A subsidy is the government forcing more resources to be allocated to something than people with money think is good. An externality is when we believe that outcomes are affecting people who weren't the buyer/seller.
The environmental lobby wants to claim that fossil fuels are subsidised therefore we must stamp them out because it is Free Market. Charitably speaking, that really just shows the environmentalists are making an effort to use other people's language but don't understand the free market philosophy at a fundamental level. If the use of something has to stop for environmental reasons then it is taxed. Claiming that it is really reversing a subsidy comes out more as trying to shout the opposition down by changing what words mean on them. It is bad form.
In common speech "subsidize" is frequently used in the context of people being made to involuntarily bear externalities.
For example, people who live in areas with a lot of truck traffic often complain that they are being forced to "subsidize" trucking due to the damage to their local roads. What they mean is that they are being forced to bear the externality of excessive road damage, not that they are literally writing a check to the trucking company.
I.e. You are demonstrating the exact same error but don't seem to understand what's going on with the use of the word.
There is value in clarifying what is meant be a specific usage of 'subsidy', (which the linked paper does in the first sentence of its summary). There is value to calling people out for not doing this clarification when they use the word in its less standard meaning.
However, there is no value in saying that a fairly widespread usage of the word "subsidy" is incorrect.
It's like trying to pretend that "literally" doesn't figuratively have the same meaning as "figuratively". That boat has sailed and all we can do now is distinguish be between literal and figurative uses of "literally".
There are a range of actions that are appropriate to take when dealing with an unwanted subsidy. If we redefine what 'subsidy' means then the range of appropriate actions changes and we have to talk about what the new actions are. It would be far easier to use the right word, so word and action line up without the need for analogies.
I can't figure out what you are trying to say. Can you give a concrete example? What is the confusion that is added by the term 'implicit subsidies'?
That money they are lobbying for comes from their taxes, especially if it's local roads, so yes, if the trucking company isn't paying for the damage, the taxpayer is indirectly subsidizing them.
If say 10% of a city's budget goes to fixing truck damage to roads without at least commensurate benefit, then it's a more important issue than whether .05% went to cleaning up cotton candy after the town fair.
It also doesn't even have to be about tax expenditure. The healthcare cost of using fossil fuels is realized in private spending on treatment for pollution triggered respiratory illnesses, and the economic cost of climate change effect mitigation, which is already being accounted for in business planning.
Electricity is considered a human right - it is required maintain the most basic modern standard of living - and the externalities of it's production with fossil fuels are borne by everyone in some way. Therefore it's a matter of massively broader consequence and greater cost than the example you used.
The US spends around $35 billion/year in actual subsidies on fossil fuels.[1] (About $20 billion to producers, and about $15 billion to consumers.
Further more, the cost of not charging the fossil fuel industry for carbon emissions should absolutely be counted as a real subsidy, although its value is harder to calculate. But we force industries to clean up other pollutants, or we otherwise regulate their environmental impact, which costs them. If we gave one industry a pass on those regulations, that would be uncontroversially a subsidy.
1. https://www.theguardian.com/environment/climate-consensus-97...