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November 10, 2015

Explaining Low Inflation: Model-Based
Decomposition
Saeed Zaman

After falling below 2 percent in early 2012, inflation as
measured by the price index for personal consumption
expenditures (PCE) has averaged 1.2 percent on a
four-quarter trailing basis. Over the last four quarters,
PCE inflation has been just 0.3 percent. A number
of analysts have attributed much of the weakness
in inflation to a sharp decline in energy prices and
a strengthening of the dollar. But inflation excluding
volatile food and energy components (core PCE) has
also been running quite low, averaging 1.5 percent
over the last four years and 1.3 percent over the last
year. These readings are significantly below the Federal Open Market Committee’s (FOMC) long-run goal
of 2 percent for PCE inflation.
In this article I use a statistical forecasting model—
called a Bayesian vector autoregression or BVAR—to
explain the factors responsible for the stubbornly low
levels of core inflation over the past four years. The
model-based decomposition allows us to see the contribution of the different factors. I focus on core inflation to abstract from temporary variations in the PCE
that may arise due to volatile food and energy prices.
The model characterizes the relationship between
core inflation and the factors that have been shown to
have some influence on core inflation, such as labor
costs, energy prices, the exchange rate, labor market
indicators, economic activity, and monetary policy. The
analysis presented here extends and updates Clark
and Zaman (2013).

Figure 1. US Inflation over the Last 10 Years
Four-quarter percent change
5.0
4.5
4.0
3.5
3.0
2.5
FOMC longer-run goal
2.0
1.5
Core PCE inflation
1.0
0.5
Headline PCE inflation
0.0
-0.5
-1.0
-1.5
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Source: Bureau of Economic Analysis; PCE (Personal Consumption Expenditures Price Index),
Core PCE (PCE excluding food and energy components)

From late 2012 to mid-2013, the factors contributing to
low inflation were a weaker-than-expected recovery in
the labor markets and weaker-than-expected energy
prices. Thereafter, the labor market recovered more
rapidly than expected, which put upward pressure on
core inflation. However, over the past year, the sharp
decline in energy prices and the stronger dollar have
exerted significant downward pressure on core inflation, equal to about a 0.9 percentage point drag on
average, which has more than offset the upward pressure coming from improving labor markets.
Figure 2. Baseline Forecast of Core PCE Inflation

We begin by estimating the model using data from
1967:Q2 to 2012:Q1 to forecast core PCE inflation
from 2012:Q2 to 2015:Q3 (the period characterized
by low inflation). We stop at 2012:Q1, because that
is when core PCE inflation peaked. The figure below
shows the core inflation forecast (i.e. the model’s
projection of the most likely path of inflation over the
forecast period), along with the 70 percent confidence
bands to characterize the normal level of uncertainty
around the forecast. Also plotted in the figure is the
path that inflation actually followed.
The baseline projection of core inflation very gradually
moves up, crossing 1.9 percent by 2015:Q3. Although
the baseline forecast tracked the path of actual inflation quite well up through the first quarter of 2013:Q1,
from then on it generally came in above it. The unexpected falloffs in 2012:Q3, 2013:Q2, the second half
of 2014, and 2015: Q1 were of sizable magnitude, but
they were not very big in a historical sense, because
those readings were within the model’s forecasted 70
percent confidence bands.
It is important to recognize that the baseline forecast
of core inflation depends on the forecasts of the other
variables in the model. By examining the various
shocks that have affected inflation and some of its
key determinants, it is possible to identify the potential
source of differences between the original forecast
and actual inflation.
Accordingly, we next generate a conditional forecast
of core PCE inflation. This forecast is conditioned on
the actual evolution of all the model’s variables except core inflation over the forecast period 2012:Q2 to
2015:Q3. The conditional forecast of core PCE inflation closely tracks the actual evolution of core PCE
inflation, suggesting that most of the falloff of core
inflation that occurred over the 2012:Q2 to 2015:Q3
period could be explained by movements in the other
variables of the model, that is, by unexpected developments in the determinants of inflation.

Quarterly percent annualized
4.0
3.5

70% probability
band

3.0
2.5

Baseline forecast
of core PCE inflation
Actual core PCE
inflation (data)

2.0
1.5
1.0
0.5
0.0
2011

2012

2013

2014

2015

Note: Estimated through 2012:Q1.
Source: Bureau of Economic Analysis; author’s calculations.

Figure 3. Conditional Forecast of Core PCE Inflation
Quarterly percent annualized
4.0
3.5

70% probability band

3.0
2.5
Baseline forecast of
core PCE inflation

2.0
1.5

Core PCE inflation (data)
Conditional forecast of
core PCE inflation

1.0
0.5
0.0
2011

2012

2013

2014

Note: Estimated through 2012:Q1.
Source: Bureau of Economic Analysis; author’s calculations.

