Estimates of the Trade and Welfare Effects of NAFTA?
I am going to construct a complicated mathematical model of the economy, and then I'm going to calibrate it using some actual data, and in the end I will be able to tell everyone how much better or worse off they are given various changes in the economy. And it will be totally and completely true. Trust me, it's math and therefore science.
My co-blogger Dave Schuler pointed me to this paper on NAFTA. The title is the same as the title of this post, but without the question mark.
Dave cited this interesting claim from the abstract,
We find that Mexico’s welfare increases by 1.31%, U.S.’s welfare increases by 0.08%, and Canada’s welfare declines by 0.06%.
Why is this interesting? Well, it claims to tell us how much the overall welfare in the U.S. increased as a result of NAFTA. I found this to be rather startling. I find it startling because to do this the authors would need some measure of welfare for each person in the U.S., a utility function if you will. Here is the thing, I don’t even know what my utility function is. I could say it is U(x,y) = a*log(x) + (1-a)*log(y) which would be a Cobb-Douglas utility function. But is that really my utility function? To be quite honest I don’t know. Nobody knows what their utility function is nor could they really write it down.
In fact, that is exactly the type of utility function the authors assume for everyone. A Cobb-Douglas utility function over J final consumption goods with a sequence of exponents denoted (abusing notation a bit here) of a(j) where the sum of these J exponents equals one. In other words, a Cobb-Douglas utility function with constant returns to scale, that is if you double all of the J final consumption goods you double your utility. This is rather restrictive, but they probably chose it to ensure there would not be any issue with increasing returns to scale. In other words, they chose this utility function, and later the production function, for mathematical tractability, vs. actually trying to measure real life changes in welfare for consumers.
Now, what is one reason why we might see a small increase in welfare, setting aside this issue of is that really the utility function of every American. Well suppose you have the following function f(x) = log(x) and suppose you go from 100, too 200 for x. How big a change is there in f(x)? You go from 2 to approximately 2.3 or you get an almost 15.1% increase in welfare…for a doubling of your input/consumption good. In fact, given this functional form for utility we can derive the functional form for marginal utility, it is 1/x. As X gets larger the marginal impact on utility will get smaller and tend towards zero in the limit. So, given the assumptions of the model it is not that startling to see the percentages quoted above. The U.S. consumer probably consumes far more of the various J final consumer goods than Mexican consumers. But of course, why should Mexicans and Americans have the same utility functions?
Now, what about production in this paper? Interestingly enough the authors do allow for different types of intermediate goods, but labor is simply labor. All labor is the same. College graduate with a degree in chemistry, the same as the high school dropout working at the car wash. Each type of labor can be interchanged with zero loss to productivity. Instead of treating capital as one big amorphous mass that can be moved around quickly and with no loss in productivity from industry to industry this is the assumption with labor. In fact, it also holds between countries too from what I can see. Labor between the N countries is entirely fungible. Lets skip over cultural norms, language barriers and the like. And yet again the authors assume constant return to scales and perfect competition.
That last one is a bit of doozy by the way. Perfect competition means not just that there is competition, but that it is perfect. That is everyone knows everything about everything. We don’t have to worry about incentive problems or informational asymmetries or even whether or not consumers know what their utility function is or producers of intermediate goods knowing their production function or their cost functions, etc. Everyone knows it all at all times.
From there the authors go on to derive equilibrium conditions and results. However, even these, while undoubtedly mathematically true, are dubious. Equilibrium in economics is kind of a fiction. What happens at equilibrium? Nothing. There is a joke about economists; a finance guy and an economist are walking down the street. The finance guys says, “Look, $20 on the ground, lets pick up and go have lunch.” The economist responds, “Ridiculous, in equilibrium somebody would have already picked it up, so it can’t be there.” In equilibrium how much food would in the grocery store? None. Why? Markets have cleared, quantity supplied equals the quantity demanded. Nothing left to put on the shelves. There would be no gasoline at the gas station, no clothing at the department store. The point is that economies are rarely if ever at equilibrium. Deriving equilibrium conditions may not be totally useless in terms of mathematical modelling, but basing analysis off of equilibrium conditions probably is.
And while the authors do estimate some trade elasticities their overall model is not empirically estimated. It is calibrated and then simulated. Much like the real business cycle and other macro economic models out there. While I suppose these can be interesting, I guess, the problem is the results can be highly misleading like that 0.08% welfare gain from NAFTA for Americans. This is treating their model as if it were a literal representation of reality. Clearly it isn’t.
Note, none of the numbers the authors present are actual real world numbers. They are all based off of their model simulations. Further, the model is simple, and actually that is not all that bad. Trying to have extremely complicated models can quickly become intractable and leave us unable to learn anything at all. But to look at these results and say, oh 0.08% for the U.S. therefore the U.S. got pretty much nothing from NAFTA is a gross misinterpretation of this model. That number is derived from this highly stylized and simple model. It is not based on trying to parse out what actually happened in the the U.S., Mexican and Canadian economies.