# Management of the macroeconomy is not “the closest without exceeding it”

In the game show “The Price Is Right”, participants guess the retail price of fabulous prizes. Unlike many guessing games where you try to make the best guess possible, the contestant who guesses the number closest to the actual prize, without exceeding it, wins. Competitors must resist the urge to make the most accurate guess without exceeding the true value.

Experts have argued that macroeconomic management has a similar dynamic.** **In a recent blog post, Alex Domash and Larry Summers argue that strong wage growth can sometimes leave workers worse off. After all, rising wages are going to be associated with further price increases. They explain that wage growth is linked to increases in real wages (inflation-adjusted wages – versus “nominal wages,” which are the simple dollar amount). However, beyond a certain threshold, this relationship is reversed. When nominal wages are very high, this is associated with *lower *real wages, probably due to adverse supply shocks or overly stimulating aggregate demand. Like “The Price Is Right” competitors, macro policymakers need to be careful when placing policy on the optimal amount.

This is not just an academic argument – it is relevant to political debates past and present. For example, a common criticism of the Obama administration (and by extension, of Summers’ tenure on the National Economic Council) is that the United States has never achieved full employment. Current levels of employment relative to population (despite the so-called “labour shortage”) are currently higher than in the Obama administration. On the other hand, some have argued that rising employment levels and wages can fuel inflation and called on fiscal and monetary policymakers to take drastic measures to reduce inflation, even at the cost of rising unemployment.

Domash and Summers’ argument suggests that policymakers should be more careful about raising wages – if they go too far, it could lead to lower real wages. The graph below illustrates this finding. There is a positive correlation between real wage growth and nominal wage growth in the previous year until nominal wage growth exceeds 4.4%. After that, further increases are likely to be canceled out by a faster rise in inflation, driving down the real wage.

Analytics like this require people to decide how to generate or present their data. While there’s nothing wrong with the way Domash and Summers posted their findings, small changes can lead to a very different outcome. Three small changes described below lead to a different outcome, with contrasting policy implications.

**Change #1: Lose polynomial fit**

Domash and Summers use a “polynomial fit” to estimate the relationship between nominal wages and real wages. You may remember a high school algebra class where you had to solve equations of the form “ax^{2} + bx + c”. A polynomial fit finds the values of “a”, “b”, and “c” that best match the data.

A polynomial adjustment might be appropriate because of the hypothetical inversion relationship between nominal and real wage increases. This allows us to find the local maximum without necessarily assuming one. If a more conventional linear fit is more accurate, the value of “a” should be very close to zero. In such cases, the equation effectively becomes “bx + c”.

An alternative to Domash and Summers’ analysis is to perform two separate linear regressions, one on either side of their proposed threshold. The graph below shows these regressions in red and the original polynomial fit in green.

This change reveals that their essential result of a change in slope after crossing the 4.4% wage growth line is preserved. We go from a slightly upward slope of 0.34 to a strongly negative slope of -0.93. Another advantage of this alternative framework is that it allows us to perform statistical tests indicating that the change in slope is statistically significant (p

**Change #2: Look at years instead of quarters**

A second change we are making is to disaggregate the data. Domash and Summers’ analysis is indexed at the quarter level. There is an observation for nominal wage growth in the fall of 1994, the winter of 1994 and the spring of 1995. But since we are looking at the change *finished *four quarters, each observation contains substantial amounts of information that is incorporated into *previous *observation. A data point from summer 1994 incorporates all changes that occurred in summer 1993, fall 1993, winter 1993, and spring 1994. Meanwhile, a data point from fall 1994 will include changes from fall 1993, winter 1993, spring 1994 and summer 1994. Three quarters of the time period overlaps.

This overlap means that the chart actually contains less data than it appears to have. We see a dense scatter plot with 224 observations, but a better representation would be to look at one data point for each year. For example, the chart below only includes the first quarter of each year, so we have 56 observations.

The slope of the second line in this specification is no longer statistically significant. This is not because the change made above reduced the slope of the line, but because we are looking at fewer observations. Fewer observations reduced the statistical power of the analysis so we are less likely to see statistical significance. Eliminating these observations is a more appropriate way to look at this data – each observation in this specification is new instead of pulling overlapping dates.

**Change #3 – Sensitivity test**

Finally, the previous specification suggests that the year 1980 is an important driver of our results. Previous iterations of the chart show four dots in the lower right corner. But all this concerns a relatively short period – from October 1979 to July 1980.

1979 and 1980 are the “Volcker Shock” years and occupy a special place in macroeconomic history. The Federal Reserve, then led by Paul Volcker, announced a new monetary policy framework in the fall of 1979 and raised interest rates dramatically over the following year. The tightening of monetary policy led to two consecutive recessions, but also to a sharp drop in inflation, from an annual increase in prices of 13.5% in 1980 to an increase of 3.1% in 1983. As my colleague Ed Dolan has argued, the Volcker shock was regime change. in monetary policy – not reflecting the Federal Reserve’s reaction to changing conditions, but a change in policy that resulted in different inflation expectations.

These four points are unusual in the construction of data. Each point reflects the evolution of real wages *after *the Volcker shock, with changes in nominal wages *before *them. A specific quirk in the way the data is presented – looking at wage growth over a four-quarter period and lagging nominal growth over the same four quarters – allows this to happen.

Due to the uniqueness of the Volcker shock, it is worth considering what the relationship looks like if we ignore these data points. By redoing our previous linear regressions, but excluding 1980, we see that the relationship between real and nominal wages is now stable after the 4.4% threshold. The negative relationship we observed earlier was entirely due to the Volcker shock alone.

The intention here is not to suggest that the inclusion of the 1980 data is inappropriate, but only to show that the proposed relationship depends entirely on a single data point. This graph suggests an alternative relationship to that proposed by Domash and Summers. Instead of real wages first rising with nominal wages and then falling, we can suggest a relationship where in most circumstances the association is initially positive and then flat.

This interpretation makes microeconomic sense. Wage growth increases until the labor market reaches full employment, which seems to correspond to an overall wage growth of around 4.4%.

Additional growth does not lead to higher real wages, but it does lead to lower real wages. People’s salaries are based on their productivity (among other factors), which will be valued in real terms. Wages do not rise instantaneously in response to price changes, but adjust over a sufficient period.

Domash and Summers present their results as a cautionary tale: they warn that the Federal Reserve is unlikely to achieve a “soft landing” – bringing inflation under control without a corresponding increase in unemployment.

They may be right. But we have to be careful not to generalize too much from the limited sample of data we have. Although today may be analogous to the period of high inflation that preceded the Volcker shock, it may not be. Yes, it will be difficult for the Federal Reserve to reduce inflation without inducing a recession. While Bob Barker might just tell a “Price Is Right” competitor to “get down,” the Federal Reserve must take action to reduce inflation. But in taking these steps, they should be aware of how little data we rely on and how difficult it is to relate it to our current unprecedented situation.

Photo credit: *iStock*