Residual seasonality in GDP and GDI findings and next steps.
Moulton, Brent R. ; Cowan, Benjamin D.
THE BUREAU OF ECONOMIC ANALYSIS (BEA) has long adjusted its widely
followed estimates of quarterly gross domestic product (GDP) and gross
domestic income (GDI) to account for seasonality. (1) Seasonal
adjustment involves a set of statistical methods designed to remove
fluctuations that normally occur at about the same time and the same
magnitude each year. Seasonal adjustment allows for economic series that
are often easier to interpret and analyze because they are not affected
by routine seasonal patterns due to factors such as seasonal weather
patterns and holidays. Quarterly data on consumer spending, for example,
are easier to compare and analyze if the effects of the holiday shopping
season are removed.
In early 2015, several reports noted that over the last decade or
longer, first-quarter GDP has tended to grow, on average, at a slower
pace, compared with other quarters. Analysts debated the extent to which
this phenomenon reflects special factors, such as unusually harsh winter
weather, and/or "residual seasonality," that is, lingering
seasonality even though the data have already been adjusted to remove
seasonal effects. (2) BEA subsequently announced a three-phase plan for
addressing residual seasonality. (3)
In the first phase, as part of the July 2015 annual revision of the
national income and product accounts (NIPAs), BEA began seasonally
adjusting several series used to calculate GDP that exhibited
seasonality but had not previously been adjusted. These series included
several from the Census Bureau's quarterly services survey, for
example. (4)
In the second phase, BEA conducted a component-by-component review,
the results of which are reported in this paper, to identify the causes
of residual seasonality in the GDP and GDI estimates.
In the third phase, BEA plans to produce estimates of GDP and its
major components that are not seasonally adjusted. These not seasonally
adjusted estimates will be released in conjunction with BEA's
seasonally adjusted GDP estimates, beginning in mid-2018. These data
will likely prove particularly helpful in identifying and analyzing
changes in seasonal trends.
What is residual seasonality?
Seasonal adjustment refers to statistical processes aimed at
removing seasonal effects from a time series--that is, the fluctuations
that normally occur at about the same time and the same magnitude each
year. Seasonal effects are estimated using procedures that decompose
time series into seasonal, trend-cycle, and irregular components. The
seasonal adjustment procedure essentially removes the seasonal effects,
leaving the trend-cycle and irregular components. Residual seasonality
refers to the presence of lingering seasonal effects even after seasonal
adjustment processes have been applied to the data.
The detection of residual seasonality can be difficult. A time
series that has been correctly seasonally adjusted may still display
unusually high or low growth for specific quarters over particular time
spans. Even after seasonal adjustment, the irregular components of a
time series are often noisy and variable. And like any series subject to
random variation, the variations in seasonally adjusted series are not
likely to balance or fully offset across quarters. Just as it is
possible when flipping a coin to obtain four tails in five flips, it is
similarly possible that a particular quarter may exhibit below average
growth in four of the most recent five years, even if the series has
been correctly seasonally adjusted. One should not expect the growth
rates of seasonally adjusted quarters to be uniform; the question is
whether the variation exceeds what would be expected by chance over
time.
The determination of whether a series exhibits residual seasonality
thus must rely on the application of statistical tests that can analyze
the variation. These tests can be quite sensitive to the period selected
for analysis. In the case of GDP, the evidence for residual seasonality
is somewhat ambiguous, with tests finding evidence for residual
seasonality over some time spans but not others.
In the remainder of this paper, we provide the following:
* An overview of the seasonal adjustment methodologies used by BEA
in preparing the NIPAs, including GDP and GDI.
* The findings of our recent component-by-component review of
residual seasonality in the NIPAs. We identify the major reasons for
residual seasonality and detail some steps that BEA and other federal
statistical agencies may take to help resolve some of the issues.
* An update of BEA's plans for addressing residual seasonality
and a rough timetable for scheduled improvements.
