Semi-Parametric Indirect Inference

We develop in this paper a generalization of the Indirect Inference (II) to semi-parametric settings and termed Semi-parametric Indirect Inference (SII). We introduce a new notion of Partial Encompassing which lays the emphasis on Pseudo True Values of Interest. The main difference with the older notion of encompassing is that some components of the pseudo-true value of interest associated with the structural parameters do correspond to true unknown values. This enables us to produce a theory of robust estimation despite mis-specifications in the structural model being used as a simulator. We also provide the asymptotic probability distributions of our SII estimators as well as Wald Encompassing Tests (WET) and advocate the use of Hausman type tests on the required assumptions for the consistency of the SII estimators. We illustrate our theory with examples based on semi-parametric stochastic volatility models.Indirect inference, partial encompassing, pseudo-true value of interest, structural models, instrumental models, Wald encompassing tests.

Noise and Competition in Strategic Oligopoly

Focusing on homogeneous beliefs, we can distinguish two commonly shared ideas that, i) the competition between informed traders destroys their trading profits, ii) trading with a noisy signal brings about a loss in the expected profits. So far, it has been proved in the latter framework, that when N strategic and perfectly informed traders compete in the financial market, i) the informativeness of prices increases with the degree of competition and, ii) the aggregate and individual profits go to 0 when N is large. In this paper, we propose a general study where N strategic informaed agents have heterogeneous beliefs, i.e. are endowed with noisy information and compete à la Nash. We prove the existence and uniqueness of a linear equilibrium generalizing Kyle (1985) results to the case of N informed traders when the insiders have heterogeneous beliefs. In this general framework, we derive the following striking results: for certain regions of noise and numbers of competitors in excess of four, i) each individual expected profit is greater than the one obtained in the perfectly informed (and homogeneous beliefs) case; ii) the aggregate profit has a finite (strictly) positive limit when N is large. iii) Even when an infinite number of insiders compete in the market, the price is no longer efficient and does not fully reveal the final liquidation value of the risky asset. iv) In the particular case where each informed agent is endowed with a signal the precision of which is the same, a) we show that there exists an optimal level of noise for which each individual expected profit is maximized; b) we show that there exists an optimal size of the market for which the aggregate expectged profit is maximized; c) the liquidity is an increasing function of the number of informed traders but has a finite limit for large N; d) the informativeness of prices is a decreasing function of the number of informed traders.Competition, optimal noise, price manipulation

Simulated Asymptotic Least Squares Theory

We develop in this paper a general econometric methodology referred to as the Simulated Asymptotic Least Squares (SALS). It is shown that this approach provides a unifying theory for 'approximation-based' or simulation-based inference methods and nests the Simulated Nonlinear Least Squares (SSNLS), the Simulated Pseudo Maximum Likelihood (SPML), the Simulated Method of Moments (SMM) in both parametric and semiparametric settings, the Indirect Inference (II) and the Efficient Method of Moments (EMM). We produce a new notion of Efficiency Bounds in Direction and provide a general study of the efficiency in the SALS framework. In the particular case of the II and the EMM methods and when the instrumental model is of a GMM type, we characterise a new weighting matrix for a more efficient estimation about the structural parameters of interest ?0. This new weighting matrix does no longer correspond, in the general case, to the classical one as characterised by Hansen (1982). Generalized global specification tests extending the previous existing ones are also proposed.Simulated Asymptotic Least Squares, Approximation-based and Simulation-based estimation, Efficiency Bounds in Direction, GMM, SNLS, SPML, SMM, II, GII, EMM.

Bullish-Bearish strategies of trading: A non-linear equilibrium.

