Evaluating threshold effects in consumer sentiment.

1. Introduction

The Consumer Sentiment Index published by the University of Michigan (hereafter the UM index) is one of the two most commonly monitored measures of consumer sentiment in the United States (the other one being the Consumer Confidence Index issued by the Conference Board). Sentiment indexes, which are constructed from answers to survey questions, are popular with the media; newspaper articles and commentaries abound following their release. The analysis often confers a primary role to consumer sentiment in determining economic fluctuations. The view among economists, however, is more equivocal. As early as 1965, Adams and Green found that the information contained in the UM index encompasses the information included in standard government statistics on employment and financial conditions. Many economists think that consumer sentiment is endogenous and is a reflection of current macroeconomic conditions. Other economists, in line with Keynes' notion of animals spirits, argue that psychological factors, which are not captured by economic variables, can influence consumers' decisions. Thus, the willingness to consume may be an important factor affecting consumption.

Few studies have found that sentiment indexes have significant explanatory power once fundamental economic factors are taken into account. Garner (1991) and Throop (1992), however, performed event studies and suggested that these indexes could be helpful during major economic or political events, as they then tend to diverge from a path consistent with other macroeconomic variables. Drawing on this literature, our study provides a new evaluation of consumer sentiment as a predictor of aggregate consumer spending.

Periods of high economic or political uncertainty are usually associated with increased volatility of consumer sentiment, suggesting that large swings in sentiment could influence consumption. We provide a formal assessment of this possibility by estimating a consumption function in which only large variations of sentiment affect spending. We find that consumer sentiment is a statistically important determinant of consumption in periods of high uncertainty, even after controlling for other determinants of consumption.

This article is organized as follows. Section 2 describes two views of consumer behavior. Section 3 reviews the relevant empirical literature. Section 4 introduces our econometric model, data, and estimation methods. Section 5 summarizes the estimation and forecasting results. Section 6 evaluates the predictive power of the UM index within the Campbell--Mankiw (Campbell and Mankiw 1990) framework. Section 7 concludes.

2. Theory

This section briefly reviews the theory of consumer behavior and discusses possible links to consumer sentiment. The permanent income hypothesis (PIH) states that consumers' expenditures depend on their permanent income. Permanent income is defined as the present value of wealth,

[Y.sub.Pt] = [A.sub.t] + [E.sub.t] [[infinity].summation over (i=o)] [beta.sup.i][Y.sub.Lt+i],

where [A.sub.t] is the real value of the individual's nonhuman wealth at the beginning of period t; [beta] is the discount factor; [Y.sub.Lt] is real disposable labor income; and [E.sub.t] is the expectation operator conditional on information available to the individual at time t.

Campbell and Mankiw (1990) test Hall's (1978) random walk hypothesis by separating consumers into two groups. A proportion of households, [lambda] (rule-of-thumbers), simply set consumption equal to income in each period, while a fraction (1--[lambda]) (life-cyclers) behave according to the PIH. In this framework, the only reason any lagged variable could have predictive power for current consumption growth is because that variable has predictive power for current income growth, and the [lambda]. consumers do not spend that income until it arrives. In that context, the usefulness of consumer sentiment should come from the fact that it captures information about expected future income. On the other hand, if consumer sentiment has explanatory power beyond that of predicting future income, then the Campbell-Mankiw framework would be rejected.

A more psychological approach to consumption was pioneered by Katona (1975). In Katona's view, consumer expenditures are a function of both capacity and willingness to consume. According to the psychological theory, willingness (as captured by sentiment) to consume cannot be explained only by the reaction of consumers to economic variables. In this view, a drop in sentiment can, by itself, cause a decline in consumption in a way not foreseen by economic variables (i.e., without a decrease in income). Willingness to consume is negatively related to uncertainty (Acemoglu and Scott 1994). Even if consumers' financial position is actually unchanged, higher perceived uncertainty can lead to a decline in consumption, as increased uncertainty reduces marginal propensity to consume. In this context, the usefulness of sentiment comes from its ability to convey consumers' assessment of uncertainty. It can therefore be linked to precautionary saving models of consumption (Carroll 1992).

