The Determinants of Consumer Confidence and Consumer Expenditure

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					      The Determinants of Consumer Confidence and
                Consumer Expenditure
                                   Saruta Benjanuvatra∗
                                    University of York
                                       February 2009



                                            Abstract
         The relation between consumer confidence and consumer expenditure has fre-
      quently been studied as these variables are important economic indicators and play
      important roles in the economy. However, little research has been done on what
      causes movements in consumer confidence itself. This paper fills this gap by finding
      determinants of consumer confidence and consumer expenditure, using the Bayesian
      Averaging of Classical Estimates (BACE) approach. The paper also re-examines
      the relation between consumer confidence and consumer expenditure. Our results
      indicate that they are not related.




Keywords: BACE, consumer confidence, consumer expenditure, model selec-
tion, Bayesian Averaging




  ∗
    I am grateful to Dick van Dijk for his valuable comments and support. Correspondence: Saruta
Benjanuvatra, Department of Economics and Related Studies, University of York, Alcuin College Block
D, Alcuin Way, York, YO10 5NB, UK; E-mail: sb652@york.ac.uk.


                                                1
1         Introduction
A typical news message:1

”Consumer confidence helps Wall Street”

New York: The American stock markets closed with profit on Wednesday due to increase
in consumer confidence in the U.S.. Investors hope that consumers will spend more money
around Thanksgiving and Christmas periods.(...)

This news message shows how people, in general, think about the relation between con-
sumer confidence and consumer expenditure. Investors believe that an increase in con-
sumer confidence will lead to an increase in consumer expenditure. In other words, people
will spend more when consumer confidence is high, and spend less when consumer con-
fidence is low. But, is it really true? In particular, does consumer confidence have any
predictive power on its own? Or does it merely reflect information that is already con-
tained in other variables?
   These questions have received much attention in economic literature, and a nice
overview is given by Ludvigson (2004). She notices that consumer confidence has only
modest information, if any, in addition to other fundamentals about the future path of
consumer expenditure. Moreover, in her conclusion she also states that a key problem
in assessing the true forecasting power is “that we don’t know what those other funda-
mentals might be.” (Ludvigson, 2004; pp. 49). The author also notes that while most
attention has been given to the predictive power of consumer confidence on expenditure,
little has been given to the determinants of consumer confidence itself.
        In this paper, we attempt to fill this gap by investigating the relation between con-
sumer confidence and consumer expenditure in the U.S., concentrating on the following
two research questions. First, what economic variables are determinants of consumer con-
fidence and consumer expenditure? Second, is there a causal relation between consumer
confidence and consumer expenditure? To answer these questions we apply the Bayesian
Averaging of Classical Estimates (BACE) approach to the Conference Board’s Consumer
Confidence Index (CB-index), the University of Michigan’s Consumer Sentiment Index
(UM-index), and total consumer expenditure for the period from February 1979 to April
2001.
        The BACE approach is very useful when one has many potential explanatory variables
but not enough theoretical guidance to enable the researcher to select the appropriate vari-
ables for the analysis. It performs many ordinary least squares (OLS) regressions with
    1
        This message appeared originally in Dutch, on Dutch Teletext on November 24th, 2005.




                                                     1
different subsets of variables, and evaluates the importance of these regressions by consid-
ering their Schwarz Information Criterion. Eventually, the BACE approach summarizes
the importance of each explanatory variable by providing posterior inclusion probabilities;
a belief that the variable should be included in the regression.
   This approach was introduced and successfully applied by Sala-i-Martin et al. (2004)
to find determinants of economic growth in a cross-country data set. Here we use this
approach to find determinants of consumer confidence and consumer expenditure, and to
examine the relation between them. The BACE approach is very useful to our analysis for
the following reasons. First, there is little economic theory suggesting what determines
consumer confidence. We therefore consider 48 different potential explanatory variables,
and we let the BACE approach “decide” which variables are likely to be determinants of
consumer confidence. Second, as mentioned by Ludvigson (2004), it is not clear which
fundamentals cause movements in consumer expenditure, and therefore it is difficult to
determine if consumer confidence really predicts consumer expenditure, or if consumer
confidence merely reflects movements in other fundamentals. The BACE approach solves
this problem by considering many different subsets of fundamentals and comparing the
importance of consumer confidence in these different regressions.
   Our results yield conclusions that are contrary to popular belief. We find that con-
sumer confidence and consumer expenditure are not related. Consumer expenditure is not
a determinant of consumer confidence, and consumer confidence variables are considered
not important for determining consumer expenditure. Moreover, they have different sets
of predictors as determined by our analysis. This means that an increase or decrease in
consumer confidence does not affect consumer expenditure, and vice versa.
    This paper is constructed as follows. Section 2 introduces the BACE approach. The
considered data set is discussed in Section 3. Section 4 presents results for consumer
confidence. Section 5 discusses the relations between consumer confidence and consumer
expenditure. Our conclusions are presented in Section 6.



2     BACE Approach
We use the Bayesian Averaging of Classical Estimates (BACE) approach, developed by
Sala-i-Martin et al. (2004), to determine what economic variables have explanatory effects
on consumer confidence and consumer expenditure. In this section we briefly explain this
approach.




                                            2
2.1       Bayesian Inference
Classical econometricians postulate a ’true’ model with ’true’ parameters, and they are
typically interested in obtaining estimates of the ’true’ parameters. On the other hand,
Bayesian econometricians postulate probabilities on different models with different pa-
rameters. These probabilities are subjective, and they indicate a degree of confidence, or
a belief, on the correctness of the model and the parameter values.
    A Bayesian analysis on parameters typically starts by specifying a prior probability
distribution on the parameter space. This prior distribution indicates a belief on the
parameter values before a data set is analyzed. It can be transformed into the posterior
distribution by conditioning the prior belief on the data realizations. To obtain the
posterior distribution of parameter vector θ, we apply Bayes’ theorem

                                                    p(y|θ)p(θ)
                                        p(θ|y) =                                                    (1)
                                                       p(y)
where p(θ|y) is the posterior density of θ given data vector y = [y1 , . . . , yT ] , p(y|θ) is the
likelihood function, p(θ) is the prior density of θ, and p(y) is the predictive density of
data y.
    The likelihood function p(y|θ) gives the probability distribution on the actually ob-
served data when the data is generated by a particular data generating process or a par-
ticular model. This process can be chosen by the researcher, and in the BACE approach,
one considers the classical linear model. This means that given X, a (T × K)-matrix of
K explanatory variables, y is generated by


                                               y = Xβ + ε                                           (2)
where ε = [ε1 , . . . , εT ] ∼ N (0, σ 2 I), and β = [β1 , . . . , βK ] is a vector of coefficients of the
explanatory variables. Hence, the parameter vector θ is given by θ = (β, σ 2 ).
   To determine what variables explain consumer confidence and consumer expenditure,
we divide the parameter space of the coefficient vector β into 2K regions, where each region
corresponds to a model. In each model, a subset of the coefficients is set to zero, which
implies that the corresponding explanatory variables are excluded from the regression.
   Then the posterior density of θ given data y becomes

                                          2K
                                                            p(y|θ)p(θ|Mi )
                               p(θ|y) =         P (Mi |y)                                           (3)
                                          i=1
                                                               p(y|Mi )
where

                                                   p(y|Mi )P (Mi )
                                 P (Mi |y) =      2K
                                                                                                    (4)
                                                  j=1   p(y|Mj )P (Mj )

                                                    3
is the posterior model probability of model Mi given data y, P (Mi ) is the prior probability
of model Mi , and p(y|Mi ) is the marginal likelihood. Thus the posterior distribution is
simply the weighted average of the 2K conditional posterior distributions, with P (Mi |y)
the weight of model Mi .
   The marginal likelihood is given as


                                 p(y|Mi ) =      p(y|θ)p(θ|Mi )dθ.                       (5)

A problem is how to choose p(θ|Mi ), the prior conditional on model Mi , because different
expressions result in different marginal likelihoods. However, it can be shown that for the
standard linear model, the marginal likelihood is approximately

                                                                 −T /2
                                   p(y|Mi ) ∝ T −ki /2 SSEi                              (6)

for large SSEi , where SSEi is the sum of squared residuals from an OLS regression, and
ki is the number of explanatory variables included in model Mi (see Sala-i-Martin et al.
(2004)). Then the posterior model probability of model Mi given data y becomes

                                                                     −T /2
                                           P (Mi )T −ki /2 SSEi
                          P (Mi |y) =     2K                                −T /2
                                                                                    .    (7)
                                          j=1   P (Mj )T −kj /2 SSEj
                      −T /2
Note that T −ki /2 SSEi       is the exponential of the Schwarz Information Criterion (SIC).
Thus, the higher the SIC, the higher the posterior model probability.
   Since it is impossible to report the posterior model probability of all 2K models, we
report posterior inclusion probability instead. The posterior inclusion probability of an
explanatory variable xk is the posterior probability that βk = 0. Thus this measure
represents the belief that xk is a determinant of y. Let Iik be one if explanatory variable
xk is included in model Mi , and zero otherwise. The posterior inclusion probability is
given by

                                                      2K
                                 P (βk = 0|y) =            Iik P (Mi |y).                (8)
                                                   i=1

We are also interested in the sign and magnitude of the coefficient. The unconditional
posterior mean of β can be defined as

                                                 2K
                                    E(β|y) =                    ˆ
                                                       P (Mi |y)βi                       (9)
                                                 i=1

      ˆ                                                                     ˆ
where βi = E(β|y, Mi ) is the posterior mean of β conditional on model Mi . βi is equal
to the OLS estimate if the prior density conditional on model Mi , p(β|Mi ), becomes

                                                  4
uninformative. In other words, the unconditional posterior mean of β can be computed
as a weighted average of OLS estimates, in which ’good’ models in terms of the SIC receive
higher weight.
    Instead of looking at the unconditional posterior mean of a coefficient βk , it is more
informative to know what the posterior mean of βk is, given that the variable xk is included
in the regression. Therefore, we report the posterior mean conditional on inclusion, which
is given by

                                                            E(βk |y)
                              E(βk |y, βk = 0) =                                       (10)
                                                          P (βk = 0|y)
The posterior variance of coefficient βk conditional on inclusion in model Mi is

                                                   2
                                               E(βk |y)
                  V ar(βk |y, βk = 0) =                   − (E(βk |y, βk = 0))2        (11)
                                             P (βk = 0|y)
where

                                      2K
                          2
                       E(βk |y)   =         P (Mi |y)(V ar(βk |Mi , y) + βˆk )
                                                                          i
                                                                           2
                                                                                       (12)
                                      i=1

From the conditional posterior mean and variance of coefficient βk , one can compute the
sign certainty probability. This is the probability that the coefficient, βk , is on the same
side of zero as its mean conditional on inclusion. If the posterior mean of βk is negative,
then the sign certainty probability of βk is

                                                 2K
                                                                   P (βk < 0|y, Mi )
                   P (βk < 0|y, βk = 0) =              P (Mi |y)                       (13)
                                                 i=1
                                                                     P (βk = 0|y)

where

                                                            ˆ
                                                            βk
                     P (βk < 0|y, Mi ) = t                                , T − ki     (14)
                                                       V ar(βk |Mi , y)
with ki the number of included variables in model Mi , and t(x, s) the cumulative distribu-
tion function of a t-distribution with s degrees of freedom evaluated at x. Similarly, one
can compute the sign certainty probability of βk when the posterior mean of βk is positive.
It then corresponds to 1 minus the p-value of a one-sided t-test in classical inference.




                                                   5
2.2    Model Size
Prior to calculation of the posterior inclusion probability in (8), we have to specify the
                                                                            ¯
prior model probability P (Mi ). We first choose a prior expected model size k, then we set
                                                                 ¯
the prior inclusion probability for each variable to be equal to k/K, as in Sala-i-Martin
et al. (2004). Consequently, the prior model probability for model Mi becomes

                                        ¯    ki      ¯    K−ki
                                        k            k
                            P (Mi ) =             1−             ,                    (15)
                                        K            K
This implies that the prior distribution of the model size is binomial with prior expected
           ¯
model size k. Thus, if we denote Kincluded as the number of explanatory variables in the
model, then the prior model size probability that the model has k explanatory variables
becomes

                                                  ¯   k      ¯       K−k
                                            K     k          k
                     P (Kincluded = k) =                  1−                          (16)
                                            k     K          K
                                                        ¯
In this paper, we choose the prior expected model size, k, to be equal to 5. To check
                                                        ¯
whether or not the BACE approach is robust for different k, we also perform a sensitivity
                                ¯
analysis on different choices of k in Section 4.

2.3    Simulation Method
Now we are ready to calculate the probabilities explained above. However, when the num-
ber of potential variables becomes large, the number of models to be estimated becomes
large with the factor of 2K . In our research, there are at least 48 explanatory variables.
Thus, the number of possible models to be estimated goes beyond 2.8 × 1014 . It is not
feasible anymore to use the BACE approach to estimate all the models exactly. So, we
need a simulation method here.
   We choose to apply simulation method Markov Chain Monte Carlo Model Composition
(M C 3 ), introduced by Madigan and York (1995), on our data set. This method constructs
an ergodic Markov chain {M0 , M1 , M2 , ...} over all possible models. Given model Mi−1 ,
the algorithm selects model Mi as follows:

   Step 1: Randomly select a variable λ from the complete set of variables, except
           the constant term, with uniform probability.
   Step 2: If the variable λ is not yet present in model Mi−1 , add this variable into
           model Mi . Otherwise, remove variable λ.
   Step 3: Replace model Mi−1 by model Mi with probability min{1, PP (Mi |y) } and
                                                                         (Mi−1 |y)
           return to step 1.




                                             6
To start up the M C 3 algorithm, we draw model M0 from the prior model distribution as
given by (15), and then we let the algorithm burn-in for 50,000 iterations. After that,
we repeat the algorithm for 25 million times to create a sample of 25 million models.
The M C 3 sample converges to the posterior distribution of the models, and the posterior
probabilities given by (8)-(14) can be calculated by computing the average results in
the M C 3 sample. However, the results of the individual M C 3 draws do not need to be
weighted.

2.4    Advantages and Disadvantages of BACE Approach
The BACE approach has several advantages in comparison with previous Bayesian Model
Averaging (BMA) methods. As the BACE approach is a combination of classical OLS
estimation and a Bayesian approach, BACE estimates can simply be calculated by using
OLS method. Results can easily be interpreted by non-Bayesian economists as the weights
are comparable to the Schwarz model selection criterion. Lastly, BACE does not require
the specification of the prior distribution of the parameters. Instead, only one prior
                                                ¯
hyper-parameter - the prior expected model size k - needs to be specified.
   However, BACE approach also has some disadvantages. First of all, it is not clear how
                                             ¯
one can choose the prior expected model size k. Even though Sala-i-Martin et al. (2004)
                                                   ¯
compare results obtained from different values of k, and claim that the BACE approach is
                            ¯
robust, the choice of these k is still arbitrary. Moreover, according to Hendry and Reade
(2005), the BACE approach performs poorly in terms of bias on coefficients and forecast
errors when outliers and structural breaks exist in the data set. Finally, Stock and Watson
(2005) suggest that the BACE approach is not suitable for forecasting purposes because
it performs poorly in terms of point forecasting when applied to macroeconomic variables.



