The size of the U.S.A. shadow economy:
A Structural Equation Approach
Adriana AnaMaria ALEXANDRU
PhD Candidate, University Assistant, Department of Statistics and Econometrics
University of Economics, Bucharest, Romania
Scientific researcher
National Scientific Institute in the field of Labour and Social Protection
E-mail: adrianaalexandru@yahoo.com
Ion DOBRE
PhD, University Professor, Department of Economic Cybernetics
University of Economics, Bucharest, Romania
E-mail: dobrerio@ase.ro
Catalin Corneliu GHINARARU
Scientific researcher I
National Scientific Institute in the field of Labour and Social Protection
ghinararu@incsmps.ro
Abstract:
This paper aims to estimate the size of the U.S.A. shadow economy (SE) using a Structural Equation Approach
using quarterly data for the period 1980-2009. In order to do that, the shadow economy is modeled like a latent
variable using a special case of the structural equation models-the MIMIC model.
The model includes tax burden (decomposed in personal current taxes, taxes on production and imports, taxes on
corporate income and contributions for government social insurance), government unemployment insurance,
unemployment rate, self-employment and government employment as causes of shadow economy and the labour force
participation ratio and currency ratio as indicators of the unreported economy.
The results confirm that taxes on corporate income, contributions for government social insurance,
unemployment rate and the self-employment are the main causes of shadow economy. The size of the SE is
estimated to be decreasing over the last two decades.
Keywords: shadow economy, MIMIC models, USA
JEL classification codes: C87, E26, H20, H50, O17
I. Measuring the shadow economy
Studies trying to measure the dimension of shadow economy face the difficulty of how to define
it. One commonly used working definition is: all currently unregistered economic activity which
contributes to the officially calculated (or observed) Gross National Product1. Smith (1994) defines
it as „market-based production of goods and services, whether legal or illegal that escapes detection
in the official estimates of GDP.“
Clandestine by her nature, the shadow economy is difficult to evaluate. In the problem of
measuring the dimension of shadow economy, there are various approaches who include using
surveys of taxation compliance, using the discrepancy between national income and national
expenditure; considering fluctuations in labour force participation rates; the monetary “transactions
approach” of Feige (1979); modifications of currency demand equations, where the pioneer was
Cagan (1958).One criticism of most of these approaches is that it focus on one cause of hidden
economic activity, and one indicator.
In contrast, The MIMIC(“Multiple Indicators, Multiple Causes”) model of Zellner(1970),
Goldberger(1972), Jöreskog and Goldberger(1975), Jöreskog and Sörbom(1993)) allows for several
1
This definition is used by Feige (1989-„ economic activities include conscious efforts to avoid official detection) and
by Schneider and Enste(2000- all economic activities which contribute to officially calculated gross national product).
indicators variables and several causal variables in forming structural relationships to explain the
latent variable. Frey and Weck-Hanneman (1984) estimated underground economy MIMIC models
for a range of OECD countries; Aigner et al.(1988) applied a dynamic MIMIC model to U.S. data;
and Tedds (1998) used this approach to model the Canadian underground economy.
II. Modeling the shadow economy
In the process of econometric modelling of U.S.A. shadow economy (SE) we used a different
type of models-Structural Equations Models (SEM).The SEM represents statistical relationships
among latent (unobserved) and manifest (observed) variables.
Bollen (1989, p.1) presents the fundamental hypothesis for structural equation modelling
as: S  () , where  is the observed population covariance matrix,  is a vector of model
parameters, and S is the covariance matrix implied by the model. When the quality expressed in the
equation holds, the model is said to “fit” the data. Thus, the goal of structural equation modelling is
to explain the patterns of covariance observed among the study variables.
A special case of SEM is the Multiple Indicators and Multiple Causes model. It allows to
consider the SE as a “latent” variable linked, on the one hand, to a number of observable indicators
(reflecting changes in the size of the SE) and on the other, to a set of observed causal variables,
which are regarded as some of the most important determinants of the unreported economic
activity(Dell’Anno, 2003).
Frey and Weck-Hanneman (1984) have been the first economists that consider the dimension of
the hidden economy as an “unobservable variable”.
This type of models is composed by two sorts of equations, the structural one and the measurement
equations system. The equation that captures the relationships among the latent variable (η) and the
causes (Xq) is named “structural model” and the equations that links indicators (Yp) with the latent
variable (non-observed economy) is called the “measurement model”.
