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Consumer expectations and cyclical durations.

In macroeconomic literature, the characterization of the ultimate sources of aggregate variability has always been a question of paramount importance. Perhaps the most significant endeavor in this context is by Pigou (1929) who categorizes the variability sources into three broad groups: "real causes," "psychological causes," and "autonomous monetary causes." Perhaps the least explored category in contemporary macroeconomics is the second category. Psychological determinants describe agents' swings of optimism and pessimism. Variations in these determinants are believed to significantly impact investment and aggregate production levels. In this study, "consumer expectations" are proposed as the covariate that illustrates the swings of optimistic and pessimistic views of consumers.

Consumers, perhaps more so than businesses and government, are increasingly regarded as the dominant force behind cyclical fluctuations in aggregate production levels. With their ever-changing expectations, consumers play a significant role in determining whether the economy will recover rapidly from a state of contraction or maintain a state of expansion and growth for a longer period.

From Figure 1 below an association between cyclical phases and the index of consumer expectations appears. Business-cycle troughs are preceded by a rise in the index measuring consumer sentiments, while declines in this index lead to cyclical peaks. This simple observation may be the first indication that deteriorations in consumer expectations lead to declines in aggregate production levels, and vice-versa. Oh and Waldman (1990), for instance, have found that expectational shocks, measured by revisions of the series of leading economic indicators, explain more than 20% of the variations in aggregate production levels. Matsusaka and Sbordone (1995) have concluded that consumer expectations account for some 13 to 26% of the innovation variance of GNP.

While numerous studies have analyzed the association between changes in aggregate production levels and variations in consumer expectations, the purpose of this study is to explore a different but related issue, that of the association between consumer expectations and business-cycle durations. Parametric hazard models are used to test whether changes in consumer sentiments about the state of the economy Granger-cause changes in cyclical durations.

The basic postulate in this analysis is that expectations are self-fulfilling. Optimistic sentiments postpone cyclical peaks and promote troughs. Pessimistic sentiments result in opposite phenomena. This analysis examines two additional issues. The first issue deals with the question of whether cyclical turning-points are more likely to happen as cyclical durations extend. The second issue involves the question of efficacy of government policy when attempting to manage business-cycle durations.

The main finding from this study is that, after controlling for fundamentals (monetary and fiscal proxies as well as inflation), a statistically significant association is found to link business-cycle durations to consumer expectations. Consumer sentiments are found to Granger-cause business-cycle durations. In particular, longer expansion-durations derive from consumers' optimistic prospects, and vice-versa. Another major finding is that U.S. postwar cyclical durations are found to exhibit significant positive duration dependence. That is, as cyclical expansions and contractions grow "older," their likelihoods of termination increase. This finding agrees partially with the conclusions from some recent studies by Diebold and Rudebusch (1989), Diebold, Rudebusch and Sichel (1993), Sichel (1991), and Watson (1992) who argue that, while recessions do exhibit positive duration dependence, expansions do not. In fact, most economists argue that business cycles are merely random fluctuations. This includes work by Fisher (1925) and McCullock (1975). Finally, while variations in inflation are determined to inversely impact expansion-durations, government discretionary policy is found to have the intended effect primarily on cyclical expansions.

The remainder of the paper is as follows. The first section offers a brief discussion of consumer expectations in association with business-cycle durations. Section II introduces the basics of the survival data analysis. Section III consists of a discussion of the data and tests for exogeneity in right-hand side variables. The basic empirical results of the study follow in Section IV. A summary and concluding remarks about the cyclical durations-consumer expectations association constitute the final section of the paper.


Before assessing the duration data used in this study, a brief explanation of why cyclical durations may associate with consumer expectations is offered. Consider a familiar scenario, that of an economy exiting a prolonged and severe contraction. If the expected duration for the upcoming cyclical expansion depends on the underlying strength of the economy, one such determinant may be the anticipation consumers form about the state of economic conditions. If the anticipations are of robustness, and if they are generalized among agents, such anticipations may result in consumers making substantial purchases, thus helping to expand aggregate production and employment levels, and consequently prolonging the duration of the cyclical expansion in question. Just as important, unfavorable anticipations about the state of the economy may also lead consumers to postpone their discretionary expenditures, thus adversely impacting aggregate production and employment levels, and thus extending contraction durations or shortening expansion durations. In essence, changes in consumer expectations are associated with business-cycle durations via changes in aggregate output and employment levels.