3     Data Analysis
Data used in this paper is monthly and available from February 1979 to April 2001. We
divide the data set into three groups. The Full period is from February 1979 to April 2001,
Period 1 is from February 1979 to March 1991, and Period 2 is from April 1991 to April
2001. For consumer confidence, the Conference Board’s Consumer Confidence Index (CB-
index) and the University of Michigan’s Consumer Sentiment Index (UM-index) are used
as the dependent variables. For consumer expenditure, we use total personal consumption
expenditure as the dependent variable.
   The CB-index and the UM-index both measure public confidence and are widely used
to determine the U.S. consumer confidence. The indices are based on five survey ques-
tions. The first two questions reflect respondents’ evaluations of present conditions of

                                            7
the economy, whereas another three questions ask the respondents about their expec-
tations. Although the survey questions are in a similar form, the questions and their
interpretations for each index are different2 . We first discuss the CB-index.

3.1       Conference Board’s Consumer Confidence Index
The first two questions for the CB-index survey the respondents’ assessment of current
business conditions and job availability in their areas. The assessment particularly reflects
current conditions in the labor markets and economic activities. Another three survey
questions ask about the respondents’ expectations of the business conditions and job
availability in their area, and their total family income over six months in comparison
with their current conditions. In other words, the expectations component of this index
asks about the expected changes in the economy. Figure 1 presents time series of the
present and expectations components of the CB-index.
                          200


                          180


                          160


                          140


                          120


                          100


                           80


                           60


                           40


                           20
                                                                                                 CB−present
                                                                                                 CB−expect
                            0
                                1980   1982   1984   1986   1988   1990   1992   1994   1996   1998   2000




Figure 1: The present and expectations components of the Conference Board’s Consumer Con-
fidence Index (CB-index) for the full period February 1979 - April 2001.

      The figure shows large fluctuations in the two series over time, with the expectations
component fluctuating relatively less than the present component. The fluctuations in
the present component can easily be related to recession periods in 1980, 1982-1983, and
1990-1991, in which the consumer confidence of present conditions shares a strong decline.
Furthermore, the two series are not closely correlated (r = 0.46). We can see that the two
series do not follow each other very closely, and in many periods they even move towards
different directions.
  2
      See Ludvigson (2004) for details about the survey questions




                                                                   8
   The fluctuations in the present component also suggest that this series might be non-
stationary. The time series of the expectations component on the other hand, seems
to be more stationary. To investigate this, we perform Dickey-Fuller tests on these two
time series, where the null hypothesis corresponds to the presence of a unit root. The
test results do not reject the null hypothesis for the present component, which suggests
that it probably is non-stationary. For the expectations component, the null hypothesis
is rejected. Thus, the time series of the expectations component is stationary. These
conclusions would suggest that we should use the first difference of the present compo-
nent and the level of the expectations component as the dependent variables to determine
consumer confidence. These conclusions also coincide with the character of the survey
questions, that the present component reflects the level of the economy while the expecta-
tions component reflects changes in the economy over six months (Ludvigson (2004)). As
a result, to make the present and expectations components comparable, we differentiate
the present component series first.

3.2    University of Michigan’s Consumer Sentiment Index

                      200


                      180


                      160


                      140


                      120


                      100


                       80


                       60


                       40


                       20
                                                                                             UM−present
                                                                                             UM−expect
                        0
                            1980   1982   1984   1986   1988   1990   1992   1994   1996   1998   2000




Figure 2: The present and expectations components of the University of Michigan’s Consumer
Sentiment Index (UM-index) for the full period February 1979 - April 2001.

   The first two questions for the UM-index ask the respondents to evaluate their current
financial status with respect to that of the previous year; and whether now is a good
time to buy major household items. These questions reflect perception of people about
the recent changes in the economy. Another three questions concentrate primarily on
the respondents’ expectations on business conditions and changes in their own financial
status over one year, as well as the country’s overall economic conditions over the next


                                                               9
five years. Figure 2 presents time series of the present and expectations components of
the UM-index.
   The two series are positively correlated (r = 0.86) and they fluctuate much less than
the present and expectations components of the CB-index. Furthermore, both series seem
to be stationary. It should be mentioned that the Dickey-Fuller tests on the two series do
not reject the null hypothesis of a unit root, which would suggest that differentiation of
the two time series is preferable. However, these tests typically have low power, and they
do not take into account the presence of level shifts due to recessions and expansions.
As it is also mentioned in Ludvigson (2004) that the UM-indices reflect changes in the
economy rather than the level of economic activities, we decide not to differentiate these
two series. Instead, we use their level as the dependent variables.

3.3    Consumer Expenditure and other explanatory variables
To determine the CB-index and the UM-index, we use 1-month lagged values of 36 vari-
ables selected out of 170 variables used in Marcellino et al. (2004). These explanatory
variables are also transformed and adjusted according to the same study. Besides these
36 variables, we also add 1-month to 12-month lagged values of the dependent variable
into our list of explanatory variables. Thus, there are 48 explanatory variables in total.


                      0.03




                      0.02




                      0.01




                        0




                     −0.01




                     −0.02



                                                                                      Consumer Expenditure
                     −0.03
                             1980   1982   1984   1986   1988   1990   1992   1994   1996   1998    2000




           Figure 3: The growth rate of total personal consumption expenditure.

   To examine whether changes in consumer confidence cause changes in consumer ex-
penditure, we perform an analysis in which we use the growth rate of the total personal
consumption expenditure as dependent variable. Figure 3 shows a plot of this time series.
In the analysis, we remove the total personal consumption expenditure out of the list of


                                                                10
explanatory variables and add 1-month to 3-month lagged values of the present and ex-
pectations components of the CB-index into the list. Therefore, there are 53 explanatory
variables in total. The complete list of the explanatory variables and their transformations
is presented in Table A1 in the Appendix.
    As mentioned in Section 2.4, the BACE approach performs poorly when outliers and
structural breaks are present in the data set. Therefore, we correct all variables for outliers
according to a method often used by Stock and Watson. The procedure is as follows. If
an observation deviates from the median of the series more than 3 times the interquartile
range (IQR), we replace the observation by the median of its six surrounding observations
and itself.
    Finally, in order to make the coefficients interpretable and comparable, we normalize
all variables by subtracting the mean and dividing by the standard deviation.



4     Results - Consumer Confidence
In this section, we present determinants of the present and expectations components of
the CB-index and UM-index. For each time series in each period, we calculate poste-
rior conclusion probability, posterior mean conditional on inclusion, posterior standard
deviation conditional on inclusion and OLS sigh certainty probability, using equation (8),
(10), (11), and (13) respectively. Most tables shown in this section are constructed in
the same manner. Column (2) presents numbers of all variables as shown in Table A1 in
the Appendix. Column (3) lists the first 15 determinants sorted in descending order with
respect to the posterior inclusion probability in the full period February 1979 to April
2001. Column (4)-(6) present the posterior inclusion probability in all three periods.
                                      ¯            ¯
   With 48 explanatory variables and k equals 5, k/K equals 0.104. The probabilities
that are equal to or higher than 0.104 are given in bold. Column (7)-(9) present the signs
of the posterior mean conditional on inclusion in all three periods. ++ or −− represents
the sign certainty probabilities that are equal to or higher than 0.95. Complete results
can be found in the Appendix.

4.1    CB-index
CB present component

Table 1 presents summary results of our analysis on the present component of the Con-
ference Board’s Consumer Confidence index. Here, the BACE approach detects two
variables that are very likely to be determinants of the CB present component. They



                                              11
                                                            Post. inclusion prob.          Sign
      Rank   No.                  Variable                  Full      1       2     Full     1     2
       (1)   (2)                    (3)                      (4)     (5)     (6)     (7)    (8)   (9)

        1     11   average unemployment duration in weeks   0.997   0.146   0.573   ++     ++     ++
        2     37   lagged dependent (t-1)                   0.953   0.528   0.098   −−     −−     −−
        3     28   interest rate 3-month u.s.treasury       0.852   0.160   0.328   ++     ++     ++
        4     20   purchasing managers’ index               0.470   0.907   0.093   ++     ++     ++
        5     17   total housing starts                     0.256   0.064   0.025   ++     ++     +
        6      9   ratio advertisement:unemployed           0.167   0.081   0.051   ++     +       +
        7     13   total civilian labor force               0.072   0.054   0.074   ++     ++     ++
        8     24   s&p stock price index                    0.062   0.088   0.012   ++     ++     +
        9     38   lagged dependent (t-2)                   0.047   0.015   0.017   −−     −       −
       10     27   interest rate federal funds              0.036   0.016   0.030   ++     +       +
       11     48   lagged dependent (t-12)                  0.032   0.016   0.356   ++     +      ++
       12     23   interest rate 10-year u.s.treasury       0.030   0.029   0.019   +       +     +
       13     10   average working hours per week           0.026   0.019   0.044   +       +     ++
       14     29   money supply: m2                         0.021   0.023   0.014   +       +     +
       15     15   new public construction put in place     0.020   0.027   0.011   −       −     −

       39     4    total personal consumption expenditure   0.008   0.011   0.013    −      −     −



Table 1: Summary results of the BACE approach on the present component of the CB-index
for the full period February 1979 - April 2001.


both have posterior inclusion probabilities of more than 95 percent. We shortly discuss
these variables.
   The variable with the highest posterior inclusion probability is the average unemploy-
ment duration in weeks of those individuals who are unemployed. This variable seems to
be robust with high posterior inclusion probability in all three sample periods. It is not
unexpected that unemployment duration is likely to be an important determinant, as the
present component of the CB-index reflects the respondents’ assessment of local business
conditions, job availability and economic activities. However, the sign of the coefficient
is quite surprising; unemployment duration has a positive effect with a sign certainty
probability of almost 1. This means that if unemployed individuals on average have been
unemployed for a long time, then the present component of consumer confidence is likely
to rise in the following month.
   It is hard to reconcile this unexpected result with existing economic theory, but it might
be understood in terms of the cyclical behavior of these variables at different stages of
the business cycle. Shortly after a trough in the business cycle, that is, after a recession,
unemployment duration is at a peak as many individuals have become and remained
unemployed during the recession period. However, it is also the period in which consumer
confidence is recovering from a trough, and hence, on the rise. Thus, unemployment
duration and the change in consumer confidence are positively correlated.
   The second determinant is 1-month lagged value of the present component of the CB-
index. Note that this variable has a negative coefficient. This means that, after a large
negative change in consumer confidence, consumers are more likely to regain confidence in
the following month. This could suggest that consumers overreact. It might also be due

                                                    12
to measurement errors in the Conference Board index. That is, after a large measurement
error, the index should be expected to revert to its true value in the following month.
   Two other variables, the short-term interest rate and the purchasing managers’ index
(PMI), are also likely to be relevant determinants with posterior inclusion probabilities of
85 and 47 percent. Moreover, these variables appear to be very robust with sign certainty
probabilities of more than 98 percent in all three considered sample periods. We shortly
discuss these two variables here as well.
   The short-term interest rate is an important indicator for the business cycle. Therefore,
it is not surprising that this variable is considered an important determinant of the present
component of consumer confidence. Changes in the 3-month interest rate have positive
effects on changes in the present component of consumer confidence. The purchasing
managers’ index is a very influential indicator for manufacturing activity and business
confidence. Not surprisingly, a high level of the PMI is associated with a rise in consumer
confidence in the following month. See Table A2 in the Appendix for a complete overview.

           No.                      Variable                             Coefficient             Std.Error      p-value
           (1)                        (2)                                   (3)                    (4)           (5)

            37   lagged dependent (t-1)                                       -0.2724                0.0615    0.0000
            11   average unemployment duration in weeks                       0.3206                 0.0602    0.0000
            28   interest rate 3-month u.s. treasury                          0.2204                 0.0615    0.0004
            20   purchasing managers’ index                                    0.2331                0.0662    0.0005


      Table 2: Results of an OLS regression of the present component of the CB-index.


                         3




                         2




                         1




                         0




                        −1




                        −2


                                                                                      CB present
                        −3                                                            fitted




                        −4
                             1980   1982   1984   1986   1988   1990   1992    1994   1996    1998    2000




Figure 4: The fit of an OLS regression of the present component of the CB-index on constant,
1-month lagged dependent, unemployment duration, 3-month interest rate and PMI.

   Since we are also interested in the relation between consumer confidence and consumer
expenditure, we report the results of the consumer expenditure in Table 1 as well. This

                                                                13
variable has a very low posterior inclusion probability and it is unlikely to be a determinant
of the consumer confidence’s present condition.
   To illustrate the performance of the four most important determinants of the CB
present component, we run an ordinary least squares (OLS) regression of CB-present on a
constant, 1-month lagged CB-present, average unemployment duration in weeks, 3-month
interest rate, and PMI. Table 2 shows the regression results. All regressors are significant
with the expected signs. A plot of the fit of this regression is shown in Figure 4. It is
clearly visible that these four variables are able to capture the up- and downturns of the
present component of consumer confidence well.

CB expectations component

Table 3 presents summary results of the BACE approach on the expectations compo-
nent of the CB-index, sorted in descending order with respect to the posterior inclusion
probability for the full period February 1979 to April 2001.

                                                            Post. inclusion prob.          Sign
      Rank   No.                  Variable                  Full      1       2     Full     1     2
       (1)   (2)                    (3)                      (4)     (5)     (6)     (7)    (8)   (9)

        1     37   lagged dependent (t-1)                   1.000   1.000   1.000   ++     ++     ++
        2     24   s&p stock price index                    0.935   0.767   0.338   ++     ++     ++
        3     23   interest rate 10-year u.s.treasury       0.461   0.018   0.364   ++     +      ++
        4     29   money supply: m2                         0.351   0.030   0.033   ++     +       +
        5     21   new orders consumer goods&materials      0.268   0.820   0.011   ++     ++      +
        6     35   consumer price index                     0.089   0.031   0.039   −−     −      +
        7     44   lagged dependent (t-8)                   0.088   0.134   0.016   ++     ++      +
        8     33   producer price index                     0.083   0.010   0.268   −−     −      −−
        9     28   interest rate 3-month u.s.treasury       0.056   0.018   0.193   ++     +      ++
       10     20   purchasing managers’ index               0.045   0.015   0.062   ++     +      ++
       11     31   money stock: m3                          0.043   0.021   0.035   ++     +       +
       12     14   total construction put in place          0.036   0.027   0.013   ++     +       +
       13      2   total capacity utilization               0.036   0.098   0.112   −       −     ++
       14     17   total housing starts                     0.029   0.016   0.040   +       +     −
       15     11   average unemployment duration in weeks   0.028   0.109   0.127   +      ++     −−

       20     4    total personal consumption expenditure   0.022   0.096   0.012    −     −−     −



Table 3: Summary results of the BACE approach on the expectations component of CB-index
for the full period February 1979 - April 2001.