A MIMIC2 model of the shadow economy is formulated mathematically as follows:
   X  
(1)
Y    
(2)
where:
 is the scalar latent variable(the size of shadow economy);
Y   (Y1 ,....Y p ) is the (1  p ) vector of indicators of the latent variable;
X   ( X 1 ,... X q ) is the ( 1  q ) vector of causes of  ;
( p1) and  ( q1) vectors of parameters;
 ( p1) and  ( q1) vectors of scalar random errors;
The  and  are assumed to be mutually uncorrelated: ( E ( t t ' )  E ( t  t ' )  0 ).
Since the structural equation model (1) only partially explains the latent variable  , the error
term  represents the unexplained component.
The MIMIC model assumes that the variables are measured as deviations from their means and
that the error term does not correlate to the causes E (t )  E ( xt )  E ( t )  0
and E ( xt t ' )  E ( t xt ' )  0 . The variance of  t is abbreviated by  and  is the
( q  q ). covariance matrix of the causes xt .
2
A detailed presentation of the MIMIC model is realized by Bühn A., Schneider F.” Mimic Models, Cointegration and
Error Correction: An Application To The French Shadow Economy”, Cesifo working paper no.2200/2008
The measurement model (2) represents the link between the latent variable and its indicators;
the latent unobservable variable is expressed in terms of observable variables. Their
( p  p ) covariance matrix is given by   .
Like the MIMIC model’s causes, the indicators are directly measurable and expressed as
deviations from their means, E ( yt )  E ( t )  0. It is assumed that the error terms in the
measurement model do not correlate either to the causes xt
or to the latent variable,  t .
E ( xt  t ' )  E ( t xt ' )  0 and E (t  t ' )  E ( tt ' )  0.
Substituting (2) into (1), the MIMIC model can be written as: Y  X  z
(3)
where:     , z     . The error term z in equation (3) is a (p ×1) vector of linear
combinations of the white noise error terms  and  from the structural equation and the
measurement model, z  (0, ) . The covariance matrix  is given as cov( z )      ,
cov(  ,  )   , cov(  ,  )   the diagonal covariance matrix of  .
The multivariate regression equation (3) has a regressor matrix of rank one, and the error
covariance matrix is also constrained, and that is the raison for which it is impossible to obtain
cardinal estimates of all of the parameters. The estimation of (1) and (2) requires a normalization of
the parameters in (1), and a convenient way to achieve this is to constrain one element of  to some
pre-assigned value (Giles, Tedds, 2000).
To facilitate the identification of SEM some conditions are available but, unfortunately, none of
these are necessary and sufficient conditions (Bollen, 1989). The necessary (but not sufficient)
condition, so-called t-rule, enunciates that the number of nonredundant elements in the covariance
matrix of the observed variables must be greater or equal to the number of unknown parameters in
the model-implied covariance matrix.3
A sufficient (but not necessary) condition of identification, is that the number of indicators is
two or greater and the number of causes is one or more, provided that is assigned a scale to η
(MIMIC rule). For assigning a scale to the latent variable it is needed to fix one λ parameter to an
exogenous value. Although several econometric improvements are introduced in the last years, the
most important criticism to the MIMIC method is the strong dependence of the outcomes by the
(exogenous) choice of the coefficient of scale (λ).
Given an estimate of the  vector, and setting the error term  to its mean value of zero,
equation (2) enables us to “predict” ordinal values for  which is the relative size of the hidden
economy, at each sample point. Then, if we have a specific value for  at some sample point,
obtained from some other source, we can convert the within-sample predictions for  into a
cardinal series. We use an average value from other estimations realized using the currency demand
model to calibrate the time-series of the hidden economy.
Giles (1999a) was the first author to “calibrate” such MIMIC model hidden economy results
formally, by using the output from a completely separate demand-for-cash model to convert the
ordinal predictions into cardinal ones in the context of New Zealand data.
III. Data issues
The variables used in the estimation are defined in Appendix A. The data series are quarterly
from 1980:Q1 to 2009:Q2. All the series have been seasonally adjusted.
