Keywords:
Abstract:
JEL Classification Code: E3
Five years after the end of the Great Recession, the rate of long-term unemployment in the United State has remained relatively elevated, while the rate of short-term unemployment has returned to a level close to historical norms. At the same time, inflation, while low, has not fallen as much as some observers expected in the aftermath of the Great Recession (e.g., Ball and Mazumder (2011)). 1 Moreover, theoretical considerations raise the possibility that short- and long-term unemployment exert different pressure on prices: For example, workers that are unemployed for long periods may become disconnected from the labor market (due, for example, to`hysteresis-type effects) or ranking practices may imply that the recently unemployed are the ``marginal'' influence on wage pressures (e.g., Blanchard and Summers (1988), Layard, Nickells, and Jackman (1991) or Blanchard and Diamond (1994)). These considerations have raised the question of whether the long-term unemployed exert less downward pressure on prices. Such questions are highly relevant in policy discussions following the Great Recession (e.g., Economic Report of the President (2014), pages 81-83). However, empirical evidence, based on estimation of Phillips curves for U.S. national data, is mixed.
The standard approach using national inflation and unemployment data faces considerable empirical challenges. In particular, rates of short- and long-term unemployment are highly correlated in U.S. data, making inference difficult in short samples. (That is, the regressors suffer from the problem of ``multicollinearity''.) We will illustrate that this empirical problem is very clear when estimating a simple Phillips curve in U.S. data, where coefficients on short- and long-term unemployment rates are very imprecisely estimated, but are jointly highly statistically significant.
However, these challenges can be overcome by bringing more data to bear on the question. As the recent policy debate does not have the luxury of waiting for more years of data to accumulate, we turn to an additional source of data: Regional variation.2 Specifically, we consider the links between inflation and various measures of unemployment across U.S. regions (as well as with national rates of unemployment) over the last 30 years. This approach yields much more precise parameter estimates. We estimate the influence of short- and long-term unemployment on inflation rather precisely (compared to earlier studies) and find no evidence that long-term unemployment exerts less pressure on prices than short-term unemployment.
The next section presents information on U.S. (national) data and estimates national-level Phillips curves, illustrating the empirical challenges associated with discriminating between the effects on inflation of short- and long-term unemployment. Section 3 presents a model to highlight the small-sample issue and how regional variation may yield more precise parameter estimates. Section 4 presents the results using U.S. metropolitan area data and section 5 concludes.
Figure 1 presents the evolution of the national unemployment rate, the rate of short-term unemployment, and the rate of long-term unemployment (where the cutoff between short- and long-term unemployment is set at 27 weeks); we focus on annual data. Short- and long-term unemployment are highly correlated. Since 2009, there has been some divergence. Notably, short-term unemployment fell to near its average level over this period by 2013, while long-term unemployment remained elevated.
To examine the inflationary pressure from unemployment rates, a
simple Phillips curve is specified, in which inflation (
) depends on its own lag and rates of unemployment (with the
rates of total, short- and long-term unemployment denoted by
,
,
, respectively):
We estimate this equation for the period from 1985 to 2013 and the
more recent period from 1998 to 2013 using annual data. We focus on
the recent period for estimation because of evidence that the nature
of the Phillips curve was importantly different over this period,
reflecting increased anchoring of inflation expectations (e.g.,
Williams (2006), Kiley (2007), and Boivin, Kiley, and Mishkin
(2010)). In our empirical specification, we allow inflation
expectations (
) to be a function of a constant and the
measure of expected inflation over the next 10 years from the Survey
of Professional Forecasters for the 1985 to 2013 period. As the
survey measure of expected inflation is essentially constant after
1998, expected inflation is proxied by the constant term in the 1998
to 2013 sample. We use the Consumer Price Index (excluding food and
energy) as our price measure.
