The Bathtub Model of Unemployment: The Importance of Labor Market Flow Dynamics
Ayşegül Şahin and Christina Patterson*
An alternative to Okun’s law to understand unemployment dynamics is to examine the evolution of the unemployment inflow and outflow rates. (For more on Okun’s law, see yesterday’s post.) A useful analogy is a bathtub: we can think of the unemployment rate (a stock) as the amount of water in a bathtub. Changes in the amount of water in the tub are determined by the rate at which water pours into the tub relative to the rate at which it drains out. For example, if the inflow of water is equal to the outflow, the amount of water in the tub remains constant. But if the rate of water flow into the tub is suddenly increased by turning the faucet to its maximum level, then the water level rises rapidly. A similar dynamic occurs in the stock of unemployed workers when there is a rapid increase in job losses during a recession. In this post, we focus on the flow dynamics in an economic recovery to help understand how the unemployment rate may evolve.
To clarify the bathtub model, we need to use a little bit of math. Let ut be the unemployment rate, st the inflow rate, and ft the outflow rate. The evolution of the unemployment rate can be written as
This identity tells us that the change in the unemployment rate is given by the difference between inflows into unemployment and outflows from unemployment. In this post, we do not distinguish between inflows caused by job separations and entry/re-entry into the labor market or between outflows caused by job finding and leaving the labor force. Thus, we abstract for the moment from the labor force participation margin, but we will return to this crucial margin in later posts.
Since 1990, the Bureau of Labor Statistics has estimated labor market flows between employment, unemployment, and “out of the labor force” (nonparticipation). However, because we focus only on the total outflow and inflow rates and want to consider the entire postwar period, we use a method attributed to Shimer (2005) that relies only on characteristics of the level and duration of unemployment. The chart below shows the path of the inflow and outflow rates produced by this method. The inflow rate st (measured on the right axis) spiked up during the recession but has mostly subsided recently. The outflow rate ft (measured on the left axis) reached its lowest level since 1972 during the 2007-09 recession and, despite recent improvements, still stands far below its pre-recession levels.
What Do Flows Tell Us?
An important concept is the flow-consistent unemployment rate (ut*), the level at which the unemployment rate would settle if the inflow and outflow rates stay constant at their current levels. This concept is sometimes called the steady-state unemployment rate, but should not be confused with a natural rate concept. Because flow rates change from month to month, the flow-consistent unemployment rate changes.
The flow-consistent unemployment rate is defined as
The actual and the flow-consistent unemployment rates generally are very close to each other over the postwar period. However, significant deviations have occurred between the two measures during periods of rapid change in labor market conditions. To explain some of the recent large drops in the unemployment rate, we look for periods in which the flow-consistent unemployment rate is far below the actual unemployment rate.
|Historical Unemployment Rate Dynamics|
Change in u
Change in u
Change in u
The table shows the largest negative deviations between u* and u for the postwar period. When this deviation was at least 0.9 percentage point (the difference in December 2011), the unemployment rate declined 0.5 percentage point on average in the following month. Because our u* calculation uses data from the following month, we expect the deviation would provide such a near-term prediction. But when we look at the change in the unemployment rate over the subsequent three months (fifth column), it declines a further 0.4 percentage point on average. Looking at the subsequent twelve months instead (last column), the unemployment rate declined a further 1.2 percentage points on average. For example, the large June 1983 deviation predicted the subsequent sharp decline in the unemployment rate in early 1984 described in the introductory post to this series.
During the most recent recovery, we have also observed some large deviations between the two measures. The first two were in November and December 2010. As happened previously, these deviations were followed by a substantial decline in the unemployment rate. More recently, in October and December 2011, the flow-consistent unemployment rates were 1.1 and 0.9 percentage points, respectively, below the actual unemployment rate.
A key question is whether this most recent deviation is a clear signal of a further decline in the unemployment rate. The answer depends on whether the behavior of the inflow and outflow rates will be different going forward.
The Importance of the Outflow Rate
While the inflow and outflow rates jointly determine the unemployment rate, historical data show that fluctuations in the outflow rate drive a majority of the fluctuations in the unemployment rate. Economic downturns are typically characterized by short-lived spikes in the inflow rate followed by prolonged weakness in the outflow rate. The inflow rate plays an important role in the rise of the unemployment rate at the onset of recessions, but is typically less important in the decline of the unemployment rate during recoveries (see Elsby, Hobijn, and Şahin ). Historical flow dynamics tell us that unless the economy gets hit with a negative shock that increases job loss, changes in the outflow rate will be the most important determinant of the path of the unemployment rate in the future.
To demonstrate how the improvement in flow rates—especially the outflow rate—can bring down the unemployment rate, we construct a hypothetical unemployment rate path under three scenarios. In these scenarios, we assume the inflow and outflow rates change at the same rate as in the recoveries following the 1981-82, 1990-91, and 2001 recessions. We start the simulations two-and-a-half years from the official NBER trough to ensure that we are comparing similar points of the business cycle. (This simulation is similar to Daly, Hobijn, and Kwok’s simulation computed in 2009 to assess how high the unemployment rate was likely to go.)
In all three scenarios, the unemployment rate declines to around 6 percent by the end of 2014. Indeed if the inflow and outflow rates improve at the same rate as they did in late 1993 and 1994, the unemployment rate will fall to close to 6 percent by early 2013. In contrast, the March 2012 Blue Chip consensus forecast has unemployment remaining above 7.5 percent through 2013.
The next chart shows the hypothetical inflow and outflow rates in the three scenarios. Although the decrease in the inflow rate contributes to the decline, the main driver of the decline in the unemployment rate in these scenarios is the improvement in the outflow rate. It is important to note that in all of these scenarios, the increase in the outflow rate is modest: it rises from 25 percent to around 33-34 percent, compared with a peak before the Great Recession of about 60 percent. One concern about these simulations is that with the inflow rate already at very low levels, it may not fall as implied in the simulation. However, even if the inflow rate stays at its current level of 2.3 percent, the outflow rate would only have to rise to 37 percent for the unemployment rate to be at 6 percent by the end of 2014.
What conclusions should we take from this analysis of the bathtub model? First, the future path of the unemployment rate will be determined primarily by movements in the outflow rate. Second, flow dynamics suggest further declines in the unemployment rate. That is because even modest increases in the outflow rate can lead to significant declines in the unemployment rate as long as there is not a big negative shock that triggers a new wave of job losses. Finally, the unemployment rate can decline regardless of whether workers find jobs or leave the labor force, and thus can fall even in the absence of improved job-finding prospects. In fact, as seen in the last chart, labor market exit has been an important factor in recent movements of the unemployment rate. We will discuss the importance of participation in Friday's post.
*Christina Patterson is a research associate in the Research and Statistics Group.
The views expressed in this blog are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System. Any errors or omissions are the responsibility of the authors.