The series in levels or differences have been tested for unit roots using the Augmented-Dickey
Fuller (ADF) test. We test I(2) against I(1) and if we reject I(2), we test I(1) against I(0) as
3
Bollen K.A. (1989), pp. 93. More clearly, the number of observed variances and covariances must be equal to or
greater than the number of parameters to be estimated (including variance of latent factor, variances of disturbances,
covariances among observed variables).
appropriate(Appendix A). All the data has been differentiated for the achievement of the
stationarity. While all the variables have been identified like integrated on first order, the latent
variable is estimated in the same transformation of independent variables (first difference).
IV. Estimating the MIMIC model of the shadow economy
In our econometrical demarche of estimating the size of shadow economy, the causal variables
considered in the model are: tax burden decomposed into personal current taxes ( X 1 ), taxes on
production and imports( X 2 ), taxes on corporate income( X 3 ), contributions for government social
insurance( X 4 ) and government unemployment insurance( X 5 ), unemployment rate( X 6 ), selfemployment in civilian labour force ( X 7 ),government employment in civilian labour force ( X 8 )
called bureaucracy index.
The indicator variables incorporated in the model are: real gross domestic product index ( Y1 ),
currency ratio M1 M 2 ( Y2 ) and civilian labour force participation rate ( Y3 ).
The main elements of tax burden, government unemployment insurance and index of real gross
domestic product are expressed as percentages of gross domestic product while government
employment, self-employment, unemployment rate and civilian labour force participation rate are
calculated like percentages of civilian labour force. A detailed presentation of the variables is
realised in (Dobre, Alexandru, 2008)4.
The identification procedure of the best model starts from the most general model
specification (MIMIC 8-1-3) and continues removing the variables which have not structural
parameters statistically significant.
The results of estimating the structural equation models, by Maximum Likelihood, using the
LISREL 8.8 package, over the period 1990-2009 appear in table 1.The estimates of the coefficients
(  ) of the causal variables(x) in the structural equation for the shadow economy (  ) in equation (2)
provides the basis for estimating  over the sample period.The coefficient of the index of real GDP5
is normalised to -1 to sufficiently identify the model ( 1  1 ).This indicates an inverse
relationship between the official and shadow economy.
The results presented in table 1 suggest a negative none statistically significant relationship
between the size of the shadow economy and civilian labor force participation rate. Also, between
the dimension of the shadow economy and the currency ratio there is a positive none statistically
significant relationship.
Although the causal variables have the anticipated signs, many of them lack individual significance.
The unemployment rate and social insurance contributions are the only causal variable positively
significant in all MIMIC models. The other causal variables from the model are not statistically
significant.
The positive sign of the unemployment rate according with the negative one obtained by the
civilian labor force participation rate point out the fact that many workers from the official economy
go underground when they are laid off. The positive sign of the unemployment rate indicates the
existence of a flow of resources from official to shadow economy in recession cycles.
4
Dobre, I., Alexandru, A., “The impact of unemployment rate on the dimension of the shadow economy in Spain: A
structural Equation Approach”, European Research Studies Journal, Volume XIII, issue 4, 2009, pg.179-197, ISSN:
1108-2976.
5
Index real GDP 
Re al GDPt
Re al GDP1990
Table 1 : Estimated Coefficients6 of the MIMIC Models
Models
Tax
personnal/
GDP
Tax
production/
GDP
X1
X2
-0.01
(-0.08)
-0.01
(-0.08)
-0.01
(-0.08)
-0.01
(0.08)
-0.02
(-0.14)
-0.02
(-0.14)
-0.02
(-0.14)
0.83
(0.89)
0.42
(0.52)
0.83
(0.89)
------
-----
MIMIC
8-1-3
MIMIC
8-1-2a
MIMIC
8-1-2b
MIMIC
7-1-3
MIMIC
6-1-3
MIMIC
6-1-2a
MIMIC
6-1-2b
MIMIC
5-1-2
MIMIC
4-1-3a
MIMIC
4-1-3b
MIMIC
4-1-3c
MIMIC
4-1-2
MIMIC
3-1-3
MIMIC
3-1-2
-----------------
Tax
corporat./
GDP
X3
-0.27
(-0.82)
-0.37
(-1.10)
-0.27
(-0.82)
-0.27
(-0.81)
-0.30
(-0.89)
-0.30
(-0.89)
-0.30
(-0.89)
-0.29
(-0.88)
Social
insurance
contr./GDP
Governm.unempl.
.insurance/GDP
Unempl.
