"Does the Fed ease monetary policy after large stock market declines? Should it?"

From the Federal Reserve Bank of Richmond Virginia,  Econ Focus-First Quarter 2023:

Market commentors noticed a pattern during Alan Greenspan's tenure as Fed chair from 1987 to 2006. The Fed, it appeared to some, had developed a policy of bailing out stock investors by injecting liquidity into the economy amid large stock market declines. This perceived tendency came to be called the "Greenspan put."

By most accounts, the notion of a Greenspan put had its genesis in the Fed's reaction to the stock market crash of Monday, Oct. 19, 1987. Concerned that the unprecedented market decline might provoke credit and liquidity problems in the broader financial markets, the Fed had opened its liquidity spigots and subsequently cut its short-term interest rate target.

The "put" notion grew in 1998, when the Fed cut rates out of concern about the deteriorating state of global credit markets.

By 2001, the idea of a Greenspan put had become widespread. In January of that year, following a Fed rate cut, the Financial Times stated, "It's official: there is a Greenspan put option. Yesterday's half a percentage point interest rate cut by the U.S. Federal Reserve may not have been designed explicitly to bail out the stock market. But that is exactly what it is in danger of doing."

The phenomenon became known as a "put" because it was seen by some observers as offering downside protection to equity investors — somewhat akin to an equity put option, which gives an investor the right to sell a stock (or basket of stocks) at a pre-specified price, thereby limiting the investor's loss in the event of a major market decline. Of course, no one took the "put" part of the "Greenspan put" phrase too literally. There was never any expectation that the Fed would offer investors the precise and bankable protection afforded by an equity put option. The idea was fuzzier: that the Fed could be counted on to provide some sort of liquidity backstop in the event of a major stock market decline.

The consensus view among economists and policymakers, then and now, is that there really is no such thing as a Greenspan put or Fed put — at least not as a policy designed to bail out stock market investors. According to this view, Fed liquidity injections to deal with liquidity crises or weakening economic activity may sometimes have the effect of buoying stock prices. However, as one economist put it, "it is a fundamental misreading of monetary policy to believe that the stock market per se is an objective of policy." Still, to the extent that market participants believe in the "put," it can shape market expectations and make things more complicated for policymakers.

Whence the Greenspan Put?
The emergence of the Greenspan put as a widespread notion about Fed behavior owed much to two factors: The first was an abiding desire among Fed policymakers to avoid repeating the perceived mistakes of the Great Depression; the second was a salutary, yet perplexing, new development that came to be dubbed "Goldilocks."

During the Fed's early years, prior to the Great Depression, many policymakers and academics were inclined to conflate macroeconomic stabilization policies with polices designed to bail out individual firms — the type of bailouts that can create moral hazard problems by shielding investors from the consequences of their bad decisions, thereby encouraging them to take excessive risks. It was this concern that informed Treasury Secretary Andrew Mellon in the early 1930s when he gave his infamous policy advice to President Herbert Hoover: "Liquidate labor, liquidate stocks, liquidate the farmers, liquidate real estate."

Some economic historians, including former Fed Chair Ben Bernanke, have pushed back against the idea that the stock market crash of 1929 was one of the primary causes of the Great Depression. Still, there is little doubt that the market's massive decline between 1929 and 1932 signaled and contributed to deepening economic distress. The Fed's failure to heed deflationary signs — particularly shrinking monetary aggregates — later came to be recognized as a major policy mistake, thanks in large part to the historical analysis of Milton Friedman and Anna Schwartz as well as later research by Bernanke.

Based on the lessons learned, the Fed developed a much more activist stance in the post-World War II period and became increasingly inclined to extend credit during crises. The Fed did some of the groundwork for expanding its lender of last resort function in the late 1960s, well before Alan Greenspan's tenure as Fed chair. And it was not long before the Fed began to act on it. In 1970, after the default of the Penn Central railroad, the Fed provided liquidity to support the commercial paper market. In 1974, the Fed made a $1.7 billion loan to Franklin National Bank to provide support for financial markets, even though policymakers recognized that the bank was likely to fail.

Upon taking his post in August 1987, Greenspan was soon confronted with an unprecedented crisis. From today's perspective, looking at a long-term price chart of the major U.S. stock indexes, it is hard to even identify Black Monday, the stock market crash of October 1987. It looks like a minor dip. Yet it was a scary event for market participants at the time. The Dow Jones Industrial Average declined by 23 percent — a record single-day loss that still holds. The stock rout — which had been exacerbated by automated sell orders associated with portfolio insurance — spread across global stock markets and raised fear among policymakers that it could have adverse effects on credit markets....

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From Climateer "Quote of the Day" Federal Reserve Edition:

"I have two problems but only one tool".
-Ben Bernanke
Testimony to the House Budget Committee
Jan. 16, 2008

From December 2007's  Central Banks to "Flood" Markets with Liquidity: