Abstract
We investigate the circumstances in which business cycle forecasting is beneficial for business by addressing both the short-run and the long-run aspects. For an assessment of short-run forecasting we make a distinction between using publicly available information of cycle probabilities and the use of resources to sharpen this outlook. A sharpened forecast can pay off because it helps the firm to optimally select its output mix. For a long-run perspective we show that firms whose optimal level of operation varies with varying selling prices gain from an accurate assessment of the likelihood of the states of expansion and recession. Petroleum refining in the U.S. is econometrically studied as an exemplary industry. The results document cyclical regularities that indicate that forecasting is advantageous for firms in this industry.
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Notes
With this choice we take the perspective that the stage of the cycle is objectively, if at times only with a lag, identifiable.
Note that a dependence on duration would not invalidate the analysis that follows but would merely make the probability p depend on the length of the expansion.
Finding one or more variables that help explain the probabilities of a continuation of the present state (and the probability of a turning point) is only one requirement for making an informed forecast. A further requirement is to find a quantitative relationship that is stable and hence reliable for out-of-sample forecasting. The results documented in Estrella and Mishkin (1998) indicate that stock price data and interest rate spreads are the potentially most informative variables for improving probability assessments for the U.S. business cycle. Information concerning these variables are not only significant for explaining the cycle in-sample but also predict out-of-sample.
One could think of other aspects relevant for decision making (not to be modeled here) where this type of analysis would apply. Besides the varying output prices the costs of inputs may also be affected by the business cycle.
Clearly, the question of forecasting during recessions could be developed as a straightforward extension of the present analysis.
An early contribution to the sensitivity of prices to cyclical changes is from Wasson (1953) who documents sizable variations across types of durable goods. See also Gordon (1990) for a major contribution to the measurement of prices of durable goods. Effective selling prices, e.g. for automobiles, have to incorporate rebates which, particularly during recessions, can be significant and furthermore prices tend to decline as customers in recessions tend to relocate purchases to low-priced retailers (see Coibion et al. 2015).
We could differentiate the parameter \(\beta \) over types of goods but for the basic insights developed here this is not material.
Expected profit, given \(Q_S +Q_L =1\), can be written as \(E\left( {\Pi } \right) =p\left[ {Q_L P_L^B +\left( {1-Q_L } \right) P_S^B } \right] +\left( {1-p} \right) \left[ {Q_L P_L^R +\left( {1-Q_L } \right) P_S^R } \right] -\alpha -\beta Q_L^2 -\beta \left( {1-Q_L } \right) ^{2}\). Maximizing expected profit rather than strategies like, e.g., downside risk control (Barro and Canestrelli 2014) is the appropriate criterion here given the repetitive nature of the decision problem and the availability of probability estimates.
Given \(p=0.95, P_S^R -P_L^R \) would need to be 19 times higher than \(P_L^B -P_S^B \) to neutralize the described effect of business cycle expectations on the output mix.
With the labels concerning goods chosen as “large” and “small” the situation of a typical firm will be that \(\delta \) is positive. However, for our analysis these labels could be changed in any way (e.g., good 1 and good 2) and \(\delta \) could also be negative.
This probabilistic perspective on the role of forecasting can intuitively be grasped when we consider forecasting as selecting a ball from an urn. In the case of the uninformed forecast we can think of nature (or fate) as drawing a ball every quarter during the expansion from an urn with 100 balls where 95 balls have the label “expansion” and 5 balls are labeled “contraction”. This makes for a probability of 0.95 in favor of a continued expansion. Think now of forecasting as affording a glimpse into the urn and perceiving that nature is drawing from one of two smaller urns termed A and B with 50 balls each and with unequal numbers of balls labeled recession. Consider as an illustration the case where urn A contains two recession balls and urn B contains three of them (implying 48 expansion balls in A and 47 such balls in B). This means that with informed forecasting we are either in the situation with \(p=0.96\) or \(p=0.94.\) In terms of the terminology introduced this is a situation with a \(\phi =0.01.\) Accordingly, an informed business cycle forecast allows us a sharper assessment of the likelihood of a continuation of a boom. If we know the choice to be from an A type situation we know with a higher probability that the expansion continues. By contrast, in a B type situation we know that a continuation of the expansion has a lower probability. Hence, the role of the forecaster is to tell management whether they face situation A or B. In the former case an informed forecast makes us—and rationally so—more optimistic regarding the expansion and in the latter it makes us more pessimistic. Clearly, if \(\phi \) is zero we are back in the non-informed situation. Also, \(\phi \) has an upper boundary of \(1-p\).
Obviously, the potential benefit of an informed forecast has to be weighed against the costs of the forecast. See Rötheli (1998) for an elaboration of this point.
The transition probabilities discussed before and (unconditional) probabilities of the two states of a Markov process are related by the equation \(\varepsilon =\left( {1-q} \right) {/}\left( {2-p-q} \right) \).
This cost function has already proved helpful in the modeling of industrial concentrations processes (Rötheli 2008).
The problem to be solved is \(\mathop {\mathrm{Max}}\nolimits _{{\bar{Q}},\underline{Q},W} E\left( \mathrm{{\Pi }} \right) = \varepsilon \left[ {{\overline{ PQ }} - \rho W - \frac{\beta }{{{W^{0.5}}}}{{{\bar{Q}}}^2}} \right] + \left( {1 - \varepsilon } \right) \Big [ \underline{ PQ } - \rho W - \frac{\beta }{{{W^{0.5}}}}{{\underline{Q}}^2} \Big ]\).
A description of this industry and the typical product mix of firms can be found in chapter 5, Office of Technology Assessment (1983). Refineries are in a position to influence the mix of output in a multistage production process and use this flexibility to adjust to changing market conditions (see Gary et al. 2007).
All estimates reported here use logs of level data. Tests for unit roots indicate that all individual prices of refinery products as well as the price of oil and real GDP are non-stationary as indicated by augmented Dickey–Fuller test statistics for the hypothesis of a unit root with a p value of at least 0.3. Hence, in order for the equation in level terms as shown in (8) to have the necessary properties for testing we need to make the case that (8) represents a cointegration equation. This proposition is supported by Dickey–Fuller test statistics concerning the residuals of the estimated equations which indicate stationarity of the residuals in all cases at the 1% level of significance.
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Data sources
NBER dating of business cycle turning points. http://nber.org/cycles/cyclesmain.html
Industry price data from the U.S. Bureau of Labor Statistics. http://data.bls.gov/cgi-bin/dsrv?pc
Crude oil price (West Texas intermediate). https://research.stlouisfed.org/fred2/series/MCOILWTICO
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I would like to thank Christoph Mölleken, James Juniper, Lukas Rosenberger, Walter von Siebenthal, Martin Watts and participants in a seminar at the University of Newcastle for comments. The detailed comments by an anonymous referee were particularly helpful.
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Rötheli, T.F. Should business rely on business cycle forecasting?. Cent Eur J Oper Res 26, 121–133 (2018). https://doi.org/10.1007/s10100-017-0477-8
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DOI: https://doi.org/10.1007/s10100-017-0477-8