Unemployment Measure | 1985-2013 Total | 1998-2013 Total | 1985-2013 Short | 1998-2013 Short | 1985-2013 Long | 1998-2013 Long | 1985-2013 Short and Long | 1998-2013 Short and Long |
a | 0.52 | 0.52 | 0.51 | 0.52 | ||||
a std error | (0.23) | (0.22) | (0.23) | (0.23) | ||||
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0.50 | 0.14 | 0.61 | 0.35 | 0.44 | 0.04 | 0.59 | 0.15 |
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(0.17) | (0.21) | (0.17) | (0.12) | (0.19) | (0.16) | (0.23) | (0.18) |
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-0.11 | -0.16 | -0.28 | -0.34 | na | na | -0.24 | -0.17 |
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(0.05) | (0.05) | (0.11) | (0.12) | (0.21) | (0.20) | ||
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-0.11 | -0.16 | na | na | -0.17 | -0.24 | -0.03 | -0.14 |
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(0.05) | (0.05) | (0.08) | (0.08) | (0.15) | (0.15) | ||
Wald test (p-value)
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0.03 | 0.01 | 0.02 | 0.01 | 0.04 | 0.01 | 0.05 | 0.01 |
Wald test (p-value)
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na | na | na | na | na | na | 0.54 | 0.92 |
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0.69 | 0.57 | 0.69 | 0.53 | 0.68 | 0.54 | 0.69 | 0.57 |
Results are reported in table 1. We consider a range of
cases: The first two columns report the case using the total
unemployment rate (i.e.,
); columns 3 and 4
report the case using only short-term unemployment (
),
while columns 5 and 6 report the case using only long-term
unemployment (
). Finally, the last two columns allow
for separate influences from short- and long-term unemployment.
A few results are clear. First, some type of Phillips curve
relationship is present in the data, as all of the specifications
with only one measure of unemployment show statistically significant
coefficients on the unemployment measure (with the reported standard
errors yielding t-statistics around 3 in all cases). In addition,
all of the equations fit quite similarly - as can be seen both in
the similarity of coefficients and standard errors, and (more
directly) in the
statistics. Finally, consistent with Williams
(2006), inertia is reduced in the most recent (1998-2013) period in
each specification. Note that this finding suggests the focus on
accelerationist specifications, in which the lag on inflation (or
sum of lags) is restricted to enter with a coefficient of unity,
is misplaced.
Several recent analyses have discussed the possible separate roles of short-term and long-term unemployment. Ball and Mazumder (2011) speculate that the differential behavior of short- and long-term unemployment after 2009 may allow for separate consideration of these factors as more data accumulate (and our model/Monte Carlo simulations in the next section will examine this conjecture). Building on this idea, Stock (2011), Gordon (2013), Watson (2014), and Linder, Peach, and Rich (2014) each estimate Phillips curves similar to those in the first four columns - that is, curves with either total unemployment or short-term unemployment, but not both short-term and long-term unemployment. An important difference is that these previous analyses emphasize and ``accelerationist'' form of the Phillips curve, in which high unemployment results in continuously falling inflation; in contrast, our analysis builds on Williams (2006) and Kiley (2007), who document how anchored expectations since the Volcker disinflation imply that high levels of economic slack result in below average. but not continuously decelerating, inflation. (This distinction is important in evaluating the claims of ``missing disinflation'' that follow the approach of Ball and Mazumder (2011). For example, this is the evidence emphasized in Gordon (2013) or Linder, Peach, and Rich (2014) or Krueger, Cramer, and Cho (2014).)
The reason previous analyses have taken the approach of looking at either short- or long-term unemployment, but not both, is clear in the last two columns: The coefficients on short- and long-term unemployment are very imprecisely estimated when each measure is allowed to enter. However, these coefficients are jointly highly significant in the statistical sense (as indicated by the p-value associated with the Wald test for the exclusion of these variables). Finally, due to the lack of precision, the Wald test for the equality of the coefficients on short- and long-term unemployment cannot reject this hypothesis - but this result is hardly dispositive on the issue, as the balance of results points to problems distinguishing the roles of short- and long-term unemployment in inflationary pressure. The next section highlights these problems and a possible solution.
