• I don't see how it's more private than publishing income?
• I don't see how knowledge of gross and taxable income allow to deduce tax fraud?
• I'm afraid publishing this information will not help in terms of tax fraud but possibly hurt general society "climate".

Do you mean publish = make available to 3rd parties or tell the citizen what their effective tax rate is?

The latter is done in Germany: the income tax statement has an information line that states average tax rate as percentage of taxable income (not before deductions). However, I'll assume you're talking about the first meaning.

In case you mean publishing to 3rd party, I don't really see where the big difference between publishing taxable income vs. publishing effective tax rate is in terms of privacy?

Personally, I'm very much in favor of privacy rights (along the line that I behave well and in concequence expect privacy), and in my culture personal income and/or wealth are considered private. From that perspective, I do see a huge difference between a (or few) tax officer(s) who took an oath that they will obey all laws and will be scrupulously correct in administering their duties knowing details of my financial situation in order to calculate my taxes and random persons getting this knowledge. (more below in section "Does it help")

Does it help detecting tax fraud?

As I understand tax avoidancefraud, it happens either by

1. not reporting income in the first place, or
2. by claiming more deductions than took place.

In other words, by illegally reducing the taxable income.

For allowing the public to find tax fraud,

1. cannot be detected by publishing reported income before deductions, and for
2. without knowing what exactly is deduced there is no way to decide whether the deduction was legal or not (which is why you have to detail this to the tax office). Not even the ratio or difference is very informative here. Consider

• a) a web developer employed somewhere around the corner: hardly any deductions but mostly mandatory social insurance and maybe some
• b) a self-employed web developer working from home: hardly any deductions but social insurance which is more variable and higher than in case a)
• c) a farmer, tradesman or shop owner: far higher income (sales), but also far higher deductions buying material/wares and writing off machinery
  As a rule of thumb, IIRC, local shops often have a margin in the lower single-digit percentages of sales.
• d) in my region, part-time farmers are quite common. Or think what happens if the web-designer a) or b) starts a small online shop from home (using the services of a logistic company like amazon: that would not even require a garage for storage).

In the end, even with publishing income before deductions and tax rate, the legal and plausible range will be so wide that I don't see how good conclusions can be drawn.
Moreover, I don't see how any conclusions can be drawn that the tax office couldn't draw far more easily as they have far more information.

Does publishing such information help or hurt?

Coming from a country (Germany) that has had governments for substantial parts (spatially and temporally) of the last century that made extensive and bad use of denounciations, I'm rather wary of the "collateral damage" of such a publication strategy for tax fraud.

Note: Anyone who knows of a tax fraud can already inform the tax office, even anonymously. (This of course may be different in different legislations)

I don't know numbers about tax fraud in this context, but there was an article in the local newspaper a few years ago about anonymous information on animal welfare issues. The interesting points in this context here are that the animal welfare officer explained:

• roughly 1/3 of the reports were actually warranted in the sense that they considered it OK for non-experts to be worried about animal welfare in the respective situation (which doesn't mean that something was actually wrong).
  For example, it's possible to keep sheep and cattle outside on pasture land in winter here. But it may not be easy for a non-farmer/non-vet to decide whether they have suitable conditions for that or not (e.g. whether they need a shed and what exactly is needed).
• another 1/3 of the reports were not warranted in the sense that from the description they could decide there is no problem, but were not able to convince the informer that everything is OK.
  Examples: people worried that ducklings may drown, or thinking that sheep need a heated stable (which is actually bad for them)
• the last 1/3 according to their assessment of the situation were denounciations* out of spite.
  I've actually witnessed a situation that fell into this category, the officer explained that this is quite frequent and that they are of course not allowed to say who informed against the owner of the animal in question. They added that it did not come from the village - and also said that they do see a decided problem with such denunciations* poisoning neighbourhood relations (not knowing who it was creates a whole lot of distrust). Needless to say that even if the animal is kept in perfectly fine conditions this is rather stressful for the holder and involves taking off from work etc.

The officers are required by law to properly make a full case every single time they receive such a report (unless they can convince the worried person that ducklings really won't drown and that sheep do get ill in heated stables and the informer after all decides to withdraw their animal cruelty report).