Overview of NIPA Seasonal Adjustment Methodology
GDP and GDI are each calculated as aggregates of many component
series. For such aggregates, there are two potential approaches for
seasonal adjustment. In the direct approach, component series that have
not been seasonally adjusted are aggregated. After this aggregation, the
seasonal adjustment processes are applied.
In contrast, the indirect approach seasonally adjusts the component
series or uses source data that have already been seasonally adjusted.
These seasonally adjusted components are then directly aggregated to
generate seasonally adjusted aggregate series, including GDP. (5)
BEA's long-standing practice has been to produce its featured
estimates of GDP and GDI using the indirect approach.
Most of the source data that are used to estimate GDP are available
in seasonally adjusted form from source agencies. When seasonally
adjusted source data are not available, BEA generally seasonally adjusts
the source data before using them in its various estimation processes,
such as interpolation, extrapolation and commodity flow, retail control,
and perpetual inventory methods. These processes are described in
chapter 4 of Concepts and Methods of the U.S. National Income and
Product Accounts.
There are several advantages to this indirect approach.
First, because the estimates are usually based on seasonally
adjusted source data, the effects of such source data on the NIPA
estimates are more transparent and intuitive to data users. For example,
BEA sometimes lacks source data in making its earliest estimate of
quarterly GDP (the "advance" estimate, which is published
about a month after the end of a quarter). To account for this missing
data, BEA makes various assumptions. When the seasonally adjusted source
data subsequently become available from the source agency, data users
can quickly infer the impact on GDP without concerns about the effect of
seasonal adjustment. In addition, the indirect approach makes it easier
to establish trends necessary to estimate components for which monthly
or quarterly source data are lacking.
Second, the consistent use of seasonally adjusted source data makes
it easier for BEA's staff to review and spot anomalies in comparing
the NIPA estimates with the source data.
Third, BEA publishes many useful GDP measures beyond nominal GDP;
"contributions to percent change" and "chained"
index values are among the most widely used. Because these measures are
derived from seasonally adjusted components, they remain generally
consistent with one another. If the estimates were directly seasonally
adjusted only at the end of the estimation and aggregation process
(direct method), such consistency would be lacking. Indeed, under the
direct approach, the seasonally adjusted component series generally
would not add up to the seasonally adjusted aggregates, even when
measured in current dollars.
There are also some disadvantages to the indirect approach to
seasonal adjustment.
Notably, because GDP is not directly adjusted as a single data
series at the end of the estimation process, it is possible that the
indirect approach can allow some residual seasonality to seep into the
aggregates. And because the seasonal adjustments take place at the
beginning of the estimation process at the source data level, the effect
of seasonal adjustment on the main aggregates can be relatively opaque
for researchers.
As part of its three-phase strategy noted above, BEA intends to
produce and publish estimates of GDP and GDI that are not seasonally
adjusted to foster even greater transparency and allow for heightened
analysis of the effects of seasonal adjustment. (6)
Component Review of Residual Seasonality
A team of BEA analysts conducted a component-by-component
investigation of residual seasonality within quarterly GDP and GDI
estimates. (7) This review represents phase 2 of BEA's three-phase
strategy for grappling with residual seasonality.
Objectives
The goal of the component-by-component review was to identify and
investigate instances of residual seasonality, to determine the causes,
and to propose solutions. The team sought to uncover broad cases of
residual seasonality that might be addressed in a systematic fashion
rather than with ad hoc fixes.
Methodology
Because BEA derives its seasonally adjusted estimates of GDP and
GDI using an indirect, or "bottom-up," approach, the team
focused on the most finely detailed series contributing to those
aggregates. The investigation ultimately examined approximately 2,000
nominal data series. For the GDP estimates, price and quantity measures
were examined for each of these series as well as nominal estimates. For
GDI, separate price and quantity estimates are not available for the
detailed component series. Instead, real GDI is derived by deflating
nominal GDI using the GDP price index.