We now provide an illustration of the problem and our approach to resolving these difficulties.
We start by observing, as in Fitzgerald, Holtemeyer, and Nicolini
(2013), that the United States is composed of many regions, and it
is plausible to consider Phillips curves at the regional level. On
its face, this is not controversial - the world economy consists of
many regions and economists estimates Phillips curves for individual
regions, even across regions sharing a common currency (e.g., the
Euro area). More fundamentally, labor markets may be somewhat
localized, implying that regional labor market conditions may affect
costs (and hence prices) within a region. In addition, non-traded
goods and services may reflect resource utilization pressures within
their regions. With these thoughts in mind, we suppose that price
inflation in region
(
) is a related to regional
and national factors in much the same way as assumed above:
To demonstrate the challenges that arise using national data, we use a Monte Carlo approach. Specifically, we parameterize equation 2, simulate data from this parameterization, and then estimate Phillips curves using national and regional data.
Our simulations assume symmetric regions. Focusing on the Phillips
curve, we assume that inflation expectations are anchored (at a
constant level), that inertia is local (with
and
), and that short- and long-term unemployment enter the
Phillips curve with equal coefficients and that these effects are
local (with
and
). Finally, we assume that the errors in the
Phillips curve have a standard deviation of 1 and that the
correlation between regions is 0.2.
For unemployment, we assume regional short- and long-term unemployment rates are the sum of a common and regional factor, both of which are auto-correlated. The common unemployment factor is an AR(2) process (where the coefficient on the first lag is 1.1 and that on the second is -0.5) whose innovation standard error is 0.4 percent. The regional factors for short-term and long-term unemployment are independent (within and across regions); this implies that the correlations between short- and long-term unemployment within and across regions are due to the common factor. The regional factors are AR(1) processes with a lag coefficient of 0.9 and an innovation standard error of 0.237.
(More details on the simulated model are provided in an appendix.)
This calibration roughly matches features of U.S. data for CPI inflation and unemployment across the regions we use in our empirical analysis. In particular, we examine 24 large metropolitan areas in the United States for which we could gather the Consumer Price Index and measures of unemployment over the 1985 to 2013 period.3 Our panel of regions contains 24 regions over 29 years; however, there are missing observations for certain regions at the beginning and end of the time period under study, so our panel is unbalanced. An appendix presents more information on the data used in this study.
Consumer Price Index (excluding food and energy), Data, National | Consumer Price Index (excluding food and energy), Data, Regional | Consumer Price Index (excluding food and energy), Data | Consumer Price Index (excluding food and energy), Simulated, National | Consumer Price Index (excluding food and energy), Simulated, Regional | Consumer Price Index (excluding food and energy), Simulated | Unemployment, Total, Data, National | Unemployment, Total, Data, Regional | Unemployment, Total, Data | Unemployment, Total, Simulated, National | Unemployment, Total, Simulated, Regional | Unemployment, Total, Simulated | Unemployment, Short-term, Data, National | Unemployment, Short-term, Data, Regional | Unemployment, Short-term, Data | Unemployment, Short-term, Simulated, National | Unemployment, Short-term, Simulated, Regional | Unemployment, Short-term, Simulated | Unemployment, Long-term, Data, National | Unemployment, Long-term, Data, Regional | Unemployment, Long-term, Data | Unemployment, Long-term, Simulated, National | Unemployment, Long-term, Simulated, Regional | Unemployment, Long-term, Simulated | |
Standard Deviation | 1.1 | 1.3 | 0.8 | 1.3 | 1.5 | 1.7 | 1.4 | 1.6 | 0.8 | 1.0 | 0.7 | 0.9 | 1.0 | 1.0 | 0.7 | 0.9 | ||||||||
Autocorrelation | 0.9 | 0.7 | 0.7 | 0.6 | 0.8 | 0.8 | 0.7 | 0.8 | 0.7 | 0.7 | 0.7 | 0.8 | 0.8 | 0.8 | 0.7 | 0.8 | ||||||||
Average pairwise correlation across regions | 0.3 | 0.3 | 0.6 | 0.8 | 0.5 | 0.6 | 0.8 | 0.6 |
Table 2 presents some summary statistics for the U.S. data and from our parameterization of the model. The simulated data has the key characteristics to U.S. data. The volatility of inflation and unemployment measures is similar to that of the data, as are the autocorrelations. (Although national inflation is somewhat less auto-correlated in the simulated data than over the 1985-2013 sample, this reflects the fact that inflation was higher in the early half of this period, and the autocorrelation of inflation is much lower in recent years; our calibration balances these considerations.) Inflation is modestly correlated across metropolitan areas; unemployment measures are more strongly correlated across metropolitan regions.