Conventionally, consumer aggregate expenditures are categorized as either necessary or discretionary expenditures. While necessary expenditures are relatively stable and predictable, discretionary expenditures are cyclical and harder to predict accurately. Because the latter often require significant debt commitments, consumers' expectations about future prices and income are vital to their decision to make or postpone large purchases. It is hypothesized that optimistic prospects translate into consumers making discretionary purchases, thus increasing the aggregate output level, which in turn is expected to extend expansion durations or shorten those of contractions. Similarly, consumers' pessimism decreases their incentive to borrow and spend, thus reducing aggregate output and consequently shortening expansion durations and extending those of contractions.


A. The Basic Model

Let T, a random variable with a continuous probability distribution, represent business-cycle phases, while t represents a typical point in its range. The hazard function [Lambda](t) is defined as the rate at which a cyclical phase is completed after duration t, assuming it lasts until t. Because it is not clear from economic theory alone whether to expect a constant, increasing, or decreasing hazard rate for cyclical durations, the choice of the distribution is critical. To handle this question of nonstationarity, this study relies on Lancaster's (1979) Weibull distribution which allows for a power dependence of the hazard on the factor time.(2) Lancaster defined the Weibull distribution by the following hazard rate:

[Lambda](t) = [Lambda][Alpha][t.sup.[Alpha]-1] (1)

where t is the duration to date of the ith cyclical phase, [Lambda] ([greater than]0) is a scale parameter, and [Alpha] ([greater than] 0) is an index. The conditional density function of T is

f(t) = [Lambda][Alpha][t.sup.[Alpha]-1] exp (-[Lambda][t.sup.[Alpha]]) (2)

Alternatively, in terms of Y [equivalent to] log(T), the above conditional density function is the linear model

ln(T) [equivalent to] Y = [Mu] + [Sigma]W. (3)

The dependent failure time is then the log of the number of quarters a cyclical phase is expected to last before the next turning point, or before censoring occurs. W has the extreme value p.d.f. exp(w-e[W.sup.w], -[infinity] [less than] w [less than] 0.

The shape of the distribution is determined by [Mu] (= -log([Lambda])), and [Alpha](= [[Sigma].sup.-1]). The hazard function is deemed increasing if [Alpha] [greater than] 1 [equivalence] ([Delta][Lambda]/[Delta]t) [greater than] 0, decreasing if [Alpha] [less than] 1 [equivalence] ([Delta][Lambda]/[Delta]t) [less than] 0, and constant if [Alpha] = 1 [equivalence] ([Delta][Lambda]/[Delta]t) = 0; the Weibull distribution simplifies to the exponential where there is no duration dependence. The interpretation of cyclical duration dependence is rather straightforward. A positive duration dependence, depicted by [Alpha] [greater than] 1, indicates that as a cyclical phase grows "older" its likelihood of termination increases. Similarly, a negative duration dependence, depicted by [Alpha] [less than] 1, indicates that as a cyclical phase grows "older" its likelihood of termination decreases. In the case of [Alpha] = 1, the likelihood of termination of a cyclical phase remains constant regardless of the age of the cyclical phase. Finally, using the hazard in Equation 1 and accounting for censoring in the data, the log-likelihood function to maximize is:

[Mathematical Expression Omitted], (4)

where [d.sub.i] = zero if the cyclical phase is censored, and one otherwise.

B. The Generalized Weibull Model

One advantage of this parametric approach is the flexibility it allows for examining other related and relevant hypotheses. To generalize the Weibull function, consider the case in which the probability of termination is determined by a vector of time-varying covariates x(s) whose value at time t is x(t).(3) Covariates x(s) may record the variations in the time-varying variables such as consumer expectations and perhaps discretionary government economic policy. The above indicators have a special feature: they are defined for a cyclical duration until the latter is terminated. The conditional hazard of the generalized Weibull distribution becomes:

