The GD has two separate major features. The first is the international series of financial crises, and massive ensuing contraction from 1929 to the early '30s. This on its own was of an extreme scale and pain, but in character not initially all that different from earlier financial panics, like 1907 in the United States, or the major financial contraction in the 1870s.
This initial part of the GD though, was so large in scale that it shook confidence in many of the world's financial systems to a massive degree. This lack of confidence and lower threshold for local panics eventually robbed economies of loanable funds from savings, and inhibited the ability of even safe institutions to function. The financial collapse spurred both nominal and real contractions--meaning there were massive deflations around the world in addition to recession. Chile for example lost more than half of its GDP.
The deflation meant that debts became ever-more-massive over time relative to incomes, but incomes across the board, from almost any source, were slashed and falling rapidly. Deflation and financial uncertainty encouraged people to save as much as they could out of fear, and because the deflation meant that even paper money sitting in or under a mattress would gain in relative value. Because nominal interest rates collapse in a deflation (the nominal interest rate is the real interest rate plus inflation, see
Fisher Equation) and banks could not either receive new deposits (panics) nor collect on previous loans, functional insolvency metastasized through economies, eating them from the inside out.
This wasn't even the end of the problem though. The panic and contraction was only the first phase. The second phase, essentially the long-term fallout from an economic nuke, was characterized by depressed commodity prices, weak labor markets, and crippled trade. Depending on the country, this phase might have lasted until the second world war, been short-circuited by domestic re-armament and militarization, or somewhere in between. Example, Japan was spending great gobs of its GDP on the military, and in any country, drafting young men into the army or navy reduced unemployment rather directly.
All that being said, the cause of the collapse can be attributed to a few factors.
1.
Fragile post-WWI international financial system: As our British delegation knows well, the Great War wasn't all that great for the-then-His Majesty's Government treasury. Being the victorious powers though, France and the UK paid their debts to the US with a new income source, reparations from Germany. This was all well and good, but Wiemar Germany was not quite in the best state in the '20s and '30s. Certain German revenues were earmarked for reparation payments, leaving not all that much for needed government ministries of administration. Aside from trying to inflate their way out of the problem, the German governments borrowed money to pay for their expenses. This might seem unremarkable, save that most of this credit... came from the United States.
So we've got the Entente, who borrowed lots of money publicly and privately for war expenses from the US paying interest out of reparations from Germany, which also incurred lots of domestic debt from the war; and lacking a good alternative was also borrowing money from the US to fill the budget gap left by reparations. This amounts to a financial perpetual motion machine, and about as effective. People of the day were in fact aware of this potential problem, as (for example) the US Federal Reserve Chairman Strong expressed concern at least at one point about a German default causing a financial crisis in the United States. But this isn't all!
2.
The rules of the re-introduced Gold Standard: The end of the Great War left the United States and the UK in possession of a great deal of the world's gold reserves. As various nations went back onto the standard, the agreement was that their central banks could redeem paper in return for American or British gold on demand, as otherwise many countries would lack a sufficient gold reserve of their own. Unlike today's floating currencies, which rise or fall in relative value in balance with interest rates and trade balances, currencies of the interwar era on the gold standard ultimately balanced differentials in interest rates or trade deficits through the movement of gold itself, or rights to transfer it. There were all sorts of ways central banks could manipulate this system, but ultimately it proved to be very inflexible, especially in times of crisis. A wordsmith possessing a superior grasp of the art explains
in detail here.
3.
Really, very, bad, no-good, awful, terrible head-bashing-against-the-wall-bad monetary policy by central banks: Let's talk about the US in particular here, where as I mentioned in #1, Fate decided it would be funny to hang world economic stability on an insular, isolationist country. Hilarity did not ensue. The Federal Reserve Banks in the US were in fact well aware of the dangerous rise in equity prices in US markets during the late '20s, and were trying to deal with the problem by constraining the growth of credit. In those days, central bankers did not quite understand the effects they could have on an economy as well as they do now (which is really saying something), and they did not have either the grand supply of statistics, nor the ability to analyze them, nor the delicate tools to make a light touch. So essentially, they were forced to take a somewhat blunt-force approach to the issue, considerably raising interest rates by absorbing monetary reserves.
Enter the Gold Standard. Given that interest rates are rising, and are set to continue rising for the foreseeable future, banks, investors, institutions and individuals moved *more* reserves into the United States. After all, they could get a better return at the higher rates in the US than those smaller ones in their home countries. This was completely at odds with what the Federal Reserve wanted to happen of course. This influx of capital, however modest, added to the rising prices for securities in the US. So, in order to deal with this second-order problem, the Federal Reserve banks 'sterilized' the inflow. This meant they essentially locked up incoming gold or gold-backed paper in order to prevent it from entering the monetary base of the economy. This all makes sense, and is reasonably logical. The breakdown came when stock prices, and later banks themselves, began to crash. Essentially, until 1933, the Federal Reserve was handcuffed to its own inertia of worrying about the overheating stock markets.
