1) The stock market is not the economy!!! More than 40% of the sales from the S&P 500 companies are now generated abroad, meaning that international factors will also have an impact on US stock market performance. Of course, recent research suggests that both the business cycle as well as asset prices, equities as well as bonds and even real estate, have become increasingly correlated across countries in recent years as the global financial cycle becomes more predominant. As a side note, maybe this also means that the benefits of diversification have somewhat decreased.
2) While it is true that every (severe) economic downturn is associated with a substantial decline in asset prices, mostly equities but also housing, the reverse is not true. There is definitely some truth to the old saying that the stock market has predicted 9 out of the last 5 recessions. Equity prices can tank without dragging the economy down with it, as shown by the famous crash of 1987 when the Fed's decisive interventions in financial markets made all the difference. Even with declining asset prices, the economy can be fine of the Fed keeps aggregate demand stable. While some economists assert that in the case of the Great Depression and maybe also the Great Recession the stock market crash led to the economic downturn, this seems to be mostly false. In both cases it was tight monetary policy, which led to a decline in economic activity and dragged equity prices down with it.
3) Some recessions are more severe than others. Stock market declines might be less consequential than a severe bust in the housing market. About 80% of the stock market in the US is hold by the top 10% who have a much lower marginal propensity to consume. The home ownership rate, on the other hand, exceeds 60%. While a large decline in equity prices might only have a very limited impact on consumption, a large decline in real estate is felt much more broadly, especially if home owners equity is wiped out and of there was a substantial amount of debt and leverage involved.
4) Debt and leverage matter, and so does liquidity. As Perry Mehrling points out in his course on money: “Liquidity kills you quick”. Macroeconomists neglected these factors to some extent before the crisis. While it is true that for the aggregate one person’s liability is another person’s asset, the distribution of debt matters a great deal as individuals and companies face different borrowing and cash constraints.
5) The financial system matters a great deal. Almost every transaction in the economy involves money in some form or other. Disruptions to the financial and payment system can have large macroeconomic effects because financial shocks will interrupt the invisible hand of the market economy as price signals get distorted during fire sales and amidst larger spikes in risk premiums and interest rates. The Central Bank’s lender of last resort function is therefore of key importance. During a panic, the Central Bank can insure that the financial network remains intact by providing enough liquidity to the system and maybe even providing a backstop to falling asset prices if deemed necessary.
6) Most modern recessions in large advancers economies are monetary in nature, very often caused by misguided monetary policy. There is definitely some truth to Dornbusch’s assertion that expansions don’t die of old age, but that every single one of them was murdered by the Fed. Most recessions are mostly negative aggregate demand shocks, meaning that the level of nominal spending in the economy has fallen for one reason or the other. Total spending falls as the propensity to hoard money increases. While there are several ways of getting rid of excess cash balances, there is only one way to increase your money stock: by buying less goods and services, meaning a decline in spending. While it is certainly possible for one person to increase their money stock, it is certainly not possible for many agents in the economy to do the same. The fallacy of compositing clicks in. As people try to increase their money stock and reduce their spending, overall spending in the economy falls as well. As one person’s expenditure is another person’s income, economy-wife GDP falls, and unemployment rises.
Of course, Central Banks would have the ability and firepower, and some of them also have a more or less an explicit mandate, to keep the economy on an even keel. However, very often Central Bankers have found themselves being behind the curve. They certainly got completely sidetracked by the Great Recession, despite the fact that the some of the root causes were monetary in nature.
7) Central Banks can always increase aggregate demand and inflation, even in a liquidity trap. The constraints they face are not economic but rather political and institutional. While most economists agree that Quantitative Easing did stimulate the economy, there is some debate about its effectiveness. Furthermore, QE1 was probably had a much bigger impact than subsequent rounds of asset purchases, the reason being that QE1 started when financial markets were still in turmoil, asset prices were falling across the board, and risk premiums were extremely high. The Fed's asset purchases reduced market volatility, put on a floor on asset prices, and reduced risk. Subsequent rounds of asset purchases provided much less bang for the buck for several reasons. First, the Fed made it abundantly clear that they were never really willing and even considering overshooting their inflation target, even for temporary catch-up growth following one of the largest recessions in modern history. This was essentially a very hawkish signal and widely reduced the effectiveness of asset purchases. Second, it is widely agreed upon that monetary injections at the zero-lower bound of interest rate will actually be ineffective if they are perceived to be temporary instead of being permanent. This is Krugman's famous irrelevance result. Insofar as the Fed always signalled that the Fed's balance sheet will go back to normal one day, they practically ensured that their asset purchases will have less of an effect. At the zero-lower bound, monetary policy is essentially all about forward guidance and expectations management, even more so than in usual times, because open market operations are just swapping one zero-interest rate bearing asset for another, Treasuries for base money, meaning that the economy-wide effect should be basically zero (There can be some effect if you buy longer-term bonds instead that have interest rates above zero. The question then is how large are the purchases going to be and how will the macroeconomy respond if Central Banks are in the business of compressing yields and managing the yield curve).
As Angel Ubide points out in his book "The paradox of risk", Central Banks that were much more conservative in the beginning of the crisis of 2008 and the subsequent recession ended up having to stimulate the economy much more and resort to more aggressive policy tools than Central Banks that moved somewhat earlier, such as the Fed. That being said, even the Fed pursued extremely tight monetary policy in 2008/2009 and only began to act more aggressively as soon as it became clear that a second Great Depression could become a reality.
As far as changing the Central Bank's mandate to a price level target or a nominal GDP level target is concerned, which both would have been much more stimulative during the downturn, the effectiveness of monetary potency was never really tested.
The ultimate weapon against a severe negative demand shock would obviously be Milton Friedman's helicopter drop, an injection of cash that is directly targeted at the consumer. While such a policy blurs to some extent the line between monetary and fiscal policy, such an extreme measure might actually have the best chance of increasing aggregate demand and rendering monetary policy more potent when interest rate changes are constrained by the effective lower bound.
8) The long-run secular downward trend in real interest rates is one of the most important macroeconomic trends in recent decades. It vastly increases the chance of Central Banks hitting the lower bound on interest rates when faced by a severe demand shock. Moreover, lower real interest rate also imply that the fundamental value of asset prices rises. This is true for equities, bonds, and both land as well as real estate. Over the last two decades, we have experienced already several "bubbles", Dot-Com followed by the housing bubble. In all likelihood, most advanced economies will continue to experience rich equity valuations in the foreseeable future. While these are not necessarily "bubbles", low real interest rates might exacerbate the financial cycle and produce boom and bust cycles in asset prices, which obviously will also affect the real economy, a phenomenon that Larry Summers has called secular stagnation.