Canadian Cattle Cycles and Market Shocks



We analyze Canadian beef cattle cycles using time-series properties of four variables: total cattle inventories, beef cow inventories, beef supply, and beef prices. Our aim is to provide up-to-date estimates of the duration of the cycles, and to determine whether or not some of the recent market shocks can be associated with changes in the nature of the cycles. Spectral decomposition of the variables reveals 10-year cycles in total cattle inventories, beef cow inventories, beef supply, and beef prices. Seasonal and annual cycles are also found in beef supply and prices, respectively. Using intervention analysis, exchange rate appreciation, feed price escalation, and bovine spongiform encephalopathy (BSE) are modeled as pure jumps. Exchange rate and feed price shocks are modeled as having started in 2002 and 2007, respectively, and persisted up to the end of the sample period, while BSE is modeled as a shift for the period 2003 to 2005. We find significant impacts of the three shocks on total inventories, but beef supply appears to have been impacted by exchange rates and BSE. A spectral comparison of the pre- and post-shock periodograms of beef supply reveals a 58% reduction in the peak amplitude of the beef supply cycle.


Dans le présent article, nous analysons les cycles du secteur canadien des bovins de boucherie par le biais des propriétés des séries chronologiques de quatre variables associées à ce secteur, à savoir le cheptel bovin total, le cheptel de vaches de boucherie, l'approvisionnement en bœuf et les prix du bœuf. Notre objectif consiste à fournir des estimations à jour de la durée des cycles et à déterminer si certains chocs ayant récemment secoué les marchés peuvent être associés ou non à des changements liés à la nature des cycles. La décomposition spectrale des variables montre que le cheptel bovin, le cheptel de vaches de boucherie, l'approvisionnement en bœuf et les prix du bœuf suivent des cycles de dix ans. L'approvisionnement en bœuf et les prix du bœuf suivent respectivement des cycles saisonnier et annuel. À l'aide de l'analyse d'intervention, nous avons modélisé l'appréciation du taux de change, la flambée des prix des aliments pour animaux et les épisodes d'encéphalopathie spongiforme bovine (ESB) comme étant des chocs. Les chocs liés au taux de change et aux prix des aliments pour animaux ont été modélisés comme ayant commencé en 2002 et en 2007 respectivement, et ayant continué jusqu’à la fin de la période d’échantillonnage, tandis que l’ESB a été modélisé comme un changement au cours de la période 2003–05. Selon nos résultats, les trois chocs ont eu des répercussions considérables sur le cheptel bovin total, tandis que le taux de change et l’ESB semblent avoir touché l'approvisionnement en bœuf. Une comparaison spectrale des périodogrammes de l'approvisionnement en bœuf avant et après les chocs révèle une diminution de 58 % de l'amplitude de crête du cycle de l'approvisionnement en bœuf.


Cycles in beef cattle production are a well-documented phenomenon that has significant implications for beef herd management for producer profitability (Canfax Research Services 2009), as well as government policy. Knowledge of the cattle cycle is especially important to prospective and newly established cow-calf producers in timing their production decisions. Existence of the cattle cycle implies that producers need to be flexible in managing their operations to ensure they survive periods of low or no profitability during a cyclical downturn. At the industry level, the cycle has implications for government intervention in response to external shocks. For example, the Federal-Provincial BSE Recovery Program implemented from June 2003 to July 2005 was meant to compensate cattle producers, but because the cattle cycle had entered the liquidation phase, the program seems to have inadvertently depressed cattle prices even further during this time (Le Roy et al 2007). This behavior suggests that perhaps any response to a shock on the industry during a downturn should occur only if the shock has the potential to significantly deepen the trough of the existing cattle cycle. Otherwise, cycle peaks and troughs may be amplified by policy interventions and not necessarily by the shocks that they are meant to counteract. For these reasons, this study re-examines the Canadian cattle cycle and investigates the impacts of exogenous shocks on these cycles.

Marsh (1999) determined that breeding cow productivity growth affected cattle cycles. The Canadian beef cattle industry has experienced considerable productivity growth; from 1972 to 2008, beef output per cow increased by 53% from about 170 kg to about 260 kg (Canada Beef Inc. 2012). More recently the industry has been contracting as a result of a lack of profitability (Duckworth 2012). Between 2006 and 2011, cattle ranches decreased by 34% from 75,598 to 49,613 operations (Statistics Canada 2011).1 Prior to and within this time period, the industry experienced five major shocks, namely, border thickening related to bovine spongiform encephalopathy (BSE) and increased transactions costs associated with the 2008 introduction of U.S. mandatory country of origin labeling,2 a surge in feed prices, exchange rate appreciation, and a decline in real income due to the 2008/09 global economic crisis.

In spite of the productivity growth and exogenous policy and market shocks that may have altered the Canadian cattle cycle, there has been virtually no recent empirical work examining Canadian cattle cycles. The last study of Canada's cattle cycle was undertaken more than 40 years ago by Kulshreshtha and Wilson (1973). Despite the paucity of Canadian research, there has been a steady stream of research focused on the U.S. cattle cycle (Hamilton and Kastens 2000; Aadland 2004; Crespi et al 2010). Historically, the two markets have been closely synchronized. However, Canfax Research Services (2009) claims that after 1987, there was a divergence in the cycles of the two industries because of an exchange rate shock. According to Canfax, expansion of the Canadian beef cow herd started in 1987 following a very low Canada/U.S. exchange rate that increased Canadian cattle prices relative to U.S. prices thereby giving Canadian cattle feeders higher profits on inventories. But expansion of the U.S. herd began in 1990 after full recovery of U.S. prices. The fact that this was a Canada/U.S. exchange rate shock that did not lead to higher prices in the U.S. market explains the divergence of the cycles in spite of the closely integrated nature of the two industries.