Instead of pausing or even easing their policies of credit tightening or sterilization, they continued and actually intensified. Then Treasury Secretary Andrew Mellon believed the fall to be reasonable and even in a sense desirable. Through liquidating various assets in the stock and initial banking crises, he (and others) believed it would "purge the rottenness out of the system." This view wouldn't be entirely without merit in a small contraction, or if the Fed wasn't continuing to tighten the screws, but the combination of credit-tightening and large contraction spelled doom.
Now, even with that in mind the *bank* collapses in the US were hardly inevitable. However, the Fed, designed and ordered to help stabilize the US banking system, was at a loss and suffused with internal disagreement when the first banks started to fail. Bank failures were perhaps the most dangerous thing about financial crises, and characterize the worst contractions in American history. Under more secure circumstances, an insolvent bank might well end up going through a clearing house process of distributing what assets remained to the creditors and depositors. Everyone takes some pain, but in a better economy, it isn't an overall problem. Unfortunately, this type of process could not occur when there was *general* suspicion of institutional (or for that matter, individual) insolvency. Further, the increased difficulty in obtaining credit prevented any financing of private deals or agreements that might ease the pain. When the first banks started to fall then, the message was broadcast far and wide, and in a chain reaction, increasing panic drove people to try saving their deposits--by getting to the bank first, or at least before it might collapse. Oops.
It did not help when increasing suspicion that the US would leave the gold standard began to encourage the movement of gold out of the US, or at least out of the monetary base (like burying a box of gold coins in the garden). The Fed was particularly squeezed when the UK left the Gold Standard in 1931, making it all too obvious that the US dropping the link to gold was a question of when, not if.
France was in fact the destination for quite a bit of this flow for a time, and this helped delay the onset of the depression there. Unfortunately for the French, France left the gold standard only in the mid-thirties; which was not helpful given that the earlier break in the link to gold promoted earlier and stronger recovery in other countries, like the UK.
4.
A bog-standard stock bubble: It seems to have been that underlying productivity growth (both labor, and multifactor/technological productivity growth in general) supported (or would have) economic growth, but the rapid rise in securities value is at best rather questionable in its foundation.
5.
Poor assessments of risk: This ties in tightly with #4. You can't have a bubble unless lots of people think that it won't lose money, especially in the short-term. Even today, with many orders of magnitude more information available to people for free, you had rather poorly supported speculation from housekeepers buying "investment properties" to financial quants failing to ask where the risk ended up in their calculations. Let me say this now: most macroeconomists are boring investors, and they'd advise you to be also. It probably was exciting to borrow money for a month, a week, a day, and pay it back with profit left over from the financial markets. It's also probably not a good idea over the long term.
6.
Politically-driven policy reactions: This is touchy, but bear with me for a moment. This category lumps in a myriad array of government actions the world over that mostly *contributed* to the Depression's severity and length, but didn't light the fuse, per se. Let's start with the easy ones. First, I think we're all aware of the unusually named Smoot and Hawley, US politicians who sponsored a dramatic boost to US tariffs on a large variety of goods. The original notion was a new tariff policy that would help the American farmer, who like anyone else, dislikes offering lower prices to compete with foreigners. In this case for food products, cotton, etc. President Coolidge vetoed such a bill during his tenure, saying in his characteristically laconic way; "Farmers never did make much money. I don't think there's anything we can do about it." Hoover on the other hand, was more receptive to the idea, but when the economy hit the shoals, Congress used it as an excuse to "protect" virtually any industry in their districts they could think of. Hoover unfortunately didn't veto the thing, and apparently no one realized that other countries might have a mild distaste for their exports being squeezed, and retaliate. Less bad, but not quite helpful to the world economy was the British Empire's Imperial Preference, for similar reasons (it disrupted trade outside the Empire, with Argentina, for example).
Beyond mutually destructive trade wars, fiscal policies were often contractionary. There might be a number of reasons for arguing that a country should have a tax rate of x. But, if the tax rate is currently <x, and there's a massive recession come to visit, now is probably not be the best time to raise it to x.
Similarly, many posters here could advance arguments that government spending either now or back in the 20s or 30s should be or have been of some value y, where y< current expenditure. All well and good, but cuts like that in the midst of a large recession may not be helpful. Governments back in '29-'3X often didn't choose one of those options though, they went double or nothing on both, often to try balancing the budget. Fiscal unpredictability and pain did not demonstrate great efficacy in either the United States or Wiemar Germany, for a couple examples.
In general, the Depression also triggered or exacerbated political problems in various countries, with disharmonious results for the economy. Political instability is not a good thing for growth on its face, even if such problems didn't ultimately affect economic policy or trade.
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So, with too much having been said, can you avoid all that caused the Great Depression? Well, no. Probably not if your POD is after Versailles. But a fair number of other changes, even taken individually, could lead to those causes fizzling into a rather forgettable typical recession in most countries. The butterflies with an economic POD of that type though are at gale-force strength very early for obvious reasons, so even if some of the grand contours of such a 20th century are familiar, the details would necessarily be scrambled beyond most recognition.