2015

Next we decompose which specific realized developments in the economy, as captured by the model’s
variables, have driven inflation lower. Specifically, we
use our forecasting model to identify the unique contributions of each variable to the unexpected realized
path of core PCE inflation from 2012:Q2 to 2015:Q3.
From the second half of 2014 to 2015:Q1, energy prices declined by 20 percent. (Alternatively, the cumulative decline was 80 percent on an annualized basis
over the three quarters). At the same time, the US
nominal broad dollar rose by 12 percent. The model
posits that these two disinflationary developments
generated a significant falloff in core inflation. The
forecast path that takes into account the evolution of
both energy prices and exchange rate (i.e., the baseline forecast into which only the information on the
evolution of energy prices and the exchange rate is
incorporated) generally does a decent job of tracking
the actual evolution of core inflation. Throughout the
forecast period, the actual evolution of energy prices
turned out to be below the model’s expectations, and
so these misses acted as a dampening force on core
inflation.
The exchange rate for most of the period under
analysis played a marginal role in applying downward
pressure on core inflation until third quarter of 2014.
Thereafter, it has been acting to push core inflation
significantly lower as evidenced by the forecast path
with exchange rate developments lying well below the
baseline forecast.
One unusual feature of this economic recovery is that
labor market slack has been diminishing much more
rapidly (especially over the past two years or so) than
in previous recoveries, despite very modest growth
in real GDP. Over the past four years, the unemployment rate has declined from 8.2 percent to 5.1 percent, while GDP growth has averaged just 2 percent
over this period. Not surprisingly, the model’s forecast
for real GDP growth made using data up to 2012:Q1
is generally higher than the actual path, which has
weighed on core inflation. This is evidenced by the
forecast path for core inflation that incorporates the
evolution of real GDP growth mostly falling below the
baseline forecast (with the exception of three quarters
in 2013).
On the other hand, the model’s expectations for labor
market variables have been worse than what actually
transpired over the last two years—lower for payroll
employment and labor costs, higher for the unem-

Figure 4. Core PCE Inflation Forecast Decomposition
Quarterly percent annualized
3.0
2.8
2.5
2.3
2.0

Baseline forecast
Forecast path with
exchange rate shocks only
Forecast path with
energy shocks only
Actual core PCE inflation (data)
Forecast path with both energy
and exchange rate shocks only

1.8
1.5
1.3
1.0
0.8
0.5
6/2012 12/2012

6/2013 12/2013

6/2014 12/2014

6/2015

Note: Estimated through 2012:Q1.
Source: Bureau of Economic Analysis; author’s calculations

Figure 5. Core PCE Inflation Forecast Decomposition
Quarterly percent annualized
3.0
2.8
2.5
Forecast path with
labor market shocks only

2.3
2.0

Baseline forecast
Forecast path with
GDP shocks only
Actual core PCE
inflation (data)

1.8
1.5
1.3
1.0
0.8
0.5
6/2012 12/2012

6/2013 12/2013

6/2014 12/2014

Note: Estimated through 2012:Q1.
Source: Bureau of Economic Analysis; author’s calculations.

6/2015

ployment rate. As a result, the rapid improvement in
the labor markets has been putting upward pressure
on core inflation as evidenced by the forecast path
with labor market developments lying well above the
baseline forecast over the last two years or so. This
is in contrast to 2012 and early 2013 when the unemployment rate declined slowly relative to the model’s
expectations and the growth rate of labor costs came
in well below expectations. Not surprisingly, from 2012
to the first half of 2013, developments in the labor
markets exerted sizable downward pressure on core
inflation.
Thus, over the last two years the downward pressure
from underperforming real GDP growth has been
more than offset by upward pressure from the rapid
recovery in labor markets, resulting in small upward
pressure on core inflation.
Lastly, to get a sense of this model’s projection for
core inflation going forward, we use the model to
generate a forecast of core inflation over the next
two years. Specifically, we estimate it with data from
1967:Q2 through 2015:Q3, to generate a forecast
trajectory of core PCE inflation from 2015:Q4 to
2017:Q4. The model projects that core PCE inflation
very gradually rises toward the FOMC’s long-term
inflation goal of 2 percent, ending 2017 at 1.8 percent.
As with any inflation forecast, there is considerable
uncertainty around this forecast, as shown by the 70
percent confidence bands.
While simple, the forecasting model used in this
analysis was able to explain most of the falloff in core
PCE inflation over the past four years as a response
to other developments in the economy. According to
the model, the sluggish pace of labor market recovery
in 2012 and 2013 had been restraining core inflation
along with lower energy prices. But over the past year
or so, the sharp falloff in energy prices and the rapid
appreciation of the nominal dollar have acted to significantly restrain core inflation, while the labor market
has been putting some upward pressure on inflation.
Historical experience suggests that the impact of both
temporary energy and dollar shocks on core inflation is usually short-lived. Therefore, to the extent we
are confident that economic activity will continue to
increase moderately and slack in labor markets will
continue to diminish, these factors should put upward
pressure on inflation during the next few years, as we
forecast inflation to rise at a very gradual pace.

Figure 6. Forecast of Core PCE Inflation Going
Forward
Quarterly percent annualized
3.5
3.0

70% probability band

2.5
2.0
1.5
1.0
0.5
0.0
3/2014 9/2014 3/2015 9/2015 3/2016 9/2016 3/2017 9/2017
Note: Estimated through 2015:Q3.
Source: Bureau of Economic Analysis; author’s calculations.

Actual core PCE
inflation (data)
Mean forecast of
core PCE inflation

Saeed Zaman is an economist in the Research Department of the Federal Reserve Bank of Cleveland. His current research focuses on
inflation measurement and forecasting, including nowcasting methods, and he contributes to the development of macroeconomic
forecasting and policy models at the bank.
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