3. Review of Empirical Literature

In this section, we summarize the empirical literature on the use of consumer sentiment indexes in a consumption function. We begin by briefly reviewing the explanatory variables typically found in these analyses.

Explanatory Variables

To evaluate the informational content unique to sentiment indexes, they must be purged of information that could come from their determinants. The inclusion of such variables in a consumption equation will ensure that the addition of sentiment indexes provides further explanatory power only to the extent that the indexes capture information relative to expected income, uncertainty, or at least information not found in standard macroeconomic data. These control variables are disposable income (a proxy for expected income), unemployment rate and inflation (proxies for uncertainty), (1) interest rates and stock prices (proxies for information from financial markets), (2) and net worth (a proxy for nonhuman wealth).

The information contained in these explanatory variables can be evaluated by calculating the [R.sup.2] of the following regression equation:

(1) U[M.sub.t] = [mu] + [beta][X.sub.t] + [v.sub.t],

where UM stands for the University of Michigan Consumer Sentiment index and X is a vector containing the aforementioned variables. Estimating Equation 1, we find that about 72% of the variation in the index can be explained by the components of X.

Thus, some of the variations in consumer sentiment cannot be explained by standard macrovariables, suggesting that [v.sub.t] could be used in a consumption equation to assess the incremental explanatory power of sentiment. In our empirical model, we use sentiment with the addition of the components of X, as this procedure involves only one estimation step.

Forecasting Value

The findings in the empirical literature on consumer sentiment indexes can be divided into three groups. First, the indexes are of negligible value. Fuhrer (1993) finds that the UM index is a statistically significant predictor of consumer spending, but that its explanatory power fades in the presence of income in the equation. Hymans (1970), Mishkin (1978), Burch and Gordon (1984), and Garner (1991) also find that sentiment indexes lose their significance with the addition of controls.

The second group includes studies finding that sentiment indexes have an incremental explanatory value. Carroll, Fuhrer, and Wilcox (1994) (hereafter CFW) find an intrinsic, but modest, predictive value for the UM index. By controlling for the predictive power of sentiment for income growth through an instrumental variable regression, they find predictive power for consumption growth in sentiment. In addressing the question of how sentiment fits into a formal maximizing model of aggregate consumption, the authors conclude that this power cannot be interpreted within the Campbell--Mankiw framework. Other studies (Matsusaka and Sbordone 1995; Bram and Ludvigson 1998; Howrey 2001; Souleles 2001; and Mourougane and Roma 2002) find that consumer sentiment indexes depict idiosyncratic variations useful to explain consumption or economic activity.

The third group of studies finds that sentiment indexes are useful because they improve forecasts of consumption during exceptional periods. In line with Garner, Throop (1992) finds that, during the Gulf War and the 1987 stock market crash, consumer sentiment moved independently from current economic conditions. Using a vector error-correction model (VECM), he finds that the variables that usually explain sentiment failed to do so during the Gulf war. Instead, consumer spending followed the path of sentiment during that period. (3) Santero and Westerlund (1996) also argue that strong variations in sentiment, which are likely driven by major events, are often followed by fluctuations in GDP.

Using the standard controls, Garner (1991) finds that the addition of consumer sentiment worsened forecasting accuracy during normal times but improved it during the Gulf War. This suggests that we should ignore the consumer sentiment during normal periods. Periods of high economic or political uncertainty are often associated with high volatility of consumer sentiment, suggesting that large swings in sentiment are particularly important for consumption.

Analyses of the usefulness of consumer sentiment during these exceptional times of high uncertainty are scant. Moreover, they are always focused on predetermined periods, often the Gulf War episode. But can we really conclude that consumer sentiment is valuable in times of major shocks based only on event studies? In the next section, we formally assess the usefulness of the UM index during extraordinary periods.

