In the middle of last week, the U.S. Federal Reserve closed one of the most controversial chapters in its 101-year history by announcing the end of quantitative easing -- an unusual monetary program designed to drive down long-term interest rates and fuel the economy.

The Committee judges that there has been a substantial improvement in the outlook for the labor market since the inception of its current asset purchase program. Moreover, the Committee continues to see sufficient underlying strength in the broader economy to support ongoing progress toward maximum employment in a context of price stability. Accordingly, the Committee decided to conclude its asset purchase program this month.

Even among people well-versed in monetary policy, it's hard to overstate the extraordinary nature of what was essentially an experiment. In three successive rounds of bond buying, the Fed bulked up its balance sheet by $3.6 trillion.

Despite the Herculean scale of these efforts, analysts and commentators have questioned the policy's effectiveness. According to Neil Irwin of The New York Times, "while the Fed's impact on financial markets can be dramatic and easy to measure, its impact on the economy, which is the real goal, can be much squishier."

The purpose of quantitative easing
Gauging the success of quantitative easing is first and foremost a matter of identifying what to measure. For this, it's helpful to go back to November 2008, when the Fed originally stated its decision to pursue the unusual course:

This action is being taken to reduce the cost and increase the availability of credit for the purchase of houses, which in turn should support housing markets and foster improved conditions in financial markets more generally.

Its primary goal, in other words, was to drive down borrowing costs -- more specifically, to reduce the interest rate on mortgages.

There's no doubt the central bank succeeded in this narrow objective. Prior to the financial crisis, the average rate on a 30-year, fixed-rate mortgage was roughly 6.5%. From late 2008 to the fourth quarter of 2012, it dropped, in fits and starts corresponding to the three successive rounds of easing, to 3.4%.

Lest there be any doubt about cause and effect, we can look to the middle of 2013, when interest rates surged after the Fed first suggested it would begin to taper its bond-buying program.

The most direct result: A refinancing boom
While it's hard to say what impact the decline in interest rates had on the housing market, there's no ambiguity when it comes to the mortgage market. This is because the record low interest rates triggered by quantitative easing led to a refinancing boom that, in depth and duration, is perhaps without precedent.

You can see this in the chart below, which shows that the undulating shape of the boom mirrored the three waves of easing. During the initial wave in 2009, the Fed purchased a net $500 billion in agency mortgage-backed securities. By the end of the second wave in 2010, its MBS holdings stood at $1 trillion. And during the third wave between 2012 and today, its holdings ratcheted up an additional $1 trillion.

We can therefore hazard a guess that in the absence of record low interest rates, mortgage refinance volumes would have been in the neighborhood of $150 billion a quarter, as was the case between peaks.

At this rate, total refinancing volume between 2009 and the middle of last year would have reached $2.9 trillion without quantitative easing. The actual figure was $5.7 trillion, suggesting quantitative easing led to $2.8 trillion in refinanced mortgages.

This freed up billions of dollars in monthly mortgage payments that homeowners could use to bolster the broader economy. In fact, we can even draw an approximate estimate of how much money was made available.

Assuming the average mortgagee reduced his or her interest rate from 6% to 4.25%, then the monthly payment on a 30-year, fixed-rate mortgage would have dropped by about 20%. On $2.8 trillion in mortgages, that translates to a cumulative $3 billion reduction in monthly interest expense and $1.1 trillion in savings over the course of a conventional mortgage.

An additional beneficiary of quantitative easing: Banks
It's worth noting, moreover, that homeowners weren't the only beneficiaries of quantitative easing, as banks also derived significant benefit from the low interest rate environment.

Take Wells Fargo as an example. Between the first quarter of 2009 and the middle of last year, 70% of its mortgage applications were requests to refinance existing mortgages, as opposed to purchase new homes. In more normal times the split is around 50-50.

It follows that a material share of the $32 billion Wells Fargo earned from the origination and sale of mortgages over this period related directly to the refinance boom triggered by quantitative easing. Let's say it is 20% of the $32 billion; that equates to $6.4 billion in noninterest income.

When you consider that Wells Fargo originates one-third of all mortgages in the United States, this means U.S. banks got nearly $20 billion in additional noninterest income from the refinance wave. That is admittedly a fraction of the bank industry's total profits over this time period. For instance, the industry earned a cumulative $154 billion in 2013 alone. But $20 billion is still $20 billion.

Now, just to reiterate, these are convoluted estimates based on multiple assumptions. They nevertheless demonstrate that quantitative easing did have a non-negligible impact on both existing homeowners and the nation's financial sector.

Was quantitative easing worth it?
Policymakers will spend decades debating whether quantitative easing succeeded or failed. But while opposing sides can cite plenty of facts and figures, the truth is that we'll never know for sure if the unusual monetary move was "worth it."

On its face, quantitative easing seems to have "cost" the nation $3.6 trillion -- I use quotations because it's far from obvious whether the expansion of the Fed's balance sheet translates into actual costs. Meanwhile, over the life of their loans, American homeowners will save upward of $1 trillion in interest expenses.

Finally, no analysis is complete without making subjective assumptions about what would have happened to the housing market and broader economy in the absence of the unprecedented move. At this point, then, I think all we can say is that things would have been worse.

John Maxfield has no position in any stocks mentioned. The Motley Fool recommends Wells Fargo. The Motley Fool owns shares of Wells Fargo. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.