Given the technological and structural changes that have occurred in the Canadian beef cattle industry over the last four decades, the purpose of this paper is to provide up-to-date information on the nature of the Canadian cattle cycle. The first objective is to estimate cycles in four industry variables: total cattle inventories, beef cow inventories, beef supply, and beef prices. The second objective is to determine whether or not recent market shocks—appreciation of the Canadian dollar relative to the U.S. currency and feed price escalation—changed the cattle cycle. The paper is organized as follows: the next section summarizes existing literature on cattle cycle estimation, and section three presents the data and the analytical procedure including intervention analysis, the framework used to model the impact of exogenous shocks on the variables of interest. Section four presents the study findings. The fifth section provides concluding remarks and draws policy implications for the federal program AgriStability and the provincial Western Livestock Price Insurance Program.


There is a long history of analysis of agricultural price cycles that predates Ezekiel's (1938) cobweb model going back to at least Gerlich (1911). While the cobweb model began to explain the dynamics of commodity cycles, its simplified structure—where demand is a function of current prices, while supply is a function of previous prices—was subject to many criticisms including diverging and oscillating regimes driven by systematic forecasting errors. The persistence and regularity of livestock price and inventory cycles nevertheless led to extensive research studying cycles. The instability of commodity prices during the 1970s proved to be fertile ground for empirical studies of livestock cycles: Rausser and Cargill (1970), Kulshreshtha and Wilson (1973), Jarvis (1974), and Griffith (1975, 1977). Despite the increase in empirical research, the conceptual problem remained that dynamic models based on cobweb style models were derived from systematic forecast errors and were inconsistent with the rational expectations hypothesis. When rational expectations are applied to this type of model, price fluctuates around its long-run steady state and there are no cycles (Gouel 2012).

A number of models developed during the last two decades addressed rational expectations, while preserving cyclical behavior. Rosen et al (1994) initiated this type of model by combining a third-order difference equation to identify stock accumulation together with an inventory decision rule that equated current cow prices to discounted expected future prices for the cow and her progeny. While the model was consistent with a rational expectations approach, it only predicted a cattle cycle of only three to four years. Subsequent conceptual models dealt with the limitations of Rosen et al, Aadland (2004) adapted a similar model that introduced the entire age distribution of the breeding herd and applied a combination of adaptive and rational expectations across heterogeneous producers. This approach resulted in a 10-year cycle. Hamilton and Kastens (2000) extended the general approach to one that considered counter-cyclical responses by producers. They considered market timing where producers strategically timed inventory expansion or contractions to take advantage of a move that is opposite to the rest of the industry. Hamilton and Kastens found that market timing had the potential to influence cattle cycles, that often cycles persisted despite counter-cyclical behavior, and that optimal producer responses depended on what drove the cycle—exogenous shocks or market timing. A final paper in this stream of literature by Crespi et al (2010) used a similar approach to examine the effect of cattle cycles on the exercise of oligopsony power. By accounting for cyclical behavior, Crespi et al established that the price-depressing effects of larger inventories magnified the extent of market power exercised in procurement behavior of packers. So in their model, population dynamics affected packer decisions as well as producer decisions.

While conceptual livestock models coalesced around a common approach, empirical measurement of cycles has taken several different forms. First, harmonic analysis involves an expansion of periodic functions by summing sine and cosine functions to recreate cycle(s) (see Kulshreshtha and Wilson 1973). Second, a related time-varying stochastic version of this approach is Harvey's (1989) Structural-Time Series approach which decomposes times series into stochastic trends, seasonal effects, and stochastic cycles. The evolution of trend and cyclical components involves a state-space model that allows parameters to evolve over time. Parker and Shonkwiler (2014) applied this method to examine German hog cycles that are allowed to vary in amplitude and phase over time. A third approach constructs cycles from the turning points of a series using a cycle-dating algorithm developed by Bry and Boschan (1971). This approach has been applied to commodity prices by Cashin et al (2002) in order to consider asymmetric price cycles where the approach distinguishes between the amplitudes and phases for price slumps and price booms.

A fourth approach involves spectral methods. Spectral analysis is a technique in which a time series is converted from the time domain to frequency domain in order to examine its cyclical patterns. The spectral approach is described in detail in the Appendix. However, it is worth noting that this is the dominant approach in measuring livestock cycles. Rosen et al (1994) employ spectral methods as an alternative approach to visualizing the cattle cycle. Other empirical examples include Purcell (1999) and Dawson (2009) for the Australian and U.K. pig cycles, Miller and Hayenga (2001) for the U.S. pork price cycle, and Mundlak and Huang (1996) for the U.S., Uruguay, and Argentina cattle cycles. It is popular because it is straightforward and flexible. Aadland (2004) describes the cattle cycle as the most regular and lengthy of economic cycles. Given these considerations, we follow the spectral approach and do not consider the added complexities of asymmetric and time-varying cycles applied with the other approaches.


Spectral analysis is performed on the four time series that are commonly used in the literature to describe the cattle cycle. These include total cattle inventories, beef cow inventories, beef supply, and beef prices. Total cattle inventories and beef cow inventories are annual data for the period 1931 to 2012 (82 observations) obtained from Statistics Canada (2012). Beef supply is calculated as a sum of three series: total monthly inspected slaughter from January 1992 to January 2012 (241 observations) obtained from the Red Meat Section of Agriculture and Agri-Food Canada (2012b), monthly fed cattle exports for January 1992 to January 2012 (241 observations), and monthly feeder cattle exports for the same period both from the Economic Research Service of the U.S. Department of Agriculture (2012). Beef prices are analyzed using the Alberta direct to packer monthly steer carcass (rail) prices for January 1988 to December 2011 (288 observations) from Agriculture and Agri-Food Canada (2012a). These are found to be highly correlated with live steer prices, with a correlation coefficient of 0.99. Nominal prices are used because the choice of deflators can change the time-series properties of the price series. Specifically, deflating prices can create spurious cycles that do not exist in the original series (Peterson and Tomek 2000). Moreover, Mundlak and Huang (1996) believe the unexpectedly large variability at higher frequencies that they find in the spectra of prices for Uruguay and Argentina is a result of using real prices. Summary statistics for the four variables are provided in Table 1.

