We address the problem of estimating the word error rate (WER) of an automatic speech recognition (ASR) system without using acoustic test data. This is an important problem which is faced by the designers of new applications which use ASR. Quick estimate of WER early in the design cycle can be used to guide the decisions involving dialog strategy and grammar design. Our approach involves estimating the probability distribution of the word hypotheses produced by the underlying ASR system given the text test corpus. A critical component of this system is a phonemic confusion model which seeks to capture the errors made by ASR on the acoustic data at a phonemic level. We use a confusion model composed of probabilistic phoneme sequence conversion rules which are learned from phonemic transcription pairs obtained by leave-one-out decoding of the training set. We show reasonably close estimation of WER when applying the ystem to test sets from different domains.