   There are two variables that turn out to be important determinants of consumer ex-
pectations as measured by the Conference Board. The variable with the highest posterior
inclusion probability is the 1-month lagged value of the expectations component of the
CB-index. This variable captures many of the dynamics of consumer expectations.
   The second determinant is the return on the S&P stock price index. A higher stock
price return results in higher consumer expectations. From a theoretical point of view,
the stock market is a very reasonable determinant as this variable directly influences


                                                    14
household’s assets. Stock market returns also receive attention from the media. People,
both financial analysts and laymen, consider this variable to be an important indicator
for the state of the economy.
  Other variables are considered less important. They even appear to be non-robust
when considering different sample periods. When we look at the results of consumer
expenditure in Table 3, we again observe that consumer expenditure has a very low
posterior inclusion probability and it is unlikely to be a determinant of the consumer
confidence’s expectations component. See Table A3 in the Appendix for more details.
   To illustrate the performance of stock market returns on consumer expectations, we
perform an OLS regression of CB-expect on a constant, 1-month lagged values of CB-
expect, and returns on the S&P stock price index. Table 4 shows the regression results.
Again, both variables are strongly significant. A good fit is illustrated in Figure 5.

                  No.               Variable                    Coefficient         Std.Error          p-value
                  (1)                 (2)                          (3)                (4)               (5)

                   37        lagged dependent (t-1)               0.8933              0.0264           0.0000
                   24        s&p stock price index                0.1034              0.0264           0.0001


Table 4: Results of an OLS regression of the expectations component of the CB-index.


                         3




                         2




                         1




                         0




                        −1




                        −2

                                                                                        CB expect
                                                                                        fitted
                        −3




                        −4
                             1980   1982   1984   1986   1988    1990   1992   1994   1996   1998   2000




Figure 5: The fit of an OLS regression of the expectations component of the CB-index on
constant, 1-month lagged dependent, and S&P stock price return.

Sensitivity analysis of BACE approach

                                                                  ¯
Our results might depend on the chosen prior expected model size, k, of 5. We therefore
test whether the BACE approach is robust for different prior expected model size for the
                                                ¯
CB-index. We choose to test the approach with k equals 2, 5, 10, 15, and 25, with k   ¯
equals 5 as benchmark.

                                                                 15
   Table A4 in the Appendix shows the results for the present component of the CB-
index. Of the variables that we mentioned in Section 4.1, lagged dependent variable,
unemployment duration, 3-month interest rate and PMI are all very robust.
  Table A5 in the Appendix shows the results for the expectations component of the
CB-index. It turns out that these results are very robust for different prior expected
                                                                                     ¯
model sizes. Therefore, we conclude that the BACE approach is robust with respect to k.

4.2    UM-index
UM present component

Table 5 presents summary results of the BACE approach on the present component of
the UM-index for the full period February 1979 to April 2001.

                                                            Post. inclusion prob.          Sign
      Rank   No.                  Variable                  Full      1       2     Full     1     2
       (1)   (2)                    (3)                      (4)     (5)     (6)     (7)    (8)   (9)

        1    37    lagged dependent (t-1)                   1.000   1.000   1.000   ++     ++     ++
        2    29    money supply: m2                         0.762   0.545   0.019   ++     ++     +
        3    20    purchasing managers’ index               0.599   0.187   0.077   ++     ++     ++
        4    42    lagged dependent (t-6)                   0.550   0.170   0.018   ++     ++     −
        5    11    average unemployment duration in weeks   0.520   0.102   0.116   ++     +      ++
        6    10    average working hours per week           0.393   0.035   0.361   ++     +      ++
        7    48    lagged dependent (t-12)                  0.308   0.055   0.019   ++     ++     +
        8    36    implicit price deflator                   0.183   0.243   0.017   −−     −−     −
        9    25    s&p’s dividend yield                     0.127   0.153   0.023   −      −−      −
       10    47    lagged dependent (t-11)                  0.125   0.044   0.018   ++     +       +
       11    24    s&p stock price index                    0.113   0.205   0.011   ++     ++     −
       12     9    ratio advertisement:unemployed           0.110   0.032   0.976   +       +     ++
       13     8    total employees                          0.100   0.041   0.250   ++     +      ++
       14    45    lagged dependent (t-9)                   0.086   0.019   0.015   ++     +       +
       15    44    lagged dependent (t-8)                   0.084   0.032   0.016   ++     +      −

       37     4    total personal consumption expenditure   0.012   0.036   0.018    +      +     −


Table 5: Summary results of the BACE approach on the present component of UM-index for
the full period February 1979 - April 2001.

   From Table 5 we first observe that the 1-month lagged dependent variable should
always be included in the regression; the posterior inclusion probability is 1. Thus, there
is a strong positive autocorrelation in the present component of the UM-index. This is
not an unexpected result, as we already noticed in Section 3 that we could not reject
a unit root in the present component of the UM-index. Further, more variables appear
to be important. For example, four more variables have posterior inclusion probability
of more than 50 percent. These are money supply, PMI, the 6-month lagged dependent
variable, and unemployment duration. We shortly discuss these variables.
   As in the analysis of the present component of the CB-index, we again observe that the
unemployment duration and the purchasing manager’s index are important determinants.
Moreover, they are robust with sign certainty probabilities of at least 93 percent in all

                                                    16
considered sample periods. As these two variables are robust determinants of present
component for both CB-index and UM-index with respect to different sample periods
and prior expected model sizes, we can firmly conclude that unemployment duration and
the PMI are important determinants of consumer confidence’s present component.
   While short-term interest rate was a determinant in the present component of the
CB-index, it is not important when considering the UM-index. Interestingly, the short-
term interest rate now seems to be replaced by another monetary variable, i.e. the money
supply (M2). However, this variable only seems to be an important determinant in Period
1 (covering the 1980s). In Period 2, the posterior inclusion probability of M2 is less than
2 percent. We also observe that 6- and 12-month lagged dependent variables are highly
ranked. This suggests that there are some seasonal effects in the UM-index that are not
filtered out. This is the case in Period 1.

           No.                     Variable                             Coefficient                Std.Error   p-value
           (1)                       (2)                                   (3)                       (4)        (5)

            37   lagged dependent (t-1)                                      0.9081                 0.0225    0.0000
            29   money supply (M2)                                           0.0754                 0.0199    0.0002
            20   purchasing managers’ index                                  0.0519                 0.0240    0.0314
            11   average unemployment duration in weeks                      0.0215                 0.0202    0.2876


      Table 6: Results of an OLS regression of the present component of the UM-index.


                        3




                        2




                        1




                        0




                       −1




                       −2
                                                                                    UM present
                                                                                    fitted

                       −3




                       −4
                            1980   1982   1984   1986   1988   1990   1992   1994    1996    1998    2000




Figure 6: The fit of an OLS regression of the present component of the UM-index on constant,
1-month lagged dependent, money supply (M2), PMI, and average unemployment duration.

   To illustrate the performance of the three determinants mentioned above, we perform
an OLS regression of UM-present on a constant, 1-month lagged values of UM-present,
money supply, PMI, and unemployment duration. Table 6 shows the regression results.
All coefficients have the correct sign and are strongly significant. The only exception is

                                                               17
the unemployment duration which is not significant in this regression. Again, a very good
fit is illustrated in Figure 6.
   Finally, we notice that consumer expenditure is unlikely to be a determinant of the
present component of the UM-index. See Table A6 in the Appendix for a complete
overview.

UM expectations component

Table 7 presents summary results of the BACE approach on the expectations component
of the UM-index for the full period February 1979 to April 2001.


                                                            Post. inclusion prob.          Sign
      Rank   No.                 Variable                   Full      1       2     Full     1     2
       (1)   (2)                   (3)                       (4)     (5)     (6)     (7)    (8)   (9)

         1    37   lagged dependent (t-1)                   1.000   1.000   1.000   ++     ++     ++
         2    24   s&p stock price index                    0.847   0.147   0.728   ++     ++     ++
         3    21   new orders consumer goods&materials      0.553   0.417   0.032   ++     ++     +
         4    29   money supply: m2                         0.206   0.061   0.024   ++     ++     +
         5    36   implicit price deflator                   0.156   0.145   0.012   −−     −−     +
         6    43   lagged dependent (t-7)                   0.148   0.043   0.032   ++     +      −
         7     6   total manufacturing&trade                0.147   0.128   0.032   ++     ++     +
         8     3   personal income                          0.125   0.039   0.275   ++     +      ++
         9     1   sales, business&manufacturing            0.103   0.119   0.021   ++     ++     +
        10    35   consumer price index                     0.088   0.227   0.012   −−     −−     +
        11    31   money stock: m3                          0.064   0.012   0.034   ++     +       +
        12    32   average hour earnings                    0.059   0.173   0.014   −−     −−     +
        13    44   lagged dependent (t-8)                   0.059   0.013   0.020   ++     +      −
        14    39   lagged dependent (t-3)                   0.053   0.015   0.023   ++     +      −
        15    16   new one-family houses for sale           0.044   0.024   0.822   −−     −      −−

        41     4   total personal consumption expenditure   0.010   0.019   0.015    +      +     +


Table 7: Summary results of the BACE approach on the expectations component of UM-index
for the period February 1979 - April 2001.

   The first determinant is the 1-month lagged value of the UM-expect. Again, this is
not unexpected as the Dickey-Fuller test in Section 3 was unable to reject a unit root
in this time series. Two other variables have a posterior inclusion probability of more
than 50 percent; new orders of consumer goods and the stock market return. We shortly
discuss these two variables.
    The second determinant is the return on the S&P stock price index. Like in the case
of CB-expect, this variable is considered an important determinant for the UM-expect
index. Moreover, this variable is very robust. With the results of CB-expect in mind,
we can therefore conclude that the stock market return is an important determinant of
expectations component of consumer confidence.
   The third determinant is the new orders consumer goods & materials. In general,
people tend to see this as an indicator for business condition. Higher new orders of


                                                   18
consumer goods & materials indicates better business and overall economic conditions.
Note that this variable appears to be less important in Period 2 (1990s).
    The total personal consumption expenditure ranks 41st and has a very low posterior
inclusion probability of 0.01. Thus again, this variable is very unlikely to be a determi-
nant of the UM expectations component. See Table A7 in the Appendix for a complete
overview.
    We also perform an OLS regression of UM-present on a constant, 1-month lagged
values of UM-expect, S&P stock price, and new orders consumer goods & materials.
Table 8 shows that all variables are strongly significant. Figure 7 illustrates a very good
fit.

            No.                    Variable                           Coefficient              Std.Error      p-value
            (1)                      (2)                                 (3)                     (4)           (5)

             37   lagged dependent (t-1)                                     0.9420                0.0182    0.0000
             24   s&p stock price index                                      0.0677                0.0181    0.0002
             21   new orders consumer goods&materials                        0.0618                0.0181    0.0007




Table 8: Results of an OLS regression of the expectations component of the UM-index.

                        3




                        2




                        1




                        0




                       −1




                       −2
                                                                                       UM expect
                                                                                       fitted

                       −3




                       −4
                            1980   1982   1984   1986   1988   1990   1992    1994    1996   1998    2000




Figure 7: The fit of an OLS regression of the expectations component of the UM-index on
constant, 1-month lagged dependent, S&P stock price index, and new orders consumer goods &
materials.



5     Relations Consumer Confidence and Consumer
      Expenditure
We use total personal consumption expenditure as an indicator for consumer expendi-
ture. We remove the total personal consumption expenditure from our list of explanatory

                                                               19
variables and extend it with 1-month to 3-month lagged values of present and expec-
tations components of the CB-index to see what variables have explanatory effects on
the growth of consumer expenditure, and whether consumer confidence predict consumer
expenditure.
                                     ¯           ¯
   With 53 explanatory variables and k equals 5, k/K equals 0.094. The probabilities
that are equal to or higher than 0.094 are given in bold. Complete results can be found
in the Appendix.

5.1    Does Consumer Confidence predict Consumer Expenditure?

                                                             Post. inclusion prob.          Sign
      Rank   No.                   Variable                  Full      1       2     Full     1     2
       (1)   (2)                     (3)                      (4)     (5)     (6)     (7)    (8)   (9)

        1    18    total inventories                         0.927   0.929   0.083   ++     ++     ++
        2     2    total capacity utilization                0.801   0.918   0.012   −−     −−     +
        3    37    lagged dependent (t-1)                    0.413   0.076   0.940   −−     −−     −−
        4    24    s&p stock price index                     0.327   0.043   0.126   ++     ++     ++
        5    35    consumer price index                      0.262   0.042   0.050   −−     −−     −−
        6    36    implicit price deflator                    0.157   0.021   0.138   −−     −      −−
        7    25    s&p’s dividend yield                      0.139   0.013   0.019   −−     −       −
        8    29    money supply: m2                          0.130   0.021   0.132   ++     +      ++
        9    33    producer price index                      0.083   0.017   0.042   −−     −      −−
       10    12    unemployment rate                         0.059   0.041   0.014   −       −     +
       11    26    s&p’s price-earnings ratio                0.036   0.012   0.049   +      −      ++
       12    17    total housing starts                      0.034   0.019   0.013   ++     +       +
       13     3    personal income                           0.031   0.011   0.074   ++     +      ++
       14    44    lagged dependent (t-8)                    0.030   0.011   0.024   ++     +       +
       15    28    interest rate 3-month u.s.treasury        0.029   0.033   0.017   ++     +       +

       18    49    lagged CB present (t-1)                   0.025   0.009   0.028    +      +     +
       19    11    average unemployment duration in weeks    0.023   0.022   0.012    +      +     +
       23    20    purchasing managers’ index                0.016   0.012   0.011    +      +     +
       25    50    lagged CB expectations (t-1)              0.014   0.015   0.011    +      +     −
       34    52    lagged CB expectations (t-2)              0.009   0.011   0.018    −      +     −
       36    54    lagged CB expectations (t-3)              0.009   0.011   0.012    +      +     −
       44    53    lagged CB present (t-3)                   0.007   0.010   0.011    +      +     −
       46    51    lagged CB present (t-2)                   0.007   0.009   0.020    −      −     −



Table 9: Summary results of the BACE approach on consumer expenditure for the full period
February 1979 - April 2001.