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|
Results for estimates of the effects of short- and long-term unemployment on inflation using simulated national data are reported in figure 2: This panel reports the empirical densities of coefficients on short- and long-term unemployment, along with those estimated when one imposes that the coefficients on these measures are equal (i.e., the total unemployment case). The top panel assumes a sample period of 20 years, the middle panel a sample period of 50 years, and the bottom panel a sample of 100 years. The thin blue (solid) and red (dashed) lines report the simulated density function for short- and long-term unemployment coefficients, respectively. (Note that these coefficients should be identical as the simulated data generating process is symmetric in these factors; the lines are very similar. indicating that our simulations are fairly accurate; the overlap of the lines makes it difficult to see the individual lines for coefficients on short- and long-term unemployment). The thin black (dashed) line reports the results for the national unemployment rate. Each coefficient is centered around 0.25, as it should be. The coefficients on short-term and long-term unemployment are very imprecisely estimated, even with 100 years of data (while the total unemployment measure estimates are more precisely estimated). Note that this result contradicts the conjecture of Ball and Mazumder (2013), who speculated that a few more years of data would provide clearer evidence of the effects of short- and long-term unemployment on inflation. According to this analysis, a great deal more data would need to accumulate before precise estimates of the effects of short- and long-term unemployment could be estimated with any precision.
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|
We now turn to an empirical analysis of U.S. regional data. As mentioned before, We examine 24 large metropolitan areas for the United States.
We estimate equation 2 over two sample periods (as in our national estimates), 1985-2013 and 1998-2013. For the 1985-2013 sample, we proxy expected inflation with a region-specific intercept and the national measure of long-run expected inflation from the Survey of Professional forecasters used in our national regression; for the 1998-2013 sample, region fixed effects are used to proxy for expected inflation (because, as in the national regressions presented earlier, the survey measure of expected inflation is essentially constant over the 1998-2013 period). Note that these regional fixed effects will also account for regional differences in the average level of the measures of unemployment. (We do not impose any structure that would allow us to disentangle estimates of expected inflation and the natural rate of unemployment).4 Finally, we also consider a specification with fixed time-period effects, which eliminates the ability of the specification to identify the coefficients on the national rates of the survey measure of inflation expectations, lagged inflation, and the unemployment measures, but controls for the possibility of omitted (time- varying) national factors.
Table 3 presents results. The first two columns repeat the results estimated using national data (reported previously in table 1). The middle columns present the estimates without time-period fixed effects, and the last two columns report results with the time-period fixed effects.
