I think it ultimately comes down to people trusting history to repeat itself.
Start with demographics. Layer on productivity growth and you have a first-order approximation of national productivity. Figure gross margins and from that net margins, as well as average corporate tax rates–boom, you have the economy's profitability. Estimate a pay-out rate and you get a high-level return estimate. It's very approximate, but it's theoretically solid for any closed economic system. (Cf: natural resource inputs are not properly accounted for.)
How do you explain why this appreciation in value isn't arbitraged away, as suggested by GP? In his words, "if 9.7% long-term returns were guaranteed, wouldn't everyone just borrow 30-year loans on margin at 5% interest rate and invest it in S&P?" This would effectively drive up the current day price and eliminate any projected future growth in index price -- invalidating the hypothesis that the S&P price will continue growing in the future.
I'm basically saying I'd like a somewhat bottoms up approach to modelling the S&P index where the inputs can explain the x% YoY increase in price.
The S&P has not always generated positive returns relative to inflation.
Sometimes there are 30 year long dips.
1968: +11%.
1969: -8.6%.
1970: +3.6%.
1971: +14.5%.
1972: +19.2%.
$1 of S&P500 in 1968 would be worth $1.23 in 1978, 10 years later.
There are large drops in some of the years, but they are usually followed by outsized rallies in the years afterwards.
Source: Moneychimp’s CAGR of the Stock Market calculator. http://www.moneychimp.com/features/market_cagr.htm
Even your link admits poor performance during periods of high inflation, and gives several other example periods.
But here was my original source:
http://www.multpl.com/inflation-adjusted-s-p-500
With your link, if you're just talking about value of the stocks and controlling for inflation, one dollar of stocks in 1969 grows to only $1.03 in December 1991.
To maintain the historical growth rate, you have to believe one of the following two things, or some combination of them:
1. The US will continue to amass a larger share of the world's wealth, indefinitely.
2. The economy of the world at large will begin to also grow ~10% a year, a number far in excess of the historical average or any well-informed estimate.
Personally, I wouldn't make that bet.
I feel like in the 21st century, a lot of folks have come to put a lot of faith in the "stocks in the long run" mantra.
But any stationary effect in the markets can be arbitraged away. If 9.7% long-term returns were guaranteed, wouldn't everyone just borrow 30-year loans on margin at 5% interest rate and invest it in S&P?
Edit: agree with sibling comment. If one loses 27% in the first year and makes 9.7% annually after that, they would be operating at net loss. So even if long-term gains were assured, volatility can still make investing on borrowed money unprofitable.