No, that”s not really what needs to happen.

US population does not have to shrink at all, rather only that it grow less than the “little over 1%” figure indicated.

US annual population growth rates have generally been below 1% since the early 70s (but for a brief & unsustained surge in the early 90s), and the historical population growth rate trend has clearly been trending downward in the US for over a century now (was nearly 2% around the turn of the last century, and has been in the lower 0.9% for the most recent decade+). During the Great Depression (the last time we went through a Fisherian debt-deflation following a Minsky-ian financial crisis), population growth rates fell from “a little over 1%” to the 0.6% range. Add to the mix the right”s antagonism towards immigration, and it not at all difficult to conceive of relatively lower population growth that the ”norm” suggested by Seth.

Ditto re: productivity gains: Productivity does not have to actually reverse into negative territory (although that has happened for brief periods of time), rather the rate of productivity gains merely has to slow from the assumed 2% rate, which is entirely reasonable (see, e.g., http://www.bls.gov/lpc/prodybar.htm).

Over the course of the “Great Moderation” [which is now long gone & replaced by the ''new normal'' of delevering our way out of a balance sheet recession] nonfarm business sector prductivity trended from approx. 1.1% during the 1973~1979 stagflation era steadily upward to 2.5% for the 2001-2007 period of the Bush policy area… only to start falling again (1.8% average for the post-bubble era). Without a clear path out of our current debt-deflation induced economic malaise, it is hard to see how 2%+ productivity gains can be sustained over the next decade in the face of dampened aggregate demand & ongoing deleveraging… unless corporate America resorts to yet more unemployment. It is not all that hard to envision an extended period of low productivity gains of, say, only 1%, as has happened for multi-year steches over the last 40 years.

As for inflation: Maybe not ”forever”, but perhaps for the next 10 years. Until the private sector”s balance sheets are sufficiently repaired – which then allows aggregate demand to rebound sufficiently to start making a run towards full employment & full use of productive capacity – it is unlikely that inflation is going to consistently generate even your ”modest” 3% target. The Fed has already set a 2% inflation target – which it has barely met even in the face of energy price spikes & a domestic drought”s impact on agricultural commodities – through 2014 ~ 2015. With Europe on its knees, unemployment stubbornly high & capacity utilization stubbornly low, and the US dollar still the reserve currency of choice, there is little if any inflationary pressure anywhere, that I can see.

So, at the end of the day, all that is needed to see 4% nominal equity returns is, let”s say (just for the sake of argument), 0.7% population growth + 0.7% productivity growth, then real stock returns are a measly 1.4%. What is unreasonable with that? A bit pessimistic, perhaps, but certainly not unreasonable.

Add back the Fed”s targeted 2% rate and you get 3.4% nominal equity returns… below Gross” estimate, without much stretch of the imagination at all. And without population shrinkage or productivity collapses of any sort.