4. Empirical Framework

Instead of focusing on periods of major economic or political events documented in the press, we propose a more general approach in which periods of high volatility are endogenously determined within a consumption function framework. Before turning to the modeling of sentiment, we introduce our benchmark model.

Benchmark Model: A Consumption Function

Our consumption function contains a long-run anchor determined by a cointegrating vector including the level of consumption, income, and net worth (all in real per capita terms). Moreover, short-run dynamics provide information coming from variables that affect consumption within the business cycle. These variables are the first difference of nominal interest rates, inflation, stock prices, unemployment, and the variables included in the cointegrating vector. We estimate the following dynamic consumption function

[DELTA][C.sub.t] = [alpha] + [pi][DELTA][L.sup.j]([C.sub.t] + [n.summation over (i=1)[[beta].sub.i][DELTA][L.sup.j]([X.sub.it]) + [gamma][[C.sub.t-1] - [[psi].sub.1][Y.sub.t-1] - [[psi].sub.2][W.sub.t-1] + [[epsilon.sub.t] j = 1, ..., m,

where [C.sub.t] is total NIPA consumer expenditures; [Y.sub.t] is disposable income; [W.sub.t] is households' net worth; and [X.sub.it] represents a vector containing the n short-run dynamic variables. The variables and lags kept for the final specification are chosen with the general-to-specific method, as in Hendry and Ericsson (1991). Note that this equation does not include any measure of consumer sentiment at this stage.

Threshold Specification

We postulate that the explanatory power of the UM index comes from its strong variations. In this context, we estimate a model in which only large swings in sentiment can affect consumption. If our thinking is correct, the explanatory and forecasting power of our model should be maintained by focusing only on large changes in the index. Moreover, if in-sample and out-of-sample properties are improved by doing so, we may conclude that small variations in the index should be ignored.

We estimate a threshold that conditions the inclusion of consumer sentiment in the consumption function in Equation 2. More precisely, we estimate [theta], [theta] > 0, in the following equality:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

The threshold ([theta]) is given by a grid search minimizing the sum of squared errors of Equation 2 with [DELA]U[M.sub.tr] added. This means that the change in consumer sentiment will enter the regression at time t only if its absolute value exceeds [theta]. Otherwise, zeros replace sentiment data. The criterion tells us at which magnitude of variation it is worthwhile to include consumer sentiment in the regression in terms of better fit. (4) However, to ensure the estimation of a threshold sentiment variable with minimal noise (such that positive shocks are not immediately followed by negative shocks or vice versa), we define a smoother criterion,

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

This criterion means that the change in consumer sentiment will enter Equation 2 at time t only if the absolute value of the difference between its level and the average level over the two previous quarters exceeds [theta].

5. Results

In this section, we present our benchmark model for measuring the usefulness of the UM index. Our threshold model is then analyzed.

Benchmark Model

When testing for cointegration with the Johansen-Juselius (1990) approach, we find cointegration at the 5% significance level (Table 1). Consequently, we use the Phillips and Loretan (1991) nonlinear least-squares methodology to estimate Equation 2 and obtain long-run parameter estimates over the sample period 1960:III-2002:I for the level of consumption, income, and net wealth.

Using the general-to-specific method, we obtain a final specification. (5) The first column of Table 2 gives the estimation results for this benchmark model. It also summarizes various diagnostic tests performed on the residuals of this equation.

The consumption equation performs reasonably well in explaining movements in consumption over the last four decades. About 33.8% of the variations in consumption can be attributed to our explanatory variables. All short-run coefficients are statistically significant and have the expected sign. Moreover, the error-correction term depicts a negative coefficient, a feature consistent with the existence of cointegration.

