Nonlinear GMM Research Articles

A note on Bayesian interpretations of HCCME-type refinements for nonlinear GMM models

In this note, we provide the application of HCCME-type refinements to nonlinear GMM models with Bayesian interpretations.

Old Wine in a New Bottle: Are Financial Variables Omitted Variables in the Production Function?

This paper examines the role of financial variables in the production function by making use of nonlinear regressions along with panel data techniques and a G7 data panel set. It offers a non-linear GMM estimator that makes use of instruments that exploit information from the levels of the variables in the production function, while it uses both one-level and two-level bootstraps to check whether the estimates are supported by the data. The results suggest that both money and credit aggregates enter significantly the aggregate production function as an input, indicating that both variables seem to facilitate the process of production.

Old Wine in a New Bottle: Are Financial Variables Omitted Variables in the Production Function?

This paper examines the role of financial variables in the production function by making use of nonlinear regressions along with panel data techniques and a G7 data panel set. It offers a non-linear GMM estimator that makes use of instruments that exploit information from the levels of the variables in the production function, while it uses both one-level and two-level bootstraps to check whether the estimates are supported by the data. The results suggest that both money and credit aggregates enter significantly the aggregate production function as an input, indicating that both variables seem to facilitate the process of production.

Departures from Rational Expectations and Asset Pricing Anomalies

We investigate the potential of the consumption CAPM with pessimism, doubt, and the availability heuristic in the agent's beliefs to resolve the equity premium and risk-free rate puzzles. Using the nonlinear GMM estimation techniques, we find that doubt and the availability heuristic play an important role in explaining the cross-section of asset returns. However, when taken alone, these deviations from rational expectations cannot resolve the equity premium and risk-free rate puzzles. This result is robust to the assumption that the expected value of an uncertain prospect is nonlinear in the subjective outcome probabilities.

Departures from Rational Expectations and Asset Pricing Anomalies

We investigate the potential of the consumption CAPM with pessimism, doubt, and the availability heuristic in the agent's beliefs to resolve the equity premium and risk-free rate puzzles. Using the nonlinear GMM estimation techniques, we find that doubt and the availability heuristic play an important role in explaining the cross-section of asset returns. However, when taken alone, these deviations from rational expectations can not resolve the equity premium and risk-free rate puzzles. This result is robust to the assumption that the expected value of an uncertain prospect is nonlinear in the subjective outcome probabilities.

Learning by Exporting: New Insights from Examining Firm Innovation

Empirical findings across many nations show that exporters have superior productivity compared to nonexporters and that this relationship is driven by productive firms becoming exporters. The conclusion drawn from these studies is that there is little learning from exporting. We, however, assess if there areex postbenefits that accrue to exporting firms by examining innovation outcomes. We argue that exporters can often access diverse knowledge inputs not available in the domestic market, that this knowledge can spill back to the focal firm, and that such learning can foster increased innovation. We examine product innovation and patent application counts of a representative sample of Spanish manufacturing firms from 1990 to 1997. To conduct the analysis, we use a nonlinear GMM estimator for exponential models with panel data that allows for predetermined regressors and linear feedback. We find that exporting is associated with innovation. Moreover, the panel data allow us to explore the temporal relationship between exporting and innovation. In contrast to existing findings, we find evidence of learning by exporting—albeit in dimensions not previously examined in the literature.

Estimating Euler equations

In this paper we consider conditions under which the estimation of a log-linearized Euler equation for consumption yields consistent estimates of the preference parameters. When utility is isoelastic and a sample covering a long time period is available, consistent estimates are obtained from the log-linearized Euler equation when the innovations to the conditional variance of consumption growth are uncorrelated with the instruments typically used in estimation. We perform a Monte Carlo experiment, consisting in solving and simulating a simple life cycle model under uncertainty, and show that in most situations, the estimates obtained from the log-linearized equation are not systematically biased. This is true even when we introduce heteroskedasticity in the process generating income. The only exception is when discount rates are very high (e.g. 47% per year). This problem arises because consumers are nearly always close to the maximum borrowing limit: the estimation bias is unrelated to the linearization and estimates using non-linear GMM are as bad. Across all our situations, estimation using a log-linearized Euler equation does better than nonlinear GMM. Finally, we plot life cycle profiles for the variance of consumption growth, which, except when the discount factor is very high, is remarkably flat. This implies that claims that demographic variables in log-linearized Euler equations capture changes in the variance of consumption growth are unwarranted.