[Lambda](t; X) = [Lambda][Alpha][t.sup.[Alpha]-1][e.sup.X[Beta]] (5)

where [Beta][prime] = ([[Beta].sub.1], [[Beta].sub.2], [[Beta].sub.3], . . ., [[Beta].sub.k]) is a vector of regression parameters. The conditional density function of T is

f(t;X) = [Lambda][Alpha][t.sup.[Alpha]-1][e.sup.X[Beta]]exp(-[Lambda][ b.[Alpha]][e.sup.X[Beta]*]) (6)

Alternatively, in terms of Y-log(T), the conditional density function of T given X is the linear model

Y = [Mu]+X[[Beta].sup.*] + [Sigma]W (7)

where [[Beta].sup.*] = - [Sigma][Beta], [Mu] = -log[Lambda], and [Sigma] = [[Alpha].sup.-1]. The hazard function, Equation 5, indicates that the log failure rate is a linear function of the covariates X.

To assess the impact of consumer expectations on the hazard function, the index of consumer expectations E is integrated into the generalized Weibull model. Other economic determinants (fundamentals) are also incorporated in the generalized model. Discretionary government monetary and fiscal policy have always been suspected by many as a significant force impacting aggregate output levels and thus cyclical durations. In this analysis it is assumed that policy-makers' concern with business cycles is that of trying to maximize expansion durations and minimize those of contractions.(4) Moreover, because to economic agents, concern over inflation may take precedent over other considerations during the later phase of a typical expansion, covariate inflation is also included in the model. Consequently, indicators of monetary and fiscal variations as well as variations in the general price level are covariates to include in the extended model. The extended hazard model will then become:

ln(T) = [Mu] + [[[Beta].sub.1].sup.*]ln(E) + [[[Beta].sub.2].sup.*]ln(M) + [[[Beta].sub.3].sup.*]ln(f) + [[[Beta].sub.4].sup.*]ln(inf) + [Sigma] W, (8)

where E is a measure of consumer expectations, M is the monetary liquidity measure, F is the fiscal stance in the economy, and inf is the inflation rate.(5)

If variations in consumer expectations do associate with failure time, In(T), the parameter estimates of [[[Beta].sub.1].sup.*] would capture such association. During expansions, if consumers' optimistic (pessimistic) sentiments translate into longer (shorter) durations, then [[[Beta].sub.1].sup.*] will be positive (negative) and significantly different from zero. Likewise, during contractions, if consumer optimism (pessimism) translates into shorter (longer) durations, then [[[Beta].sub.1].sup.*] will be negative (positive) and significantly different from zero.

Moreover, to maximize an expansion duration, policy-makers would begin with an accommodating monetary and fiscal policy to enhance the recovery at its early stage. Later during the expansion, a shift to a tight policy to slow down the overheated economy is likely to be considered as well. If such a policy is successfully conducted, the association between the dependent failure time, In(T), and the covariates ln(M) and ln(F), would be undetermined (i.e., [[[Beta].sub.2].sup.*], [[[Beta].sub.2].sup.*] [[[Beta].sub.3].sup.*] [greater than] = [less than] 0).(6) On the other hand, to minimize the duration of a contraction, policy-makers would prescribe an accommodating monetary and fiscal policy. In this case, a successful economic policy would be depicted by an inverse relationship between ln(T) and covariates ln(M) and ln (F) (i.e., [[[Beta].sub.2].sup.*], [[[Beta].sub.3].sup.*] [less than] 0). Finally, if inflation does indeed cut short expansion durations, the parameter [[[Beta].sub.4].sup.*] will be negative and statistically significant. Because inflation is not characteristic of contractions, it is believed to play no significant role during their durations.

The decision on what constitutes "good" proxies for monetary stance, in particular, is controversial. A variety of indicators is used. Leeper and Gordon (1992) use M1, M2, and the monetary base as measures of monetary liquidity. Christiano and Eichenbaum (1992) use nonborrowed reserves to establish the association between monetary liquidity and interest rate variations. Romer and Romer (1989) suggest the "narrative approach." Sims (1992) and Bernanke and Blinder (1992) advocate the federal funds rate instead.

In the present analysis F is proxied by Federal government expenditures, and M is proxied by M2, the broader definition of the money supply. The ratio of nonborrowed reserves (NBR) over total reserves (TR) is also selected to proxy monetary liquidity. Government expenditures and M2 are both normalized by real GNP (Y) to allow for cyclical adjustment.

