Update 11/09/2021: Over a year later, Iceland now reports 34 total deaths / 14757 total infections for a naive IFR of 0.23%, or a least 50% higher than the mean of this old simple estimate, and roughly 2x seasonal flu.
EDIT: updated with wider estimates to reflect potential sample bias
deCODE Genetics has tested a random-ish sample of about ~5K Icelanders for COVID-19 and about 0.9% tested positive, which naively indicates ~3K true infections in a population of ~330K.
However, if we consider that the volunteer based sample is perhaps biased (the article suggests they would control for this but doesn't describe if/how), that suggests an estimate closer to the ~1k confirmed cases - say 2K.
On the other hand, if we consider the potential of false negatives from failed tests for those who already recovered, that suggests a higher range, perhaps up to ~5k. (The PCR test is highly specific, so we can ignore false positives)
Iceland has only 2 deaths so far for a naive IFR in the range of 0.04% to 0.2% to (we can probably ignore false negatives for deaths - as they are harder to miss in Iceland). Iceland's cumulative case count is clearly in a linear growth regime (past midpoint of sigmoid). They have 6 patients in ICU (Iceland data), which has about a 30% fatality rate, and 19 in hospital with a 10% fatality rate so we can estimate the future total death count in the 2 to 8 range.
This results in a mean predicted IFR of 0.17% (6/3500)and a range of 0.04% to 0.4% (2/5k to 8/2k), similar to influenza but potentially a bit (2x) higher. The uncertainty range will eventually tighten as we know more about survival in their current hospitalizations.
This agrees with the Diamond Princess data which rules out IFR much higher than influenza. (see my analysis here, or a more detailed analysis here) In that same post I also arrived at a similar conclusion by directly estimating under-reporting (the infection/case ratio) by comparing the age structure of confirmed cases to the age structure of the population and assuming uniform or slightly age-dependent attack rates similar to other viruses. That model predicts under-reporting of ~20X or more in the US, so it's not surprising that the under-reporting in Iceland is still in the ~4X range.
The infection hospitalization rate of COVID-19 in Iceland is also in the vicinity of ~1%, similar to influenza.
This also puts bounds on how widespread C19 can be - with IHR and IFR both similar to influenza, there couldn't be tens of millions of infected in the US as of a few weeks ago or we would be seeing considerably more hospitalizations and deaths than we do.
The 'common cold' is actually caused by over 200 virus strains of different orders, so I wonder if years from now SARS-CoV-2 will be lumped in as a non-influenza virus strain in the 'flu' category.