Investigating production cycles in the U.S. softwood lumber industry: 1965-2017

Softwood lumber is one of the most essential forest products and plays a fundamental role in the construction industry in the U.S. In 2019, softwood species accounted for 83% of the total lumber consumed in the U.S. (Brandeis et al., 2021). In 2017, about 69% of softwood lumber consumption was allocated to the housing sector. Specifically, 30% was used for new residential construction, while 39% was dedicated to the maintenance and improvement of existing homes. Additionally, new nonresidential construction accounted for another 11% of total softwood lumber consumption (Howard and Liang, 2019). Therefore, softwood lumber significantly influences the U.S. real estate sector, and its prices serve as both an input cost and an indicator of future housing demand (Liu et al., 2012).

However, the softwood lumber supply chain is a complex system that includes harvesting, processing, distribution, and market selling, each determined by diverse economic and environmental decisions (Adhikari and Ozarska, 2018; Bajgiran et al., 2016; Boukherroub et al., 2015; Silver et al., 2015). Each stage of the supply chain presents challenges. Harvesting is sometimes regulated to ensure sustainability (Paluš et al., 2020; Stupak et al., 2011), while processing depends on efficiency, labor, and technology (Wieruszewski et al., 2023; Daniels, 2010). Distribution is influenced by fuel costs, infrastructure, and shipping supplier and lastly, the consumption is driven by trends in construction and manufacturing (Bajgiran et al., 2016). During this process, the significant time lag between harvesting and final product delivery poses a challenge for producers. Converting standing timber into finished lumber can take up to one year, making it difficult for producers to respond quickly to shifts in market demand (Holtkamp, 1984). As the product is processed, storage costs rise at each stage, but products become more vulnerable to quality degradation from moisture (Previati et al., 2012), pests (Geib et al., 2008) or improper management (Appiah-Kubi et al., 2021) over time. As a result, underproduction may cause shortages during high demand periods, but overproduction increases storage costs and leads to quality deterioration. Therefore, efficient supply chain management is imperative. This research aims to analyze the production cycles within the U.S. lumber industry from 1965 to 2017, offering valuable insights into industry trends and sustainable development.

Numerous studies have examined the softwood lumber industry, identifying several key factors that influence its demand and supply. These include construction activities (Manning, 1975; Uri and Boyd, 1990), economic conditions (Lewandrowski et al., 1994), landowner type and behavior (Liao and Zhang, 2008; Zhang et al., 2015a), trade policies and global market dynamics (Devadoss et al., 2005; Godwin and Zhang, 2012), and applied technologies (Stier, 1982). From a methodological perspective, economists have emphasized the importance of capturing cyclical components in time series to better understand underlying economic phenomena (Ardeni and Wright, 1990; Beveridge and Nelson, 1981; Proietti, 2006). Within the context of the lumber industry, however, existing studies have largely focused on short-term trends and seasonal fluctuations (Banaś and Kożuch, 2019; Banas and Utnik-Banas, 2021; Chudy and Hagler, 2020; Cleveland and Tiao, 1976; Heshmatol et al., 2022; Verly et al., 2021; Mehrotra et al., 2014; Kożuch and Banaś, 2020). These studies commonly employ nonparametric filtering techniques, such as Census-class methods, which rely on seasonal adjustment and deterministic assumptions, limiting their ability to capture stochastic behavior or adapt to structural change in the data. To the best of our knowledge, Mehrotra et al. (2014) is the only study to explicitly examine long-term industry cycles in the lumber sector, reporting a 5–6 year cycle using the Census X-11 method. However, this approach cannot represent stochastic dynamics or allow for structural variability over time.

Given these limitations, there is a clear need for more flexible methodologies capable of capturing long-term stochastic cycles in the lumber market. Unobserved Components Model (UCM), by contrast, offers a model-based framework that can uncover latent stochastic features through a more adaptive and data-driven decomposition. Accordingly, this study seeks to investigate how such cyclical patterns influence the softwood lumber industry and whether alternative modeling approaches can more effectively capture these dynamics beyond traditional time series techniques.

The primary objective of this study is to adopt the UCM with an extended regression term as a stochastic approach to analyzing time series behavior of U.S. softwood lumber production. By decomposing time series data into different latent components, UCM provides a more flexible and realistic representation to capture long-term dynamics. A second objective is to empirically identify and assess the stochastic cycles in softwood lumber production and evaluate the influence of macroeconomic shocks. We tested several candidate regressors, including indicators of household purchasing power, construction activity, and input costs, and selected GDP growth based on model-fit criteria. Together, these objectives offer new insights into the cyclical dynamics of the lumber industry and contribute to more informed decision-making and strategic planning within the sector.

To investigate the cyclical behavior of the U.S. lumber production, we compiled yearly softwood lumber production series data from the USDA published lumber report (Howard and Liang, 2019). It contained 53 annual observations, measured in billion board feet, with each observation representing the national softwood production volume from 1965 to 2017. The analysis also incorporated GDP growth as an exogenous economic variable. The original GDP values, expressed in billions of 2009 dollars, were taken from the same USDA lumber report. We computed the annual GDP growth rate as the year-over-year percentage change:

As a key indicator of overall macroeconomic performance, GDP growth is expected to influence both the demand for housing, closely tied to lumber consumption, and investment activity in the broader economy.

Figure 1 illustrates the trends of two observed variables over time: softwood lumber production and GDP growth. To reduce the variability for the trend in later years, Box et al. (2015) suggested using log-transformed data instead of original series. We therefore transformed the response variable, production volume, before implementing the econometric model.

