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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 34

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