Economic growth and wages are distinct---studies cite correlation and not causation.

We first consider the connections between wages and inflation or economic activity using cross-correlations. Cross-correlations allow for a simple examination of the lead or lag structure between two series as well as the strength of the connections between the series. If wage inflation reliably comes ahead of price inflation in the data, then the strongest cross-correlation should be between wage inflation in quarter t and price inflation in some k-th quarter after t.

When working with price inflation and wage inflation, there are important long-run trends and short-term volatility that we would like to remove from our analysis. As a general rule, wages and prices have followed roughly similar long-term trends: both accelerated from the 1960s into the 1970s and then decelerated in the 1980s. The forecasting literature has found gains in inflation forecasting accuracy by specifying inflation in gap form as a deviation from a slow-moving long-run trend (see, e.g., Kozicki and Tinsley 2001, Clark 2011, and Zaman 2013). We borrow from this literature and construct wage inflation gaps as quarterly annualized growth in a particular wage measure less a shared long-run trend.3 To remove high-frequency fluctuations in food and energy prices in our measure of price inflation, we define the price inflation gap as quarterly annualized core PCE inflation less the shared long-term trend. We then look at cross-correlations between quarterly price inflation gaps at time t+k and quarterly wage inflation gaps at time t.

Our measures have been moderately positively correlated since 1960: both price inflation and wage inflation tend to be above (or below) trend at the same time (figure 2). The strongest correlations have been between core PCE inflation and the ECI. The weakest correlations have been with the CPH measure, which is not surprising given its volatility. Depending on the measure, wages either lead core PCE inflation very slightly or are contemporaneous with it: the correlation peaks come in quarter t+1 or t.