   Table 9 shows summary results of the BACE approach on consumer expenditure. The
first two variables are likely to be determinants of the growth of consumer expenditure,
in particular in Period 1 (1980s). The determinant with the highest posterior inclusion
probability (93 percent) is the growth in total manufacturing and trade inventories. Thus a
high growth in the inventories is a good predictor of a high growth in consumer expenditure
in the following month. The determinant with the second-highest posterior inclusion
probability (80 percent) is total capacity utilization. A low capacity utilization leads to
a high growth of consumer expenditure.



                                                        20
   It should be mentioned, though, that only few variables seem to be very robust.
Particularly in Period 2, only the 1-month and 10-month lags of consumer expenditure
growth have posterior inclusion probability of more than 15 percent. The effect of the
stock market return seems to be robustly positive, whereas the effect of the inflation rate
seems to be robustly negative with sign certainty probabilities of more than 95 percent in
each sample period.
   For our analysis here, the results of the consumer confidence variables are the most
interesting. All six lagged values of the present and expectations components of the
CB-index are unlikely to be determinants of the consumer expenditure, neither for the
full period nor in each sub-period. Among these variables, 1-month lagged value of the
present condition of the CB-index has the highest posterior inclusion probability (0.025).
However, this probability is still very low. See Table A8 in the Appendix for a complete
overview.
   To test the lack of predictive power discussed above, we perform an OLS regression
of consumer expenditure on a constant, 1-month lagged dependent, total inventories,
capacity utilization, stock price return, inflation, and 1-month to 3-month lagged values
of CB-present and CB-expect. The regression results are shown in Table 10.


                 No.            Variable               Coefficient     Std.Error   p-value
                 (1)              (2)                     (3)            (4)        (5)

                  37   lagged dependent (t-1)              -0.2418     0.0622     0.0001
                  18   total inventories                    0.2634     0.0727     0.0004
                   2   total capacity utilization          -0.2162     0.0630     0.0007
                  24   s&p stock price index                0.1683     0.0592     0.0048
                  35   consumer price index                -0.1675     0.0613     0.0068
                  49   lagged CB present (t-1)              0.0570     0.0677     0.4004
                  50   lagged CB expectations (t-1)         0.1989     0.1533     0.1956
                  51   lagged CB present (t-2)              0.0071     0.0691     0.9184
                  52   lagged CB expectations (t-2)        -0.2187     0.2018     0.2795
                  53   lagged CB present (t-3)              0.0144     0.0622     0.8176
                  54   lagged CB expectations (t-3)         0.0634     0.1476     0.6679


            Table 10: Results of an OLS regression of consumer expenditure growth.

   The results in Table 10 show that the five ‘baseline’ regressors are all strongly sig-
nificant at the 0.05 level of significance, while the consumer confidence regressors are
not significant. To test the joint significance of these CB variables, we perform an F -
test. It has a test value of 0.8277 with p-value equals 0.5493. Hence, the null hypothesis
that consumer confidence is not a predictor of consumer expenditure growth cannot be
rejected.




                                                      21
Sensitivity analysis of BACE approach

With the same approach applied in Section 4.1, we test whether BACE is robust for differ-
                                                                     ¯
ent prior expected model sizes for consumer expenditure. Results for k = {2, 5, 10, 15, 25}
are reported in Table A9 in the Appendix.
    While the order of variables with posterior inclusion probabilities higher than prior
inclusion probability change only slightly, the number of variables with high posterior
                                                  ¯
inclusion probabilities substantially decrease as k increases. There are only four variables
                                                                    ¯
that have high posterior inclusion probability for all five different k tested here. These
variables are total inventories, total capacity utilization, 1-month lagged value of total
personal consumption expenditure, and S&P stock price index.
   When we consider the consumer confidence variables, we observe that these variables
                                                                      ¯
are very robust in having low posterior inclusion probabilities. When k is 25, and hence
the prior inclusion probability is 47 percent, no consumer confidence variable obtains pos-
terior inclusion probability higher than 16 percent. Therefore, we conclude that consumer
confidence does not predict consumer expenditure.

5.2    Comparison determinants of Consumer Confidence and Con-
       sumer Expenditure
It is quite surprising that we do not find a relation between contemporaneous consumer
confidence and future consumer expenditure. In Section 4, we find that there is no
predictive effect of consumer expenditure on future consumer confidence either. However,
a contemporaneous relation between these two variables is still possible. In this sub-section
we explore this possibility. If there is a contemporaneous relation between consumer
confidence and expenditure, then one might expect some overlap in the set of (lagged)
determinants of these two variables.
   To see whether consumer confidence and consumer expenditure are determined by the
same variables, we compare the determinants of each series. In Section 4 we observed
that unemployment duration and the purchasing manager’s index are strong indicators
of consumer confidence in consumers’ present condition. Therefore, we report the results
of these two variables in the analysis on consumer expenditure growth in Table 9 as well.
These two variables are unlikely to be determinants of consumer expenditure growth.
   Things are a bit different for the main indicator of the expectations component of
consumer confidence, namely the stock market returns. Table 9 shows that this variable
ranks 4th in the ability to predict consumer expenditure, with a posterior inclusion prob-
ability of 33 percent. Thus it is possible that both consumer confidence’s expectations




                                             22
component and consumer expenditure have the stock market returns as a common deter-
minant. However, the evidence is not very strong.



6     Conclusion
In this paper, we apply the Bayesian Averaging Classical Estimates (BACE) approach
to the data set to answer two research questions; what are the determinants of consumer
confidence and consumer expenditure, and whether consumer confidence and consumer
expenditure are related. The present component and the expectations component of
the Conference Board’s Consumer Confidence Index (CB-index) and the University of
Michigan’s Consumer Sentiment Index (UM-index) are used as dependent variables for
consumer confidence. The dependent variable for consumer expenditure is the growth of
the total personal consumption expenditure.
    We consider a set of 48 economic variables as potential determinants. The BACE
approach is very useful in determining what economic variables are likely to be predictors
of the consumer confidence and consumer expenditure, particularly when there is not
enough theoretical guidance for the researcher to select the appropriate variables for the
analysis. Our results show that the BACE approach is able to select a small set of robust
determinants. For the present component of consumer confidence, these determinants are
the unemployment duration and the purchasing manager’s index. For the expectations
component of consumer confidence, this determinant is the return on stock prices.
    Furthermore, our results show that consumer confidence and consumer expenditure
are unlikely to be related. The total personal consumption expenditure has very low
posterior inclusion probability in the present and expectations components of both CB-
index and UM-index. Therefore, consumer expenditure is very unlikely to be included
in the model for consumer confidence. Furthermore, none of the consumer confidence
variables is considered an important determinant of consumer expenditure. This means
that changes in consumer confidence have no effects on consumer expenditure and vice
versa.
    Sensitivity analyses show that our main results are robust for both CB-index and
UM-index in all sample periods with respect to all prior expected model sizes tested here.
Thus this paper shows that the BACE approach can also be successfully applied in other
contexts than that of economic growth regressions as done in Sala-i-Martin et al. (2004).




                                           23
7     References
Hendry, David F. and J. James Reade. 2005. ‘Problems in Model Averaging with
  Dummy Variables’, mimeo, University of Oxford.
Ludvigson, Sydney C. 2004. ‘Consumer Confidence and Consumer Spending’, Jour-
    nal of Economic Perspectives, 18(2), pp. 29-50.
Madigan, D. and J. York. 1995. ‘Bayesian Graphical Models for Discrete Data’,
  International Statistical Review, 63, pp. 215-232.
Marcellino, Massimiliano; James H. Stock and Mark W. Watson. 2004. ‘A
    Comparison of Direct and Iterated Multistep AR Methods for Forecasting Macroeco-
    nomic Time Series,’ CEPR Discussion Papers 4976.
Sala-i-Martin, Xavier; Gernot Doppelhofer and Ronald I. Miller. 2004. ‘De-
   terminants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE)
    Approach’, The American Economic Review, 94(4), pp. 813-835.
Stock, James H. and Mark W. Watson. 2005. ‘An Empirical Comparison of Methods
    for Forecasting using Many Predictors’, mimeo, Harvard University.
Stock, James H. and Mark W. Watson. 1999. ‘Forecasting Inflation’, Journal of
   Monetary Economics, 44, pp. 293-335.



8     Appendix
This section presents a complete overview of the results obtained in Section 3, 4 and 5.
We first explain how each table is constructed and what it represents.
  Table A1 presents the complete list of explanatory variable we use. The first column
indicates the ID number of the variables in our research. All other columns are shown
as in Marcellino et al. (2004). Variables are divided into seven categories. The last six
variables are in use only when determining consumer expenditure.
   Table A2, A3, A6, A7 and A8 are constructed in the same way. Each table presents
a complete overview of determinants for each series of the dependent variables. Column
(2) lists number of variables corresponding with the numbers shown in the first column of
Table A1. Column (3) shows all variables sorted in descending order with respect to the
posterior inclusion probability of the full period. Column (4)-(6) presents the posterior
inclusion probability for each sub-period. Probabilities equal to or higher than the prior
inclusion probability are given in bold. The posterior mean conditional on inclusion prob-
abilities are shown in column (7), (9) and (11) whereas the posterior standard deviation
conditional on inclusion probabilities are shown in column (8), (10) and (12). The last




                                           24
three columns present the sign certainty probabilities. The probabilities equal to or higher
than 0.95 are given in bold.
   Table A4, A5 and A9 respectively present the posterior inclusion probability obtained
from different prior expected model sizes for the series CB-present, CB-expect and con-
sumer expenditure. The first two rows indicate which prior expected model size is used to
calculate the posterior inclusion probabilities. The variables are sorted in descending order
with respect to the posterior inclusion probabilities obtained with a prior expected model
size equals 5. All probabilities equal to or higher than the prior inclusion probability used
in each column are given in bold.




                                             25
Table A1: 36 explanatory variables, 12 lagged values of dependent variables and 6 lagged
values of CB-present and CB-expect. An explanation of the transformations and the
acronyms is given in Marcellino et al. (2004).

        No.   Trans.                                  Description                              Series
                              Income, Output, Sales, Capacity Utilization
         1    ∆ Ln     sales, business - manufacturing (chained)                               msmq
         2    Lev      capacity utilization total index                                         utl10
         3    ∆ Ln     personal income (chained) (series#52) (bil 1992$,saar)                  gmpyq
         4    ∆ Ln     personal consumption expend (chained) - total (bil 1992$, saar)          gmcq
         5    ∆ Ln     merch wholesalers: total (mil of chained 1996$) (sa)                      wtq
         6    ∆ Ln     mfg&trade: total (mil of chained 1996$) (sa)                            msmtq
         7    ∆ Ln     industrial production index - total index                                ips10
                                     Employment and Unemployment
          8   ∆ Ln     employees on nonag. payrolls: total (thous.,sa)                          lpnag
          9    Ln      employment:ratio; help-wanted ads:no.unemployed clf                       lhelx
         10    Dif     avg.weekly hrs.of prod. wkrs.: total private (sa)                           lw
         11   Lev      unemploy.by duration: average(mean)duration in weeks (sa)               lhu680
         12   Lev      unemployment rate: all workers, 16 years&over (%, sa)                      lhur
         13   ∆ Ln     civilian labor force: employed, total (thous, sa)                         lhem
                                   Construction, Inventories and Orders
         14   ∆ Ln     construct.put in place: total priv&public 1987$ (mil$, saar)             contc
         15   ∆ Ln     new construction put in place - public (c30)                             conqc
         16    Ln      new 1 - family houses for sale at end of month (thous,sa)                 hniv
         17    Ln      housing starts:nonfarm(1947-58);total farm&nonfarm(1959-)(thous,sa)       hsfr
         18   ∆ Ln     mfg&trade inventories: total (mil of chained 1996) (sa)                  ivmtq
         19   ∆ Ln     inventories, business, mfg (mil of chained 1996$, sa)                   ivmfgq
         20   Lev      purchasing managers’ index (sa)                                           pmi
         21   ∆ Ln     new orders (net)-consumer goods&materials, 1996$ (bci)                  mocmq
         22   ∆ Ln     mfg new orders:all manufacturing industries,total,real(mo/pwfsa)(AC)      moq
                                      Interest Rates and Asset Prices
         23    ∆       interest rate: u.s.treasury const maturities, 10-yr. (% per ann, nsa)    fygt10
         24   ∆ Ln     s&p’s common stock price index: composite (1941-43=10)                  fspcom
         25   Lev      s&p’s composite common stock: dividend yield (% per annum)                fsdxp
         26   Lev      s&p’s composite common stock: price-earnings ratio (%,nsa)                fspxe
         27    ∆       interest rate: federal funds (effective) (% per annum, nsa)                 fyff
         28    ∆       interest rate: u.s.treasury bills, sec mkt, 3-mo.(% per ann, nsa)        fygm3
         29   ∆ Ln     money supply - m2 in 1996 (bci)                                          fm2dq
         30   ∆ Ln     united states;effective exchange rate(merm)(index no.)                     exrus
                                    Nominal Prices, Wages, and Money
         31   ∆   Ln   money stock:m3(m2+lg time dep,term rp’s&inst only mmmfs)(bil$,sa)         fm3
         32   ∆   Ln   avg hr earnings of prod wkrs:total private nonagric ($,sa)                 leh
         33   ∆   Ln   producer price index: finished goods (82=100, sa)                         pwfsa
         34   ∆   Ln   index of sensitive materials prices (1990=100)(bci-99a)                 psm99q
         35   ∆   Ln   cpi-u:all items (82-84=100,sa)                                          punew
         36   ∆   Ln   pce,impl pr defl: pce (1987=100)                                          gmdc
                                              Lagged dependent
         37            lagged dependent (t-1)
         38            lagged dependent (t-2)
         39            lagged dependent (t-3)
         40            lagged dependent (t-4)
         41            lagged dependent (t-5)
         42            lagged dependent (t-6)
         43            lagged dependent (t-7)
         44            lagged dependent (t-8)
         45            lagged dependent (t-9)
         46            lagged dependent (t-10)
         47            lagged dependent (t-11)
         48            lagged dependent (t-12)
                                       Lagged Consumer Confidence
         49     ∆      lagged consumer confidence present (Conference Board)(t-1)
         50    Lev     lagged consumer confidence expectations (Conference Board)(t-1)
         51     ∆      lagged consumer confidence present (Conference Board)(t-2)
         52    Lev     lagged consumer confidence expectations (Conference Board)(t-2)
         53     ∆      lagged consumer confidence present (Conference Board)(t-3)
         54    Lev     lagged consumer confidence expectations (Conference Board)(t-3)