Augmented Model

We first reproduce the analysis commonly found in the literature, that is, by measuring the improvement to the goodness of fit and forecasts of a consumption equation resulting from the addition of a sentiment index. We include four lags of the UM index (in first difference because we are interested in changes in the index). As can be seen in the second column of Table 2, the sum of the coefficients on these lags is small, but positive and statistically significant. In-sample performance is assessed by the increment in the [R.sub.2] statistic, while out-of-sample performance is examined using the root-mean-squared error (RMSE) over the 1990s. (6) We compute one-step-ahead forecasts. (7)

Results are given in the first and second lines of Table 3. The RMSEs are shown in parentheses and expressed relative to the benchmark's RMSEs. The results are broadly consistent with the literature's view that, taken on its own, consumer sentiment has modest incremental explanatory power. The addition of the UM index yields a slightly higher [R.sup.2] but increases the RMSE.

Threshold Model

We now estimate a model as in Equation 3. The focus of the analysis is to measure the improvement to our consumption equation when we replace consumer sentiment with the threshold variable in the augmented model.

The simultaneous estimation of Equations 2 and 3 over the 1960-2002 period yields a value of 10.51 for the parameter [theta]. With this estimate of [theta], we can construct a series that contains only values that meet the criterion in Equation 3. Figure 1 depicts the transformed UM index series actually replacing the sentiment index in the consumption equation. The third column of Table 2 shows that the coefficients for the threshold variables are more positive and even more significant than in the augmented model.

The graph on the left shows the sentiment variable entering in the augmented model, and the graph on the right shows the sentiment variable entering in the threshold model. A relatively small number of periods that can be associated with major economic or political events are identified with this threshold. In four of the last five recessions, sharp positive increases in sentiment were useful in explaining higher consumption during early recovery periods, thereby suggesting that sentiment could be a good proxy for pent-up demand. Although the UM index dropped markedly following 11 September, this drop was not large enough to exceed the threshold. (8) This is consistent with Garner (2002). This result is reasonable, given that consumption held up very well during the last quarter of 2001. The adjusted series coincides with several turning points in the U.S. economy. This is in line with the view that consumer sentiment could proxy uncertainty because turning points are, by definition, periods of elevated uncertainty.

The third line of Table 3 summarizes the results with the threshold model. The in-sample performance is improved relative to both the benchmark and augmented models. The increment to the [R.sup.2] is of about two percentage points relative to the augmented model. As in Garner (1991), our results suggest that small fluctuations in sentiment should be ignored.

Results with respect to the out-of-sample performance also depict an improvement. The RMSE decreases by three percentage points relative to the augmented model. (9,10) Moreover, following Ericsson's (1991) forecast encompassing test, we find that our threshold model provides statistically significant smaller forecasting errors relative to both the augmented and the benchmark models. Thus, replacing the sentiment index by the threshold variable improves the equation, confirming that the relevant information for future consumption coming from sentiment is indeed found in its large variations.

(6.) Threshold Sentiment in the Campbell-Mankiw Framework

The Campbell-Mankiw model implies that consumer sentiment has predictive power only to the extent that it appears in the forecasting equation for consumption indirectly, through its role as a predictor of income. In this section, we follow CFW and test whether the Campbell-Mankiw framework provides an admissible explanation for the fact that lagged threshold sentiment has some explanatory power for current changes in household spending.

As in section 2, the Campbell-Mankiw model assumes that rule-of-thumb consumers receive a constant fraction [lambda] of total income such that aggregate consumption is given by

(4) [DELTA][C.sub.t] = [lambda][DELTA][Y.sub.t] + [[epsilon.sub.t]

where [[DELTA][C.sub.t] is the change in aggregate consumption; [DELTA][Y.sub.t] is the change in income; and [[epsilon.sub.t] is the error term. The error term [[epsilon].sub.t] is orthogonal to lagged variables but not necessarily to [DELTA][Y.sub.t], so an ordinary least squares (OLS) estimate of [lambda] will generally be inconsistent. A consistent estimate can be obtained by using the instrumental variable (IV) technique. The IV estimate of [lambda] obtained by Campbell and Mankiw is of about 0.5. Because consumption follows an IMA(1,1) process, subsequent articles (Christiano, Eichenbaum, and Marshall 1991 as well as CFW) modified Equation 4 to be

(5) [DELTA][C.sub.t] = [[lambda][DELTA][Y.sub.t] + [[mu].sub.t] [[mu].sub.t] ~ MA(1).