Rate
X4
X5
X6
2.88*
(3.85)
-1.80*
(-2.85)
2.88*
(3.85)
3.06*
(4.22)
2.98*
(4.20)
2.98*
(4.20)
2.98*
(4.20)
2.97*
(4.20)
2.89
(1.89)
-0.41
(-0.28)
2.89
(1.89)
2.89
(1.89)
2.89
(1.89)
2.89
(1.89)
2.89
(1.89)
2.85
(1.89)
2.75
(1.68)
-----
-----
-----
----
-----
-0.13
(-0.79)
1.93
(1.68)
-----
-----
-----
-----
-0.99*
(-2.58)
-0.24
(-0.73)
-0.24
(-0.73)
-0.15
(-0.46)
-0.15
(-0.46)
2.21*
(2.41)
3.00*
(4.17)
3.00*
(4.17)
2.93*
(4.03)
2.93*
(4.03)
-----
----
-----
----
---------------
Self
Empl.
Index
Bureac.
M1/M2
Lab.Force
Partic.
X7
X8
Y2
Y3
1.06*
(3.73)
1.48*
(4.99)
1.06*
(3.73)
1.09*
(3.82)
1.08*
(3.80)
1.08*
(3.80)
1.08*
(3.80)
1.09*
(3.83)
1.14*
(3.92)
0.98
(1.67)
0.85
(1.72)
0.98
(1.67)
1.02
(1.73)
1.01
(1.73)
1.01
(1.73)
1.01
(1.73)
1.01
(1.72)
0.70
(1.12)
0.62
(0.53)
-0.15
(-0.15)
0.62
(0.53)
0.61
(0.51)
0.05
(1.11)
-0.01
(-0.89)
-0.02
(-0.79)
----
----
-----
1.49*
(7.99)
1.49*
(7.99)
1.45*
(7.74)
1.45*
(7.74)
1.01
(1.70)
1.01
(1.70)
-----
----0.05
(1.11)
0.05
(1.11)
0.05
(1.11)
------
------
------
0.05
(1.11)
------
------
-0.24
(-0.19)
0.05
(1.11)
0.05
(1.11)
0.05
(1.11)
---------
------
------
------
0.05
(1.11)
------
------
-------
-----0.01
(-0.89)
-0.01
(-0.89)
-0.01
(-0.89)
------0.01
(-0.89)
-0.01
(-0.89)
-0.01
(-0.89)
-0.01
(-0.89)
-0.01
(-0.89)
-0.01
(-0.89)
-0.01
(-0.89)
Chi-square
RMSEA
(p-value)7 (p (p-value)8
39.18
(0.0017)
27.66
(0.000)
10.49+
(0.232)
35.67
(0.002)
15.50+
(0.28)
7.44+
(0.28)
7.02+
(0.31)
7.44+
(0.19)
26.88
(0.001)
13.81+
(0.13)
10.20+
(0.33)
4.41+
(0.35)
8.83+
(0.27)
4.05+
(0.26)
0.11
(0.021)
0.15
(0.0049)
0.052+
(0.42)
0.11
(0.021)
0.041+
(0.53)
0.046+
(0.45)
0.038+
(0.49)
0.065+
(0.33)
0.13
(0.011)
0.07+
(0.30)
0.034+
(0.55)
0.03+
(0.50)
0.047+
(0.45)
0.055+
(0.37)
AGFI9
Df10
0.78
17
0.69
8
0.88
8
0.79
15
0.90
13
0.91
6
0.91
6
0.90
5
0.81
9
0.90
9
0.92
9
0.93
4
0.93
7
0.93
3
6
The estimations has been made with the software LISREL 8.8
The SEM permits to consider and estimate the correlations between the X-variables and between the Y’s. In our analysis greater number of models estimated, the covariances between the observed
variables are often not statistically different from zero. Yet, if we decide to estimate these parameters changes in the estimates of structural coefficients are slightness, therefore the covariances are fixed
equal to zero in order to have more degrees of freedom (Dell’Anno, 2004). If the structural equation model is correct and the population parameters are known, then the matrix S(Sample covariance
7
matrix) will equal to
 ( ) (model implied covariance matrix) therefore the perfect fitting correspond to p-value=1.0.This test has a statistical validity if there are large sample and multinormal
distributions.
8
P-value for Test of Close Fit (RMSEA<0.05). + means good fitting (p-value>0.05).
