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Desrtopa comments on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 - Less Wrong
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My guess is that rather than policing any of various muggle institutions, they investigate, as we do in our own world, whenever anyone appears to suddenly come into possession of large amounts of money for no clear reason, and if they find out they did something illegal, they throw them in jail.
Maybe people are already using wizardry to get huge amounts of money through the muggle world, but if so they may have to store and use the money very inconspicuously.
This is by far the likeliest explanation I've seen. It does lead one to wonder how many wizards are sitting on huge piles of muggle money and slowly converting it into galleons as needed.
I wonder if they do. The wizarding world is a bizarre mix of modern and ancient traditions. It seems just as likely for them to have an income tax as not. So, they may or may not have the bureaucratic apparatus in place to know how much money people have and make.
I also wonder what the official stance would be on, say, bilking the stock market. It seems like standing up for muggle rights would be an unpopular political stance. Since there's no direct victim and you're doing things that aren't even illegal in the muggle world (nevermind they don't have time-travel), it seems unlikely the authorities would care to stop you, unless they have a blanket ban on anything that would result in inflation.
God, I'm such a double-nerd. There's a dark lord to be fought and I'm hoping the next plot arc is about wizard tax law and how magical Britain handles inflation.
The funny thing is, it's not really bilking the stock market. The whole argument for stock trading is that traders create value by accurately pricing securities, and thus allocating capital efficiently. Time travel is just a ridiculously efficient means of doing so. Given common access to Time-Turners, the stock market would literally be perfectly efficient(assuming that using turner-induced stock prices doesn't violate the 6-hour rule). People without them would be very pissed off, but I'd actually argue it as being the right and proper way to run a stock market if the technology existed.
The only thing is, once you have enough time turners to control most of the volume of the market, there are no longer any linear-time causal inputs (read: people) deciding what directions the market will take. Market fluctuations would literally come from nowhere, though it might be best said that they would come from Time. And given Harry's previous scary experiment (DO NOT MESS WITH TIME, ch. 17), I'm not sure it's such a good idea to let Time be the one to control this.
Bolded word is redundant. This is a service being provided and nobody is having wealth that they have 'rights' to taken away. This is different in nature to using using time travel or to win at cards or roulette.
The muggles end up better off than they were AND Harry is better off. Almost as though it is a trade.
(Essentially I just agree with Alsadius.)
There's another motivation for secrecy. Anyone who makes money off the Muggle world benefits from being the only one making money off the Muggle world. If they're making lots of money, they don't want other people to start thinking about how.
This would require a wizarding equivalent of the IRS, which I've never heard of. I've never seen mention of taxes, but they obviously have to pay the ministry employees something. One of the consequences of their primitive monetary system is that it is very easy to obtain money without the government knowing it. Perhaps they could use muggle taxes to buy gold to be minted into galleons, and pay employees that way. In cannon, the prime minister knows about the wizarding world, and it's possible that information of it is just highly classified.
I suppose money could be magically tracked, but there would still need to be a ministry department. And if that is possible, it easily defeats most money-making strategies.
If any money tracking is going on, I suspect it's done by the goblins, who I believe canonically have means of magically tracking things.
You don't need to magically track money though, to keep record of how much money is in people's bank accounts, and take notice if someone who's not supposed to have lots of money suddenly starts making a lot of very expensive purchases.
That's assuming you put it in a bank account.
If you don't put it in a bank account, then assuming no magical tracking, you could spend lots of money so long as you don't reach a point where anyone starts asking "Hey, where did you get all this expensive stuff?"
Since the wizarding world has so much smaller a population than ours and seems to be quite class stratified, it's quite conceivable that every person who's supposed to be really wealthy is already known and identifiable, and any Joe Shmoe who tries making a thousand galleon purchase is instantly flagged as suspicious.
In canon there is a Misuse of Muggle Artifacts office, but it's not terribly competent.
However, the Minister of Magic also liaises with the Muggle Prime Minister; and presumably there is some exchange of information between their staffs. Any financial irregularities large enough to register on a national level could register that way.
In canon at least, it's pretty clear that there is few interaction from Muggle Prime Minister and Minister of Magic, unless exceptional events occur. IIRC, in first 5 years, there is only two interactions : the Minister of Magic informing the Prime Minister about the escape of Sirius Black, and the dragons for the Triwizards Tournament. And there seems that not once did the Muggle Prime Minister directly contact the Minister of Magic, it only went the other way around.
So I'm sceptical about that. More likely the Ministry of Magic has someone working in the staff of the Muggle Prime Minister and informing the Ministry if something odds is happening.