                                                    26
     Table A2: Results of the BACE analysis on the present component of the CB-index for all periods.
                                                           Post.inclusion prob.             Posterior conditional on inclusion            Sign certainty prob.
                                                           Full      1      2            Full                1                 2          Full     1       2
     Rank   No.                     Variable                                       Mean     StDev     Mean     StDev    Mean     StDev
      (1)   (2)                        (3)                  (4)     (5)     (6)      (7)       (8)      (9)     (10)     (11)     (12)     (13)    (14)    (15)
       1    11    average unemployment duration in weeks   0.997   0.146   0.573   0.3743    0.1020   0.2943   0.1501   0.3127   0.1161   1.000   0.974   0.996
       2    37    lagged dependent (t-1)                   0.953   0.528   0.098   -0.2635   0.0654  -0.2697   0.0871  -0.2078   0.0987   1.000   0.999   0.981
       3    28    interest rate 3-month u.s.treasury       0.852   0.160   0.328   0.2456    0.0663   0.2087   0.0888   0.2677   0.0970   1.000   0.990   0.997
       4    20    purchasing managers’ index               0.470   0.907   0.093   0.2519    0.0808   0.4928   0.1271   0.2228   0.1052   0.999   1.000   0.982
       5    17    total housing starts                     0.256   0.064   0.025   0.1906    0.0644   0.2526   0.1383   0.1312   0.1420   0.998   0.965   0.821
       6     9    ratio advertisement:unemployed           0.167   0.081   0.051   0.2330    0.0971   0.1336   0.3813   0.2770   0.3264   0.991   0.637   0.801
       7    13    total civilian labor force               0.072   0.054   0.074   0.1365    0.0634   0.1591   0.0867   0.1817   0.0924   0.984   0.966   0.974
       8    24    s&p stock price index                    0.062   0.088   0.012   0.1251    0.0633   0.1650   0.0800   0.0346   0.0907   0.975   0.980   0.648
       9    38    lagged dependent (t-2)                   0.047   0.015   0.017   -0.1274   0.0672  -0.0534   0.1130  -0.0905   0.1058   0.971   0.681   0.803
      10    27    interest rate federal funds              0.036   0.016   0.030   0.1211    0.0696   0.0774   0.0839   0.1396   0.1085   0.958   0.821   0.900
      11    48    lagged dependent (t-12)                  0.032   0.016   0.356   0.0989    0.0585   0.0739   0.0777   0.2524   0.0899   0.954   0.828   0.997
      12    23    interest rate 10-year u.s.treasury       0.030   0.029   0.019   0.1261    0.0798   0.1314   0.0990   0.0874   0.1069   0.942   0.907   0.792
      13    10    average working hours per week           0.026   0.019   0.044   0.0889    0.0562   0.0882   0.0784   0.1520   0.0903   0.943   0.869   0.953
      14    29    money supply: m2                         0.021   0.023   0.014   0.0852    0.0634   0.1181   0.0989   0.0313   0.1258   0.910   0.883   0.598
      15    15    new public construction put in place     0.020   0.027   0.011   -0.0806   0.0582  -0.1166   0.0920  -0.0343   0.0902   0.916   0.897   0.648
      16     2    total capacity utilization               0.019   0.657   0.022   -0.1118   0.1418  -0.3472   0.1594   0.1155   0.1361   0.785   0.984   0.801
      17    21    new orders consumer goods&materials      0.018   0.035   0.011   0.0802    0.0628   0.1363   0.0920   0.0204   0.0966   0.899   0.930   0.583
      18    12    unemployment rate                        0.018   0.077   0.044   -0.0673   0.1339   0.1502   0.2552   0.0105   0.4575   0.692   0.721   0.509
      19    25    s&p’s dividend yield                     0.016   0.017   0.031   -0.0786   0.0782  -0.1025   0.1358  -0.0876   0.2176   0.842   0.774   0.656
      20    45    lagged dependent (t-9)                   0.016   0.018   0.018   0.0699    0.0568   0.0834   0.0778   0.0941   0.0924   0.890   0.857   0.845
      21    47    lagged dependent (t-11)                  0.015   0.011   0.015   -0.0716   0.0593  -0.0380   0.0802  -0.0750   0.0953   0.886   0.682   0.784
      22    31    money stock: m3                          0.013   0.016   0.015   0.0607    0.0614   0.0789   0.0857   0.0283   0.1324   0.838   0.821   0.584




27
      23    30    u.s.effective exchange rate               0.013   0.025   0.012   0.0612    0.0583   0.1064   0.0811  -0.0044   0.1044   0.853   0.904   0.517
      24    26    s&p’s price-earnings ratio               0.012   0.013   0.023   0.0612    0.0661  -0.0291   0.1667   0.1025   0.1308   0.822   0.569   0.783
      25    34    index of sensitive materials prices      0.012   0.013   0.015   0.0609    0.0687   0.0543   0.1134   0.0696   0.0981   0.812   0.684   0.760
      26    43    lagged dependent (t-7)                   0.012   0.015   0.012   -0.0544   0.0621  -0.0712   0.0815  -0.0316   0.0967   0.809   0.808   0.628
      27     8    total employees                          0.012   0.013   0.015   -0.0278   0.1132  -0.0696   0.1304   0.0410   0.1281   0.597   0.703   0.625
      28    39    lagged dependent (t-3)                   0.011   0.012   0.020   0.0561    0.0656   0.0542   0.0920   0.1018   0.0996   0.803   0.722   0.846
      29    40    lagged dependent (t-4)                   0.010   0.022   0.013   -0.0459   0.0619  -0.1050   0.0839   0.0512   0.0942   0.771   0.894   0.706
      30     7    total industrial production              0.010   0.016   0.012   -0.0449   0.0730  -0.0889   0.1036   0.0290   0.0984   0.731   0.804   0.616
      31    46    lagged dependent (t-10)                  0.010   0.013   0.013   0.0387    0.0581   0.0558   0.0781   0.0564   0.0952   0.747   0.762   0.723
      32    18    total inventories                        0.009   0.029   0.082   -0.0076   0.0776  -0.1364   0.0987   0.1961   0.0968   0.539   0.915   0.978
      33    44    lagged dependent (t-8)                   0.009   0.012   0.012   0.0357    0.0600   0.0480   0.0803   0.0453   0.0933   0.724   0.725   0.686
      34    22    new orders in manufacturing              0.008   0.011   0.013   0.0339    0.0572  -0.0239   0.0890   0.0602   0.0888   0.723   0.606   0.750
      35    16    new one-family houses for sale           0.008   0.047   0.011   0.0079    0.0842  -0.0616   0.2488  -0.0106   0.0991   0.537   0.598   0.542
      36    19    inventories, business&manufacturing      0.008   0.021   0.018   -0.0014   0.0697  -0.1136   0.1115   0.0898   0.0984   0.508   0.845   0.818
      37    32    average hour earnings                    0.008   0.010   0.082   0.0279    0.0578  -0.0217   0.0801   0.1966   0.0975   0.685   0.606   0.977
      38    14    total construction put in place          0.008   0.012   0.013   0.0121    0.0734   0.0576   0.1328   0.0517   0.0890   0.565   0.667   0.719
      39     4    total personal consumption expenditure   0.008   0.011   0.013   -0.0247   0.0587  -0.0411   0.0834  -0.0442   0.0890   0.663   0.689   0.690
      40    42    lagged dependent (t-6)                   0.008   0.013   0.013   -0.0223   0.0626  -0.0621   0.0842   0.0451   0.0946   0.639   0.769   0.683
      41     1    sales, business&manufacturing            0.008   0.011   0.014   -0.0279   0.0696  -0.0328   0.1072  -0.0663   0.0948   0.655   0.620   0.757
      42    35    consumer price index                     0.008   0.012   0.011   0.0078    0.0686  -0.0375   0.1050   0.0238   0.0921   0.545   0.639   0.602
      43    41    lagged dependent (t-5)                   0.008   0.013   0.014   -0.0023   0.0632   0.0622   0.0881  -0.0650   0.0966   0.514   0.759   0.749
      44    36    implicit price deflator                   0.008   0.012   0.013   0.0014    0.0691   0.0240   0.1008  -0.0530   0.0937   0.508   0.594   0.714
      45     6    total manufacturing&trade                0.008   0.010   0.011   -0.0145   0.0645  -0.0046   0.0928  -0.0198   0.0933   0.589   0.520   0.584
      46     3    personal income                          0.007   0.010   0.015   0.0053    0.0638  -0.0037   0.0864   0.0647   0.0965   0.533   0.517   0.748
      47     5    total merchandise wholesalers            0.007   0.010   0.011   -0.0139   0.0575  -0.0091   0.0800   0.0157   0.0892   0.596   0.545   0.570
      48    33    producer price index                     0.007   0.026   0.014   0.0046    0.0626   0.1171   0.0868  -0.0652   0.0894   0.529   0.910   0.766
     Table A3: Results of the BACE analysis on the expectations component of the CB-index for all periods.
                                                           Post.inclusion prob.             Posterior conditional on inclusion            Sign certainty prob.
                                                           Full      1      2            Full                1                 2          Full     1       2
     Rank   No.                     Variable                                       Mean     StDev     Mean     StDev    Mean     StDev
      (1)   (2)                        (3)                  (4)     (5)     (6)      (7)       (8)      (9)     (10)     (11)     (12)     (13)    (14)    (15)
       1    37    lagged dependent (t-1)                   1.000   1.000   1.000   0.8662    0.0363   0.8868   0.0534   0.7302   0.0980   1.000   1.000   1.000
       2    24    s&p stock price index                    0.935   0.767   0.338   0.1130    0.0303   0.1043   0.0312   0.1302   0.0473   1.000   0.999   0.997
       3    23    interest rate 10-year u.s.treasury       0.461   0.018   0.364   0.0915    0.0296   0.0334   0.0437   0.1462   0.0509   0.999   0.778   0.998
       4    29    money supply: m2                         0.351   0.030   0.033   0.0876    0.0301   0.0501   0.0351   0.0921   0.0713   0.998   0.922   0.900
       5    21    new orders consumer goods&materials      0.268   0.820   0.011   0.0753    0.0273   0.1380   0.0486   0.0096   0.0494   0.997   0.997   0.577
       6    35    consumer price index                     0.089   0.031   0.039   -0.0751   0.0331  -0.0559   0.0397   0.0982   0.0726   0.988   0.919   0.911
       7    44    lagged dependent (t-8)                   0.088   0.134   0.016   0.0777    0.0356   0.1528   0.0679   0.0315   0.0808   0.985   0.987   0.651
       8    33    producer price index                     0.083   0.010   0.268   -0.0692   0.0310  -0.0011   0.0372  -0.1272   0.0529   0.987   0.512   0.991
       9    28    interest rate 3-month u.s.treasury       0.056   0.018   0.193   0.0642    0.0321   0.0375   0.0376   0.1401   0.0565   0.977   0.840   0.993
      10    20    purchasing managers’ index               0.045   0.015   0.062   0.0729    0.0396   0.0404   0.0544   0.1250   0.0734   0.967   0.770   0.954
      11    31    money stock: m3                          0.043   0.021   0.035   0.0553    0.0311   0.0385   0.0320   0.0982   0.0724   0.962   0.885   0.911
      12    14    total construction put in place          0.036   0.027   0.013   0.0495    0.0277   0.0507   0.0367   0.0283   0.0483   0.962   0.915   0.720
      13     2    total capacity utilization               0.036   0.098   0.112   -0.0593   0.0416  -0.0892   0.0689   0.2491   0.1407   0.923   0.901   0.960
      14    17    total housing starts                     0.029   0.016   0.040   0.0543    0.0338   0.0361   0.0411  -0.1445   0.1450   0.945   0.810   0.839
      15    11    average unemployment duration in weeks   0.028   0.109   0.127   0.0482    0.0304   0.0860   0.0403  -0.2325   0.1191   0.943   0.983   0.973
      16    45    lagged dependent (t-9)                   0.027   0.021   0.025   0.0542    0.0390   0.0682   0.1111   0.0803   0.0765   0.917   0.730   0.852
      17    36    implicit price deflator                   0.025   0.016   0.014   -0.0524   0.0406  -0.0331   0.0431   0.0113   0.0653   0.901   0.778   0.569
      18    43    lagged dependent (t-7)                   0.024   0.030   0.019   0.0506    0.0404   0.0719   0.0592  -0.0595   0.0872   0.894   0.887   0.752
      19     1    sales, business&manufacturing            0.022   0.031   0.012   0.0380    0.0349   0.0573   0.0504  -0.0120   0.0501   0.861   0.871   0.594
      20     4    total personal consumption expenditure   0.022   0.096   0.012   -0.0428   0.0295  -0.0739   0.0344  -0.0211   0.0463   0.926   0.983   0.675
      21     3    personal income                          0.019   0.010   0.143   0.0406    0.0300   0.0020   0.0359   0.1189   0.0514   0.911   0.523   0.989
      22    16    new one-family houses for sale           0.017   0.023   0.041   -0.0382   0.0320  -0.0151   0.0712  -0.0946   0.0771   0.883   0.584   0.889




