We propose a novel statistic that equals a quadratic form of the first order derivative of the generalized method of moments (GMM) objective function. It is an asymptotically pivotal statistic for testing hypothezes on all parameters in the GMM moment equations. Its chi-squared limiting distribution has as many degrees of freedom as the number of parameters in the moment equations. The statistic is equal to zero when the hypothesized value of the parameters is equal to the continuous updating estimator. The specification of the statistic involves unknown covariance parameters which we can estimate using either parametric or heteroscedasticity autocorrelation consistent covariance matrix estimators. We conduct size and power comparisons for testing the risk aversion parameter in a stochastic discount factor model and the autocorrelation parameter in a panel autoregressive model of order 1.