous-time stochas- tic games with a finite number of states, and show that continuous time has substantial computational and conceptual advantages. Most important, continuous time avoids the curse of dimensionality, thereby speeding up the computations by orders of magnitude in games with more than a few state variables. Overall, the continuous-time approach opens the way to analyze more complex and realistic stochastic games than currently feasible.

Avoiding the Curse of Dimensionality in Dynamic Stochastic Games

Continuous-time stochastic games with a finite number of states have substantial computational and conceptual advantages over the more common discrete-time model. In particular, continuous time avoids a curse of dimensionality and speeds up computations by orders of magnitude in games with more than a few state variables. The continuous-time approach opens the way to analyze more complex and realistic stochastic games than is feasible in discrete-time models.

R&D and productivity: Estimating endogenous productivity

We develop a model of endogenous productivity change to examine the impact of the investment in knowledge on the productivity of firms. Our dynamic investment model extends the tradition of the knowledge capital model of Griliches (1979) that has remained a cornerstone of the productivity literature. Rather than constructing a stock of knowledge capital from a firm’s observed R&D expenditures, we consider productivity to be unobservable to the econometrician. Our approach accounts for uncertainty, nonlinearity, and heterogeneity across firms in the link between R&D and productivity. We also derive a novel estimator for production functions in this setting. Using an unbalanced panel of more than 1800 Spanish manufacturing firms in nine industries during the 1990s, we provide evidence of nonlinearities as well as economically significant uncertainties in the R&D process. R&D expenditures play a key role in determining the differences in productivity across firms and the evolution of firm-level productivity over time