28
      23    15    new public construction put in place     0.015   0.010   0.018   0.0322    0.0271   0.0027   0.0338   0.0472   0.0466   0.882   0.532   0.843
      24    25    s&p’s dividend yield                     0.014   0.017   0.025   -0.0403   0.0456  -0.0518   0.0786  -0.0796   0.1463   0.811   0.745   0.706
      25    27    interest rate federal funds              0.013   0.032   0.017   -0.0311   0.0313  -0.0484   0.0323   0.0345   0.0682   0.840   0.932   0.693
      26     6    total manufacturing&trade                0.013   0.017   0.012   0.0134    0.0435  -0.0172   0.0610  -0.0127   0.0495   0.621   0.611   0.601
      27     9    ratio advertisement:unemployed           0.011   0.030   0.378   0.0007    0.0689   0.0153   0.1179   0.2847   0.1204   0.504   0.551   0.990
      28    26    s&p’s price-earnings ratio               0.011   0.011   0.030   0.0245    0.0310  -0.0070   0.0717   0.0888   0.0743   0.785   0.539   0.883
      29    42    lagged dependent (t-6)                   0.011   0.015   0.023   0.0186    0.0465   0.0171   0.0646  -0.0647   0.1057   0.655   0.604   0.729
      30    41    lagged dependent (t-5)                   0.011   0.013   0.267   -0.0278   0.0493   0.0216   0.0551  -0.1997   0.0752   0.713   0.652   0.995
      31    12    unemployment rate                        0.011   0.037   0.176   0.0141    0.0772   0.0525   0.0590  -0.2580   0.1393   0.572   0.812   0.967
      32    48    lagged dependent (t-12)                  0.010   0.029   0.170   0.0232    0.0341  -0.0624   0.0560   0.1540   0.0622   0.752   0.867   0.993
      33    19    inventories, business&manufacturing      0.010   0.013   0.012   -0.0193   0.0302  -0.0129   0.0428  -0.0028   0.0551   0.738   0.618   0.520
      34    34    index of sensitive materials prices      0.010   0.012   0.023   -0.0210   0.0323  -0.0187   0.0342  -0.0626   0.0577   0.742   0.707   0.860
      35     7    total industrial production              0.010   0.094   0.033   0.0177    0.0357  -0.0873   0.0412   0.0742   0.0525   0.690   0.982   0.920
      36    22    new orders in manufacturing              0.010   0.274   0.012   -0.0018   0.0371  -0.1100   0.0408   0.0218   0.0463   0.519   0.996   0.680
      37    46    lagged dependent (t-10)                  0.010   0.038   0.019   0.0014    0.0495  -0.1180   0.0897   0.0343   0.0945   0.511   0.905   0.641
      38    30    u.s.effective exchange rate               0.009   0.010   0.016   0.0183    0.0280  -0.0061   0.0308   0.0387   0.0532   0.743   0.579   0.766
      39    47    lagged dependent (t-11)                  0.009   0.131   0.085   0.0086    0.0378  -0.1413   0.0671   0.1358   0.0666   0.590   0.981   0.978
      40    10    average working hours per week           0.009   0.013   0.034   0.0165    0.0278  -0.0217   0.0335   0.0690   0.0463   0.724   0.741   0.930
      41    38    lagged dependent (t-2)                   0.009   0.045   0.098   -0.0226   0.0740   0.1549   0.0944  -0.2291   0.1096   0.620   0.949   0.981
      42    40    lagged dependent (t-4)                   0.009   0.013   0.062   -0.0027   0.0473   0.0242   0.0613  -0.1526   0.0895   0.523   0.653   0.954
      43    39    lagged dependent (t-3)                   0.008   0.013   0.020   -0.0034   0.0524  -0.0439   0.0828  -0.0731   0.1082   0.526   0.701   0.750
      44     8    total employees                          0.008   0.012   0.043   -0.0085   0.0391  -0.0166   0.0438  -0.1007   0.0688   0.586   0.647   0.927
      45     5    total merchandise wholesalers            0.008   0.012   0.017   -0.0046   0.0312   0.0126   0.0393  -0.0433   0.0471   0.558   0.625   0.820
      46    32    average hour earnings                    0.008   0.013   0.042   -0.0073   0.0298  -0.0228   0.0335   0.0852   0.0535   0.596   0.752   0.943
      47    18    total inventories                        0.008   0.011   0.013   -0.0056   0.0309   0.0072   0.0383   0.0109   0.0589   0.572   0.575   0.574
      48    13    total civilian labor force               0.007   0.010   0.011   0.0024    0.0284  -0.0093   0.0331  -0.0138   0.0468   0.534   0.611   0.616
Table A4: Posterior inclusion probability obtained from different prior expected model
sizes for the present component of the CB-index.


                   Prior expected model size                  2       5      10      15      25
                   Prior inclusion probability              0.042   0.104   0.208   0.313   0.521

      Rank   No.                   Variable                    Posterior inclusion probability

        1    11    average unemployment duration in weeks   0.984   0.997   0.999   0.999   0.998
        2    37    lagged dependent (t-1)                   0.802   0.953   0.988   0.995   0.999
        3    28    interest rate 3-month u.s.treasury       0.718   0.852   0.889   0.879   0.823
        4    20    purchasing managers’ index               0.453   0.470   0.516   0.581   0.739
        5    17    total housing starts                     0.181   0.256   0.284   0.300   0.312
        6     9    ratio advertisement:unemployed           0.109   0.167   0.213   0.243   0.389
        7    13    total civilian labor force               0.046   0.072   0.116   0.159   0.265
        8    24    s&p stock price index                    0.021   0.062   0.134   0.228   0.432
        9    38    lagged dependent (t-2)                   0.013   0.047   0.120   0.214   0.466
       10    27    interest rate federal funds              0.023   0.036   0.062   0.095   0.203
       11    48    lagged dependent (t-12)                  0.017   0.032   0.060   0.094   0.196
       12    23    interest rate 10-year u.s.treasury       0.013   0.030   0.065   0.114   0.253
       13    10    average working hours per week           0.011   0.026   0.056   0.091   0.228
       14    29    money supply: m2                         0.008   0.021   0.048   0.082   0.157
       15    15    new public construction put in place     0.007   0.020   0.044   0.075   0.162
       16     2    total capacity utilization               0.008   0.019   0.044   0.077   0.214
       17    21    new orders consumer goods&materials      0.007   0.018   0.042   0.077   0.211
       18    12    unemployment rate                        0.009   0.018   0.033   0.053   0.119
       19    25    s&p’s dividend yield                     0.006   0.016   0.033   0.054   0.113
       20    45    lagged dependent (t-9)                   0.006   0.016   0.030   0.049   0.096
       21    47    lagged dependent (t-11)                  0.006   0.015   0.036   0.059   0.120
       22    31    money stock: m3                          0.005   0.013   0.029   0.047   0.098
       23    30    u.s.effective exchange rate               0.005   0.013   0.031   0.054   0.149
       24    26    s&p’s price-earnings ratio               0.005   0.012   0.026   0.044   0.094
       25    34    index of sensitive materials prices      0.006   0.012   0.025   0.041   0.092
       26    43    lagged dependent (t-7)                   0.005   0.012   0.026   0.045   0.110
       27     8    total employees                          0.005   0.012   0.029   0.054   0.209
       28    39    lagged dependent (t-3)                   0.005   0.011   0.021   0.033   0.073
       29    40    lagged dependent (t-4)                   0.003   0.010   0.023   0.040   0.098
       30     7    total industrial production              0.004   0.010   0.023   0.041   0.115
       31    46    lagged dependent (t-10)                  0.004   0.010   0.021   0.035   0.079
       32    18    total inventories                        0.004   0.009   0.020   0.034   0.082
       33    44    lagged dependent (t-8)                   0.004   0.009   0.020   0.033   0.072
       34    22    new orders in manufacturing              0.003   0.008   0.019   0.033   0.080
       35    16    new one-family houses for sale           0.004   0.008   0.019   0.033   0.077
       36    19    inventories, business&manufacturing      0.003   0.008   0.018   0.031   0.073
       37    32    average hour earnings                    0.003   0.008   0.018   0.030   0.074
       38    14    total construction put in place          0.003   0.008   0.018   0.032   0.083
       39     4    total personal consumption expenditure   0.003   0.008   0.018   0.031   0.075
       40    42    lagged dependent (t-6)                   0.003   0.008   0.018   0.033   0.079
       41     1    sales, business&manufacturing            0.003   0.008   0.018   0.035   0.091
       42    35    consumer price index                     0.003   0.008   0.017   0.031   0.074
       43    41    lagged dependent (t-5)                   0.002   0.008   0.017   0.029   0.067
       44    36    implicit price deflator                   0.003   0.008   0.017   0.031   0.075
       45     6    total manufacturing&trade                0.003   0.008   0.017   0.031   0.080
       46     3    personal income                          0.003   0.007   0.016   0.028   0.066
       47     5    total merchandise wholesalers            0.002   0.007   0.016   0.030   0.070
       48    33    producer price index                     0.002   0.007   0.017   0.028   0.069




                                                  29
Table A5: Posterior inclusion probability obtained from different prior expected model
sizes for the expectations component of the CB-index.


                   Prior expected model size                  2       5      10      15      25
                   Prior inclusion probability              0.042   0.104   0.208   0.313   0.521

      Rank   No.                   Variable                    Posterior inclusion probability

        1    37    lagged dependent (t-1)                   1.000   1.000   1.000   1.000   1.000
        2    24    s&p stock price index                    0.823   0.935   0.980   0.992   0.998
        3    23    interest rate 10-year u.s.treasury       0.164   0.461   0.725   0.845   0.937
        4    29    money supply: m2                         0.177   0.351   0.449   0.470   0.472
        5    21    new orders consumer goods&materials      0.140   0.268   0.411   0.522   0.701
        6    35    consumer price index                     0.036   0.089   0.140   0.172   0.212
        7    44    lagged dependent (t-8)                   0.024   0.088   0.199   0.294   0.447
        8    33    producer price index                     0.033   0.083   0.135   0.173   0.227
        9    28    interest rate 3-month u.s.treasury       0.032   0.056   0.067   0.074   0.103
       10    20    purchasing managers’ index               0.013   0.045   0.101   0.171   0.384
       11    31    money stock: m3                          0.018   0.043   0.079   0.113   0.185
       12    14    total construction put in place          0.018   0.036   0.059   0.079   0.132
       13     2    total capacity utilization               0.013   0.036   0.088   0.152   0.351
       14    17    total housing starts                     0.012   0.029   0.054   0.080   0.136
       15    11    average unemployment duration in weeks   0.010   0.028   0.058   0.088   0.156
       16    45    lagged dependent (t-9)                   0.009   0.027   0.062   0.095   0.170
       17    36    implicit price deflator                   0.009   0.025   0.048   0.068   0.117
       18    43    lagged dependent (t-7)                   0.007   0.024   0.051   0.076   0.126
       19     1    sales, business&manufacturing            0.010   0.022   0.039   0.058   0.101
       20     4    total personal consumption expenditure   0.005   0.022   0.065   0.129   0.331
       21     3    personal income                          0.009   0.019   0.036   0.060   0.136
       22    16    new one-family houses for sale           0.006   0.017   0.037   0.060   0.109
       23    15    new public construction put in place     0.006   0.015   0.034   0.058   0.124
       24    25    s&p’s dividend yield                     0.005   0.014   0.035   0.063   0.152
       25    27    interest rate federal funds              0.004   0.013   0.033   0.055   0.133
       26     6    total manufacturing&trade                0.006   0.013   0.029   0.047   0.108
       27     9    ratio advertisement:unemployed           0.004   0.011   0.028   0.053   0.147
       28    26    s&p’s price-earnings ratio               0.003   0.011   0.024   0.041   0.096
       29    42    lagged dependent (t-6)                   0.003   0.011   0.025   0.041   0.087
       30    41    lagged dependent (t-5)                   0.004   0.011   0.024   0.046   0.125
       31    12    unemployment rate                        0.003   0.011   0.030   0.056   0.153
       32    48    lagged dependent (t-12)                  0.004   0.010   0.024   0.043   0.100
       33    19    inventories, business&manufacturing      0.004   0.010   0.020   0.036   0.075
       34    34    index of sensitive materials prices      0.003   0.010   0.027   0.056   0.177
       35     7    total industrial production              0.003   0.010   0.021   0.035   0.074
       36    22    new orders in manufacturing              0.004   0.010   0.022   0.038   0.083
       37    46    lagged dependent (t-10)                  0.003   0.010   0.025   0.043   0.103
       38    30    u.s.effective exchange rate               0.003   0.009   0.019   0.030   0.069
       39    47    lagged dependent (t-11)                  0.003   0.009   0.020   0.036   0.078
       40    10    average working hours per week           0.003   0.009   0.020   0.035   0.080
       41    38    lagged dependent (t-2)                   0.004   0.009   0.018   0.029   0.067
       42    40    lagged dependent (t-4)                   0.004   0.009   0.019   0.033   0.075
       43    39    lagged dependent (t-3)                   0.003   0.008   0.018   0.031   0.071
       44     8    total employees                          0.003   0.008   0.021   0.040   0.106
       45     5    total merchandise wholesalers            0.002   0.008   0.019   0.035   0.081
       46    32    average hour earnings                    0.003   0.008   0.019   0.030   0.074
       47    18    total inventories                        0.003   0.008   0.018   0.032   0.079
       48    13    total civilian labor force               0.003   0.007   0.016   0.029   0.072




                                                  30
     Table A6: Results of the BACE analysis on the present component of the UM-index for all periods.
                                                           Post.inclusion prob.             Posterior conditional on inclusion            Sign certainty prob.
                                                           Full      1      2            Full                1                 2          Full     1       2
     Rank   No.                     Variable                                       Mean     StDev     Mean     StDev    Mean     StDev
      (1)   (2)                        (3)                  (4)     (5)     (6)      (7)       (8)      (9)     (10)     (11)     (12)     (13)    (14)    (15)
       1    37    lagged dependent (t-1)                   1.000   1.000   1.000   0.7285    0.0641   0.8202   0.0894   0.5114   0.0958   1.000   1.000   1.000
       2    29    money supply: m2                         0.762   0.545   0.019   0.0802    0.0218   0.0931   0.0292   0.0424   0.0453   1.000   0.999   0.824
       3    20    purchasing managers’ index               0.599   0.187   0.077   0.0934    0.0275   0.0945   0.0381   0.0750   0.0396   1.000   0.993   0.970
       4    42    lagged dependent (t-6)                   0.550   0.170   0.018   0.1445    0.0438   0.1429   0.0596  -0.0763   0.0977   0.999   0.991   0.782
       5    11    average unemployment duration in weeks   0.520   0.102   0.116   0.0931    0.0394   0.1135   0.0737   0.0958   0.0451   0.991   0.937   0.982
       6    10    average working hours per week           0.393   0.035   0.361   0.0547    0.0183   0.0419   0.0274   0.0866   0.0307   0.998   0.936   0.997
       7    48    lagged dependent (t-12)                  0.308   0.055   0.019   0.1451    0.0509   0.1071   0.0639   0.0468   0.1095   0.998   0.952   0.665
       8    36    implicit price deflator                   0.183   0.243   0.017   -0.0833   0.0295  -0.0966   0.0347  -0.0305   0.0322   0.997   0.997   0.828
       9    25    s&p’s dividend yield                     0.127   0.153   0.023   -0.0970   0.0660  -0.1072   0.0463  -0.0629   0.1466   0.928   0.989   0.666
      10    47    lagged dependent (t-11)                  0.125   0.044   0.018   0.1303    0.0543   0.0984   0.0637   0.0249   0.1122   0.991   0.938   0.588
      11    24    s&p stock price index                    0.113   0.205   0.011   0.0434    0.0184   0.0650   0.0256  -0.0031   0.0305   0.990   0.994   0.540
      12     9    ratio advertisement:unemployed           0.110   0.032   0.976   0.1432    0.0875   0.1138   0.1201   0.5299   0.1762   0.949   0.827   0.998
      13     8    total employees                          0.100   0.041   0.250   0.0732    0.0303   0.0587   0.0366   0.0979   0.0361   0.992   0.945   0.996
      14    45    lagged dependent (t-9)                   0.086   0.019   0.015   0.1161    0.0516   0.0522   0.0649   0.0207   0.1130   0.987   0.789   0.572
      15    44    lagged dependent (t-8)                   0.084   0.032   0.016   0.1142    0.0501   0.0835   0.0632  -0.0622   0.1010   0.988   0.906   0.730
      16     7    total industrial production              0.083   0.062   0.022   0.0558    0.0254   0.0647   0.0350   0.0390   0.0384   0.985   0.966   0.844
      17    17    total housing starts                     0.063   0.113   0.018   0.0645    0.0328   0.0786   0.0357   0.0540   0.0788   0.975   0.985   0.753
      18    46    lagged dependent (t-10)                  0.057   0.018   0.021   0.1077    0.0552   0.0412   0.0671   0.0851   0.1140   0.974   0.730   0.772
      19    26    s&p’s price-earnings ratio               0.042   0.026   0.099   0.0506    0.0315   0.0406   0.0596   0.1008   0.0527   0.945   0.751   0.971
      20    27    interest rate federal funds              0.038   0.019   0.033   0.0378    0.0213   0.0306   0.0275   0.0536   0.0374   0.961   0.866   0.923
      21     3    personal income                          0.036   0.135   0.012   0.0402    0.0233   0.0656   0.0284  -0.0071   0.0338   0.957   0.989   0.583
      22    41    lagged dependent (t-5)                   0.036   0.247   0.096   0.0874    0.0577   0.1540   0.0581  -0.1667   0.0790   0.935   0.996   0.981




