How do governments reconcile money that flows out of their country?
Australia has a lot of foreign businesses and it has a lot of immigrants. Both earn Australian dollars and huge amounts would be sent back their country of origin.
His does Australia balance its books on something like this? How do the economics of it work? Would it lower Australian inflation but shortening the money supply, and raise inflation of the destination country as it prints more money to exchange the Australian dollar?
Well those australian dollarydoos aren't useful in their home countries, so it is used to buy domestic money at an exchange.
The other responses are missing this point. This is the right answer. The AUD does not actually leave the country. If money is being sent to America, it is converted to USD first. In theory, the value of USD increases since there is greater demand and the value of AUD decreases. This is the mechanism of exchange rates.
Obviously, it gets a little more complicated than this, but in theory that is what is happening.
The amount that is sent out is just irrelevant. Furthermore, not all immigrants send money out. The second biggest group of immigrants are from the UK, they aren't sending much money home and any they do is offset by Australians who emigrated to the UK sending money to Australia. Other immigrants even bring in more money. For example, overseas students bring a lot of money into Australia, often at a premium. The same degree costs a domestic student 45k but an overseas student 170k. The business and innovation visa requires a minimum of 2.5 million investment. While there are probably more immigrants sending money home, the amount others bring in offsets a lot of that. It's similar to tourism. Yes, Australian tourists going abroad spend money elsewhere, but many tourists are coming into the country and spending money.
With companies, the situation is more difficult. While in theory, they are subject to paying taxes in Australia and aren't any different than local companies there are indeed ways around it. Most notably, having to pay the foreign parent company huge "franchising fees" or other "consultation fees" that reduce profit inside Australia, and then the profit gets taxed in a country with little or no corporate tax. And Australian companies use the same loophole as well. Registering an offshore company isn't particularly difficult. That is indeed something countries try to work against.
Any legitimate money sent abroad is mostly offset by Australian companies doing the same. It's not like there aren't any Australian companies working globally.
The reason why most countries don't go harder against that is that it would hurt foreign relations. And the damage to foreign relations would hurt the economy more. If everyone starts to count pennies and tries to maximize their own profits, every international trade becomes more expensive.
For example, the Indian-Australia trade agreement is vastly in favor of Australia. Australia is exporting goods worth over 19 billion a year while only importing around 7.5 billion. If Australia suddenly started to make it harder for Indian immigrants to send money to India, you can be sure that India will start taxing Australian goods more in retaliation.
In conclusion, going after this hard would mostly be penny-pinching and hurt the economy more in the long term. And countries that make this harder are suffering because of it. Look at China, where it's impossible to operate a foreign business. Any business needs to have a 51% share owned by a Chinese. And while this worked in the short term, companies are now leaving China en mass and taking their business elsewhere.
Example: literally any country in west Europe
Counter-example: Russia, China, Hong Kong
The effect is deflation but that's usually offset by deficit spending.
There's a LOT that goes into global monetary policy. I know more than some, but it's complicated in a way that's not easy or quick to explain here.
So to try and keep it short, there's at least a couple major trade-offs. First, it would be somewhat offset by Australian immigrants working in other foreign countries and sending money home to Australia. Second, Australia has global trade partners for a multitude of things and can offset imbalances through borrowing or lending through international trade if and when needed.
There's really so much more that goes into it and it's a bit different for every country, but that's a broad idea of how it can balance out.