The Census Bureau's widely used X-12 ARIMA seasonal adjustment
program was applied to the seasonally adjusted NIPA series to test for
residual seasonality. (8) Because of the large number of series
involved, simplified criteria were used to standardize and automate the
process. (9) Seasonal adjustment tests were applied on several data
ranges, focusing especially on 10-year, 15-year, and 30-year ranges
(2006-2015, 2001-2015, and 1986-2015, respectively). Several other
timespans were also examined (for example, a 5-year range was calculated
to investigate the effects of the recent availability of data from the
quarterly services survey). In general, results of residual seasonality
tests were often quite sensitive to the period selected for analysis,
especially for series, such as real GDP, that yield test statistics
quite close to the critical threshold values.
Results
Table 1 presents the results of tests for residual seasonality for
the major aggregates of real GDP and its price index. The results
indicate that (1) real GDP exhibits residual seasonality when tested
over either a 10-year or a 30-year time span, (2) the GDP price index
exhibits residual seasonality over the 30-year time span, and (3)several
real GDP components--such as nonresidential structures, exports of
goods, federal government spending (especially defense spending), and
state and local government spending--exhibit residual seasonality over
various time spans.
Table 2 presents tests for residual seasonality in current-dollar
GDI and its components. (10) GDI does not exhibit residual seasonality
over any of the time periods. The only major components exhibiting
significant residual seasonality are "net interest and
miscellaneous payments" and "current surplus of government
enterprises," which exhibit residual seasonality over some periods.
Within the major components, some more detailed GDI components not shown
in the table also exhibited residual seasonality.
These results, along with the team's analysis of the more
detailed deflation-level components, will guide BEA's efforts in
addressing residual seasonality moving forward.
Detailed series exhibiting residual seasonality were flagged for
further examination. For each flagged series, team members worked with
the BEA analysts to determine the specific cause of the residual
seasonality. This effort allowed the team to identify broad categories
of causes of residual seasonality.
Causes of residual seasonality
The team identified two main categories of factors that caused
residual seasonality. The most pervasive problem involved the manner in
which monthly frequency source data are treated in the derivation of
quarterly NIPA estimates. In the most common case, the monthly data are
tested for seasonality (either by BEA or by the source data agency) with
the conclusion that the monthly series does not exhibit seasonality.
However, when the data are aggregated to a quarterly frequency for use
in preparing the NIPA estimates, the resultant series exhibits
seasonality that was not detected at a monthly frequency. A somewhat
less common variant of this problem is that a series may be seasonally
adjusted at a monthly frequency, but when the seasonally adjusted
monthly series is aggregated to a quarterly frequency, the resultant
series still exhibits significant seasonality. The solution to this
problem will involve testing all monthly source data series for
seasonality at both monthly and quarterly frequencies. BEA will also
communicate and cooperate with source data agencies to attempt to
harmonize seasonal adjustment processes by applying consistent seasonal
adjustment criteria across agencies. The development of optimal criteria
for seasonal adjustment of data that are used at both monthly and
quarterly frequencies is also a subject for research.
Another source of residual seasonality arises when seasonal
adjustment is not applied consistently over time due to limitations on
the number of years that are open to revision. This problem can reflect
either BEA's own revision policies or the policies of the source
data agency. For example, in the 2015 NIPA annual revision, BEA
seasonally adjusted several series that had recently begun exhibiting
seasonality, but carried those revisions back for only 3 years. Residual
seasonality can still be detected in a test of those series over a
10-year span because the earlier years have not yet been seasonally
adjusted. Another example is the revision policy for the Census
Bureau's survey of value of construction put-in-place. The revision
policy for this survey is to revise monthly estimates for only the
previous 2 years, even though the seasonal adjustment procedure is
performed over a longer time span. In both cases, the published series
did not reflect consistent seasonal adjustment. Rather, the series was
essentially spliced together based on the revision policy for the
statistical product.