Table 1. Summary statistics for variables used in spectral and intervention analysis
VariableMeanStd. dev.MinimumMaximum
  1. aSource: Statistics Canada (2012); annual data from 1931 to 2012.

  2. bSource: Agriculture and Agri-Food Canada (2012b); U.S. Department of Agriculture (2012); monthly data from January 1992 to January 2012.

  3. cSource: Agriculture and Agri-Food Canada (2012a); monthly data from January 1988 to December 2011.

  4. dSource: Bank of Canada (2013); monthly data from January 2000 to December 2012.

  5. eSource: Agriculture and Agri-Food Canada (2013); monthly data from January 2000 to December 2012.

Total cattle inventories (‘000 head)a12,1522,4717,97316,880
Beef cow inventories (‘000 head)a2,8581,5525075,436
Beef supply (head)b328,20449,422180,351450,937
Rail steer price (Cdn $/cwt)c147.5616.6462.02197.29
Exchange rate (Cdn $/1 U.S. $)d1.230.210.961.60
Canadian barley price (Cdn $/MT)e179.3739.91117.66304.00

A population spectrum can be estimated from a sample of observations using one of three different approaches. The first approach is the parametric approach in which the given time-series variable is assumed to be generated by a univariate autoregression model such as an autoregressive moving average (ARMA) (p, q). The population spectrum is then expressed in terms of the parameters of the ARMA model, and upon estimation, the parameter estimates are substituted into the expression for the population spectrum. We begin by using this approach, and although for each variable we obtain the typical spectral shape3 of a time series, we are unable to observe significant peaks corresponding to long cycles. The second approach is the nonparametric approach used by Mundlak and Huang (1996). It involves specifying a bandwidth parameter that indicates the number of the different frequencies that would be sufficient for estimating the population spectrum, and a kernel term for weighting each frequency. One such kernel term is the modified Bartlett kernel, which yields an estimate of the spectrum that assumes that the time series is generated by an MA (q) process. However, the process of determining the number of frequencies to be used is fraught with bias (Hamilton 1994). Therefore we use the third approach, the so-called periodogram analysis, in which actual data are applied to the sample analog of the population spectrum to obtain sample periodogram values.

In estimating periodogram values, we follow Hamilton (1994). For a sample series with T observations (math formula, there are frequencies math formula and coefficients math formula such that the value of y at time t can be expressed as the following sample analog to the spectral representation theorem shown in the Appendix:

display math(1)

Thus the sample periodogram, which is the sample analog of the population spectrum (Equation [A7] in the Appendix) is

display math(2)

Equation (1) can be estimated by ordinary least squares, and the portion of the sample variance of the series that is due to frequency math formula is obtained from the regression coefficients as math formula. This value is proportional to the sample periodogram evaluated at math formula. In this study, sample periodogram values corresponding to all possible natural (temporal) frequencies for each variable are estimated.

We expect to find cycles of similar duration in all the four series. Total inventories are a linear combination of beef cow inventories, and slaughter cattle, backgrounders, and calves. Although adjustment of total inventories to an intermediate shock tends to occur over a long interval compared to beef cow inventories (Rosen et al 1994), adjustment of the two series to a permanent shock takes roughly the same time. For a permanent increase in demand, beef supply initially declines as ranchers increase their breeding inventories, leading to an equivalent increase in total inventories. Rosen et al (1994) show that cyclical movements of de-trended total inventories and beef supply are identical. And when the authors assume a rising supply price of beef (inelastic supply of factors of production [feed, forage, and land], with static price expectations), the resulting fully simultaneous model implies similar cycles in breeding stock, beef supply, and beef prices.

Several estimation issues arise in spectral analysis, two of which are important in the context of this study. First, is the size of data sufficient for spectral analysis? According to Granger and Hatanaka (1964), the technique requires data that are at least seven times the length of the longest cycle. However, it is not always possible to conjecture the length of the longest cycle. In the context of nonparametric estimation using either the Parzen or Tukey-Hanning estimates of spectra, the authors suggest at least 100 to 200 observations, but note that crude spectra have been estimated with as few as 80 observations. Later, Granger (1966) observes that the typical spectral shape of a time series is independent of the size of the data. Therefore, the size of data used in this study is adequate for spectral analysis, and compares with series used elsewhere.4

Second, unit roots (nonstationary data) are a problem in any estimation exercise because the moments of a distribution change over time. Stochastic trends mean that unrelated series may be spuriously correlated. Trends in either the mean and/or variance of a time series are of a particular concern in spectral analysis because low-frequency components yield large spectral values and leak bias to neighboring frequencies (Granger and Hatanaka 1964). The usual approach to deal with nonstationarity is to remove stochastic trends by differencing. The problem is that differencing amplifies the high-frequency components of a series (Pedregal 2000). Therefore to analyze cycles, an alternative approach is used that filters data to separate stochastic trends from cyclical behavior. A Hodrick–Prescott high-pass filter decomposes a time series by minimizing the sum of squared deviations from the trend plus a multiple of the sum of squares of the second differences of the trend components (Hodrick and Prescott 1981, 1997). Analysis is then performed on the cyclical component of the data.

