Should the Fed placate the markets? Yes and no.

Let’s start with the no. Today’s Bloomberg has a piece by Mohamed El-Erian with the following title and subtitle:

The Fed Should Resist Placating Markets
The central bank needs to avoid being rushed into another policy mistake by making an emergency interest-rate cut.

The Financial Times has a similar piece by Barry Eichengreen:

The Federal Reserve will not let markets dictate a rate cut

Stock moves are not a reliable signal of looming economic downturn
I mostly agree with both commentators.  The Fed should not be in the business of trying to prevent big moves in the stock market, and yesterday’s 3% decline in the S&P500 was not even a particularly large move.   (Yes, it was significantly larger than average, but I’ve seen numerous moves that were far larger.  As I write this, the S&P500 is up over 2%.)
 
So why do I say “yes and no” at the beginning of this post?  I think it depends on exactly what one means by “placate the markets.”  Imagine there were a NGDP futures market.  In that case, I would strongly support having the Fed adopt a monetary policy that placated the NGDP futures market.
  
Of course we do not have an NGDP futures market.  But we do have many markets that indirectly provide information as to market expectations of NGDP growth.  Start with the fact that NGDP growth is the sum of inflation and real GDP growth.  And then note that we have (admittedly imperfect) market indicators of expected inflation.  In addition, there are many market indicators that are substantially correlated with expected real and nominal growth.  Yesterday I recall a market commentator mentioning that risk spreads in the bond market had increased.  Risk spreads are certainly correlated with NGDP growth, as borrowers have more trouble servicing debt when NGDP growth slows sharply.
 
Suppose the Fed constructed a model to estimate market expectations of NGDP growth, which used a weighted average of all sort of relevant market prices.  It might make sense to try to stabilize that index, without trying to stabilize any single individual component of that index.  Would that be “placating the markets”?  I think that’s sort of a question of terminology.  The Fed would not have market stability as a primary goal; rather they would merely be trying to stabilize markets to the extent that doing so would stabilize NGDP growth.  As a practical matter, they might occasionally respond to severe stock or bond market movements, but not because they cared about the plight of investors.