9
Adjusted goodness-of-fit index, AGFI.This indicator takes values into the interval [0, 1].
10 The degrees of freedom are determined by 0.5(q+p)(q+p+1)-t, where p=number of indicators, p=numbers of causes, t=number of free parameters..
V. Obtaining the size of the U.S.A. shadow economy
The econometrical results reveal that the main causes of shadow economy are: taxes on corporate
income, contributions for government social insurance, unemployment rate and self-employment.
Starting from MIMIC 8-1-3 and removing the variables which have not structural parameters
statistically significant, we obtain MIMIC 4-1-2 as the best model.
The MIMIC 4-1-2 model has four causal variables (taxes on corporate income, contributions for
government social insurance, unemployment rate and self-employment) and two indicators (index
of real GDP and civilian labour force participation rate).
The choice of the model is based on: the statistical significance of parameters, the parsimony of
specification, the p-value of chi-square, and the Root Mean Square Error of Approximation
(RMSEA) test, adjusted goodness-of-fit index (AGFI).
Fig.1.Path diagram of 4-1-2 MIMIC
Taking into account the reference variable ( Y1 ,
Re al GDPt
) the shadow economy is
Re al GDP1990
scaled up to a value in 1990, the base year, and we build an average of several estimates from this
year for the U.S.A. shadow economy.
Table 2: Estimates of the size of U.S.A. shadow economy (1990)
Author
Johnson et. Al(1998)
Method
Size of Shadow Economy
Currency Demand
13.9%
Approach
Lacko(1999)
Physical
10.5%
Input(Electricity)
Schneider and Enste(2000) Currency Demand
7.5%*
Approach
Mean 1990
10.6%
*means for 1990-1993
The index of changes of the shadow economy in United States measured as percentage of GDP in
the 1990 is linked to the index of changes of real GDP as follow:
GDPt  GDPt 1
~  ~t 1
 t
Measurement Equation:
(4)
GDP1990
GDP1990
The estimates of the structural model are used to obtain an ordinal time series index for latent
variable (shadow economy):
~t
 0.24X 3t  3.00X 4 t  1.49X 6t  1.01X 7 t
Structural Equation:
(5)
GDP1990
The index is scaled to take up to a value of 10.6% in 1990 and further transformed from changes
respect to the GDP in the 1990 to the shadow economy as ratio of current GDP.These operations are
show in the benchmark equation11:
*
~t
1990
GDP
GDP1990
ˆt
(6)

 ~ 1990 

GDP1990 GDP1990
1990
GDPt
GDPt
where:
~t
I.
is the index of shadow economy calculated by eq. (5).
GDP1990
*
1990
 10.6% is the exogenous estimate of shadow economy.
GDP1990
~
III. 1990 is the value of index estimated by eq.(5).
GDP1990
GDP1990
IV.
is to convert the index of changes respect to base year in shadow economy respect to
GDPt
current GDP.
̂
V. t is the estimated shadow economy as a percentage of official GDP.
GDPt
II.
11
As the variables are all differenced to same degree, to calculate the levels of the latent variable multiplying the
structural coefficients for raw (unfiltered) data, it is equivalent to compute the changes in the index by multiplying
coefficients for the differenced causes and then to integrate them.
Fig.2. U.S.A. shadow economy as % of official GDP
18
16
% of official GDP
14
12
10
8
6
4
2
0
1980 1981 1983 1984 1986 1987 1989 1990 1992 1993 1995 1996 1998 1999 2001 2002 2004 2005 2007 2008
The shadow economy measured as percentage of official GDP records the value of 13.41% in
the first trimester of 1980 and follows an ascendant trend reaching the value of 16.77% in the last
trimester of 1982. At the beginning of 1983, the dimension of USA shadow economy begins to
decrease in intensity, recording the average value of 6% of GDP at the end of 2007. For the last two
year 2008 and 2009, the size of the unreported economy it increases slowly, achieving the value of
7.3% in the second quarter of 2009.
The results of this estimation are not far from the last empirical studies for USA (Schneider
1998, 2000, 2004, 2007, Schneider and Enste 2001).Schneider estimates in his last study, the size of
USA shadow economy as average 2004/05, at the level of 7.9 percentage of official GDP.
