## Friday, January 17, 2014

### Second order effects

There has been a lot of discussion about inequality lately, some of which could use some careful thinking about distributions and effect order.

I think the easiest way to describe what I am thinking about is an example.  Consider two groups, call them A and B.  At the beginning A and B have the same number of people and the same average share of some sort of measure of wealth.  So A has 50 people and 50 income units, as does B.

Now consider a policy that added 20 wealth units to B and subtracted 10 wealth units from A.  Call it free trade.  Now the size of the wealth pool is 110 units (higher) but group B is 50% wealthier than group A.  This could happen if you opened up competition for factory workers but no lawyers (as a random example).

The good outcome has group B giving between 10 and 20 units of wealth to group A (redistribution) so everyone is better off.  But imagine group B thinks they worked hard for their 60 units of wealth?  So they argue for letting people keep what they earn.  But they also think opposition to these policies by group A is an anti-growth stance.  Yet group A is worse off.  They also lose political power (less wealth) and so have less opportunity to fight for redistribution, making a "trust me, we'll share" argument less than convincing.

Now any real example will not have these simple inference available.  But it does make a big difference when you think about why people might oppose a policy that increase aggregate wealth for the society as a whole.

Now consider first versus second order effects.  Let us pretend that Group B grows wealth faster than group A.  Under the old system (even division), the pool would grow by 5 wealth units per decade.  In the new system, wealth grows by 6 units, but it is proportional to the pool of wealth that the group has.  This is the efficiency harvested by the new policy (it increased wealth and increased the growth rate).

So under the old system, groups A and B grow at 5 wealth units and end up with 55 units.  In the new system, Group A has 42.4 units and group B has 63.6 units.  The gap between A and B is actually larger even if both groups grew by a faster rate.  For group A to reach 55 units, this fast growth rate would have to be sustained for many iterations (4 or 5, by my calculations).  So just speeding up the growth rate doesn't mean that everyone is better off, if the intervention has distributional effects.

So I think that this leads to two important policy conclusions.  In any ordered society, the rules will help some groups and hurt others groups (even a lack of rules will have a differential impact).  Just saying that a policy increases average wealth can be quite misleading.  The second is that second order, like higher growth, have to be really large to overcome first order effects.  Now, if you are completely neutral as to distribution (the size of the pool is all that matters) then okay -- but is anybody really neutral given they will be advantaged or disadvantaged by any actual policy?

Now, I re-emphasize that you can't actually get clean numbers in the real world.  Macroeconomics has measurement error, noise, confounding, and many groups with a vested interest in obscuring actual associations.  But it does mean that very simple narratives may not fully engage with the complexity involved in real world problems.  These are very simple thought experiments and they already make ideas like "target the maximum growth rate" seem to be less deadly obvious than you might expect them to be.