1985-2013 National | 1998-2013 National | 1985-2013 Metropolitan | 1998-2013 Metropolitan | 1985-2013 Metropolitan | 1998-2013 Metropolitan | |
a | 0.52 | 0.42 | na | na | ||
a std error | (0.23) | (0.22) | ||||
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0.43 | 0.42 | 0.44 | 0.15 | ||
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(0.23) | (0.09) | (0.05) | (0.28) | ||
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0.59 | 0.15 | 0.25 | -0.18 | na | na |
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(0.23) | (0.28) | (0.22) | (0.27) | ||
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-0.21 | -0.17 | -0.22 | -0.17 | ||
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(0.05) | (0.09) | (0.05) | (0.15) | ||
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-0.27 | -0.29 | -0.27 | -0.14 | ||
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(0.07) | (0.09) | (0.07) | (0.15) | ||
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-0.24 | -0.17 | -0.14 | -0.13 | na | na |
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(0.21) | (0.20) | (0.21) | (0.25) | ||
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-0.03 | -0.14 | 0.29 | 0.20 | na | na |
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(0.15) | (0.15) | (0.17) | (0.18) | ||
Wald test (p-value),
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0.05 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
Wald test (p-value),
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0.54 | 0.92 | 0.28 | 0.54 | 0.57 | 0.46 |
Wald test (p-value),
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0.11 | 0.47 | na | na | ||
Regional fixed effects | No | No | Yes | Yes | Yes | Yes |
Time-period fixed effects | No | No | No | No | Yes | Yes |
Several results are apparent. First, the Phillips curve is very
strong across metropolitan areas, with the null hypothesis of no
Phillips curve (
,
,
,
) very strongly rejected. Second, the coefficients on
metropolitan (local) unemployment rates are estimated precisely at
around
(with, for example, t-statistics around 4 typical for
and
). Third, these local factors are much
more important than the national rates of unemployment (where the
Wald test does not reject the hypothesis that national unemployment
rates should be excluded (
and
), as
reported in the last row containing Wald tests). Note this also
implies that the last two columns with fixed regional and
time-period effects (and therefore which control for national
conditions not included) provide a good gauge of the effect of
unemployment rates on inflation.
Finally, it is notable that the coefficients on local unemployment rates are precisely estimated and very similar, and the data do not reject the hypothesis that short- and long-term unemployment rates have similar effects on inflation. The national results on this issue were very imprecise because of the correlation between short- and long-term unemployment. As suggested by our model and simulation results, this difficulty can be overcome by examining regional data.
The elevated rate of long-term unemployment following the Great Recession has re-kindled interest in the question of whether long-term unemployment exerts similar effects on price inflation as short-term unemployment in the United States. Because short- and long-term unemployment rates are highly correlated in the United States, it has been difficult to answer this question.
We show, with a simple model and set of Monte Carlo exercises. that this difficulty is predictable given the sample sizes typically available using national data and that regional variation may help inference. We then exploit data on U.S. metropolitan regions to estimate the effects of short- and long-term unemployment on inflation. The results suggest that long-term unemployment has exerted similar downward pressure on inflation to that exerted by short-term unemployment in recent decades.
Finally, our analysis has highlighted how regional data can shed light on important questions facing the macroeconomy.5
We use the following data for the United States (sources in parentheses):
All data are annual (e.g., averages of underlying monthly or quarterly data).
We use the same CPI series for the metropolitan regions. We create metropolitan estimates of our unemployment series using the Current Population Survey. (In this case, short-term unemployment is defined as less than 27 weeks, as in the national data.)
The metropolitan areas we consider are New York-Northern New Jersey-Long Island, Philadelphia-Wilmington-Atlantic City,Boston-Brockton-Nashua, Pittsburgh, Chicago-Gary-Kenosha, Detroit-Ann Arbor-Flint, St. Louis, Cleveland-Akron, Minneapolis-St. Paul, Milwaukee-Racine, Cincinnati-Hamilton, Kansas City, Washington-Baltimore, Dallas-Fort Worth, Houston-Galveston-Brazoria, Atlanta, Miami-Fort Lauderdale, Los Angeles-Riverside-Orange County, San Francisco-Oakland-San Jose, Seattle-Tacoma-Bremerton, San Diego, Portland-Salem, Honolulu, and Denver-Boulder-Greeley.
The equations for the simulated model are presented in this appendix.
We assume 20 regions. Total unemployment in each region i is the sum
of short- and long-term unemployment in each region (
). The process for short-term unemployment reflects an aggregate
(
)
and region specific (
) factor,
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The process for inflation is governed by a simple Phillips curve in each region
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