So for animal welfare, we observe a situation where the officers need to deal with 2 unnecessary cases for every case that actually should be looked into, i.e. the 3fold workload. Plus there's a problem with spiteful denounciations.

Now one difference between the animal health officer and a tax officer is that the tax officer has already far more detailed information available together with far more sophisticated tools to search for suspicious points in the details of the tax declaration. Thus the ratio of reasonable-to-look-into cases to clearly unnecessary cases would probably be far worse than for animal welfare.
As for the spiteful denunciations: just imagine your competitor is tempted to think competition may be much easier if you spend less time on improving your products/serving your customers because you're in the back office serving tax officers due to an extra tax audit...

* denounciation in English seems to be a rather neutral term according to the Wikipedia definition, whereas in German (Denunziation) it is not neutrally reporting someone's (perceived) wrongdoings to the authorities (that would be anzeigen = reporting/informing), but doing so from personal low motives. (I did not find an English translation with this meaning)

Maybe Norwegians are better behaved than Germans in this respect. Or maybe they don't have such anonymous tax fraud reporting possibilities.

• I don't see how it's more private than publishing income?
• I don't see how knowledge of gross and taxable income or tax rate allow to deduce tax avoidance?
• I'm afraid publishing this information may hurt general society "climate" more than it helps.

I don't really see where the big difference between publishing taxable income vs. publishing effective tax rate is in terms of privacy?

So, publishing effective tax rate (as in taxes : taxable income) leaves the reader to guess a bit about the size of capital gains vs. other sources of income, but is almost as good as publishing taxable income in terms of information content.

Personally, I'm very much in favor of privacy rights (along the line that I behave well and in concequence expect privacy), and in my culture personal income and/or wealth are considered private. From that perspective, I do see a huge difference between a (or few) tax officer(s) who took an oath that they will obey all laws and will be scrupulously correct in administering their duties knowing details of my financial situation in order to calculate my taxes and random persons getting this knowledge. (more below in section "Does it help").
But that's certainly a political opinion and as such open to discussion.

Does tax rate or tax payed to gross before deductions help detecting tax avoidance/loopholes?

As I understand tax avoidance, it happens via deductions that are legal but reduce the taxable income in a way that was not envisioned when the respective tax law was made (loophole). So all that distinguishes them from normal deductions is that they were not intended for the situation where they are employed.
Which means in turn that detecting a loophole needs sufficient information to distinguish whether a deduction is used as intended or not. This is impossible without knowing what exactly is deducted. In other words, far more detailed information than tax ratio or taxes paid to income before deductions is needed.

Even the tax office may not be able to detect this loophone immediately but they look for unusual patterns and routinely request further documentation (or discard deductions) - which would allow them to detect the loophole.

The ratio of tax to income before deductions proposed in the question is not very informative without additional information. Consider the following situations without tax avoidance:

• a) a web developer employed somewhere around the corner: hardly any deductions but mostly mandatory social insurance: high tax to income before deduction ratio (and that is ≈ tax rate)
• b) a self-employed web developer working from home: hardly any deductions but social insurance which is more variable and higher than in case a): somewhat lower tax to income before deduction ratio
• c) a farmer, tradesman or shop owner: far higher income before deductions (sales), but also high deductions buying material/wares and writing off machinery
  As a rule of thumb, IIRC, local shops often have a margin in the lower single-digit percentages of sales. This would put the tax to income before deduction ratio close to zero.
• d) in my region, part-time farmers are quite common. Or think what happens if the web-designer a) or b) starts a small online shop from home (using the services of a logistic company like amazon: that would not even require a garage for storage). We get a tax to income before deduction ratio anywhere between a) and 0, all is as intended and (in contrast to the CEO in the comment the difference between web-developers a) or b) vs. d) is hardly visible to the public.

In the end, even with publishing income before deductions and tax rate, the legal and plausible range will be so wide that I don't see how good conclusions can be drawn.

Moreover, I don't see how any conclusions would be possible for this tax to income before deduction rate (or effective tax rate) that the tax office couldn't draw far more easily as they have far more information at hand and the right (and duty) to ask for more documentation in case anything is not clear.