The most straightforward method for resolving this problem is to
modify the revision policies of BEA and, to the extent possible, of the
source data agencies to allow for consistent and complete seasonal
adjustment. That change will require longer time periods to be opened
for revision to incorporate revised seasonal adjustments and to reflect
changes to the seasonal status of component series. For example, each
year the current employment statistics from the Bureau of Labor
Statistics typically allow for revisions over the most recent 5-year
period to capture revisions to the seasonal adjustment factors. Five
years is probably the minimum period over which data should be revised
so that the published seasonally adjusted estimates maintain consistency
with estimates derived from the most recent seasonal adjustment
procedures.
The review also found that other, less common factors can
contribute to residual seasonality in some cases.
BEA has, by convention, intentionally avoided seasonally adjusting
certain series related to government policy in order to make the effects
of policy changes more transparent to users. For example, for federal
government employees, a general pay raise is often scheduled to take
place in January. The NIPA estimates show these pay increases as step
increases in nominal government wages and salaries in the first quarter.
Thus, these federal pay increases are reflected without seasonal
adjustment in nominal GDP and in the GDP price index and are potentially
a source of residual seasonality for the affected series. A potential
solution would be for BEA to start seasonally adjusting these series,
recognizing that such a change in estimation methods may make it more
difficult for interested users to detect easily the effects of policy
changes in the relevant data series. This problem may be ameliorated by
BEA's plan to begin publishing not seasonally adjusted estimates
concurrently with seasonally adjusted estimates.
Residual seasonality can occur when seasonally adjusted source data
are used as inputs into an estimation process that involves additional
estimation steps--such as aggregation, interpolation, or deflation. This
can result in residual seasonality, despite a lack of seasonality in the
source data. BEA can address this problem by regularly testing estimates
for residual seasonality even when seasonally adjusted source data are
used. In some cases, modifications to the estimation process may need to
be considered, for example, applying seasonal adjustment later in the
estimation process. In addition, if the input data include both
seasonally adjusted and unadjusted source data, it may be necessary to
modify the criteria for determining whether the input series is
seasonal.
BEA's Updated Plan for Addressing Residual Seasonality
BEA will continue to move forward with its three-phase
comprehensive strategy to improve its seasonal adjustment techniques.
The first phase of that strategy was completed in the July 2015 annual
revision.
In this report, we have embarked on the second phase of this
strategy by describing the results of the component-by-component review
of the GDP and GDI estimates and the main sources of residual
seasonality. The second phase will include additional steps:
* BEA will use the results of the component-by-component review to
identify and implement improvements to seasonal adjustment in the
upcoming 2016 annual revision of the NIPAs. For example, BEA may begin
seasonally adjusting certain series that exhibit seasonality at a
quarterly frequency but not at a monthly frequency. The 2016 annual
revision will also include the regular updating of seasonal factors for
the period open to revision--the most recent 3 years, 2013 through 2015
as well as the first quarter of 2016.
* BEA will communicate the findings of this component-by-component
review to the Census Bureau and to other source data agencies. BEA will
work with these agencies to implement strategies for removing residual
seasonality in source data. In particular, BEA will take advantage of
new research results from the Census Bureau and new diagnostics
available in the updated X-13 program.
* BEA will review and modify its own revision policies, and it will
work with other agencies to develop revision policies that will allow
longer time periods for revision to reflect updated seasonal adjustments
in published estimates.
BEA will introduce revisions to the historical time series to
remove any remaining residual seasonality as part of the 2018
comprehensive revision of the NIPAs. The third phase in BEA's
strategy is to develop methods and procedures for compiling estimates
for GDP and its major components that are not seasonally adjusted. These
estimates will be released concurrently with BEA's seasonally
adjusted GDP estimates and could be particularly useful to identify
changes in seasonal trends over time. These estimates will allow users
to isolate data revisions more distinctly from revisions to seasonal
factors. The expected completion date for this project and publishing
the not-seasonally-adjusted estimates is also July 2018.
