Price-Quantity Competition with risk-averse firms
Dávid Kopányi (University of Amsterdam)

We consider the market for a homogeneous good in which two firms simultaneously decide on both the price and the production level of the good. It is known from the literature that, under complete information and with profit-maximizing firms that are risk neutral, there exists no pure-strategy Nash equilibrium in this model (see e.g. Gertner, 1986). In this paper we show that a Nash equilibrium in pure strategies may exist when firms are risk averse and hold noisy conjectures about the action of the other firm. We calculate the Nash equilibrium in pure strategies numerically for the case where firms have mean-variance preferences and analyze how this equilibrium depends on important parameters of the model such as the risk aversion parameter in the objective function and the distribution of the noisy conjectures about the action of the other firm. Contrary to the mixed-strategy Nash equilibrium under risk neutrality and complete information, each firm now produces less than the market demand at the equilibrium price. Aggregate production, however, may be larger as well as smaller than the market demand, depending on the preferences and beliefs of the firms. We find that the more risk averse the firms are, the less they produce and the higher price they ask in equilibrium. Aggregate production exceeds market demand for low degrees of risk aversion and firms have some unsold products. As firms become more risk averse, aggregate production will not satisfy the demand in equilibrium. Thus, given the beliefs of firms, there exists an optimal level of risk aversion for which aggregate production equals equilibrium demand so no consumer or producer will be rationed.

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Accuracy and efficiency of various GMM inference techniques in dynamic micro panel data models
Rutger Poldermans (University of Amsterdam)

The performance in finite samples is examined of inference obtained by variants of the Arellano-Bond and the Blundell-Bond 2-step GMM estimation techniques for single dynamic panel data models with possibly endogenous regressors and cross-sectional heteroskedasticity. By simulation the effects are examined of using less (against more) robust implementations of the GMM weighting matrix, and also of particular instrument strength enhancing transformations of the matrix of instrumental variables. We compare the root mean squared errors of the resulting coefficient estimators and also the size of tests on coefficient values and of different implementations of overidentification restriction tests. Also the size and power of a test on the validity of the additional orthogonality conditions exploited by the Blundell-Bond technique are assessed over a pretty wide grid of relevant cases. Surprisingly, particular asymptotically optimal and relatively robust weighting matrices are found to be superior in finite samples to ostensibly more appropriate versions. Most of the variants of tests for overidentification restrictions show serious deficiencies. A recently developed modification of GMM is found to have great potential when the cross-sectional heteroskedasticity is pronounced and the time-series dimension of the sample not too small. Finally all techniques are employed to actual data and lead to new insights.