How does the stock market correlate with the economy?

Question

What's the Correlation Coefficient between the Canadian and US stock and economy? Don't hesitate to discuss other stock exchanges.

On Apr 30 2020, Paul Krugman wrote Opinion | Crashing Economy, Rising Stocks: What’s Going On?

Yet stock prices, which fell in the first few weeks of the Covid-19 crisis, have made up much of those losses. They’re currently more or less back to where they were last fall, when all the talk was about how well the economy was doing. What’s going on?

Well, whenever you consider the economic implications of stock prices, you want to remember three rules. First, the stock market is not the economy. Second, the stock market is not the economy. Third, the stock market is not the economy.

That is, the relationship between stock performance — largely driven by the oscillation between greed and fear — and real economic growth has always been somewhere between loose and nonexistent. Back in the 1960s the great economist Paul Samuelson famously quipped that the market had predicted nine of the past five recessions.

I know it's $< +1$, because

1. The stock market only consists of publicly traded companies, which is a subset of the economy (generally large businesses). Economic activity can also come from private companies (most small businesses are private), government activity, and not-for-profit organizations. A US stock index can also track companies that have a lot of foreign production, so the value of a company can increase from production that's not measured in US GDP.

2. The current economy can mismatch what investors expect the economy to be in the future. Stock prices don't only reflect current wealth but also future payoffs. After all, people invest to transfer wealth from one time period to another. That is one of the tasks (if not the most important task) of financial markets.

Answer 1

This study, "Is There a Link between GDP Growth and Equity Returns?", compares a number of advanced economies over the period 1969-2009. On average, the growth in stock prices was just 0.3% higher than the growth in GDP. However this ratio varies considerably between individual countries. Stock price growth was 4.5% higher than GDP growth in Spain, but -3.5% in Sweden. Here's the relevant data table.