Historically, major drops in oil do not equate to causing a U.S. recession. However, cheap oil can tear down an over valued stock market, which is what is happening right now.
For recent evidence, look at Black Monday in October 1987. Twenty-one (21) months after the Saudis started a similar oil pricing strategy as the market faces today, where the Saudis raise production to maintain market share, the U.S. stock market plummeted 40%. But there was no U.S. recession.
Fast forward to 1998, oil prices plummet 55% over a two year period (1997-1998) as emerging markets faced a currency crisis. Russia defaulted; however, there was no U.S. recession. The stock market swooned in sympathy intra-year by over 20%, with the peak of the decline happening 20 months after oil prices began to crater. We are now at month 18 of the time frame in which oil prices started their decent starting in August of 2014. I estimate that $20-$25 per barrel in oil would force a similar emerging market crisis today, and trigger a similar U.S. stock flash crash as experienced in 1998.
Three years after 1998, the U.S. went into recession. In the interim, oil reversed course, the dollar began to weaken, and geopolitical issues created enough economic stress to drive the country into recession.
This time may be different because the Fed is at the zero bound. However, I estimate that interest rate levels at this point don't have much to do with the problem other than the fact that because they have been too low for too long, the emerging markets and oil sector has become over leveraged world-wide, and now the market must correct in order to resolve an oversupply issue. Is the steep oil drop a problem for overvalued stocks? Yes. Is it enough of a problem to cause a U.S. recession? Probably not.
If you want a historical time frame when a shut down of the U.S. oil patch may have led to a recession, you have to go all the way back to 1957. At that time the U.S. was a net exporter of oil in a time frame when the disruptions in the world market for oil caused a surge in U.S. production that went away after the Suez Crisis was resolved. Does the impact on the U.S. shale industry equate to the economic impact on the oil sector felt in 1957? If you are arguing that the oil patch is going to lead the U.S. into recession, the relative similarities between the time periods may be worth further study for those trying to figure out the current economic path. But for stocks, the outcome is the same. Stocks fell over 20%, as a recession was logged from September 1957 to April 1958.
When does cheap oil best correlate with a U.S. recession? Look at time periods during or just after oil spikes upward in conjunction with a weak dollar, which then crash. My bet is these elements will be present in the next U.S. economic cycle.