Motivated by an article in yesterday's NY Times , a reader asks me to clarify the linkage between real wages and productivity as a matter of economic theory. Here is the basic logic taught in economics textbooks:Economic theory says that the wage a worker earns, measured in units of output, equals the amount of output the worker can produce. Otherwise, competitive firms would have an incentive to alter the number of workers they hire, and these adjustments would bring wages and productivity in line. If the wage were below productivity, firms would find it profitable to hire more workers. This would put upward pressure on wages and, because of diminishing returns, downward pressure on productivity. Conversely, if the wage were above productivity, firms would find it profitable to shed labor, putting downward pressure on wages and upward pressure on productivity. The equilibrium requires the wage of a worker equaling what that worker can produce.Why don’t real wages and productivity always line up in the data? There are a several reasons:1. The relevant measure of wages is total compensation, which includes cash wages and fringe benefits. Some data includes only cash wages. In an era when fringe benefits such as pensions and health care are significant parts of the compensation package, one should not expect cash wages to line up with productivity.2. The price index is important. Productivity is calculated from output data. From the standpoint of testing basic theory, the right deflator to use to calculate real wages is the price deflator for output. Sometimes, however, real wages are deflated using a consumption deflator, rather than an output deflator. To see why this matters, suppose (hypothetically) the price of an imported good such as oil were to rise significantly. A consumption price index would rise relative to an output price index. Real wages computed with a consumption price index would fall compared with productivity. But this does not disprove the theory: It just means the wrong price index has been used in evaluating the theory.3. There is heterogeneity among workers. Productivity is most easily calculated for the average worker in the economy: total output divided by total hours worked. Not every type of worker, however, will experience the same productivity change as the average. Average productivity is best compared with average real wages. If you see average productivity compared with median wages or with the wages of only production workers, you should be concerned that the comparison is, from the standpoint of economic theory, the wrong one.4. Labor is, of course, not the only input into production. Capital is the other major input. According to theory, the right measure of productivity for determining real wages is the marginal product of labor--the amount of output an incremental worker would produce, holding constant the amount of capital. With the standard Cobb-Douglas production function , marginal productivity (dY/dL) is proportional to average productivity (Y/L), which is what we can measure in the data. (See Chapter 3 of my intermediate macro text for a discussion of the Cobb-Douglas production function.) Keep in mind, however, that the Cobb-Douglas assumption of constant factor shares is not perfect. In recent years, labor’s share in income has fallen off a bit. (Between 2000 and 2005, employee compensation as a percentage of gross domestic income fell from 58.2 to 56.8 percent.) From the Cobb-Douglas perspective, this means that the marginal productivity of labor has fallen relative to average productivity. This modest drop in labor’s share is not well understood, but its importance should not be exaggerated. The Cobb-Douglas production function, together with the neoclassical theory of distribution, still seems a pretty good approximation for the U.S. economy.Update: If you want to look at data on factor income shares, go to the BEA . Click on "List of All NIPA Tables." Then click on Table 1.11. You can then judge for yourself whether the changes in income shares are large or small.Update 2: Economists Russell Roberts and David Altig also blog on this topic.