Theory, data, demand and supply
The following is a slightly altered version of a column I wrote for the December 2011 issue of our student newspaper Nekst.
In 1925, economist Henry Schulz wrote in the Journal of Political Economy that “The common method of fitting a straight line to data involves the arbitrary selection of one of the variables as the independent variable X and the assumption that an observed point fails to fall on the line because of an “error” or deviation in the dependent variable Y alone, the X variable being allowed no deviation.”
At first glance, one may wonder whether this can be right. Haven’t we all learned that we regress Y on X when we are interested in “the effect” of X on Y? In his article, Schulz was interested in estimating demand for sugar. He faced the problem that both, demand Y and price X were measured with error. In such a case, indeed, there is no reason to prefer one of the two regressions described by him to the other. Here, “errors” come about—people realized later—not only because variables are not correctly measured, but also because there were aspects of the relationship between prices and quantities sold in that market that were not explained by a simple model saying that there is a one-to-one relationship between prices and demand.
Here comes the role of theory, and it is fascinating to see in the literature how the following ideas developed. It all started with a book Henry Moore wrote in 1914, entitled Economic Cycles: Their Law and Cause. In there, we can find a regression of the quantity of pig iron sold on its price. The coefficient on price was positive, and Moore interpreted it as a “new type” of dynamic demand curve. Philip Wright, a Harvard economist, reviewed the book in the following year in the Quarterly Journal of Economics and explained that it is very plausible that demand for pig iron was very volatile, whereas the production technology, and hence the supply curve, was not changing much over time. Therefore, the shifts in the demand curve trace out the supply curve, and that is why we are estimating a supply curve when regressing quantities on prices.
A discussion followed and then, after more than 10 years, Appendix B of Philip Wright´s 1928 book The Tariff on Animal and Vegetable Oils contained two derivations of what we know today as the instrumental variables estimator. The idea is that when we regress quantities on prices and use factors shifting the supply curve as instruments for prices (e.g. weather conditions for corn production), then we will estimate a demand curve. Conversely, when we use factors shifting the demand curve as instruments (e.g. a change in value added taxes), then we will estimate a supply curve. Carl Christ provides more details on the history in his 1985 AER article.
One thing one can take away from this is that theory matters. Once we see the world through the lens of theory—here a simple model of supply and demand—we can progress in our understanding of it. It also restrains us, because not everything that can be done should be done. The above example shows that first, we need to understand what we are estimating when we regress one variable on another. This is guided by theory. If we do not know this a priori, i.e. before we have performed this regression, then there is probably no point in buying expensive data sets, collecting data, conducting experiments, studying asymptotic properties of the estimator, or developing more fancy estimation procedures. This is also what Marshak had in mind when he started his 1953 paper by saying that “Knowledge is useful if it helps to make the best decisions.” Highly recommended.
CHRIST, C. (1985): “Early progress in estimating quantitative economic relationships in America,” American Economic Review, 75(6), 39–52.
MARSCHAK, J. (1953): “Economic measurements for policy and prediction,” in Studies in Econometric Method, ed. by W. Hood, and T. C. Koopmans, pp. 1–26. Wiley, New York.
MOORE, H. (1914): Economic Cycles: Their Law and Cause. Macmillan, New York.
SCHULTZ, H. (1925): “The statistical law of demand as illustrated by the demand for sugar,” Journal of Political Economy, 33(6), 577–631.
WRIGHT, P. G. (1915): “Moore’s Economic Cycles,” Quarterly Journal of Economics, 29(3), 631–641.
WRIGHT, P. G. (1928): The Tariff on Animal and Vegetable Oil. MacMillan, New York.