Bertel Schjerning

Productivity Measurement in Manufacturing and the Expenditure Approach

This paper studies conversion factors based on the expenditure approach and evaluates the appropriateness for international comparisons of output levels in manufacturing. We apply a consistency check based on the insight that relative productivity levels should be invariant to the choice of base year. Consequently, convergence parameters and dispersion of productivity across countries should also be unaffected by this choice. The results are disappointing: relative measures of productivity depend heavily of the choice of base year and change systematically as the base years roll forward. The conclusion is insensitive to the applied method for developing conversion factors. The implication is that we cannot measure relative productivity levels in manufacturing across countries using the expenditure approach.

Comment on “Constrained Optimization Approaches to Estimation of Structural Models”

We revisit the comparison of mathematical programming with equilibrium constraints (MPEC) and nested fixed point (NFXP) algorithms for estimating structural dynamic models by Su and Judd (2012). Their implementation of the nested fixed point algorithm used successive approximations to solve the inner fixed point problem (NFXP‐SA). We redo their comparison using the more efficient version of NFXP proposed by Rust (1987), which combines successive approximations and Newton–Kantorovich iterations to solve the fixed point problem (NFXP‐NK). We show that MPEC and NFXP are similar in speed and numerical performance when the more efficient NFXP‐NK variant is used.

The Dynamics of Bertrand Price Competition with Cost-Reducing Investments

We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to “leapfrog�? their rival to attain low-cost leadership – at least temporarily. We show that leapfrogging occurs in equilibrium, resolving the Bertrand investment paradox., i.e. leapfrogging explains why firms have an ex ante incentive to undertake cost-reducing investments even though they realize that simultaneous investments to acquire the state of the art production technology would result in Bertrand price competition in the product market that drives their ex post profits to zero. Our analysis provides a new interpretation of “price wars�?. Instead of constituting a punishment for a breakdown of tacit collusion, price wars are fully competitive outcomes that occur when one firm leapfrogs its rival to become the new low cost leader. We show that the equilibrium involves investment preemption only when the firms invest in a deterministically alternating fashion and technological progress is deterministic. We prove that when technological progress is deterministic and firms move in an alternating fashion, the game has a unique Markov perfect equilibrium. When technological progress is stochastic or if firms move simultaneously, equilibria are generally not unique. Unlike the static Bertrand model, the equilibria of the dynamic Bertrand model are generally inefficient. Instead of having too little investment in equilibrium, we show that duopoly investments generally exceed the socially optimum level. Yet, we show that when investment decisions are simultaneous there is a “monopoly�? equilibrium when one firm makes all the investments, and this equilibrium is efficient. However, efficient non-monopoly equilibria also exist, demonstrating that it is possible for firms to achieve efficient dynamic coordination in their investments while their customers also benefit from technological progress in the form of lower prices.

The endogenous grid method for discrete‐continuous dynamic choice models with (or without) taste shocks

We present a fast and accurate computational method for solving and estimating a class of dynamic programming models with discrete and continuous choice variables. The solution method we develop for structural estimation extends the endogenous grid‐point method (EGM) to discrete‐continuous (DC) problems. Discrete choices can lead to kinks in the value functions and discontinuities in the optimal policy rules, greatly complicating the solution of the model. We show how these problems are ameliorated in the presence of additive choice‐specific independent and identically distributed extreme value taste shocks that are typically interpreted as “unobserved state variables” in structural econometric applications, or serve as “random noise” to smooth out kinks in the value functions in numerical applications. We present Monte Carlo experiments that demonstrate the reliability and efficiency of the DC‐EGM algorithm and the associated maximum likelihood estimator for structural estimation of a life‐cycle model of consumption with discrete retirement decisions. Life‐cycle model discrete and continuous choice Bellman equation Euler equation retirement choice endogenous grid‐point method nested fixed point algorithm extreme value taste shocks smoothed max function structural estimation C13 C63 D91

THE DYNAMICS OF BERTRAND PRICE COMPETITION WITH COST-REDUCING INVESTMENTS: THE DYNAMICS OF BERTRAND PRICE COMPETITION

We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to “leapfrog” their rival to attain low-cost leadership—at least temporarily. We show that leapfrogging occurs in equilibrium, resolving the Bertrand investment paradox., i.e. leapfrogging explains why firms have an ex ante incentive to undertake cost-reducing investments even though they realize that simultaneous investments to acquire the state of the art production technology would result in Bertrand price competition in the product market that drives their ex post profits to zero. Our analysis provides a new interpretation of “price wars”. Instead of constituting a punishment for a breakdown of tacit collusion, price wars are fully competitive outcomes that occur when one firm leapfrogs its rival to become the new low cost leader. We show that the equilibrium involves investment preemption only when the firms invest in a deterministically alternating fashion and technological progress is deterministic. We prove that when technological progress is deterministic and firms move in an alternating fashion, the game has a unique Markov perfect equilibrium. When technological progress is stochastic or if firms move simultaneously, equilibria are generally not unique. Unlike the static Bertrand model, the equilibria of the dynamic Bertrand model are generally inefficient. Instead of having too little investment in equilibrium, we show that duopoly investments generally exceed the socially optimum level. Yet, we show that when investment decisions are simultaneous there is a “monopoly” equilibrium when one firm makes all the investments, and this equilibrium is efficient. However, efficient non-monopoly equilibria also exist, demonstrating that it is possible for firms to achieve efficient dynamic coordination in their investments while their customers also benefit from technological progress in the form of lower prices.

Constrained Optimization Approaches to Estimation of Structural Models: Comment

We revisit the comparison of mathematical programming with equilibrium constraints (MPEC) and nested fixed point (NFXP) algorithms for estimating structural dynamic models by Su and Judd (SJ, 2012). They used an inefficient version of the nested fixed point algorithm that relies on successive approximations. We re-do their comparison using the more efficient version of NFXP proposed by Rust (1987), which combines successive approximations and Newton-Kantorovich iterations to solve the fixed point problem (NFXP-NK). We show that MPEC and NFXP-NK are similar in performance when the sample size is relatively small. However, in problems with larger sample sizes, NFXP-NK outperforms MPEC by a significant margin.