In Equation 5, [[mu].sub.t], is serially correlated and is therefore not likely to be orthogonal to variables lagged one period. Test statistics can be corrected for serial correlation in the residuals by lagging instruments one extra period. However, as emphasized by CFW, estimating Equation 5 would ignore the most up-to-date predictors of the change in income. We therefore estimate the following equation using the IV technique:

(6) [[DELTA][C.sub.t] = [[lambda][DELTA][Y.sub.t] + [[upsilon.sub.t] - [PHI][[upsilon.sub.t]-1.

According to the Campbell-Mankiw model, sentiment should enter Equation 6 only as an instrument for current growth of income. We test this in three steps. First, we estimate Equation 6 using the IV technique. Second, we reestimate Equation 6 with lagged sentiment added both directly and indirectly as an instrument (as in CFW). Finally, we estimate Equation 6 with the threshold sentiment variable added both directly and indirectly. Results are shown in Table 4.

The estimates for [lambda] and [PHI] are in line with the literature. For example, CFW find for the various components of consumption values for [lambda] and [PHI] ranging from 0.276 to 1.786 and -0.012 to 0.532, respectively. A coefficient for [lambda] exceeding one is clearly not consistent with the original interpretation of [lambda] as being the fraction of aggregate income accruing to rule-of-thumb consumers. However, CFW explain this discrepancy by the presence of durable goods in consumption and assume that rule-of-thumbers move their consumption, as distinct from their outlays, in line with contemporaneous changes in income.

In both regressions in which the UM index appears directly and indirectly as an instrument (either on its own or as the threshold variable), we strongly reject the hypothesis that consumer sentiment predicts the growth rate of consumption only through its predictive power for income growth.(11) Therefore, in line with CFW, we conclude that the threshold sentiment variable's explanatory power found in section 5 cannot be interpreted within the Campbell-Mankiw framework. We further conclude that the Campbell-Mankiw-breaking power of sentiment is due to the few episodes when there have been large movements in sentiment and not to the underlying regular movements in sentiment.

7. Conclusion

Few studies have found that sentiment indexes have significant explanatory power once fundamental factors of the economy are taken into account. In line with the literature, we found that, taken on its own, the UM index contains modest information to forecast aggregate consumer spending in the United States.

Some researchers, however, have suggested that sentiment indexes could be helpful during major economic or political events, as they tend to diverge from a path consistent with other macroeconomic variables in such periods. These periods of high uncertainty are usually associated with strong volatility in consumer sentiment, suggesting that large swings in sentiment matter for consumption. We have formally tested this by constructing a simple threshold model that takes into account the magnitude of variation of consumer sentiment to forecast consumer expenditures. We found that insample and out-of-sample properties of a consumption equation are improved relative to equations that include sentiment as it is.

Finally, we tested the Campbell-Mankiw model and found that lagged threshold consumer sentiment is a useful predictor for current consumption growth not solely through the income channel.

It is during periods of elevated uncertainty that consumer sentiment is most likely to affect spending. Consequently, economists and forecasters should pay attention to consumer sentiment especially in times of high uncertainty.

Appendix A: Sources and Definitions of Variables

We use quarterly NIPA time series from 1960:III to 2002:I.

Dependent variable

* Change in the log of real consumption (U.S. Department of Commerce, Bureau of Economic Analysis, National Income and Product Accounts) per capita (U.S. Department of Labor, Bureau of Labor Statistics Household Data).

Explanatory Variables

* Change in the log of real disposable personal income (U.S. Department of Commerce, Bureau of Economic Analysis, Personal Income & Outlays) per capita.

* First difference of the nominal short-term interest rate (U.S. 90-day commercial paper rate, AA-nonfinancial closing rate, Federal Reserve Website).