By Brent R. Moulton and Benjamin D. Cowan
Summary
This paper presents the results of a component-by-component review
of seasonally adjusted estimates of gross domestic product (GDP) and
gross domestic income (GDI), two widely followed economic measures
published by the Bureau of Economic Analysis (BEA). The goal of the
review was to test specific components for "residual
seasonality" and, if present, to identify the main causes. The
review found that the two most important causes of residual seasonality
were (1) inconsistencies arising from the manner in which monthly source
data are utilized in the compilation of quarterly GDP estimates and (2)
issues arising from revision policies and practices that prevented the
most recent seasonal adjustments from being applied to historical time
series. This paper also discusses BEA's on-going three-phase
strategy to improve its seasonal adjustment methods. The strategy, which
was announced in the June 2015 SURVEY OF CURRENT BUSINESS, includes this
review as well as a plan to release GDP and GDI estimates that are not
seasonally adjusted. Such estimates will provide a valuable reference
point when assessing the seasonally adjusted estimates. The three-phase
strategy is scheduled to conclude in July 2018.
(1.) GDI is calculated as the sum of the costs incurred and the
incomes earned in the production of GDP. In theory, GDI should equal
GDP, but in practice they differ because their components are estimated
using largely independent and less-than-perfect source data.
(2.) See, for example, Jason Furman, "Second Estimate of GDP
for the First Quarter of 2015," Council of Economic Advisers Blog,
May 29, 2015; Charles E. Gilbert, Norman J. Morin, Andrew D. Paciorek,
and Claudia R. Sahm, "Residual Seasonality in GDP," FEDS Notes
(May 14, 2015); Glenn D. Rudebusch, Daniel Wilson, and Tim Mahedy,
"The Puzzle of Weak First-Quarter GDP Growth," FRBSF Economic
Letter, May 18, 2015; and Jan Groen and Patrick Russo, "The Myth of
First-Quarter Residual Seasonality," Liberty Street Economics, June
8, 2015.
(3.) See the box, "Seasonality in the National Income and
Product Accounts (NIPAs)," in Stephanie H. McCulla and Shelly
Smith, "Preview of the 2015 Annual Revision of the National Income
and Product Accounts," SURVEY OF CURRENT BUSINESS 95 (June 2015):
4.
(4.) See Stephanie H. McCulla and Shelly Smith, "The 2015
Annual Revision of the National Income and Product Accounts,"
SURVEY OF CURRENT BUSINESS 95 (August 2015).
(5.) For further discussion of these two approaches, see chapter 8
of Adriaan M. Bloem, Robert J. Dippelsman, and Nils O. Maehle, Quarterly
National Accounts Manual--Concepts, Data Sources, and Compilation
(Washington, DC: International Monetary Fund, 2001).
(6.) BEA formerly published GDP data without seasonal adjustment as
a service to users. However, it discontinued publication of such data
due to budget cutbacks in 2008.
(7.) The team members were Steve Andrews, Kyle Brown, Ben Cowan,
Ryan Howley, Andrea Julca, Kate Pinard, and Andy Vargo.
(8.) The X-12 ARIMA program was used instead of the more recent
Census Bureau X-13 program because the NIPA database was already linked
to the X-12 ARIMA program. For the residual seasonality diagnostics
analyzed in this paper, the two programs are essentially identical, and
the distinction would not have influenced the findings.
(9.) In particular, based on criteria recommended by the Census
Bureau, values of the M7 statistic that were less than 1.0 and values of
the F-test statistic for stable seasonality from table D8 that were
greater than 7.0 were interpreted as evidence of residual seasonality.
Census Bureau, Seasonal Adjustment Diagnostics: Census Bureau Guideline,
version 1.1, 5 (March 2010).
(10.) Real GDI is calculated by deflating current-dollar GDI by the
GDP price index.