A distinguishing feature of duration data is that some observations may be censored. Censoring takes place when a cyclical phase is not observed for the full time to failure (turning point.) When a phase is censored at duration ti, the only information available is that the duration is at least t) old. The last cyclical phase in the sample would then be the only censored observation for the purpose of this analysis. Finally, taking into consideration censoring, the parameters [Lambda], [Alpha], and [[Beta].sup.*] are estimated by maximum likelihood.


A. Data

To examine the impact of consumer expectations on cyclical durations in the U.S. economy, NBER business-cycle chronology data are adapted to create failure time observations. The NBER determines cyclical peaks and troughs; its monthly chronology of turning points dates back to 1854. Broadly defined, a business cycle consists of two consecutive cyclical phases linking either two peaks or two troughs. Business cycles represent recurrent sequences of synchronized upturns and downturns in a great number of economic activities. In general, upward movements in business activity last longer than downturns. Typically, because of a secular trend in growth, each expansion brings a new record high or peak to aggregate economic activity, and the troughs tend to bottom out at successively higher levels of economic activity as well. The observed cyclical fluctuations do, however, vary in amplitude and duration.

This study relies on the NBER business-cycle chronology which indicates that over the last 50 years, the U.S. economy has experienced only nine cycles. Such a fact renders statistical testing of hypotheses involving duration data rather difficult. To overcome this barrier, cyclical duration data are adapted to conventional time-series data, thus allowing for higher degrees of freedom in hypothesis testing. Time failures or cyclical durations are constructed so they correspond to the progression in the expected duration of expansions, contractions, and whole-cycles. Cyclical durations then become compatible with ordinary time series data such as the consumer expectations index.

At each cyclical turning-point, the duration of a cyclical phase is set to its already observed age T, that is its expected length of time until failure. In the succeeding quarter's period, this duration takes a value of (T-l), and so forth. For instance, a cyclical phase that lasts 12 quarters will be represented by the (T-i) with i ranging from 11 to 0. Duration analysis also requires that all variables are defined in natural logarithmic values. Log(T-i) will then constitute the dependent failure time in the log-linear survival regression model.

To measure consumer expectations, the Index of Consumer Expectations (ICE) constructed by the Survey Research Center at the University of Michigan is selected.(8) Instead of the Index of Consumer Sentiment (ICS), this analysis uses the ICE to allow for the sample to include as many business-cycle durations as possible. The ICE dates back to January 1953. The survey questions cover three broad areas: personal finances, business conditions, and buying conditions. The stock of money is defined as the broader definition of money. Finally, the data sample used in the study ranges from 1955.I to 1994.II using quarterly observations.

B. Granger-Causality Tests

Before proceeding with the empirical analysis of this study, it is critical that the issue of identification be addressed. After all, it is plausible that one may attempt to explain the apparent effect of consumer expectations on cyclical durations by reverse causality. Granger causality, the most common causality inference used by economists, is employed here to explore this issue.(7)

To test for the exogeneity of the right-hand side variables of the main model (Equation 5), the one-sided distributed lag test of Granger (1969) is employed. The null hypothesis to test is that the cyclical duration does not Granger-cause consumer expectations or any other independent variable specified in the basic model. Results from the Granger-causality tests are reported in Table 1 below. The findings indicate that consistently the null hypothesis is not rejected at convincing statistical significance levels(9) These findings will then support the utilization of Equation 5 as the basic framework for analyzing the question of consumer expectations and their association with business cycle durations.


A. Empirical Check for the Weibull Distribution

The appeal of the Weibull distribution is its simple relation to the parameter [Alpha] and the duration dependence of the hazard. An empirical check for the [TABULAR DATA FOR TABLE 1 OMITTED] Weibull distribution may be provided by the plot of [Mathematical Expression Omitted] see page 11 large hat over both s and t versus log(t) (Kalbfleish and Prentice, 1980, p. 24) where

[Mathematical Expression Omitted], (9)

is the Kaplan-Meier estimate of the survivor function (also known as the product-limit estimator). The plot should give approximately a straight line. Figure 2 below offers a validation of the selection of the Weibull distribution. The relatively straight line shown,justifies the use of the Weibull distribution instead of more complex distributions.