* Inflation calculated as the change in the log of the CPI--all items (U.S. Department of Labor, Bureau of Labor Statistics).

* Change in the log of net worth per capita (Balance Sheets for the U.S. Economy, Flow of Funds data (C.9)), divided by the GDP deflator. (The University of Michigan index is added in first difference. Source: DRI.)

Table 1. Cointegration Tests (1960:III-2002:I)
                                                          Unit Root
                                                           Tests (b)

Long-Run Parameter Estimates (a)                              ADF

-0.4349 + 0.3104[wealth.sub.t] + 0.6778[income.sub.t]       -3.529
(-1.111)       (2.629)               (4.552)
                                                          Unit Root
                                                           Tests (b)

                                                            Dflags

-0.4349 + 0.3104[wealth.sub.t] + 0.6778[income.sub.t]          1
(-1.111)       (2.629)               (4.552)

Long-Run Parameter Estimates (a)                           Johansen
                                                           Test (c)
                                                        [lambda]-Trace

-0.4349 + 0.3104[wealth.sub.t] + 0.6778[income.sub.t]        30.11
(-1.111)       (2.629)               (4.552)             ([H.sub.0]:
                                                            r = 0)

Long-Run Parameter Estimates (a)                           Johansen
                                                           Test (c)
                                                        [lambda]-Trace

-0.4349 + 0.3104[wealth.sub.t] + 0.6778[income.sub.t]        12.18
(-1.111)       (2.629)               (4.552)              ([H.sub.0]:
                                                            r = 1)

(a) t-Statistics are reported below the parameters estimates.

(b) The ADP statistic tests the null hypothesis of noncointegration
([H.sub.0]: unit root in the residuals). Critical values for the 1, 5,
and 10% levels are -3.46, -2.88, and -2.57 (Hamilton 1994). The
optimal lag length for the ADF regression is given by the Bayesian
information criteria.

(c) Critical values for the 5% level are 26.79 and 13.33 for r=0 and
r= 1, respectively (where r is the number of cointegrating vectors).

Table 2. Error-Correction Models (With and Without Consumer
Sentiment) Dependent Variable: Aggregate Consumption
Growth (1960:III-2002:I)

                             Base Case Model    Augmented Model

e[c.sub.t-1]                 -0.0642 (-3.901)   -0.0716 (-4.050)
[Income.sub.t-1]              0.1054 (1.904)     0.0856 (1.514)
[Consumption.sub.t-2]         0.2287 (3.282)     0.1731 (2.336)
[Consumption.sub.t-3]         0.2801 (4.261)     0.2810 (4.013)
Interest [rate.sub.t-1]      -0.0012 (-2.366)   -0.0014 (-2.856)
Interest [rate.sub.t-2]      -0.0015 (-3.034)   -0.0016 (-3.024)
CPI [inflation.sub.t-1]      -0.0024 (-2,881)   -0.0016 (-1.683)
UM [index.sub.t-1 to t-4]           -            0.0004 (2.513)
[[bar]R.sub.2]                    0.338              0.358
LM ARCH(4)                        0.591              0.529
Jaryue-Bera                       3.183              5.082
Breusch-Godfrey                   0.236              0.491
White heteroskedasticity          1.323              1.328

                             Threshold Model

e[c.sub.t-1]                 -0.0727 (-4.190)
[Income.sub.t-1]              0.0722 (1.260)
[Consumption.sub.t-2]         0.1930 (2.727)
[Consumption.sub.t-3]         0.2757 (4.124)
Interest [rate.sub.t-1]      -0.0013 (-2.636)
Interest [rate.sub.t-2]      -0.0016 (-3.193)
CPI [inflation.sub.t-1]      -0.0016 (-1.854)
UM [index.sub.t-1 to t-4]     0.0009 (2.789)
[[bar]R.sub.2]                    0.375
LM ARCH(4)                        0.434
Jaryue-Bera                       6.388
Breusch-Godfrey                   0.761
White heteroskedasticity          1.377

The figures in parentheses are r-statistics.

