I feel that the question as framed is so broad that it may not be possible for any historian to answer in an objective way.

While this is definitely a historical question, it is also a question of economics. Aside from the usual challenge of analyzing records from the past, you are also facing the difficulty unpacking a couple hundred years of economic theory, much of which is still hotly debated. Furthermore, even a hypothetically sound economic theory is subject to so many situational variables that predictions tend to be less accurate over shorter time-horizons (and more accurate over longer ones).

I’m not well-versed enough in the exact historical circumstances of the Great Depression to answer your question in full, but I can provide you with context on the relevant economic theory. Rather than getting into a nuts-and-bolts debate on Keynesian versus Austrian versus Monetarist schools of thought, we need to talk about cause and effect, and how difficult it can be to parse from a specific time and place.

Almost any economist will agree with the following statement:

Expansion of the monetary supply causes inflation in the price of consumer goods.

The caveat to that statement i, “Eventually.” The net impact of printing currency, will eventually devalue the individual units of that currency. Unfortunately, the world is incredibly complex, and by the time “eventually” comes around, so many forces have acted upon the market that individual causes and affects can appear hopelessly intertwined.

To demonstrate the problem, allow me to lay out a hypothetical scenario:

There is a magical town called “Anytown,” in which the citizens possess all of the raw materials, climatic conditions, and technologies in order to operate as a completely self-contained economy. Anytown uses silver as its currency, and there were only 100 silver coins ever minted.

Anytown has a bakery that sells bread to the other citizens. Baker Fred knows how many loaves he can comfortably bake and self in a day, and sets the price at 1 silver coin per loaf.

This goes on for a while in perfect equilibrium, until Prospector Bob finds a vein of silver. Enough to mint another 100 coins! Bob mints the coins and goes on a spending spree. After Bob spends his windfall, the citizens of Anytown have a lot more silver jingling in their pockets. They would usually limit themselves to one loaf per day, but they are happy to eat more if they can afford it. Some citizens start to buy two loaves per day. Baker Fred sells out early for a few days, but doesn’t have the ability to bake more loaves. Eventually he raises his price to 2 coins per loaf. Voila. Inflation has taken place. The bread has not changed fundamentally in real value, but the price has gone up nonetheless.

This is all fine in theory, but nothing is ever so simple.

Imagine that while Prospector Bob is still minting his coins, several things happen:

Baker Fred invents a new oven that bakes double the loaves in one day for the same effort. (Bread gets cheaper?)

A hurricane strikes the town’s wheat field and destroys half the crop. (Wheat gets more expensive, and so does bread?)

A subset of the town’s populace is discovered to have a genetic predisposition to Celiac disease. (Less people want bread anyway??)

A factory totally unrelated to bread production lays off half of it’s workforce. (Less people have money to spend on bread? Maybe? It depends on if those factory workers were bread consumers! Maybe they prefer apples anyway? Need more data.)

Changing technology, consumer preferences, and other variables all act upon the price of bread so that by the time Prospector Bob spends his coins, it may not be clear at all to an outside observer what his impact on the economy was. We can safely assume that his net impact across time was to raise inflation, but we can’t necessarily determine when or to what degree.

We also cannot rule emotion out of the equation. Consumer mindset can have massive impacts on an economy that may appear to contradict economic theory. For example, in times of crisis when governments tend to print more money, consumers are often in a state of panic. Occasionally this can lead to a massive uptick in consumers saving more money rather than spending it which effectively removes currency from circulation in the short-term. This can lead to a paradoxical deflationary reaction from inflationary monetary policy (again, in the short-term).

Anyway, There are virtually infinite ways to interpret the question, “Did FDR prolong the Great Depression?”

Did he expand the monetary supply? Absolutely. But that is only one piece of a massive puzzle.

The U.S. also entered the Second World War, which obviously necessitated massive government spending, but also helped position the United States to rise from the ashes as the only Western nation with completely intact infrastructure. Suddenly the U.S. is exporting consumer goods to Europeans desperate for them. That equals American jobs, a stronger dollar, and political hegemony in the Western world.

To what degree was FDR personally responsible for those effects? If he was responsible for them, to what degree was that his intent versus a happy by-product?

How do we separate political realities from economic realities? When the Great Depression hit, there were very real questions as to which way the political wind would blow regarding the the spread of socialism into the United States.

If I could provide a hypothetical that makes some bold claims for the sake of demonstrating the problem:

Imagine for a moment that indisputably sound economic theory states that a completely laissez-faire monetary policy would end the Great Depression as quickly as possible. But then imagine that the average citizen has lost his job, can’t feed his family, and if he doesn’t at least perceive the government action to help him, he is going to vote in a populist demagogue who wants to print a billion dollars for each American citizen, which will undoubtedly deepen the depression.

Could you argue that FDR knowingly implemented irrational monetary policy in order to maintain political power and prevent even worse policy down the road? Yes, and people have made that argument. But these aren’t provable claims. You can chase these hypotheticals for ever, but they aren’t entirely frivolous either.

Picking the apart the question of FDR’s personal culpability for a lengthening/shortening of the Great Depression essentially requires the historian to take a position on economic theory that is still argued over and bleeds into current events.

Not to mention the challenge of separating FDR’s personal agency from forces of change outside his control.

None of this is to say that you won’t get some fascinating context from this community, but you may wish to pursue information from trained economists as well as historians.

I apologize if this comment is outside the purview of the sub, but I felt it was important to point out the extremely broad nature of this question.

Good luck!