An MCMC approach to classical estimation

This paper studies computationally and theoretically attractive estimators called the Laplace type estimators (LTE), which include means and quantiles of Quasi-posterior distributions defined as transformations of general (non-likelihood-based) statistical criterion functions, such as those in GMM, nonlinear IV, empirical likelihood, and minimum distance methods. The approach generates an alternative to classical extremum estimation and also falls outside the parametric Bayesian approach. For example, it offers a new attractive estimation method for such important semi-parametric problems as censored and instrumental quantile, nonlinear GMM and value-at-risk models. The LTE's are computed using Markov Chain Monte Carlo methods, which help circumvent the computational curse of dimensionality. A large sample theory is obtained for regular cases.

GMM Estimation of Dynamic Panel Data Models with Persistent Data

This paper considers GMM based estimation and testing procedures for two versions of the AR(1) model with Fixed Effects, henceforth abbreviated as ARFE(1): the conditional ARFE(1) model, and the inclusive ARFE(1) model, which contains the stationary ARFE(1) models and the ARFE(1) model with a unit root. First, the paper presents a two-step Optimal Linear GMM (OLGMM) estimator for the inclusive model, which is asymptotically equivalent to the optimal nonlinear GMM estimator of Ahn and Schmidt (1997). Then the paper examines the properties of the GMM estimators for both versions of the model when the data are persistent. Among other things, we find that the OLGMM estimator is superefficient in the unit root case. Furthermore, under stationarity the covariances of the instruments of the Arellano-Bond estimator and the first differences of the dependent variable are not weak. We also derive new approximations to the finite sample distributions of the Arellano-Bond estimator (for both versions of the model), the Arellano-Bover estimator, and the System estimator. We employ local-to-zero asymptotics (cf Staiger and Stock (1997)) for the Arellano-Bond estimator for the conditional model, because its instruments are weak in this context, and we employ local-to-unity asymptotics, which is developed in this paper, for the estimators for the stationary model. The new approximations agree well with the Monte Carlo evidence in terms of bias and variance. Finally, various GMM based unit root tests against stationary and conditional alternatives are proposed.

Initial conditions and moment restrictions in dynamic panel data models

Estimation of the dynamic error components model is considered using two alternative linear estimators that are designed to improve the properties of the standard first-differenced GMM estimator. Both estimators require restrictions on the initial conditions process. Asymptotic efficiency comparisons and Monte Carlo simulations for the simple AR(1) model demonstrate the dramatic improvement in performance of the proposed estimators compared to the usual first-differenced GMM estimator, and compared to non-linear GMM. The importance of these results is illustrated in an application to the estimation of a labour demand model using company panel data.

Efficient estimation of dynamic panel data models: Alternative assumptions and simplified estimation

This paper considers the estimation of dynamic models for panel data. It shows how to count and express the moment conditions implied by a variety of covariance restrictions. These conditions can be imposed in a GMM framework. Many of the moment conditions are nonlinear in the parameters. We derive a simple linearized estimator that is asymptotically as efficient as the nonlinear GMM estimator, and convenient tests of the validity of the nonlinear restrictions.

Efficient estimation of models for dynamic panel data

In this paper we consider a dynamic model for panel data. We show that, under standard assumptions, there are more moment conditions than are currently exploited in the literature. Some of these are linear, but others are quadratic, so that nonlinear GMM is required. We also show that exogenous regressors generate a larger number of relevant moment conditions in a dynamic model than they would in a static model.

Dynamic Count Data Models of Technological Innovation

This paper examines the application of count data models to firm level panel data on technological innovations. The model we propose exhibits dynamic feedback and unobserved heterogeneity. We develop a fixed effects estimator that generalises the standard Poisson and negative binomial models allowing for dynamic feedback through both the firm's stock of knowledge and its product market power. By using the long pre-sample history of innovation information this "entry stock" estimator is shown to control for correlated fixed effects and is compared with an alternative nonlinear GMM estimator. We find evidence of history dependence in innovation activity although variables reflecting the company's economic environment are also found to play a major role.