  Quality estimation models have been developed to assess the corrections made
by grammatical error correction (GEC) models when the reference or
gold-standard corrections are not available. An ideal quality estimator can be
utilized to combine the outputs of multiple GEC systems by choosing the best
subset of edits from the union of all edits proposed by the GEC base systems.
However, we found that existing GEC quality estimation models are not good
enough in differentiating good corrections from bad ones, resulting in a low
F0.5 score when used for system combination. In this paper, we propose GRECO, a
new state-of-the-art quality estimation model that gives a better estimate of
the quality of a corrected sentence, as indicated by having a higher
correlation to the F0.5 score of a corrected sentence. It results in a combined
GEC system with a higher F0.5 score. We also propose three methods for
utilizing GEC quality estimation models for system combination with varying
generality: model-agnostic, model-agnostic with voting bias, and
model-dependent method. The combined GEC system outperforms the state of the
art on the CoNLL-2014 test set and the BEA-2019 test set, achieving the highest
F0.5 scores published to date.