31
      23    12    unemployment rate                        0.034   0.029   0.186   0.0967    0.1919  -0.1044   0.1636   0.3359   0.1541   0.693   0.738   0.984
      24    43    lagged dependent (t-7)                   0.032   0.023   0.024   0.0815    0.0613   0.0570   0.0759  -0.1033   0.0900   0.908   0.773   0.873
      25    35    consumer price index                     0.029   0.031   0.011   -0.0485   0.0349  -0.0461   0.0548   0.0065   0.0335   0.917   0.799   0.576
      26    16    new one-family houses for sale           0.028   0.018   0.108   -0.0428   0.0327  -0.0196   0.0857  -0.0800   0.0377   0.905   0.590   0.982
      27    13    total civilian labor force               0.027   0.033   0.011   -0.0331   0.0209  -0.0453   0.0297  -0.0104   0.0315   0.943   0.935   0.629
      28    34    index of sensitive materials prices      0.022   0.012   0.034   -0.0310   0.0232   0.0048   0.0329  -0.0489   0.0340   0.909   0.558   0.923
      29    31    money stock: m3                          0.022   0.019   0.012   -0.0112   0.0387  -0.0186   0.0493   0.0107   0.0481   0.614   0.647   0.588
      30    15    new public construction put in place     0.020   0.017   0.012   0.0251    0.0180   0.0254   0.0270   0.0177   0.0311   0.917   0.826   0.715
      31    38    lagged dependent (t-2)                   0.020   0.016   0.026   0.0918    0.0683   0.0777   0.0972   0.1370   0.1091   0.910   0.787   0.894
      32    21    new orders consumer goods&materials      0.019   0.109   0.012   0.0253    0.0187   0.0600   0.0271   0.0018   0.0385   0.911   0.986   0.519
      33    14    total construction put in place          0.019   0.041   0.011   0.0262    0.0200   0.0487   0.0299   0.0002   0.0307   0.904   0.947   0.503
      34    22    new orders in manufacturing              0.017   0.075   0.011   0.0234    0.0181   0.0542   0.0268  -0.0094   0.0308   0.902   0.977   0.619
      35     2    total capacity utilization               0.017   0.025   0.099   -0.0379   0.0639  -0.0667   0.0911   0.1682   0.0971   0.723   0.767   0.957
      36    32    average hour earnings                    0.016   0.022   0.015   -0.0242   0.0223  -0.0397   0.0347   0.0258   0.0352   0.861   0.873   0.768
      37     4    total personal consumption expenditure   0.012   0.036   0.018   0.0186    0.0191   0.0441   0.0283  -0.0285   0.0303   0.835   0.940   0.826
      38    40    lagged dependent (t-4)                   0.011   0.035   0.052   0.0228    0.0663   0.0959   0.0742  -0.1428   0.0827   0.635   0.901   0.957
      39    28    interest rate 3-month u.s.treasury       0.011   0.013   0.059   0.0171    0.0222   0.0167   0.0310   0.0631   0.0344   0.779   0.704   0.965
      40    33    producer price index                     0.010   0.021   0.011   -0.0110   0.0263  -0.0387   0.0367   0.0088   0.0312   0.662   0.853   0.611
      41     6    total manufacturing&trade                0.009   0.034   0.037   0.0111    0.0211   0.0448   0.0313  -0.0486   0.0325   0.700   0.922   0.931
      42    19    inventories, business&manufacturing      0.009   0.013   0.012   -0.0109   0.0223  -0.0159   0.0357   0.0014   0.0355   0.687   0.672   0.516
      43     5    total merchandise wholesalers            0.009   0.012   0.070   -0.0102   0.0201   0.0047   0.0324  -0.0591   0.0306   0.693   0.557   0.972
      44    23    interest rate 10-year u.s.treasury       0.009   0.015   0.029   -0.0023   0.0220  -0.0197   0.0324   0.0431   0.0316   0.541   0.728   0.913
      45    39    lagged dependent (t-3)                   0.008   0.015   0.048   -0.0065   0.0623   0.0385   0.0886  -0.1564   0.0927   0.541   0.668   0.953
      46    18    total inventories                        0.008   0.024   0.019   0.0020    0.0240   0.0398   0.0330  -0.0406   0.0479   0.534   0.885   0.801
      47     1    sales, business&manufacturing            0.008   0.060   0.022   0.0052    0.0200   0.0515   0.0275  -0.0371   0.0348   0.603   0.968   0.855
      48    30    u.s.effective exchange rate               0.008   0.015   0.015   -0.0047   0.0181  -0.0237   0.0275   0.0247   0.0307   0.603   0.805   0.789
     Table A7: Results of the BACE analysis on the expectations component of the UM-index for all periods.
                                                           Post.inclusion prob.             Posterior conditional on inclusion            Sign certainty prob.
                                                           Full      1      2            Full                1                 2          Full     1       2
     Rank   No.                     Variable                                       Mean     StDev     Mean     StDev    Mean     StDev
      (1)   (2)                        (3)                  (4)     (5)     (6)      (7)       (8)      (9)     (10)     (11)     (12)     (13)    (14)    (15)
       1    37    lagged dependent (t-1)                   1.000   1.000   1.000   0.8967    0.0458   0.9033   0.0462   0.5341   0.1184   1.000   1.000   1.000
       2    24    s&p stock price index                    0.847   0.147   0.728   0.0681    0.0188   0.0608   0.0257   0.0952   0.0295   1.000   0.990   0.999
       3    21    new orders consumer goods&materials      0.553   0.417   0.032   0.0639    0.0191   0.0799   0.0267   0.0431   0.0308   1.000   0.998   0.917
       4    29    money supply: m2                         0.206   0.061   0.024   0.0564    0.0212   0.0578   0.0302   0.0540   0.0458   0.996   0.971   0.880
       5    36    implicit price deflator                   0.156   0.145   0.012   -0.0647   0.0258  -0.0851   0.0354   0.0037   0.0321   0.994   0.991   0.546
       6    43    lagged dependent (t-7)                   0.148   0.043   0.032   0.0831    0.0333   0.0963   0.0672  -0.1144   0.0867   0.993   0.923   0.905
       7     6    total manufacturing&trade                0.147   0.128   0.032   0.0565    0.0213   0.0687   0.0292   0.0429   0.0308   0.996   0.990   0.917
       8     3    personal income                          0.125   0.039   0.275   0.0493    0.0204   0.0483   0.0299   0.0774   0.0297   0.992   0.946   0.995
       9     1    sales, business&manufacturing            0.103   0.119   0.021   0.0518    0.0212   0.0660   0.0287   0.0315   0.0315   0.992   0.988   0.840
      10    35    consumer price index                     0.088   0.227   0.012   -0.0559   0.0253  -0.0880   0.0332   0.0094   0.0323   0.986   0.995   0.614
      11    31    money stock: m3                          0.064   0.012   0.034   0.0443    0.0217   0.0153   0.0291   0.0703   0.0494   0.979   0.700   0.921
      12    32    average hour earnings                    0.059   0.173   0.014   -0.0423   0.0209  -0.0713   0.0289   0.0221   0.0336   0.978   0.993   0.744
      13    44    lagged dependent (t-8)                   0.059   0.013   0.020   0.0670    0.0346   0.0133   0.0696  -0.0618   0.0902   0.973   0.576   0.753
      14    39    lagged dependent (t-3)                   0.053   0.015   0.023   0.0992    0.0496   0.0554   0.0760  -0.1035   0.0974   0.977   0.766   0.855
      15    16    new one-family houses for sale           0.044   0.024   0.822   -0.0409   0.0229  -0.0355   0.0404  -0.2016   0.0483   0.962   0.810   1.000
      16    11    average unemployment duration in weeks   0.044   0.096   0.016   0.0446    0.0279   0.0746   0.0429  -0.0375   0.0789   0.945   0.958   0.682
      17    25    s&p’s dividend yield                     0.038   0.014   0.071   -0.0515   0.0315  -0.0425   0.0903  -0.2779   0.1645   0.948   0.681   0.953
      18    42    lagged dependent (t-6)                   0.037   0.013   0.015   0.0623    0.0395   0.0070   0.0671  -0.0294   0.1239   0.942   0.542   0.593
      19    17    total housing starts                     0.034   0.028   0.026   0.0454    0.0274   0.0472   0.0345   0.0835   0.0807   0.950   0.913   0.848
      20    26    s&p’s price-earnings ratio               0.033   0.012   0.032   0.0423    0.0253  -0.0295   0.0731   0.0741   0.0566   0.952   0.657   0.904
      21    33    producer price index                     0.027   0.018   0.017   -0.0355   0.0229  -0.0306   0.0355  -0.0288   0.0351   0.939   0.805   0.793
      22    40    lagged dependent (t-4)                   0.026   0.015   0.115   0.0676    0.0465   0.0496   0.0627  -0.2619   0.1168   0.926   0.785   0.987




