Did Jesus call himself God?

It is sometime said that while NT writers attribute deity to Jesus, Jesus never explicitly calls himself "God". 

i) People who say this would generally reject the deity of Christ even if Jesus explicitly called himself "God" in the Gospels. They'd say that was the narrator writing a script. Inventing a speech and putting that on Jesus' lips. Or they'd say that Roman emperors called themselves "god", so there's nothing that special about calling yourself "God" in the NT era. The designation could be used in a watered down or honorific sense. 

ii) Before Jesus begins making divine claims, it's necessary for him to lay the groundwork. Imagine, at the outset of his ministry, if he went around claiming to be the Deity. Most folks would either regard him as a blasphemer or madman. So he first needs to do things that will lend credibility to that claim. So often he says things that remind the observer of Yahweh, and that's backed up by doing things that remind the observer of Yahweh. By a later stage in his ministry, there's something "about" Jesus that now makes that comparison eerily and irresistibly plausible.

iii) From a tactical and psychological standpoint, implicit claims can be more effective than explicit claims. In the Gospels, Jesus says and does things that invite comparison with things Yahweh says and does. 

Instead of just coming out and saying, "I am Yahweh", he resorts to insinuations that leave it up to the listener to complete the thought. That's more effective because it draws the listener into the dialectic, forcing him to publicly recognize and affirm the implications of what Jesus said. 

That shifts the emphasis from what Jesus says to what the listener discerns. A tactic that involves and implicates the listener in the flow of argument, so that Jesus doesn't have to say that about himself because they say it about him, in response to broad hints and clues. Even hostile accusers draw that conclusion. It puts it on the listener, including the accuser, to articulate it. Even to accuse him of blasphemy, they must unwittingly cooperate with Jesus, play on his turf, by verbalizing and explicating the thrust of what he says and does. They confess that they caught the drift. 

So they complete the trajectory, the train of thought, that he initiated–which puts them at a psychological disadvantage if they then wish to extricate themselves from complicity in the conclusion. It's a tactic that throws his accusers off balance because they have to play his game. They have to enter the game and make a move or countermove. To engage Jesus they must take the bait. Accept that coercive dilemma. Now they're on the hook. 

If he said it all himself, they'd be able to maintain their distance, but to press the charge, they must finish his sentences (as it were). In the process, they become unintended evangelists. 

iv) In addition, it's more effective in winning converts. There's a cumulative impact to his words and deeds, where it gradually dawns on the observer that God is in their midst. Not just something they hear Jesus say about himself, but something they themselves perceive, as the evidence piles up. That's more powerful than just telling someone what to believe.