# Trade and income inequality

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.