Chart 1. BEA's Three-Phase Plan To Enhance Its Seasonal Adjustment
Approach
Phase 1 Phase 2 Phase 3
BEA began seasonally BEA conducted a BEA plans to produce
adjusting several component-by-component estimates of GDP and its
series used to review to identify the major components that are
calulate GDP that causes of residual not seasonally adjusted.
had not previously seasonality in the These data will likely be
been adjusted. These GDP and GDI estimates. helpful in identifying
series included and analyzing changes in
several from the seasonal trends.
Census Bureau's
quarterly services
survey, for example.
Status Status Status
These adjustments The results were These estimates will
were included as reported in a paper be released in
part of the July released via the BEA conjunction with BEA's
2015 annual revision Web site (reproduced seasonally adjusted GDP
of the national in this article) in estimates, beginning in
income and product June 2016. Residual mid-2018.
accounts. seasonality in
historical series will
be removed in the
2018 comprehensive
update.
Table 1. Tests for Residual Seasonality of Real Gross Domestic Product
(GDP) and Price Indexes
Real GDP
10 year 15 year 30 year
M7 F M7 F M7
Gross domestic product (*) 0.8 (*) 13.1 1.1 5.3 (*) 0.8
Personal consumption
expenditures 3.0 0.3 2.6 0.9 1.8
Goods 3.0 0.4 3.0 0.4 2.1
Durable goods 2.1 1.3 2.0 1.6 1.6
Nondurable goods 3.0 0.3 1.5 2.4 2.4
Services 1.3 3.0 1.4 2.8 3.0
Gross private
domestic investment 1.1 5.5 1.9 1.5 1.8
Fixed investment 1.4 5.3 1.1 5.8 (*) 0.9
Nonresidential 1.0 5.4 (*) 0.8 (*) 8.0 (*) 0.9
Structures 1.0 6.9 1.0 (*) 7.4 (*) 0.9
Equipment 1.9 1.7 1.2 3.2 1.3
Intellectual
property products 1.6 2.0 2.6 0.7 2.4
Residential 2.7 1.3 2.9 0.9 1.9
Change in private
inventories 1.6 2.4 3.0 0.2 1.6
Net exports of goods
and services 1.2 4.1 1.7 1.7 1.5
Exports (*) 0.7 (*) 14.1 1.3 3.6 1.1
Goods (*) 0.7 (*) 12.1 1.2 4.2 1.3
Services 1.2 5.5 1.5 2.4 1.4
Imports 1.8 2.2 2.5 1.1 2.2
Goods 1.9 1.9 2.1 1.4 1.8
Services 1.3 3.0 2.9 0.7 2.5
Government
consumption
expenditures and
gross investment (*) 0.4 (*) 31.6 (*) 0.6 (*) 15.3 (*) 0.5
Federal (*) 0.6 (*) 12.3 (*) 0.9 6.8 (*) 0.6
National defense (*) 0.6 (*) 14.6 (*) 0.7 (*) 10.6 (*) 0.5
Nondefense 1.5 2.1 1.2 3.6 1.3
State and local (*) 0.6 (*) 14.7 1.0 (*) 7.5 1.5
Price indexes
10 year 15 year
F M7 F M7 F
Gross domestic product (*) 9.2 1.3 3.2 1.1 4.5
Personal consumption
expenditures 1.9 1.1 4.5 1.1 4.9
Goods 1.5 1.1 5.3 1.1 5.2
Durable goods 2.6 1.4 2.8 1.2 3.4
Nondurable goods 0.9 1.1 5.5 1.0 5.7
Services 0.3 1.6 1.8 1.5 2.1
Gross private
domestic investment 1.8 1.3 6.6 1.1 (*) 8.8
Fixed investment 5.9 1.2 6.6 1.0 (*) 9.6
Nonresidential 6.1 1.8 2.6 1.8 2.7