The incorporation of shocks is central to this analysis. We follow the approach of the rational expectations methods where exogenous shocks propagate the cyclical effects. The incorporation of exogenous shocks is illustrated with a modified stylized model developed by Rosen et al (1994) and adapted to the Canadian situation where price determination occurs in the United States and exports are determined endogenously. More sophisticated models such as Aadland (2004) or Hamilton and Kastens (2000) would provide a similar illustration at the expense of more complexity. The basics of the Rosen et al (1994) approach are contained in Equations (3) to (5).

display math(3)
display math(4)
display math(5)

Equation (3) is a stylized version of a breeding stock accumulation identity, which requires the current breeding herd to equal last year's stock times the survival rate (1−δ) plus last period's calf crop (g·xt−3), which is shared between breeding heifers and other animals destined for slaughter less demand for slaughter animals less exports. In this stylized version, demand for slaughter animals (D) includes both fed animals and cull breeding stock, and live exports (EX) are assumed exogenous. From Equation (4), the share of retained heifers (math formula) is a function of future net return for mature offspring. Equation (5) represents an inventory decision rule that equates the current net return for a breeding cow with the present value of selling her and her offspring in the future. After substituting Equation (4) into (3), two third-order difference equations remain, which are solved simultaneously across all periods to produce a rational expectations solution. The complex roots, which are a solution to these equations, produce cyclical responses to exogenous shocks.5

While Rosen et al (1994) solve endogenously for cattle prices and breeding inventory, in the case of Canada the price of cattle is determined in the United States and exports (EX) are endogenously determined. So the model is solved recursively from exogenous U.S. prices. Equation (6) links the price of Canadian cattle to the price of U.S. cattle, while the price of Canadian feed grains is linked to the price of U.S. feed grains in Equation (7). Both price linkage equations depend on the exchange rate (XR)

display math(6)
display math(7)

where as Rosen et al (1994) employ exogenous shifts in consumer demand and production costs to drive inventory cycles, we employ exogenous shocks to exchange rates and feed prices. The impact of the feed price shock would involve the same process as Rosen et al employ where the shocks are introduced as autoregressive processes for each exogenous variable that are driven by its last observation times a serial correlation coefficient plus an independent and identically distributed drawn innovation. The permanence of the shock depends on the relative size of these serial correlations and the roots of the solution for the difference equation. So shocks cause ranchers to vary their breeding stock and alter its age composition and reproductive capacity. Cycles are “demographic ‘echo effects’ of the current age distribution on future reproductive capacity” (Rosen et al 1994, p. 476). The exchange rate shock is slightly more complicated because currency changes affect both cattle and feed prices through price linkages to U.S. prices. Differences in price transmission between cattle prices and feed grain prices can produce differential effects on the breeding herd depending on whether the effect on cattle prices is greater than the effect on feed prices or vice versa. As explained by Coleman and Meilke (1988), an appreciation of the Canadian dollar would depress cattle prices but also reduce feed costs. The net effect on profitability depends on these relative effects, which in turn generate cyclical behavior through demographic echoes.6 When feed price shocks are introduced at the same time, the complexity of these interactions is increased.

The May 2003 outbreak of BSE closed the border for Canadian exports—initially banning beef and cattle exports with gradual liberalization of first boxed beef market, then exports of fed cattle under 30 months, and finally exports of cull animals. These events can be traced through Equations (3) to (7), first by exogenously setting exports to zero and solving for prices endogenously and then gradually liberalizing price linkages. However, the complexity of the process cannot be captured by this stylized model because it does not differentiate between breeding/cull animals and fed cattle and the associated prices of each. The Canadian BSE shock caused a sharp decline in domestic cattle prices and it occurred roughly two years before the peak observed in the last cycle. Thus the shock may have reduced the expansion phase of the cycle.

Schaufele et al (2009) found that concurrent exchange rate fluctuations caused far greater losses to the equity (net worth) of cattle producers than did the BSE crisis. Klein et al (2006) too reveal that appreciation of the Canadian dollar adversely affected cow-calf producers, feedlot operations, and beef packers in the short-run, with the greatest impact being felt by cow-calf producers. The structural impact of the dollar appreciation will be seen in a decline in the beef cow inventory. Therefore a sustained appreciation of the Canadian dollar is likely to have tempered the consolidation and/or expansion phases of the cycle.

While Rosen et al's (1994) conceptual analysis provides explanations of why exogenous shocks drive cycles, the empirical problem remains how to incorporate the shocks into the spectral procedures, which estimate cycles for each variable. We apply a Box-Tiao (1975) intervention analysis. The Box-Tiao method fits a time series as the sum of an autoregressive integrated moving average (ARIMA) process plus an intervention term. The procedure follows standard ARIMA analysis with three steps: model the underlying data generating process; estimate the appropriate model with an interaction dummy variable to account for the exogenous shock; and undertake diagnostics tests. This approach is consistent with Rosen et al's (1994) model in that both approaches introduce exogenous shocks as autoregressive processes for each variable.

Unlike the conventional Box–Jenkins technique, we do not have to difference the series because the Hodrick–Prescott filter has already been applied. Therefore only ARMA processes are considered. Sample autocorrelation functions (correlograms) and partial autocorrelation functions (PACFs) are used to determine the stochastic process (Hamilton 1994; Yaffee and McGee 2000; Enders 2004; Box et al 2008; Greene 2008). However, results of the preliminary data analysis are inconclusive and the correlograms and PACFs do not decay in prescribed patterns. Box et al (2008) suggest when this problem occurs to use information criteria (Akaike Information Criterion or Bayesian Information Criterion) to determine optimal model structure and lag order. For all four variables, autoregressive (AR) models are found to be appropriate. Greene (2008) notes that most empirical work has been based on the AR(1) model partly because it is widely believed to be a reasonable approximation of most data generating processes.

Given an AR(1) model structure, intervention dummies can be introduced following Enders (2004):7

display math(8)

where math formula is the intervention dummy8 that takes on the values 0 and 1 before and after the exogenous shock, respectively, math formula is white noise, and math formula.

