Georgeanne M. Artz, Kevin D. Duncan, Arthur P. Hall and Peter F. Orazem have a new paper on that topic. The answer seems to be that state-level business conditions do not matter so much, at least not in their currently measurable forms:
This study submits 11 business climate indexes to tests of their ability to predict relative economic performance on either side of state borders. Our results show that most business climate indexes have no ability to predict relative economic growth regardless of how growth is measured. Some are negatively correlated with relative growth. Many are better at reporting past growth than at predicting the future. In the end, the most predictive business climate index is the Grant Thornton Index which was discontinued in 1989.
While I don’t think this is the final word on the topic, the burden of proof clearly lies on the side which claims they do matter a good deal.