## thoughts on economic models

A typical, very simple economic model is a demand curve, Dx = f(Px). It states that, other things equal, an increase in the price of x will result in a decrease in demand for x. I other things are not equal, the assumptions of the model do not hold. Suppose, writes blogger Arnold Kling, that x stands for tuition charged by a school, and we observe that demand went up rather than down when tuition increased. What may have happened is that scholarships became more generous, so the full tuition – net of student aid – fell. Other things did not remain equal.

Most economic models contain more variables. Consider the aggregate production function X = f(K,L). The quantity of output is a function of the quantity of physical capital plus the quantity of labour.

[This model] is used to predict that differences in output per worker will be proportionate to differences in capital per worker. When this fails, there are many possible reasons: workers may differ in their human capital; physical capital may not be measured or aggregated correctly; output may not be measured or aggregated correctly; institutional differences may matter. etc.

In fact, the primary use of the aggregate production function model is to examine its failure, which is called “the residual.” Economists place an interpretation on this residual, calling it “total factor productivity.” They interpret the rate of change in this residual over time as “productivity growth.” They interpret the change in the rate of change in this residual as “change in the trend rate of productivity growth.”

Arnold Kling, “Thoughts on the use of Models in Economics“, askblog, 9 July 2016.

Arnold’s explanation of how economists use models is useful, but I think he is too easy on model-building. It is very difficult – probably impossible – to measure output, labour and capital without using prices. This is necessary, because if prices are used, the model becomes close to a tautology. The value of the quantity demanded, for example, is always equal to the value of the quantity supplied (plus or minus abnormal profits or losses). Similarly, the value of output is equal to the cost of the rental of machines plus the wages of labour (adjusted for any abnormal profit or loss).

Think how difficult it is to measure (without prices!) the heterogeneous output of a factory, or the hours of equivalently productive workers. Physical capital is even more difficult to measure. Without prices or interest rates, what is the unit of measure. Kilos of capital? Number of shovels, hammers or machines?

Economic models are helpful, but only as toy models, useful for understanding, but not predicting, how a real economy functions.

See here for past posts on production functions.