The exogenous shocks considered in this study are the effect of feed prices and exchange rates on cattle inventories, beef supply, and prices. The integrated nature of the cattle supply chain with multiple markets and long production lags means that the exact sequence of exogenous shock effects throughout the system is unclear. Therefore this study estimates these effects separately for each variable.

Summary statistics on monthly exchange rates and nominal barley prices for January 2000 to December 2012 are provided in Table 1 and their graphs are shown in Figures 1 and 2. All shocks are modeled as pure jumps, whereby the exogenous variable takes on the dummy variable values 0 and 1 before and after the shock, respectively. The intervention dummies for the exchange rate and feed price shocks are assigned a value of 1 from June 2002 and January 2007, respectively, up to the end of the sample period in January 2012. In the regression models of the two annual variables (total cattle inventories and cow inventories), we simply consider the exchange rate shock as having occurred in 2002, and the feed price shock in 2007. In determining the effect of exchange rate and feed price shocks on cattle inventories, beef supply and prices, the effect of the May 2003 BSE crisis is accounted for using a dummy variable, since the crisis was observed to have had a direct impact on these variables. In the beef supply and price equations, the BSE dummy takes on the value 1 from May 2003 to June 2005 when the U.S. border was closed to imports of Canadian cattle, and 0 for the pre- and post-BSE periods. In the inventory equations, however, the dummy takes on the value 1 for the years 2003, 2004, and 2005 and 0 otherwise.

Figure 1.

Exchange rates, January 2000 to December 2012

Source: Bank of Canada (2013).

Figure 2.

Feed barley nominal producer prices, January 2000 to December 2012

Source: Agriculture and Agri-Food Canada (2013).


An augmented Dickey–Fuller test is used to test for unit roots. When a variable is found to be nonstationary, the Hodrick–Prescott high-pass filter is used to decompose the time series into a stochastic trend and cyclical components. The augmented Dickey–Fuller test is then performed on the cyclical component to ascertain if it has been made stationary.

Nature of Cycles

We begin by examining the autocorrelation function of each variable for initial clues to the nature of the cycles. These autocorrelations are shown in Figures 3 through 6 and are derived using Bartlett's formula (Berlinet and Francq 1997). With the length of a cycle measured from one trough to another, it is likely that total cattle inventories and beef cow inventories have one cycle almost every 10 years. Beef supply has three peaks in every 10 months, pointing to the possibility of a three-month seasonal cycle. The autocorrelations of steer prices decline with increasing lags and seem to have a cycle every 10 to 12 months.

Figure 3.

Autocorrelations of total cattle inventories, 1931–2012

While autocorrelation functions provide us with a rough idea of the nature of cycles, periodogram estimates provide precise determination of important cycles. A periodogram is a plot of the sinusoidal amplitudes on the vertical axis set against temporal (natural) frequencies of the time series on the horizontal axis. In any periodogram, a significant cycle is represented by a distinct peak (reflecting a large periodogram value) at a temporal frequency that corresponds to the length of the cycle. In other words, in explaining the oscillation of the time series using a periodogram, the dominant cycles are those that show up as single peaks. The other peaks are not true sinusoidal components and may be regarded as background noise. The period, T, of the cycle is calculated as the inverse of the temporal frequency. Figures 7 through 10 show the sample periodograms of the different variables, and Table 2 provides a summary of the estimated cycles. In all four periodograms, the first distinct peaks are observed at low frequencies. For total cattle inventories, the observed peak corresponds to a temporal frequency of 0.097. Taking the inverse of this frequency yields a 10-year cycle. Similarly, a 10-year cycle is evident in beef cow inventories. These cycles are consistent with those anecdotally observed by Canfax for Canadian cattle inventories, and empirically by Mundlak and Huang (1996) for U.S. inventories. Beef supply also has a 10-year cycle as shown by the first peak, and a three-month seasonal cycle indicated by the peak at a frequency of 0.33. Fed steer carcass prices have an annual cycle as seen in the autocorrelation function, and an eight-year cycle.

Table 2. Estimated beef cattle cycles
Total cattle inventories10 years
Beef cow inventories10 years
Beef supply10 years; 3 months
Rail steer prices10 years; 12 months
Figure 4.

Autocorrelations of beef cow inventories, 1931–2012

Figure 5.

Autocorrelations of beef supply, January 1992 to January 2012

Figure 6.

Autocorrelations of rail steer prices, January 1988 to December 2011

Figure 7.

Periodogram of total cattle inventories, 1931–2012

Overall, these results are consistent with most prior empirical studies despite the technological and institutional changes that have occurred in the beef cattle industry. The cattle cycle, as commonly defined by cattle inventories and beef supply, is persistent and lasts 10 years on average. Cattle inventory and beef supply cycles tend to move together although the latter has been observed to lag the former by about one year (Petry 2004). Kulshreshtha and Wilson (1973) found two beef price cycles for Canada: a 12-month cycle similar to the one obtained by this study, and a longer cycle of nine and a half years. Franzmann and Walker (1972), Mundlak and Huang (1996), and Stockton and Van Tassell (2007) found that the U.S. beef price cycle had a period of 10 years, similar to the U.S. inventory cycle.

The beef price cycle runs counter to and leads both inventory and beef supply cycles. For instance, in the 1990–2004 U.S. cattle cycle, cattle inventories peaked five years after the price peak in 1991 (Anderson et al 1996). The Canadian situation can at times be somewhat different from U.S. price cycles because of the possibility that border measures will temporally break the link between prices in the two markets. This situation occurred from May 2003 until July 2005 when the U.S. market was closed to imports of live Canadian fed (under 30 months of age) cattle. The border closed prices for all Canadian cattle declined sharply because animals previously slaughtered in the United States had to compete for spots in Canadian plants. The down-turn in the Canadian steer price cycle preceded that in the United States by almost two years. This effect shows up in the estimated eight-year price cycle. When the same model is estimated after removing the price observations for the period when the border was closed to live cattle trade, the estimated cycle is 10 years.

