The sentence would sound more natural with "it" as the subject: It might have been better if he had said...

This sentence illustrates the use of "better" as an adverb meaning "more wisely". Normally, "better" is an adjective, but not here. I like the sentence a lot, and would not change it one iota. As an adverb, "better" can modify any verb or adjective. In this sentence, there are two candidates: 1. "better" could modify "have" 2. "better" could modify "said" The speaker can influence the listener's choice by changing the position of "better" in the sentence. He can say A. He might better have said... B. He might have better said it. C. He might have said it better. All are correct. In B and C, the listener will interpret "better" as modifying "said". It means he could have found better words and said it better. Sometimes this is good enough. However, using the wrong words is not the only thing that the speaker might have done better. Perhaps the words he used were perfect but the points he made were the wrong ones. In that case, B and C do not serve the purpose. Hence A is my favorite, in which "better" modifies "have" (or "have said"). "Have + said" is the present perfect tense, which speaks of experiences. "He might better have said" means that his experience of saying (whatever it is that he said) might have been better, had he done things differently.

‘Better’ here means ‘in a more good way’. ‘Good’ is a vague word. A more precise adverb or adverbial phrase would be clearer. This use of ‘might’, though correct, is rather high brow. The more common could/should is more natural, though slightly changing the meaning. He could have more accurately said … He should have said, to be more precise,.. The original does have the advantage of brevity and would be understood by an Economist reader though.