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[Economics] Is 'New Keynesian' economics actually Keynesian?

I ask because Post-Keynesian economists claim New Keynesians aren't Keynesian at all.
gpt
Modern New Keynesian models derive from multiple sources, some harkening back to Keynes in the 1930s, but most emerging out of the work of the 1970s. To fix ideas, let's use Woodford's and Gali's books as prototypes.

The basic building blocks of a standard three-equation New Keynesian model are:

1. Milton Friedman's permanent income hypothesis, as interpreted in Robert Hall's intertemporal optimizing consumer. This part is Monetarist, almost chapter and verse. (Friedman 1957, Hall 1978 JPE, 1988 JPE)

2. A model of firms' pricing decisions that combines elements of imperfect competition, forward-looking behavior, and price stickiness. This part is largely "Keynesian," though most writers accept some form of sluggish nominal adjustment. It is the key piece that differentiates New Keynesian models from their New Classical and RBC cousins. (Dixit-Stiglitz 1977, Taylor 1977, Calvo 1983, Rotemberg 1982). [Later edit: imperfect competition is *the fundamental thing* that separates NK macro from New Classical macro. Sluggish price adjustment is *the fundamental thing* that separates NK macro from RBC macro. More comments on request.]

3. A monetary rule that focuses exclusively on interest-rate adjustment and focuses on feedback rules. This part is truly "Keynesian" in multiple senses.  (Taylor 1993)

4. A focus on rules over discretion, which is largely a holdover from New Classical thought. (Friedman 1968, Kydland-Prescott 1977, Barro-Gordon 1983) 

5. Rational expectations, largely taken from the New Classicals. (Lucas 1972, Lucas 1975)

6. The key macroeconomic mismatch being deviations of the interest rate from its natural rate. This part harkens all the way back to Wicksell.

7. Macroeconomic fluctuations as emanating from both "real" and "nominal" sources. Half of this part emerges from the real business cycle literature; the other half from the nascent New Keynesian literature of the late 1970s and early 1980s. (Kydland-Prescott 1982 (real), Taylor 1980 (nominal))

One could certainly call New Keynesian macroeconomics "New Wicksellean macroeconomics" without much loss of substance. Similarly, about two-thirds of New Keynesian economics is monetarist (the consumption block is all Friedman, the Phillips Curve is half Friedman, and the Taylor Rule is half Friedman).

However, New Keynesian economics is "Keynesian" in the sense that it recognizes the importance of coordination failure, price stickiness, real rigidities, and other imperfections that can lead output to deviate from full-employment equilibrium. It is *not* Keynesian in that NK economics does not have a role for *permanent* deviations of output from full-employment equilibrium (though the adjustment process can take time). It is not Keynesian in that NK economics requires inflexible wages and/or prices to generate welfare-relevant business cycles, while Keynes believed that there could be welfare-relevant business cycles even in a situation of fully flexible wages and prices. 

Nontechnical readings:

1. DeLong, "The Triumph of Monetarism," JEP 2000.
2. Woodford, "Revolution and Evolution in Twentieth-Century Macroeconomics," 1999.
3. Woodford, *Interest and Prices,* 2003, chapter 1. He spends a bit too much time distancing himself from New Classical and Real Business Cycle theories, but the history of thought in his introduction is useful.