The conventional wisdom in economics is that trade is mutually beneficial to all parties and the freer the trade the better. However, as David Autor and collaborators have empirically shown, the benefits of trade can be unevenly distributed. A simple way to think about this is to consider a simple model of a nation’s income ($I$) as a function of socio-economic status ($S$), $I = \alpha +\beta S$. Here, $S$ can be distributed in anyway but has zero mean. The mean income of the nation is $\alpha$ while $\beta$ is a measure of inequality (i.e. proportional to standard deviation). Generally, it was presumed that trade increases $\alpha$. However, as Autor finds, trade can also increase $\beta$ and then it becomes a quantitative game as to whether you personally will do better or worse with trade. Your change in income will be $\Delta I = \Delta \alpha +\Delta\beta S$. Thus, if you are above the mean $S$ then trade is always beneficial and increasing $\beta$ helps you even more.  However, where the mean is with respect to the median is strongly dependent on the tails of the distribution of $S$. So if people with high $S$ are very far away from the median, then the mean could also be high with respect to the median. If you are below the mean then gains from $\Delta \alpha$ are offset by decreases in $\Delta \beta S$ and if you’re $S$ is more negative than $-\Delta \alpha/\Delta\beta$ then you will do worse in absolute terms. This could explain what has been happening in the US. The nation benefits from trade by having cheaper goods but some sectors like manufacturing and textiles are greatly hurt and the cheaper goods cannot make up for the decrease in income. Those above the mean are benefitting from a mean shift in income due to trade as well as any increases in inequality. Those below the mean are getting smaller gains and in some cases doing worse as a result of trade. Thus, it may not be surprising that there are divergent views on the benefits of trade.

## 2 thoughts on “Trade and income inequality”

1. I once read an old article by Krugman on this; his view was ‘free trade’ was on the whole good, and also said that rising inequality in USA was due mostly to technological change, skill change, etc. He relied on the Stolper-Samuelson theorem from the 30’s to justify that. I think using SST once can show traide will increase mean income of trading nations, and also may have ‘all boats rise’ (ie Gini will not increase within nations). However it hink that requires some additional conditions (some of which i think are addressed by people who like NAFTA and such but see its imperfections). Also the worst aspect of applying SST to the real world is it essentially requires ‘full employment’ to work. Thats not the case in the wolrd–usa, mexico, india, china..
Samuleson (of MIT, one of SS) wrote one of his last papers i J Ec Perspecs in 2004 said basically his theorem did not apply to the real world–its like a simple ‘mass balance argument’ in chemstry for a closed system at equiibrium. All markets clear, all chemicals end up where they belong.

The logic of the same argument above i think applies essentially within the USA. Much of this goes down to why thin king in terms of mean rather than median income is either incomplete scientifically–since means are not the only things of interest; variances also are, etc. One reason why these arguments are employed so often may be ‘ideological’—-economists writing these papers like a rising average and dont care about the variance. They see their boat rise up say the trump hotel, and dont see those almsot drowning below . .

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2. p.s. 1. i looked up SST–my charcterization of it may be half correct (i may have put a + instead of a -). I could never remember what a ‘factor of production’ and ‘goods’ were. Tere are a few old thories of trade, tariffs, etc.
2. I don’t really think that way (behavioral economists/psychologists note people make routine cognitive mistakes and also have different styles of thinking—i guess S Hsu said people good in math are also good in music, while other people may be good in other things (or bad in everything)).
I did glance at one paper which looks along the lines i’d formulate it.
i think the real issue with trade and inequality for me is exactly what kinds of trade are needed and for who (usa has an ‘opiate epidemic’ i hear, and cattle farmers want to export to china) and how you measure inequality. (current money i don’t think measures up any more than GDP).

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