This paper develops quasi-likelihood estimation for generalized varying coefficient partially linear models when the response is not always observable. The paper considers two estimation methods and shows that under the assumption of selection on the observables the resulting estimators are asymptotically normal. As an application of these results the paper proposes a new estimator for the average treatment effect parameter. A simulation study illustrates the finite sample properties of the

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... osed estimators. ) and Wooldridge (2007) for M -estimation with missing data. The probabilities of the weighting method are typically unknown and therefore have to be estimated either with parametric or with nonparametric methods. In this paper we consider the parametric approach because as opposed to the nonparametric one it does not suffer from the curse of dimensionality and it is less negatively affected by a high proportion of missing data in the sample, making it perhaps more useful from an empirical point of view. Furthermore, as noted by Wooldridge (2007) , as long as the conditional mean is correctly specified and the assumption of selection on the observables holds misspecification of the parametric estimator for probabilities does not cause inconsistency of the weighted estimator for the parameters of the generalized varying coefficient partially linear estimator. The results of this paper are rather general and can be seen as a semiparametric extension of some of the results obtained by Wooldridge (2007) . The results are based on backfitting and profiling, which are the two main approaches to estimate parameters for general semiparametric models and differ in the way they deal with the infinite dimensional parameter. To be specific, backfitting involves iterating between the estimation of the infinite dimensional parameter and that of the finite dimensional one until convergence, see for example Hastie & Tibshirani (1990 ), Mammen, Linton & Nielsen (1999 ) and Opsomer (2000 . Profiling involves reparameterizing the infinite dimensional parameter as a certain function of the finite dimensional parameter and then estimate simultaneously the resulting reparameterized infinite dimensional parameter as well as the finite dimensional one, see for example Severini & Staniswalis () compare backfitting and profiling and note that in certain situations they result in asymptotically equivalent estimators as long as different level of smoothing is applied. The new results of the paper are the following: First we show that the proposed estimators defined as the solutions to a set of local quasi-scores are consistent. This result is based on a generalization to infinite dimensional parameters of the same approach used by Foutz (1977) , and complements the standard approach based on the global concavity of the quasi-likelihood function. Second, we show that both backfitting and profiling lead to estimators that are asymptotically normal but they are not asymptotically equivalent even if we consider different level of smoothing. Third, as an application of these results we propose a new semiparametric estimator for the average treatment effect parameter. This new estimator is motivated by some recent literature in health economics (see e.g. Basu, Polsky & Manning (2008) and references therein) advocating the use of parametric generalized linear models to capture potential nonlinear effects and interactions between outcomes and covariates as well as specific structures of the outcomes. Our estimator is flexible enough to capture these important features while preserving some of the advantages of using parametric methods. Furthermore for Normal, Bernoulli and Poisson quasi-likelihoods the new estimator enjoys the so-called doubly-robust property as noted by Wooldridge (2007) . Finally we use simulations to investigate the finite sample properties of the estimators based on backfitting and profiling and for the new average treatment effect estimator. The latter are compared with those based on commonly used alternatives. The results of this paper generalize and/or complement a number of results including those obtained by Cai et alamong others. The results can be used to show consistency and asymptotic normality for estimators defined as the solutions to a set of semiparametric smooth estimating equations, which could be, for example, the result of some economic theory restriction. The results can also be used to characterize the asymptotic behavior of the solutions to a set of local first order conditions that are often easier to find than those corresponding to global