In this paper, we study a financial market where risk neutral traders are endowed with a signal which is perfectly revealing of the direction (but not the exact amount) of the liquidation value of a normally distributed risky asset. This type of information is known as bullish or bearish. When the signal is positive (negative) the traders buy (sell) the asset. This type of information is different with the type of information which is classically considered in the literature where informed traders are endowed with a perfect or a noisy signal. In this model, since the optimal trading strategy is not linear, the pricing schedule is also a non-linear function of the volumes. The main results are the following i) the price function is a non-linear Sigmo¨ıd-shaped function. ii) A monopolistic bullish-bearish type trader makes nearly thirty six percent of the profits she would have made with a perfect signal in a linear model `a la Kyle (1985). iii) In the presence of competition, the market reveals his private information quicker than in a noisy informed strategic oligopoly. Moreover, liquidity is no longer a monotonic increasing function of the number of competitors

Noise and competition in strategic oligopoly

In this paper, we propose a model where N strategic informed traders who are endowed with heterogeneous noisy signals with different precisions compete in a market with a single risky asset. We explicitly describe the unique linear equilibrium that exists in this setup and derive its properties. Moreover, we focus on the effects of noise on the competition between traders. We show that noise softens the competition between traders. In particular, for N exceeding three and for certain sets of noise in traders' signals, each trader's individual profit is greater than the one obtained in the case of perfect information

Simulated asymptotic least squares theory

We develop in this paper a general econometric methodology referred to as the Simulated Asymptotic Least Squares (SALS). It is shown that this approach provides a unifying theory for 'approximation-based' or simulation-based inference methods and nests the Simulated Nonlinear Least Squares (SSNLS), the Simulated Pseudo Maximum Likelihood (SPML), the Simulated Method of Moments (SMM) in both parametric and semiparametric settings, the Indirect Inference (II) and the Efficient Method of Moments (EMM). We produce a new notion of Efficiency Bounds in Direction and provide a general study of the efficiency in the SALS framework. In the particular case of the II and the EMM methods and when the instrumental model is of a GMM type, we characterise a new weighting matrix for a more efficient estimation about the structural parameters of interest ?0. This new weighting matrix does no longer correspond, in the general case, to the classical one as characterised by Hansen (1982). Generalized global specification tests extending the previous existing ones are also proposed

Noise and competition in strategic oligopoly

Focusing on homogeneous beliefs, we can distinguish two commonly shared ideas that, i) the competition between informed traders destroys their trading profits, ii) trading with a noisy signal brings about a loss in the expected profits. So far, it has been proved in the latter framework, that when N strategic and perfectly informed traders compete in the financial market, i) the informativeness of prices increases with the degree of competition and, ii) the aggregate and individual profits go to 0 when N is large. In this paper, we propose a general study where N strategic informaed agents have heterogeneous beliefs, i.e. are endowed with noisy information and compete à la Nash. We prove the existence and uniqueness of a linear equilibrium generalizing Kyle (1985) results to the case of N informed traders when the insiders have heterogeneous beliefs. In this general framework, we derive the following striking results: for certain regions of noise and numbers of competitors in excess of four, i) each individual expected profit is greater than the one obtained in the perfectly informed (and homogeneous beliefs) case; ii) the aggregate profit has a finite (strictly) positive limit when N is large. iii) Even when an infinite number of insiders compete in the market, the price is no longer efficient and does not fully reveal the final liquidation value of the risky asset. iv) In the particular case where each informed agent is endowed with a signal the precision of which is the same, a) we show that there exists an optimal level of noise for which each individual expected profit is maximized; b) we show that there exists an optimal size of the market for which the aggregate expectged profit is maximized; c) the liquidity is an increasing function of the number of informed traders but has a finite limit for large N; d) the informativeness of prices is a decreasing function of the number of informed traders

Semi-parametric indirect inference

We develop in this paper a generalization of the Indirect Inference (II) to semi-parametric settings and termed Semi-parametric Indirect Inference (SII). We introduce a new notion of Partial Encompassing which lays the emphasis on Pseudo True Values of Interest. The main difference with the older notion of encompassing is that some components of the pseudo-true value of interest associated with the structural parameters do correspond to true unknown values. This enables us to produce a theory of robust estimation despite mis-specifications in the structural model being used as a simulator. We also provide the asymptotic probability distributions of our SII estimators as well as Wald Encompassing Tests (WET) and advocate the use of Hausman type tests on the required assumptions for the consistency of the SII estimators. We illustrate our theory with examples based on semi-parametric stochastic volatility models