A mean-variance approach to forecasting with the consumer confidence index

Abstract

This article refines the way consumer confidence survey data are used in forecasting models. The refinement is easy to describe: it extends existing models by controlling for statistically significant changes in consumer confidence index values. The motivation behind this refinement is simply that not all changes in the confidence index are statistically significant, and mean index values alone provide a noisy signal. Using Michigan Index of Consumer Confidence from 1967 through 2013, we show that controlling for significant versus insignificant changes in the consumer confidence index materially enhances the explanatory power of household expenditure forecasting models.

Keywords:

• consumer confidence index
• forecasting consumer spending
• mean-variance approach

JEL Classification:

• E270
• D84
• D120
• C83

Acknowledgements

We are grateful to Sydney Ludvigson for providing some of the data used in the study, to Lafayette College for an Excel Scholar Fellowship, to Nicole Crain for constructive feedback on earlier drafts and to James MacGee for useful comments.

Notes

¹ For example see Lovell (2001).

² For studies that examine the forecasting power of consumer confidence, see Fuhrer (1993), Bram and Ludvigson (1998), Howrey (2001), Ludvigson (2004), Croushore (2005), Cotsomitis and Kwan (2006), Gelper et al. (2007), Al-Eyd et al. (2009), Ҫelik and Özerkek (2009), Fornell et al. (2010), Dees and Brinca (2011), Chen (2011), Starr (2012), Dreger and Kholodilin (2013), Vosen and Schmidt (2011), Bruno (2014), and Møller et al. (2014).

³ Unlike the rest of the literature, Croushore (2005) found that the consumer confidence index does not have any forecasting power on consumer expenditures. Even if this is correct, it does not contradict the findings of our article, because he does not look at significant changes in the consumer confidence index.

⁴ Survey B indicates a split among households that is in line with the framework posited by Campbell and Mankiw (1989). In their model, half of households follow a rule of thumb of consuming their current income and half are forward-looking and consume their permanent income.

⁵ Dominitz and Manski (2004) looked at the transitions between ‘yes’, ‘no’ and ‘maybe’ in the index and found a transition matrix. They concluded that the transitions between ‘yes’, ‘no’ and ‘maybe’ was also volatile between months, which also shows that there can be big differences between months with the same aggregate ICS.

⁶ Equation 8 scales the SD to conform to the specific formula used by the University of Michigan in computing their various indices of consumer attitudes. In their computations, if $y=100\mathrm{\%}$, then the DUR index would be 200. If $n=100\mathrm{\%}$, then the DUR index would be 0. And if $m=100\mathrm{\%}$ then the DUR index would be 100. In each of these cases, the SD would obviously be zero, since there is no deviation. Thus, Equation 8 adjusts the typical SD formula to conform to the values assigned by the University of Michigan and the fact that the sum of all response shares must equal 100%. See the Appendix for further details on how the Michigan indices are computed.

⁷ Curtin et al. (2000) examined the error of the consumer sentiment tied to an increasing refusal rate (of interviews). In a more complex model, the SE might take this into account. For the purposes of the analysis in this article, we assume such effects are negligible.

⁸ Equation 13 derives from the total area under the product of the heights of two normal error curves determined by the means and SEs. This area approximates the sum of the probabilities that both means reflect parameters within the same index point.

⁹ In alternative specifications, not reported in the article, we examined other critical cut-off values such as the 1% and 10% confidence levels. The results were largely unchanged, and the 5% confidence level is of course a commonly used convention.

¹⁰ Alternatively, if the survey results for the five questions were available at the level of the individual respondent, we could compute the covariances as follows: $\mathrm{c}\mathrm{o}\mathrm{v}(A,B)=400P(y_A,y_b)+200P(y_A,m_b)+200P(m_A,y_b)$, where P(1, 2) is the number of occurrences that someone polled answered both 1 in Index A and 2 in Index B. This is based on the standard formula $cov(X,Y)=E(XY)-E(X)E(Y)$ and the values for y, n and m discussed in Note 6. Because this information is not reported on the individual basis, we are forced to assume that the correlation coefficients are constant over time. This assumption makes the correlation coefficients between variables over time equal to the correlation coefficients between variables at every survey level.

¹¹ Dominitz and Manski (2004) also looked at correlations among the indices across time. They also found a high correlation between the expected business condition variables (in our case BUS12 and BUS5).

¹² Michigan computes the index as follows: $\mathrm{I}\mathrm{C}\mathrm{S}=2.0+\frac{I_1+I_2+I_3+I_4+I_5}{6.7558}$. We divide the SD of the sum of the Indices by 6.7558 to transform the SD into the same units as the Index of Consumer Sentiment.

¹³ We examined other critical cut-off values, as explained in Note 9, and the results are not materially different from those reported in the text.

¹⁴ Labour income is wages and salaries plus transfers minus personal contributions for social insurance, as is appears in the quarterly components from the Department of Commerce’s National Income and Product Accounts. Stock prices are quarterly averages of the daily adjusted close of the Standard and Poor’s 500 index. The interest rate is the quarterly average based on the 3-month Treasury bill rate, reported monthly by the Board of Governors of the Federal Reserve System. Nominal labour income and the Standard and Poor’s 500 index are deflated by the personal consumption expenditure implicit price deflater, as reported quarterly in the National Income and Product Accounts. This data set is available at the link provided in the supplemental data set section of the article.

¹⁵ The 1990 recession ran from the third quarter of 1990 through the first quarter of 1991. The 2007 recession ran from the fourth quarter of 2007 through the second quarter of 2009.

¹⁶ Mankiw (1982) suggests that the growth in expenditures on durable goods may be passively autocorrelated, with the error term following a first order moving average process. Such first-order autocorrelation may cause the error to be correlated with the one-period-lagged endogenous variable, a condition that could skew in-sample statistical tests of joint marginal significance of the explanatory variables (the reported p-values).

¹⁷ For example, Bram and Ludvigson (1998) excluded these early observations so that they could compare it to the Confidence Board’s measure of consumer sentiment, which started in 1967.

¹⁸ For lagged values in the early part of our data set, we use data values before 1967.

¹⁹ The DUR Index question asks: ‘About the big things people buy for their homes – such as furniture, a refrigerator, stove, television, and things like that. Generally speaking, do you think now is a good or bad time for people to buy major household items?’ The VEH Index question asks: ‘do you think now is a good or bad time for people to buy a motor vehicle?’