Table 3. In-Sample and Out-of-Sample Performance
Adjusted [R.sup.2] and Relative RMSE

Base case          0.3380 (1.0000)
Augmented          0.3577 (1.0092)
Threshold          0.3747 (0.9793)

Numbers in parentheses represent relative RMSEs
(i.e., divided by the base case model's RMSE). Out-of-sample
per-formance: estimation period, 1960:III-1989:IV;
forecasting period, 1990:I-2002:I. RMSE for the
case model is 0.435%.

Table 4. Campbell-Mankiw Model Estimates (1960:III-2002:I)

                                                         p-Value on
                                                         Joint
                                                         Significance
                                                         of the
                                                         Coefficients
                              [lambda]       [PHI]       on Sentiment

Without sentiment          1.054 (0.000)  0.315 (0.000)     --
With sentiment             0.801 (0.000)  0.302 (0.002)    0.000
With threshold sentiment   1.059 (0.000)  .0339 (0.000)    0.007

Instrument list contains a constant and three lags of: income,
consumption, unemployment rate, inflation rate, S&P500, and the
UM index for specification with sentiment and with threshold.
See Appendix A for more details on the variables.

The authors wish to thank Jeannine Bailliu, Denise Cote. Yanick Desnoyers, Robert Lafrance, Rent Lalonde, John Murray, Jean-Francois Perrault, Larry Schembri, David Tessier, Bank of Canada, and Canadian Economics Association (Calgary, 2002) seminar participants, and two anonymous referees for several valuable comments and suggestions. The views expressed in this article are those of the authors. No responsibility for them should be attributed to the Bank of Canada.

(1) As the volatility of inflation increases with its level, higher inflation generates uncertainty around expectations of real wage gains.

(2) The value of the consumer confidence index might come from the timeliness of its monthly release, as it is available with almost no time lag. Financial variables can be used to control for this. This advantage is relatively small (Fuhrer 1993). For details on links between consumer sentiment and the stock market, see Otoo (1999).

(3) Decreasing interest rates and inflation led the model to forecast an increase in consumption at that time.

(4) By construction, finding a value of [theta] different from zero guarantees that the deletion of low-volatility observations is profitable in terms of the equation's fit.

(5) Stock prices and the unemployment rate are nonsignificant and do not improve the fit.

(6) RMSEs are calculated using rolling regressions, starting with 1960:III-1989:IV as the sample period, moving up one quarter each time to generate a new forecast.

(7) This is a reasonable forecasting horizon because we use quarterly data and we do not expect confidence to affect consumption more than one quarter out.

(8) This situation has also been observed during the recent war in Iraq.

(9) Our results are not sensitive to small changes in [theta] nor to a change in the sample period for the estimation of the thresholds. Indeed, changing the threshold estimation period from 1960:III-2002:I to 1960:III-1979:IV with separate estimation of the consumption function over the 1980:1-2002:1 and forecasting over the 1990s yields similar results.

(10) Another method can be used to identify periods of high volatility in consumer sentiment indexes. In addition to the above threshold specification, we analyzed a method based on conditional variance estimation, as in Worrell and Leon (2001). The results obtained using a GARCH(1,1) model reinforce our premise that large swings in consumer sentiment are particularly useful. The [R.sup.2] rises by as much as four percentage points in that case, and out-of-sample performance is also reasonably good, as the relative RMSE falls to 0.9816.

(11) The parameter estimates and the significance of consumer sentiment are robust to different instrument lists. Upon performing over-identifying restrictions tests, we find no evidence against the specification.

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Brigitte Desroches * and Marc-Andre Gosselin ([dagger])

* International Department, Bank of Canada, 234 Wellington Street, Ottawa, Ontario, Canada K1A 0G9, E-mail [e-mail]; corresponding author.

([dagger]) International Department, Bank of Canada, 234 Wellington Street, Ottawa, Ontario, Canada K1A 0G9, E-mail [e-mail]

Received December 2002; accepted June 2003.