Shorter price cycles have been observed before. Mundlak and Huang (1996) found price cycles of six years for Argentina and Uruguay. Differences between breeding stock and price cycles can be explained conceptually. Rosen et al (1994) suggest circumstances where cycles are more important for breeding stock than for prices, where the model is solved recursively and factor supplies are perfectly elastic, so the price process is of a lower order than the process for the breeding stock.9 In practice, after the BSE border closure, prices adjusted very quickly to the change in market structure, while the breeding inventory adjusted much more slowly and in fact, the first response was to expand despite depressed market conditions. At that time, slaughter facilities for cull cows were in very short supply. If the animal could not be sold, it was bred again and retained until the calf was born and weaned. So cow inventories could not adjust, while the price cycle appears to have been affected by BSE. Despite the border closure, by September 2003, Canada was able to export boxed beef to the United States and sales of the meat product helped to close the price gap between markets.

Cycle Effects of Market Shocks

Although we considered the impact of the BSE shock anecdotally above, the effects of feed price escalation and exchange rate appreciation can be examined more formally with intervention analysis.10 Each of the endogenous variables is estimated with an autoregressive specification with intervention dummies for feed prices and exchange rates. Estimated results for each variable are summarized in Table 3. All models are statistically significant, and so are all the lagged variable parameter estimates.

Table 3. Maximum likelihood estimates of the underlying AR (p) processes


  1. Figures in parentheses are standard errors.

Total cattle inventories: AR(2); N = 82, Prob math formula = 0.000
Exchange rate−158.95−1.970.049
Feed price239.231.900.058
Beef cow inventories: AR(2); N = 82, Prob math formula = 0.000
Exchange rate−17.18−0.420.673
Feed price35.360.720.473
Beef supply: AR(5); N = 241, Prob math formula = 0.000
Exchange rate25,922.712.110.035
Feed price−2,372.66−0.130.894
Rail steer prices: AR(5); N = 288, Prob math formula = 0.000
Exchange rate−2.97−0.370.709
Feed price9.521.380.168

Total cattle inventories and beef cow inventories follow an AR(2) process. Total cattle inventories are significantly affected by exchange rate, feed price, and BSE shocks. Exchange rate appreciation has two effects on profitability. A stronger Canadian dollar lowers cattle prices but it also lowers input prices. In addition to affecting input prices, additional capital investments may occur, increasing productivity. In the case of total cattle inventories—which include breeding animals, stocks of young animals, and cattle on feed—the sustained appreciation of the Canadian dollar appears to have reduced overall profitability and reduced overall stocks. However, the effect on profitability depends on a number of factors: output and input prices and the composition of the total cattle stock.

Higher feed prices appear to have had a significant positive effect on total cattle inventories. Although this result at first appears counterintuitive, the impact of feed prices has different impacts depending on the type of cattle in the herd. Feed prices would have the greatest effect on fed steers and heifers. Higher feed prices would result in animals sold at lower weights and more animals held back as backgrounders so that older animals are put on feed. These effects would actually increase the total cattle herd as it takes longer to get an animal to market.11

Breeding cow inventories are not significantly affected by the shocks. Breeding cows are not large consumers of feed grains and although higher feed prices affect the future profitability of their progeny, current feed prices only have an indirect effect on future profitability.

Beef supply and steer carcass prices are generated by an AR(5) process. Exchange rate appreciation has a significant positive effect on beef supply. Some of this effect is explained by liquidating total cattle inventories and some of the effect would be from reduced exports of feeder calves. However, the overall effect of exchange rates is a complex process that works through the entire system with the potential to either increase or decrease supplies. A further complication is that the exchange rate shock is entered as a dummy over a long time period with the potential to pick up other unspecified effects that occurred concurrently. So although we describe the shock as driven by exchange rates, it is in fact an amalgam of factors that occurred over the period which exchange rates appreciated. Neither exchange rate appreciation nor feed price escalation appears to have a statistically significant effect on steer carcass prices.

The next step is to determine if the changes in cycles can be associated with the shocks. From the above results, we speculate that the total cattle inventory cycle may have been altered by exchange rate appreciation or feed price escalation or both, whereas the beef supply cycle may have been altered by exchange rate appreciation, the effect of the BSE outbreak notwithstanding. Establishing these changes requires estimating and comparing the cyclical nature of the two variables before and after the respective shocks. However, the sample size of cattle inventories does not permit meaningful spectral analysis of sub sample cycles. Therefore the analysis is restricted to beef supply. In any case, beef supply is a function of cattle inventories, and both series have a similar cycle, and have been significantly affected by the exchange rate shock.

The initial and long-run effects of the exchange rate shock result in increased beef supply, and the decline in inventories is reflected in changes in the beef supply cycle. Figures 11 and 12 show cycles in beef supply before and after the shock in exchange rates. The seasonal three-month cycle is evident in both time periods. The long cycle was 125 months long prior to the shock, and 116 months long after the shock implying a nine-month reduction in the duration of the beef supply cycle. Given the variety of shocks that the industry has faced over the last decade, a nine-month change in the period of a cycle is not substantial. However, our intervention analysis describes a 58% reduction in the amplitude of the beef supply cycle, which has important implications. First, this change in amplitude is unlikely to be solely due to exchange rate effects. The dummy variable accounting for the sustained appreciation in the exchange rate is probably accounting for a significant number of other factors that improved the potential of the sector. Productivity growth in the Canadian livestock sector in general has been reported by Stewart et al (2009), and has been attributed to both scale effects and technical change. This productivity growth occurred over periods of depreciating and appreciating exchange rates.

Figure 8.

Periodogram of beef cow inventories, 1931–2012

Figure 9.

Periodogram of beef supply, January 1992 to January 2012

Figure 10.

