SB argues that PG overstates the case, saying that to eliminate inequality you have to eliminate innovation. SB says that PG is correct, but no one says inequality should be eliminated, only reduced. That seems reasonable. So, "the conversation is about what level of economic inequality is desirable in a society, and how to limit inequality — not about how to end it entirely."

So we are talking about what is "desirable in a society." PG makes it absolutely clear in the simple version of the essay: "economic inequality per se is not bad."

Economic inequality does not cause poverty. But increasing poverty tends to increase inequality. I believe that the institutions which best promote wealth creation lead to both inequality and reduction in poverty. The rich get richer and the poor get richer.

I’m sure PG himself supports some policies that reduce inequality (progressive system of taxation, social security, medicare).

PG may support these policies, but not necessarily because they reduce inequality. These may reduce poverty, which almost everyone advances as a desirable goal. Reducing poverty will tend to reduce inequality as a side effect, unless the rich are getting richer faster than the poor are getting richer. If everyone is getting richer, I am not going to quibble about differences in rates.

Further, there are an abundance of studies that show that reducing economic inequality (even through redistributive means) actually boosts overall prosperity. This study by the IMF shows that countries with lower levels of economic inequality show higher levels of economic growth over the long term,

I didn't look at it, because countries with higher economic growth tend to be poorer, immature, developing economies. A weight lifter wanting to gain strength does not emulate an infant, which doubles in strength every few months.

while this report by the OECD found that “income inequality has a sizable and statistically significant negative impact on growth.”

This "report" is actually a book. Sorry, this is my lunch hour. The summary says "lower income households have been left behind," a typical statement suggesting that things are getting worse for the poor, when the reverse is generally true.

Many studies have shown that income inequality is bad, even controlling for other factors — too many to include in a short blog post. For example this one, which shows economic inequality is bad for health.

When you have "many studies" to choose from, you should choose the best one and it should be good. This one, the article anyway, is a classic example of conflating correlation and causation: "the researchers found that people in unequal communities were more likely to die before the age of 75 than people in more equal communities, even if the average incomes were the same."

There is no justification to conclude that the inequality causes poor health.

Say we consider two communities, A and B. Community A is pretty homogeneous, with most incomes close to the average. Unsurprisingly, people there have average health. Community B is highly unequal: a few very high earners live there. If the average income is the same as Community A, there must be very many low earners in Community B. Obviously, with this large quantity of poor people the average health status is inferior. In both communities, an individual with average income will have the same health status.

The problem is poverty, not inequality. When a rich family moves into town, people don't get sicker.

The Gates review looks good.

Contrary to Piketty’s rentier hypothesis, I don’t see anyone on the list whose ancestors bought a great parcel of land in 1780 and have been accumulating family wealth by collecting rents ever since.