VI. Conclusions
In this paper, we estimate the size of the shadow economy in the U.S.A. using the MIMIC
model. Our results show that the size of the shadow economy varies from thirteen to seventeen
percent between 1980 and 1983 and then decreases steadily up to 7 percent of official GDP in 2009.
The results of this estimation are not far from the last empirical studies for USA (Schneider
1998, 2000, 2004, 2007, Schneider and Enste 2001).Schneider estimates in his last study, the size of
USA shadow economy as average 2004/05, at the level of 7.9 percent of official GDP.
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*** www.bea.gov , U.S.Economic Accounts
*** www.bls.gov , U.S. Department of Labor
*** Federal Reserve banks
*** Eviews 6.0 software
*** Lisrel 8.80 software
Appendix A: Analysis Of Non-Stationarity
In order to discover the unit roots and the order of integration of the time series used in the
model the Augmented Dickey-Fuller (ADF) Test is used; to choose a number of lags sufficient to
remove serial correlation in the residuals and the automatic selection of bandwidth we have
employed the Schwarz information criterion (ADF) and the Newey-West test using Bartlett Kernel
(KPSS).
We have reported in the following table the p-value of the ADF test, while the null hypothesis is
the presence of the unit root, and therefore a value greater than 0.05 indicates non-stationary time
series. A second unit root test is applied, the Kwiatkowski, Phillips, Schmidt and Shin Test. This
test differs from the others in that the series is assumed to be (trend-) stationary, according to the
null hypothesis. The table 1 shows the statistical test: we test I(2) against I(1) and if we reject I(2),
we test I(1) against I(0) as appropriate, if the estimated values exceed the respective critical values,
stationarity must be rejected. The critical values for the LM test statistics are:
- KPSS test equation with constant critical values: 0.347 (10%), 0.463 (5%), 0.739 (1%);
- KPSS test equation with constant and trend: 0.119 (10%), 0.146 (5%), 0.216 (1%).
The econometric software Eviews 6.0 was used in to perform this analysis.
Table 1: Unit-root analysis
Source
CAUSES
X1
Tax burden/GDP
( X2  X3  X4
X2
Personal current taxes/GDP
X3
Taxes on production and
imports/GDP
Taxes on corporate income/GDP
X4
X5
X6
X7
X8
X9
 X5 )
Contributions for government
social insurance/GDP
Government unemployment
insurance
Unemployment rate
Self-employment/Civilian labour
force
Index of bureaucracy
Unit root
analysis
Level
First diff.
Second diff.
ADF
KPSS
ADF
KPSS
ADF
KPSS
Transf..
used
BEA
I(1)
C
0.128
0.162*
0.052
0.171*
0.000*
0.172*
( X 1 )
BEA
I(1)
C
0.119
0.098*
0.000*
0.143*
0.000*
0.212*
( X 2 )
BEA
I(1)
C
0.045*
0.301*
0.000*
0.182*
0.000*
0.110*
( X 3 )
BEA
I(1)
C
0.001*
0.046*
0.000*
0.076*
0.000*
0.240*
( X 4 )
BEA
I(1)
T&C
0.415
0.314
0.000*
0.092*
0.000*
0.050*
( X 5 )
BEA
I(1)
C
0.020*
0.401*
0.002*
0.155*
0.000*
0.269*
( X 6 )
BLS
I(1)
C
0.227
0.677
0.001*
0.169*
0.000*
0.318*
( X 7 )
BLS
I(1)
C
0.782
0.848
0.000*
0.352*
0.000*
0.195*
( X 8 )
BLS
I(1)
T&C
0.239
0.081*
0.000*
0.111*
0.000*
0.099*
( X 9 )
I(1)
T&C
0.527
0.248
0.130
0.079*
0.000*
0.092*
(Y1 )
I(1)
T&C
0.737
0.262
0.000*
0.063*
0.000*
0.095*
(Y2 )
I(1)
T&C
0.983
0.304
0.000*
0.054*
0.000*
0.086*
(Y3 )
INDICATORS
Y1
M1/M2
Y2
Index of Real GDP12
Civilian labour force participation
rate
Y3
Federal Reserve
Banks
BEA
BLS
For ADF show the MacKinnon (1996) one-sided p-values; the statistical tests are shown for KPSS; * means stationary at 0.05 level
12
Real Gross Domestic Product, Chained Dollars. Billions of chained (2500) dollars. Seasonally adjusted at annual rates/ Re al GDP1990Q1