My understanding is that if an ETF pays dividends, then the money I will get from the ETF will be dividend*(1 - expense ratio). What about an ETF of stocks whose only value comes from capital gains, not dividends? When and how are these expenses collected?
The expense ratio an ETF charges is simply deducted from the assets it holds. This reduces the net asset value which, by market forces and the redemption mechanism, drives the market value of ETF shares down.
The key is the expenses are paid daily and therefore in such small increments it's hard to notice. However, over a long term, you will see that an ETF yields slightly lower returns than the assets it holds due to expenses.
This daily process also fairly allocates expenses to people who hold onto shares for short periods, like days or weeks. If they subtracted fees only when dividends were issued, people who bought and sold between the dividend dates would pay zero fees, at the expense of others
The expense ratio is based off of the amount of money you have invested in the fund. For example, if an ETF that tracks the S&P 500 has an expense ratio of 0.75% and you invest $50,000 your fee will be $375, regardless of dividends. So regardless of if the ETF pays dividends or not, your expense ratio is based off of how much money you have invested in that particular ETF.