Periodogram of rail steer prices, January 1988 to December 2011

Figure 11.

Pre-exchange rate shock periodogram of beef supply, January 1992 to May 2002

Figure 12.

Post-exchange rate shock periodogram of beef supply, June 2002 to January 2012

Second, Klein et al (2006) suggest that appreciation of the Canadian dollar would be beneficial to the beef cattle industry to the extent that it drives investments and productivity growth. Productivity growth would in turn dampen fluctuations in the cattle cycle. For instance, Marsh (1999) found that productivity growth in the U.S. beef cattle industry, measured by increased carcass weight of steers, heifers, and cull cows, significantly reduced the price elasticity of supply for beef cow inventories over a 10-year cycle. McCullough et al (2012) attributed the significant reduction in the amplitude of the U.S. cattle inventory cycle to efficiency gains from technological advancements.

Third, the reduction in the amplitude of the beef supply cycle has to be put in the context of the negative impact of BSE shown in Table 3. The ban on Canadian beef and live cattle exports due to BSE, coupled with limited domestic slaughter capacity, meant a contraction in total beef supply. Between January 1992 and January 2012, the highest post-BSE beef supply of 433,691 head of slaughter cattle recorded in September 2005 is about 4% less than the pre-BSE record high observed in September 2002. Therefore the reduction in amplitude of beef supply may be partly attributed to BSE.


The existence of cattle cycles has been well documented in the literature. In this paper, we argue that since cycles are an important feature of the Canadian beef cattle industry, examining the impact of shocks should take into account, among other things, the extent to which they may alter the cycles. This paper recognizes cycles in not only cattle inventories, but also in beef supply and beef prices.

The paper accomplishes two goals: first, it uses spectral analysis to describe cycles in four variables: total cattle inventories, beef cow inventories, beef supply, and rail steer prices. Second, it combines intervention analysis with spectral analysis to investigate the association between cattle cycles and two market shocks, appreciation of the Canadian dollar relative to the U.S. currency, and feed price escalation.

Analyses show that 10-year cycles exist in total cattle inventories, beef cow inventories, beef supply, and steer prices. Also, a seasonal three-month cycle exists in beef supply, and an annual cycle exists in steer prices. Results of the intervention analysis indicate that both exchange rate appreciation and feed price escalation have significantly affected total cattle inventories, but neither shock has had an effect on beef cow inventories. Specifically, exchange rate appreciation has caused a reduction in total inventories, but increasing feed prices have increased inventories. Also, controlling for the effect of the 2003 BSE crisis, the study finds that a shock that corresponds to that period when the exchange rate appreciated has significantly increased beef supply. When the beef supply series is examined for changes in the beef supply cycle following the exchange rate shock, the study finds a reduction of nine months in the duration of the cycle, and a 58% reduction in the cycle's peak amplitude. However, the seasonal three-month cycle remains intact.

Knowledge of this cyclical behavior should be helpful to producers in managing their herds through the different stages. Currently, the industry appears to be at the beginning of another cycle since inventories are at their lowest, with herd liquidation having begun in 2008 and continued through 2012.

Adjusting stabilization policy to the cyclical behavior described in this paper is, to say the least, challenging. Current business risk management policy offers a margin based program, AgriStability, which stabilizes net returns over a five-year period.12 Although this approach has some potential to smooth cycles, the mismatching of time periods between the cycle and the stabilization mechanism reduces the effectiveness of the program. Given the whole farm nature of Canadian stabilization programs, it is unlikely that policy makers would extend the length of the moving average of the trigger mechanism for AgriStability to accommodate the cattle sector because of the potential to distort production decisions in other less cyclical sectors. Furthermore, short-term stabilization is also available through the Western Livestock Price Insurance Program which provides short-term (within year) price insurance for calves, feeders, and feed cattle. Individuals can also use private hedging strategies through the Chicago Mercantile Exchange.

The complexity and multi-leveled markets of the cattle industry make policy design to reduce cycles a perilous venture because of the potential for mistakes and unintended consequences. Hamilton and Kastens (2000) demonstrate how difficult it is to design counter-cyclical behavior. However, more information provides researchers and policy makers an opportunity to better understand the effects of market shocks on the industry. The finding that exchange rate appreciation, which in most of the literature is considered to be a negative shock, may be associated with a reduction in the long-term fluctuations in beef supply is informative. Certainly, improvement in productivity not only helps the industry grow, but may also reduce the amplitude of the cyclical behavior of the sector.

  1. 1

    In the current U.S. cattle cycle, herd liquidation that began in 2006 (after a two-year herd expansion) caused a 5% decline in beef cattle farms from 764,984 in 2007 to 727,906 in 2012 (U.S. Department of Agriculture 2014).

  2. 2

    Pouliot and Sumner (2014) find that country of origin labeling has significantly widened the price basis of Canadian fed cattle and reduced the ratio of U.S. imports of Canadian feeder cattle to domestic use.

  3. 3

    After de-trending and removing seasonality, parametric spectral analysis of most economic time series yields large spectral values that correspond to low frequencies and vice versa, resulting in a downward sloping asymptotic curve. However, periodogram analysis does not necessarily produce such a curve.

  4. 4

    In estimating spectra of four beef industry variables for the United States, Argentina, and Uruguay, Mundlak and Huang (1996) use 62, 57, and 70 observations, respectively.

  5. 5

    The interested reader should see Rosen et al (1994) for illustrations of simulated impacts of exogenous shocks.

  6. 6

    The impact of an exchange rate appreciation will decrease prices of outputs and any inputs that are traded. The price of nontradable inputs will not change. The net effect of dollar appreciation, at each level of the cattle supply chain, will depend on the relative size of these price changes, any productivity improvements resulting from increased investments, and any overall macroeconomic effects that change disposable income.

  7. 7

    Enders (2004) specifies a more general ARMA (p, q) with more extensive lag operators on yt and εt.