32
      23    38    lagged dependent (t-2)                   0.024   0.013   0.017   0.1010    0.0676   0.0672   0.0983  -0.0867   0.1068   0.932   0.752   0.791
      24    45    lagged dependent (t-9)                   0.018   0.015   0.051   0.0361    0.0412  -0.0331   0.0673  -0.1177   0.0759   0.809   0.688   0.938
      25    20    purchasing managers’ index               0.018   0.018   0.030   0.0320    0.0268   0.0376   0.0393   0.0721   0.0595   0.883   0.830   0.886
      26    48    lagged dependent (t-12)                  0.017   0.016   0.015   0.0364    0.0324  -0.0336   0.0473   0.0231   0.0859   0.869   0.761   0.606
      27    19    inventories, business&manufacturing      0.017   0.014   0.178   -0.0261   0.0215  -0.0214   0.0328  -0.0764   0.0318   0.887   0.743   0.991
      28     2    total capacity utilization               0.016   0.059   0.812   -0.0409   0.0521  -0.0639   0.0572   0.2453   0.0590   0.784   0.867   1.000
      29    46    lagged dependent (t-10)                  0.015   0.015   0.042   0.0320    0.0372  -0.0340   0.0558  -0.1024   0.0749   0.804   0.728   0.913
      30    41    lagged dependent (t-5)                   0.015   0.013   0.743   0.0347    0.0494   0.0357   0.0571  -0.3138   0.0810   0.759   0.733   1.000
      31    12    unemployment rate                        0.015   0.026   0.846   -0.0536   0.0829   0.0035   0.1161  -0.6142   0.1551   0.740   0.512   1.000
      32    14    total construction put in place          0.014   0.013   0.013   0.0221    0.0201   0.0179   0.0305   0.0165   0.0298   0.864   0.721   0.710
      33    47    lagged dependent (t-11)                  0.013   0.024   0.018   0.0284    0.0351  -0.0595   0.0546  -0.0288   0.0851   0.790   0.861   0.632
      34    22    new orders in manufacturing              0.012   0.016   0.017   -0.0165   0.0264  -0.0014   0.0425  -0.0260   0.0307   0.734   0.513   0.800
      35    10    average working hours per week           0.012   0.011   0.014   0.0194    0.0201  -0.0002   0.0290   0.0184   0.0351   0.832   0.502   0.699
      36     5    total merchandise wholesalers            0.011   0.028   0.012   0.0091    0.0290   0.0399   0.0315   0.0078   0.0316   0.623   0.896   0.598
      37     9    ratio advertisement:unemployed           0.011   0.026   0.114   -0.0062   0.0407  -0.0273   0.0546   0.2527   0.2414   0.560   0.691   0.851
      38    23    interest rate 10-year u.s.treasury       0.011   0.036   0.067   0.0161    0.0233  -0.0437   0.0280   0.0589   0.0315   0.755   0.940   0.968
      39     7    total industrial production              0.011   0.021   0.036   0.0162    0.0272  -0.0363   0.0393   0.0609   0.0441   0.724   0.822   0.915
      40    15    new public construction put in place     0.010   0.012   0.014   0.0153    0.0189   0.0162   0.0267   0.0185   0.0302   0.791   0.728   0.729
      41     4    total personal consumption expenditure   0.010   0.019   0.015   0.0127    0.0228   0.0309   0.0292   0.0208   0.0308   0.711   0.855   0.749
      42    30    u.s.effective exchange rate               0.010   0.013   0.012   0.0144    0.0189   0.0195   0.0262   0.0115   0.0322   0.776   0.772   0.639
      43     8    total employees                          0.009   0.023   0.033   0.0116    0.0267   0.0450   0.0389  -0.0558   0.0419   0.668   0.875   0.907
      44    27    interest rate federal funds              0.009   0.017   0.013   -0.0126   0.0207  -0.0272   0.0271   0.0057   0.0414   0.729   0.841   0.555
      45    28    interest rate 3-month u.s.treasury       0.009   0.013   0.026   -0.0104   0.0216  -0.0176   0.0295   0.0434   0.0352   0.685   0.724   0.890
      46    18    total inventories                        0.009   0.012   0.013   0.0105    0.0230   0.0182   0.0314   0.0110   0.0482   0.676   0.718   0.590
      47    34    index of sensitive materials prices      0.008   0.011   0.016   -0.0013   0.0198   0.0006   0.0284  -0.0261   0.0331   0.526   0.508   0.784
      48    13    total civilian labor force               0.007   0.013   0.016   0.0034    0.0197   0.0199   0.0283  -0.0246   0.0292   0.569   0.759   0.800
     Table A8: Results of the BACE analysis on consumer expenditure for all periods.
                                                           Post.inclusion prob.             Posterior conditional on inclusion            Sign certainty prob.
                                                           Full      1      2            Full                1                 2          Full     1       2
     Rank   No.                     Variable                                       Mean     StDev     Mean     StDev    Mean     StDev
      (1)   (2)                        (3)                  (4)     (5)     (6)      (7)       (8)      (9)     (10)     (11)     (12)     (13)    (14)    (15)
       1    18    total inventories                        0.927   0.929   0.083   0.3048    0.0770   0.3869   0.0890   0.1911   0.0929   1.000   1.000   0.979
       2     2    total capacity utilization               0.801   0.918   0.012   -0.2827   0.0982  -1.0945   0.3638   0.0350   0.1175   0.998   0.998   0.617
       3    37    lagged dependent (t-1)                   0.413   0.076   0.940   -0.2018   0.0683  -0.1753   0.0876  -0.3489   0.0897   0.998   0.976   1.000
       4    24    s&p stock price index                    0.327   0.043   0.126   0.1797    0.0614   0.1452   0.0837   0.1963   0.0850   0.998   0.957   0.989
       5    35    consumer price index                     0.262   0.042   0.050   -0.2026   0.0696  -0.2065   0.1214  -0.1609   0.0922   0.998   0.954   0.958
       6    36    implicit price deflator                   0.157   0.021   0.138   -0.1809   0.0679  -0.1414   0.1257  -0.2076   0.0875   0.996   0.869   0.990
       7    25    s&p’s dividend yield                     0.139   0.013   0.019   -0.1920   0.0801  -0.0688   0.1372  -0.1129   0.1354   0.991   0.691   0.797
       8    29    money supply: m2                         0.130   0.021   0.132   0.1807    0.0721   0.1388   0.1183   0.2161   0.0943   0.994   0.879   0.988
       9    33    producer price index                     0.083   0.017   0.042   -0.1597   0.0692  -0.1119   0.1115  -0.1589   0.0950   0.989   0.841   0.951
      10    12    unemployment rate                        0.059   0.041   0.014   -0.1384   0.2348  -0.4265   0.3896   0.0218   0.3046   0.722   0.862   0.528
      11    26    s&p’s price-earnings ratio               0.036   0.012   0.049   0.1266    0.0896  -0.0492   0.1437   0.1639   0.0936   0.921   0.634   0.959
      12    17    total housing starts                     0.034   0.019   0.013   0.1289    0.0748   0.0952   0.1407   0.0468   0.1154   0.957   0.750   0.657
      13     3    personal income                          0.031   0.011   0.074   0.1188    0.0704   0.0484   0.0887   0.1840   0.0909   0.954   0.707   0.977
      14    44    lagged dependent (t-8)                   0.030   0.011   0.024   0.1072    0.0615   0.0474   0.0834   0.1161   0.0884   0.959   0.715   0.904
      15    28    interest rate 3-month u.s.treasury       0.029   0.033   0.017   0.1068    0.0638   0.1394   0.0932   0.0947   0.0923   0.952   0.931   0.847
      16    27    interest rate federal funds              0.028   0.009   0.016   0.1069    0.0626   0.0063   0.0834   0.0909   0.0956   0.955   0.530   0.828
      17     9    ratio advertisement:unemployed           0.028   0.756   0.018   0.0650    0.1830   0.8941   0.2502   0.1360   0.2323   0.639   1.000   0.720
      18    49    lagged CB present (t-1)                  0.025   0.009   0.028   0.1038    0.0643   0.0111   0.0837   0.1290   0.0901   0.946   0.553   0.922
      19    11    average unemployment duration in weeks   0.023   0.022   0.012   0.1201    0.0962   0.0475   0.2168   0.0500   0.1232   0.894   0.587   0.657
      20    45    lagged dependent (t-9)                   0.021   0.022   0.020   -0.0920   0.0613  -0.1032   0.0777   0.1077   0.0955   0.933   0.907   0.869
      21    15    new public construction put in place     0.018   0.014   0.014   -0.0849   0.0590  -0.0707   0.0774  -0.0778   0.0888   0.924   0.819   0.809
      22    30    u.s.effective exchange rate               0.017   0.015   0.021   -0.0821   0.0593  -0.0877   0.0872  -0.1078   0.0898   0.916   0.842   0.884
      23    20    purchasing managers’ index               0.016   0.012   0.011   0.1033    0.0874   0.0820   0.1324   0.0242   0.1100   0.881   0.732   0.587
      24     7    total industrial production              0.014   0.010   0.060   -0.0818   0.0711  -0.0449   0.0901  -0.1724   0.0908   0.875   0.690   0.970




33
      25    50    lagged CB expectations (t-1)             0.014   0.015   0.011   0.0930    0.0965   0.1043   0.1332  -0.0167   0.1128   0.832   0.782   0.559
      26    16    new one-family houses for sale           0.013   0.051   0.013   -0.0042   0.1319   0.4010   0.2605  -0.0662   0.0903   0.513   0.937   0.768
      27    31    money stock: m3                          0.012   0.011   0.017   0.0367    0.0923   0.0463   0.0943   0.0723   0.1245   0.654   0.688   0.719
      28    40    lagged dependent (t-4)                   0.011   0.014   0.010   -0.0614   0.0604  -0.0751   0.0778  -0.0142   0.0911   0.845   0.832   0.562
      29    23    interest rate 10-year u.s.treasury       0.011   0.016   0.010   -0.0582   0.0727  -0.1001   0.1051   0.0019   0.0924   0.788   0.829   0.508
      30    13    total civilian labor force               0.011   0.010   0.010   0.0588    0.0608   0.0457   0.0828  -0.0398   0.0888   0.833   0.709   0.673
      31     6    total manufacturing&trade                0.010   0.012   0.033   -0.0471   0.0765  -0.0478   0.1740  -0.1678   0.1430   0.731   0.608   0.879
      32    39    lagged dependent (t-3)                   0.010   0.010   0.011   -0.0523   0.0614  -0.0385   0.0827  -0.0477   0.0932   0.802   0.679   0.695
      33    21    new orders consumer goods&materials      0.010   0.011   0.051   -0.0522   0.0623   0.0531   0.0852  -0.1681   0.0937   0.799   0.733   0.962
      34    52    lagged CB expectations (t-2)             0.009   0.011   0.018   -0.0286   0.1067   0.0176   0.1213  -0.1234   0.1296   0.606   0.558   0.829
      35    19    inventories, business&manufacturing      0.009   0.012   0.026   -0.0303   0.1053  -0.0734   0.1645   0.1242   0.0914   0.613   0.672   0.912
      36    54    lagged CB expectations (t-3)             0.009   0.011   0.012   0.0029    0.0909   0.0357   0.1196  -0.0454   0.1228   0.513   0.617   0.644
      37    38    lagged dependent (t-2)                   0.008   0.019   0.042   -0.0323   0.0693  -0.0961   0.0836  -0.1663   0.1010   0.679   0.874   0.949
      38    32    average hour earnings                    0.008   0.011   0.010   0.0113    0.0757   0.0337   0.0925  -0.0166   0.0997   0.559   0.642   0.566
      39     8    total employees                          0.008   0.011   0.012   -0.0221   0.0866  -0.0551   0.0993  -0.0527   0.1026   0.601   0.710   0.696
      40    14    total construction put in place          0.008   0.010   0.018   -0.0277   0.0652  -0.0124   0.0871  -0.0957   0.0874   0.664   0.556   0.862
      41    34    index of sensitive materials prices      0.008   0.009   0.010   0.0317    0.0616  -0.0021   0.0819  -0.0063   0.0915   0.696   0.510   0.528
      42    48    lagged dependent (t-12)                  0.008   0.015   0.015   0.0393    0.0592   0.0838   0.0793  -0.0822   0.0880   0.746   0.854   0.824
      43    41    lagged dependent (t-5)                   0.008   0.021   0.014   0.0300    0.0590   0.1037   0.0793  -0.0723   0.0883   0.694   0.903   0.793
      44    53    lagged CB present (t-3)                  0.007   0.010   0.011   0.0310    0.0654   0.0434   0.0839  -0.0380   0.0932   0.682   0.697   0.658
      45    42    lagged dependent (t-6)                   0.007   0.014   0.018   -0.0261   0.0612  -0.0752   0.0780   0.0985   0.0891   0.665   0.832   0.865
      46    51    lagged CB present (t-2)                  0.007   0.009   0.020   -0.0207   0.0632  -0.0185   0.0861  -0.1074   0.0882   0.628   0.585   0.887
      47    46    lagged dependent (t-10)                  0.007   0.010   0.242   0.0292    0.0587  -0.0469   0.0774   0.2275   0.0868   0.691   0.727   0.995
      48    47    lagged dependent (t-11)                  0.007   0.010   0.035   0.0242    0.0598  -0.0370   0.0788   0.1514   0.0984   0.657   0.680   0.937
      49     1    sales, business&manufacturing            0.007   0.032   0.085   -0.0029   0.0653   0.1424   0.1083  -0.1966   0.0968   0.518   0.905   0.978
      50     5    total merchandise wholesalers            0.007   0.009   0.011   -0.0012   0.0659  -0.0061   0.0842   0.0274   0.1043   0.507   0.529   0.603
      51    10    average working hours per week           0.007   0.010   0.039   -0.0125   0.0637   0.0405   0.0784  -0.1449   0.0876   0.578   0.697   0.950
      52    43    lagged dependent (t-7)                   0.007   0.009   0.010   -0.0010   0.0586  -0.0182   0.0772  -0.0023   0.0877   0.507   0.593   0.511
      53    22    new orders in manufacturing              0.007   0.009   0.014   -0.0004   0.0626   0.0264   0.0836  -0.0720   0.0937   0.502   0.624   0.778
Table A9: Posterior inclusion probability obtained from different prior expected model
sizes for consumer expenditure.


                   Prior expected model size                  2       5      10      15      25
                   Prior inclusion probability              0.038   0.094   0.189   0.283   0.472

      Rank   No.                   Variable                    Posterior inclusion probability

        1    18    total inventories                        0.887   0.927   0.947   0.961   0.974
        2     2    total capacity utilization               0.714   0.801   0.852   0.885   0.915
        3    37    lagged dependent (t-1)                   0.158   0.413   0.728   0.871   0.964
        4    24    s&p stock price index                    0.116   0.327   0.604   0.746   0.857
        5    35    consumer price index                     0.231   0.262   0.287   0.287   0.279
        6    36    implicit price deflator                   0.093   0.157   0.203   0.223   0.231
        7    25    s&p’s dividend yield                     0.079   0.139   0.177   0.204   0.258
        8    29    money supply: m2                         0.096   0.130   0.172   0.203   0.266
        9    33    producer price index                     0.053   0.083   0.129   0.168   0.279
       10    12    unemployment rate                        0.030   0.059   0.086   0.114   0.179
       11    26    s&p’s price-earnings ratio               0.018   0.036   0.058   0.082   0.144
       12    17    total housing starts                     0.014   0.034   0.072   0.106   0.174
       13     3    personal income                          0.010   0.031   0.074   0.118   0.204
       14    44    lagged dependent (t-8)                   0.012   0.030   0.069   0.115   0.216
       15    28    interest rate 3-month u.s.treasury       0.008   0.029   0.072   0.121   0.235
       16    27    interest rate federal funds              0.008   0.028   0.079   0.133   0.256
       17     9    ratio advertisement:unemployed           0.011   0.028   0.061   0.091   0.164
       18    49    lagged CB present (t-1)                  0.008   0.025   0.059   0.093   0.154
       19    11    average unemployment duration in weeks   0.011   0.023   0.040   0.053   0.092
       20    45    lagged dependent (t-9)                   0.008   0.021   0.041   0.066   0.132
       21    15    new public construction put in place     0.007   0.018   0.038   0.063   0.127
       22    30    u.s.effective exchange rate               0.007   0.017   0.037   0.060   0.132
       23    20    purchasing managers’ index               0.006   0.016   0.038   0.059   0.108
       24     7    total industrial production              0.006   0.014   0.028   0.043   0.095
       25    50    lagged CB expectations (t-1)             0.006   0.014   0.028   0.040   0.080
       26    16    new one-family houses for sale           0.006   0.013   0.028   0.041   0.082
       27    31    money stock: m3                          0.004   0.012   0.025   0.041   0.079
       28    40    lagged dependent (t-4)                   0.004   0.011   0.029   0.052   0.148
       29    23    interest rate 10-year u.s.treasury       0.004   0.011   0.020   0.036   0.080
       30    13    total civilian labor force               0.004   0.011   0.023   0.037   0.071
       31     6    total manufacturing&trade                0.004   0.010   0.020   0.030   0.058
       32    39    lagged dependent (t-3)                   0.004   0.010   0.024   0.042   0.124
       33    21    new orders consumer goods&materials      0.004   0.010   0.020   0.034   0.080
       34    52    lagged CB expectations (t-2)             0.004   0.009   0.019   0.034   0.079
       35    19    inventories, business&manufacturing      0.004   0.009   0.019   0.029   0.058
       36    54    lagged CB expectations (t-3)             0.003   0.009   0.017   0.031   0.064
       37    38    lagged dependent (t-2)                   0.003   0.008   0.024   0.050   0.148
       38    32    average hour earnings                    0.004   0.008   0.018   0.030   0.062
       39     8    total employees                          0.003   0.008   0.018   0.031   0.069
       40    14    total construction put in place          0.003   0.008   0.018   0.029   0.067
       41    34    index of sensitive materials prices      0.003   0.008   0.018   0.030   0.062
       42    48    lagged dependent (t-12)                  0.003   0.008   0.019   0.030   0.068
       43    41    lagged dependent (t-5)                   0.003   0.008   0.017   0.028   0.060
       44    53    lagged CB present (t-3)                  0.003   0.007   0.017   0.026   0.058
       45    42    lagged dependent (t-6)                   0.002   0.007   0.016   0.025   0.058
       46    51    lagged CB present (t-2)                  0.003   0.007   0.016   0.025   0.056
       47    46    lagged dependent (t-10)                  0.003   0.007   0.015   0.025   0.055
       48    47    lagged dependent (t-11)                  0.003   0.007   0.014   0.026   0.057
       49     1    sales, business&manufacturing            0.002   0.007   0.015   0.026   0.056
       50     5    total merchandise wholesalers            0.002   0.007   0.016   0.024   0.057
       51    10    average working hours per week           0.002   0.007   0.015   0.027   0.060
       52    43    lagged dependent (t-7)                   0.002   0.007   0.015   0.024   0.054
       53    22    new orders in manufacturing              0.002   0.007   0.015   0.025   0.054




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