Structures 6.7 1.2 5.2 1.0 (*) 7.8
Equipment 3.3 1.8 2.1 2.1 1.5
Intellectual
property products 0.9 2.7 0.4 2.4 0.8
Residential 2.3 1.1 (*) 8.5 (*) 0.8 (*) 10.4
Change in private
inventories 2.1
Net exports of goods
and services 2.7
Exports 4.1 1.1 6.6 1.0 (*) 7.2
Goods 3.1 1.1 (*) 7.3 1.1 (*) 7.1
Services 2.8 1.4 2.8 1.1 4.3
Imports 1.2 1.5 2.5 1.8 1.7
Goods 1.8 1.5 2.5 1.9 1.5
Services 0.9 1.4 4.1 1.2 5.2
Government
consumption
expenditures and
gross investment (*) 15.8 1.2 3.1 (*) 0.8 (*) 7.8
Federal (*) 14.5 1.5 3.6 (*) 0.8 (*) 16.6
National defense (*) 24.0 1.1 (*) 7.3 (*) 0.6 (*) 19.5
Nondefense 3.7 2.8 0.8 1.0 (*) 9.4
State and local 2.6 1.2 3.3 1.6 1.8
30 year
M7 F
Gross domestic product (*) 0.9 (*) 7.6
Personal consumption
expenditures 1.4 3.2
Goods 1.3 3.8
Durable goods 2.0 1.1
Nondurable goods 1.2 4.3
Services 2.1 1.2
Gross private
domestic investment 1.1 (*) 7.3
Fixed investment 1.0 (*) 8.1
Nonresidential 1.3 4.3
Structures 1.3 5.6
Equipment 1.3 3.6
Intellectual
property products 1.9 1.5
Residential 1.3 3.9
Change in private
inventories
Net exports of goods
and services
Exports 1.0 (*) 7.8
Goods 1.1 (*) 8.3
Services 1.5 2.6
Imports 3.0 0.1
Goods 3.0 0.0
Services 1.1 5.4
Government
consumption
expenditures and
gross investment (*) 0.7 (*) 11.2
Federal (*) 0.6 (*) 24.7
National defense (*) 0.5 (*) 31.5
Nondefense (*) 0.8 (*) 9.3
State and local 2.7 0.5
* Null hypothesis of no residual seasonality rejected if M7 < 1.0,
F > 7.0. F Statistical test for stable
seasonality M7 Statistical diagnostic for identifiable seasonality
Table 2. Tests for Residual Seasonality
of Nominal Gross Domestic Income (GDI)
Nominal GDI
10 year 15 year 30 year
M7 F M7 F M7 F
Gross domestic income 1.6 1.6 2.3 0.6 2.4 1.0
Compensation of
employees 2.9 0.3 3.0 0.2 2.9 0.6
Taxes on production
and imports 2.0 1.2 2.4 0.9 2.7 0.6
Less: Subsidies 2.2 2.2 1.8 2.7 1.7 2.8
Net operating
surplus 1.5 2.0 2.0 1.4 1.7 1.9
Private enterprises 1.6 1.9 2.0 1.2 1.9 1.6
Net interest and
miscellaneous
payment (*) 0.7 (*) 10.2 1.0 (*) 8.3 1.3 6.5
Business current
transfer payments 3.0 0.2 3.0 0.1 2.2 1.5
Proprietors income
with IVA and CCAdj 1.5 2.6 2.8 0.8 2.4 1.0
Rental income of
persons with CCAdj 2.5 1.8 2.1 1.8 2.7 1.0
Corporate profits
with IVA and CCAdj 1.6 2.8 1.7 2.5 1.3 3.9
Current surplus of
government enterpris (*) 0.8 (*) 7.5 1.3 4.0 (*) 0.9 6.9
Consumption of fixed
capital 1.6 2.7 1.8 2.2 3.0 0.7
Private 1.8 3.1 1.8 2.6 3.0 0.8
Government 1.2 3.5 3.0 0.1 3.0 0.3
* Null hypothesis of no residual seasonality rejected if M7 < 1.0,
F > 7.0.
CCAdj Capital consumption adjustment
F Statistical test for stable seasonality
IVA Inventory valuation adjustment
M7 Statistical diagnostic for identifiable seasonality