  8. 8

    When math formula, the intercept is math formula, and the long-run mean of the series is math formula. After the shock, the intercept shifts to math formula. Thus the initial or impact effect of the shock is math formula. Its long-run effect, math formula, is the new long-run mean less the original long-run mean. That is, math formula.

  9. 9

    The degree of oscillation is a function of the relative size of the persistence of the shock (autocorrelation between periods) and the roots of the third-order difference equation describing the evolution of the shock. If persistent measure is smaller than the root, the shock dies out quicker than the market adjusts (Rosen et al 1994, p. 477).

  10. 10

    To analyze the events around the BSE border closure, it is not as simple as applying an autoregressive specification of one exogenous variable but numerous interacts have to be considered to account for the shock. In the case of exchange rates and feed prices, intervention analysis can be applied.

  11. 11

    There are two reasons why inventories could increase. First, heavier feeders are brought into the feedlot to lower overall cost of feeding. This extends the time period of backgrounding. The second reason relates to a narrowing of the price slide between different weights and backgrounders have an incentive to sell their feeders at a heavier weight when feed grain prices are high.

  12. 12

    Although a five-year period is applied to determine the trigger mechanism, a moving average of three years of prices is calculated with highest and lowest average dropped from the calculation.

  13. 13

    This implies a short memory process. The counterpart is a long memory process (i.e.,math formula); its spectral density function is unbounded at the zero frequency, and therefore its autocorrelation function decays very slowly—hyperbolically rather than exponentially—and the differencing parameter, d, can take on a fraction (Geweke and Porter-Hudak 1983; Janacek 1994; Chiawa et al 2010).


In the strict sense, the term cycle implies perfect regularity or periodicity. But according to Granger and Hatanaka (1964), what is usually referred to as cycles in economic time series are simply fluctuations that may or may not exhibit regularity. For instance, the cattle cycle cannot be precisely predicted, and that is because no two cattle cycles are exactly similar in terms of duration and amplitude. This probably explains the persistence of the cattle cycle. The lack of perfect periodicity is what underlies the spectral technique used in analyzing economic time-series data.

Spectral analysis is a technique in which a time series is converted from the time domain to the frequency domain in order to examine its cyclical patterns. It is a generalization of Fourier analysis (also called harmonic analysis or periodogram analysis) initially used in the physical sciences to study the time dependence of physical processes (Fishman and Kiviat 1967). In Fourier analysis, any time series is assumed to contain different frequencies. When the time series is plotted against time, the time domain view is obtained, but when it is plotted against frequency, a frequency domain (or signal spectrum) view is attained (Langton 2012). Therefore Fourier analysis with respect to a time series is the decomposition of the time series into its harmonic components, and then determining their amplitudes. The harmonic components are the different pairs of sine and cosine terms that constitute the Fourier series equation. These trigonometric sine and cosine functions exhibit complete autocorrelation, and are by definition periodic. The Fourier series equation represents the so-called Fourier decomposition, and the sine and cosine terms of each harmonic have the same frequency, and therefore their coefficients (amplitudes) can be added together to obtain the power of the harmonic (Langton 2012).

According to Hamilton (1994), the value of a time-series variable, math formula, is a weighted sum of periodic functions of the form cos(math formula) and sin(math formula), where ω denotes a particular angular frequency

display math(A1)

Equation (A1) is the spectral representation theorem. Let math formula be a covariance stationary process with mean math formula and jth autocovariance

display math(A2)

If these autocovariances are absolutely summable13 (i.e., math formula), the autocovariance generating function is given by

display math(A3)

where the complex scalar math formula. Dividing the above function by 2π (the interval over which trigonometric functions repeat themselves) and evaluating it at some z with math formula and ω a real scalar, we obtain the population power spectrum of math formula

display math(A4)

The power spectrum is a function of ω, and for any given value of ω and a sequence of autocovariances math formula, the value of math formula can be calculated. Thus, the power spectrum and autocovariance functions are Fourier transforms of one another. The latter and hence variance can be recovered through an inverse transformation. Using De Moivre's theorem, which states that math formula, Equation (A4) can be rewritten as

display math(A5)

For a covariance stationary process, math formula, Equation (A5) implies

display math(A6)

Using the trigonometric relations: math formula, math formula, math formula, and math formula, Equation (A6) becomes

display math(A7)

Thus the power spectrum is nonnegative and a periodic function of ω with a period 2π; if the value of math formula is known for all ω from 0 to π, then the value of math formula for any ω can be inferred. In sum, the power spectrum is a Fourier cosine transformation of the autocovariance, and corresponds to particular frequencies (Naylor et al 1969). It shows the contribution (power) of a particular frequency to (in) the total variance of the time series since the area under the population spectrum is the total variance of the series. And the variance of a given frequency is equal to half the square of its amplitude (Sovereign et al 1971), implying that it is directly proportional to the amplitude.

Alternatively, an autocorrelation function (which can be derived from the autocovariance function) can be used to generate what is referred to as a spectral density function (Box et al 2008). And just like the power spectrum, an estimate of the spectral density measures the contribution of a particular frequency component to the total variance of a time series (Fishman and Kiviat 1967). In essence, the spectral density is a Fourier transformation of the autocorrelation function, and may simply be calculated as the power spectrum divided by the variance (McPheters and Stronge 1979).

From Equation (A7), it can be seen that generally, low frequencies yield large spectral values and therefore contribute more to the variance of the series than do higher frequencies. This leads to the typical spectral shape of an economic time series as illustrated by Granger (1966) and Naylor et al (1969), obtained by plotting the sample power spectra or spectral density estimates against frequencies. If a time series contains an important cycle, its power spectrum or spectral density function will have a peak at the frequency of the cycle (Granger 1990) since a cycle corresponds to a specific frequency and period.