Moreover, the Weibull distribution allows only for monotonic variation in the hazard with duration. A more flexible distribution, the log-logistic function for instance, with a nonmonotonic variation is examined as well. The hazard function of this distribution is defined as

[Mathematical Expression Omitted] (10)

The hazard increases then decreases with duration if [Alpha] [greater than] 1. It decreases if 0 [less than] [Alpha] [less than] 1, and is constant if [Alpha] = 1. Formulations II and IV in Tables 2 and 3 below are from the log-linear survival regression model using log-logistic function. The parameter estimates of [Alpha] confirm the duration dependence finding from the Weibull distribution. Also, the parameter estimates of the [[[Beta].sub.i].sup.*] reiterate the basic results revealed under the Weibull distribution.

There is no "natural" duration in which business-cycle surprises (cyclical turning points) occur. Thus, both the Weibull and log-logistic models are appropriate in the context of business-cycle duration analysis. The simplicity in the algebra of the survival and hazard functions of either model also facilitates computations when censoring of the data is required. The empirical findings - in particular the impact of consumer expectations on cyclical expansions in the log-logistic model - confirm the findings from the Weibull model. However, it may be more appropriate to focus on the latter. Duration dependence as well as the empirical check of the Weibull distribution are easier to establish compared to the log-logistic distribution.

B. Basic Results

If the parameter estimate of [[[Beta].sub.1].sup.*] in Equation 5 is significantly different from zero, then there is evidence that cyclical durations are impacted by consumer expectations. In the case of expansion durations, a positive and statistically significant coefficient estimate of [[[Beta].sub.1].sup.*] would indicate that higher levels in consumer expectations (optimistic views) associate with longer expansion durations, and vice-versa. Similarly, in the case of contractions, a negative and statistically significant coefficient estimate of [[[Beta].sub.1].sup.*] would indicate that higher levels in consumer expectations (optimistic views) associate with shorter contraction durations, and vice-versa.

Table 2 clearly indicates that consumers' optimistic sentiments translate into longer expansion durations, and vice-versa. The parameter estimate of [[[Beta].sub.1].sup.*] is positive and significantly different from zero at a better than one percent level. After controlling for other determinants (economic fundamentals) in the model (Specification III), the association linking expansion-durations and expectations remains highly significant indicating robustness in the results.

Table 3 shows a tendency for optimistic sentiments to result into shorter contraction durations, and vice-versa. The parameter estimate of [[[Beta].sub.1].sup.*], though negative as hypothesized, is only marginally significant. Moreover, after controlling for the economic fundamentals in the model, the association linking contraction-durations to consumer expectations remains marginally significant.

C. Related Results

Are cyclical-phase durations more likely to terminate when they grow "older?" Stated differently: do business cycles exhibit positive duration dependence? The intuitive concept behind this hypothesis is that the expected duration of a cyclical phase is thought to vary with the underlying strength of the economy. For instance, when the economy recovers from a severe recession and enters a robust expansion, this economy is less likely to slip back into another recession. Tables 2 and 3 offer an answer to this question of duration dependence. Parametric Regression results show supporting evidence that cyclical durations exhibit positive duration dependence. The parameter estimates of [Rho], significantly different from zero, and consistently less than 1 (making [Alpha] [greater than] 1), depict a case of significant positive duration dependence for postwar business cycles.

The analysis offers other significant results as well. The parameter estimates of [[[Beta].sub.2].sup.*] and [[[Beta].sub.3].sup.*] are included to assess whether government monetary and fiscal policies are efficacious. From Table 2 it is clear that the parameter estimates of [[[Beta].sub.2].sup.*] and [[[Beta].sub.3].sup.*] are positive and significantly different from zero, which indicates that active monetary and fiscal policies tend to extend expansion durations, and vice-versa. Table 3 reveals that the parameter estimates of [[[Beta].sub.3].sup.*] are negative and marginally different from zero. Active fiscal policy tends to marginally shorten [TABULAR DATA FOR TABLE 2 OMITTED] [TABULAR DATA FOR TABLE 3 OMITTED] contraction durations, and vice-versa. Finally, the parameter estimates of [[[Beta].sub.4].sup.*], as depicted in Tables 2 and 3, reveal that while inflation tends to shorten expansion durations, it does not seem to have a significant impact on contraction durations.


