Previous installments in this series posed the question and examined potential components of an answer: first, long-term trend in GDP and labor demand and supply curves, next, cultural influences. It is time to put it all together and analyze quantitatively the relative contributions, if any, of the three factors.
What I will do now is called the stepwise analysis: I will build the model in a series of steps, adding a single explanatory variable in each step. This approach allows us to understand whether any of the explanatory factors are necessary to explain the dynamics of the response variable (which is, in our case, the real wage from 1927 to 2012). We will also be able to see which features of the data each explanatory variable helps us to understand.
The first step is to look into the effect of growth in GDP per capita:
What we see is that the growth of GDP per capita explains why real wages in 2012 are higher than in 1927, but not much of anything else. Over the last 85 years GDP per capita grew fairly steadily, although sometimes at a faster, and at other times at a slower rate. There is not a hint of a break in the GDP curve during the late 1970s, when the real wage abruptly shifted from the fast growth regime into that of stagnation and decline. Why did the growth rate of real wages outpace that of GDP per capita before 1970s? Why did the growth rate of GDP per capita outpace that of real wages after the 1970s? We need to look to other factors for possible explanations.
The model that takes into account both GDP (per capita) and labor supply/demand ratio yields the following results:
Statistical analysis says that this model explains data substantially better than the model with just GDP. The predicted curve hints that demand/supply ratio may be responsible for some of the trend reversals in the data, but overall, the model is not particularly satisfactory.
The next step is to add the proxy for non-market forces (“culture”):
Adding this variable results in a dramatic improvement of the model-generated trajectory. But we are not done yet. Notice that the break point in the model curve, when it shifts from the growth to the stagnation regime, occurs several years before the break point in the data. As I discussed in a previous installment, this is precisely the expected pattern. As economic conditions change (for example, supply begins to overtake demand for labor), wages do not adjust to the new situation immediately. Contracts need to run their course and be renegotiated, and both employers and employees don’t yet know whether this year’s conditions are part of the long trend, or just a temporary spike. This means that real wage this year actually reflects the social and economic conjuncture that obtained several years ago.
It looks like the lag time involved in the response by wages is at least five years. Re-analyzing the model by regressing real wages on the values of explanatory variables lagged by five years, yields the following result:
We now see that the model now accurately predicts the break point, which is not surprising, because I introduced the delay parameter to account for this feature. What is surprising is that the model now predicts the wage dynamics during the stagnation phase: down during the 1980s, up until the early 2000s, and then down again. Such fine-scale correspondence between the model trajectory and data is entirely unexpected, and serves to further strengthen our confidence in the ability of the model to capture the forces driving the dynamics of real wages.
Additional exploration of various combinations of explanatory variables confirms that all three components are needed to replicate the data pattern. The conclusion is that real wages grow faster, or slower than “per capita income” (GDP per capita) due to an interplay between market forces (captured by the labor demand/supply ratio) and cultural influences (proxied by the real minimum wage).
What’s new here is the use of the real minimum wage as a proxy for ‘cultural’ forces (remember, that this is my shorthand notation for such non-market factors as social norms and values, political and legislative landscape, and the balance of power between employers and employees). As far as I know, nobody has attempted to include ‘culture’ in a quantitative analysis of forces affecting real wages. But once we do so, we find that culture is of paramount importance (quantitatively, its effect is greater than that of the demand/supply ratio).
It would be desirable to do two other things. First, the model is very simple, which is definitely a virtue. It folds a number of factors that have been discussed by economists and reporters (immigration, trade deficit, labor productivity, etc.) into a single measure, demand/supply ratio (and similarly with the cultural influences). I need to ‘unpack’ this aspect of the model so that we can weigh the relative contributions of such factors to the overall outcome (whether wages grow or stagnate). This looks like a good topic for the next blog.
Second, the model does not incorporate (at least explicitly) the effect of technological evolution. Some of it is folded into the growth of the GDP, which I take as given, but it would be extremely interesting to look at its effect as a separate explanatory variable. Does anybody know of a good proxy for this very important factor?
As I promised in a previous blog, I plan to post a document that provides technical details of the statistical analysis that generated the results I discuss above. This has been delayed due to heavy teaching and demands on my time last week, but I will get to it as soon as I can. For those who can’t wait, the regression model looks like this:
where W is the real wage, G/N is GDP per capita, D/S is the labor demand/supply ratio, and C is the real minimum wage; τ is the time lag. The predictor variables were smoothed by kernel regression with bandwidth = 4 y (the response variable, naturally, is not smoothed).