From parametric hazard functions, this study has examined several interrelated hypotheses that involve business-cycle durations in postwar U.S. experience. The findings from the Granger-causality tests indicate that the null hypothesis that cyclical durations do not Granger-cause consumer expectations is not rejected at convincing significance levels. The same conclusion is obtained in the case of the other covariates used in the main model.

First, the study examines and establishes an association between cyclical durations and consumer expectations. Consumer sentiments are found to Granger-cause business-cycle durations. In particular, it is shown that consumers' optimistic sentiments tend to lead to longer expansion durations, and vice-versa. Though the association is only marginal, consumers' optimistic expectations do tend to result in shorter contraction durations, and vice-versa.

Second, the analysis reveals the presence of a significant positive duration dependence. Expansion and contraction durations are thus more likely to terminate as their durations are prolonged. Such a conclusion supports the popular paradigm that cyclical phases are not prone to termination at their early stages.

Third, active monetary and fiscal policies do have the intended effect on cyclical expansion durations. Easy monetary and fiscal policies tend to prolong durations for expansions, and vice-versa. Fiscal policy seems to have only a marginal effect on contraction durations. While inflation is found to shorten expansion durations, it does not seem to impact contraction durations as hypothesized. Finally, further studies may address the question of whether false announcements by decision-makers tend to impact cyclical durations.

Acknowledgment: The author would like thank Dr. F.K. Vinlove and two anonymous referees for constructive comments.


Direct all correspondence to: Ali Abderrezak, The Pennsylvania State University, DuBois, Department of Economics, College Place, DuBois, PA 15801-3199.

1. The succeeding discussion of the properties of the Weibull distribution draws principally from Amemiya (1985), Kalbleisch and Prentice (1980), Greene (1991, 1993), Kiefer (1988), Cox and Oakes (1984).

2. The hazard function for the exponential distribution is constant, and that of the Weibull is monotonically increasing or decreasing depending on ti. The hazard functions for the lognormal and log-logistic distributions first increase, then decrease.

3. Trond Petersen (1986) offers an algorithm that allows for a flexible treatment of time-dependent covariates in fully parametric models. Tony Lancaster (1990) has a detailed exposition of this complicated issue. He notes, however, that some time-varying covariates in the context of duration analysis can be treated in the same way as time-invariant ones.

4. While policy makers may recognized the importance of other, and perhaps more deserving, considerations such as the fostering of healthy long-term growth, their attention to cyclical durations (attempts to shorten contractions and lengthen expansions) may be take precedent in most cases. Unpopular economic policies are challenging even to the Federal Reserve Bank.

5. Given that some values of the inflation rate are negative, a constant was added to the variable inf, so that ln(inf) is computable throughout.

6. If [[[Beta].sub.2].sup.*] [greater than] 0 and [[[Beta].sub.3].sup.*] [greater than] 0, then a predominantly expansionary monetary and fiscal policy is in place. Likewise, a mainly restrictive monetary and fiscal policy will be reflected by [[[Beta].sub.2].sup.*] [less than] 0 and [[[Beta].sub.3].sup.*] [less than] 0. If [[[Beta].sub.2].sup.*] [greater than] 0 and [[[Beta].sub.3].sup.*] [less than] 0, an expansionary monetary policy is combined with a restrictive fiscal policy. Finally, if [[[Beta].sub.2].sup.*] [less than] 0 and [[[Beta].sub.3].sup.*] [greater than] 0, then a mainly restrictive monetary policy and expansionary fiscal policy are in effect.

7. The most commonly used definition of causality is the Granger definition of causality (see Granger, 1969). Granger's test is based on the simple premise that the future cannot cause the present or the past. It may be simplified to the following: ceteris paribus, [X.sub.t] is a Granger cause of [Y.sub.t], if [Y.sub.t] can be predicted with better accuracy using [X.sub.t-1] i [greater than] 0) rather than not doing so. However, Granger causality is neither a necessary nor a sufficient condition for true causality to exist.

8. See Curtin (1992) for a discussion of the University of Michigan Surveys of Consumers.

9. Because the Granger-causality test implies temporal precedence, causality in the context of this analysis implies that consumer expectations are either causing cyclical durations or simply anticipating them.


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Author:Abderrezak, Ali
Publication:Quarterly Review of Economics and Finance
Date:Dec 22, 1997
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