In this study, we implemented the Unobserved Components Model (UCM) ^[1], a powerful econometric model to perform the analysis. Also known as a structural model in time series literatures, UCM already has a long history in the last century. It was formalized by Harvey (Harvey, 1990) and others in the early 1990s. Since then, various extensions and applications have appeared across different fields such as economics, finance, and environmental science. However, to our knowledge, this is the first study to apply the UCM framework to forest economics.

UCM has several key advantages over traditional time series models. As its name implies, UCM additively decomposes the observable response series into several unobserved components, i.e. trend, seasonal, cyclical, and irregular components. Each component captures distinct features of the series dynamics and therefore allows for a more transparent and interpretable analysis (Jalles, 2009). This structural transparency enables researchers to assess whether each predicted component aligns with expectations derived from the data. Compared to fixed linear filtering approaches ^[2], which are widely used in applied economics, UCM provides a more flexible, model-based approach. One key advantage is that it enables the simultaneous extraction of business cycles and forecasting within in a consistent framework. Another strength is its flexibility. UCM can either impose assumptions about the cycle, such as its frequency and persistence, as fixed linear filtering approaches do, or estimate these characteristics directly from the data (Pelagatti, 2015). Moreover, UCM can accommodate both stationary and non-stationary time series, whereas other traditional methods, such as ARIMA and GARCH, typically assume stationarity (Hooda and Verma, 2019). It is also robust in handling missing observations (Bian et al., 2019; Jalles, 2009), although we do not have this issue.

The flexibility of UCM extends to its ability to customize each component based on data patterns and each one can be included or excluded or adjusted in scale accordingly. By properly setting up components, UCM can generate a rich variety of different time series patterns and explain the time varying behaviors. In this study, given that our data consists of yearly observations without seasonal effects, the seasonal component is excluded. The response variable, total production volume, therefore, can be expressed in the following general form:

where $yt$ is the observed annual lumber production at year t, $μt$ is the trend component, $ψt$ is the cyclical component, and $εt$ is the irregular component. These hidden components will be estimated simultaneously from the annual production $yt$⁠.

Trend describes the generalized tendency of the time series data, where the slope can change dynamically across time. To better capture the local variations and nonlinear behaviors over time, the trend component is specified as a local linear trend consisting of a stochastic level $μt$ and a stochastic slope $βt$⁠, with their disturbances $ηt$ and $ξt$⁠, respectively. It can be expressed by the following equations:

The cyclical component is intended to capture stochastic cyclical patterns. A stochastic generalization of the cycle can be obtained by introducing a damping factor $ρ$ to the cycle recurrence and then adding the random noises $κt$ and $κt∗$⁠. It can well capture the complex cyclical behaviors in economic time series without introducing many additional parameters.

Here $ψt$ and $ψt∗$ represent the cyclical component in two orthogonal dimensions; the bivariate recursion implies a univariate AR(2) representation for $ψt$⁠. The parameter $ρ∈[0,1)$ is the damping factor that controls cycle persistence, while $λ∈(0,π)$ is the frequency of the cycle in radians, so the period is $2π/λ$⁠. $κt$ and $κt∗$ are two mutually independent Gaussian white noise disturbances along with zero means and common variance $σk2$⁠. The resulting stochastic cycle has a time-varying amplitude $At=ψt2+(ψt∗)2$ and phase $pt=arctan(ψt∗/ψt)$⁠. The stationarity properties of the random sequence $ct$ depend on the damping factor $ρ$⁠. If $ρ<1$⁠, $(ψt,ψt∗)$ is covariance-stationary with zero mean; each component has variance $σκ2/(1−ρ2)$⁠. If $ρ=1$⁠, then the cyclical process is nonstationary.

Subsequently, the general form equation (1) is extended by incorporating a regression term $∑j=1Jδjxjt$⁠, which can add explanatory power to the model. The regression component can explain the variations in the time series that are not captured by other components, and corresponding coefficients will be implicitly estimated through the following state space framework.

Variable selection within the UCM framework is typically guided by empirical fit rather than a strict theoretical prescription. Prior studies have employed data-driven approaches, such as backward/forward elimination, forecast performance, and Bayesian stochastic search (Fenz and Spitzer, 2006; Harvey and Durbin, 1986; Johnston and Harrison, 1980; Proietti and Grassi, 2015). In the context of lumber studies, researchers have adopted varied strategies for the variable selection: Song et al. (2011) excluded GDP from their demand model, whereas Buongiorno (2015) included GDP but omitted construction-related indicators. In contrast, Ince et al. (2011) and Prestemon et al. (2018) incorporated both GDP and housing starts to improve explanatory power.

In our study, we began with a set of candidate regressors drawn from the USDA Report (Howard and Liang, 2019) and Federal Reserve Economic Data (FRED), which includes a wide range of economic and housing-related indicators. To reduce redundancy and avoid multicollinearity, particularly among overlapping measures of housing activity, we focused on the following eight regressors ^[3]: population, GDP, disposable personal income (DPI), new construction expenditure, housing starts, interest rate, energy costs and inflation. These variables represent distinct economic mechanisms: residential construction and housing starts indicate downstream demand generated by new building activity; GDP and DPI represent household purchasing power; interest rate implies financing conditions that shape mortgage costs, investment in construction, and inventory decisions; energy costs proxy variable input prices for milling, producing, and transportation, thereby shifting supply; inflation characterizes the broader macroeconomic environment and real price dynamics.

To avoid the convergence issue, we implemented a stepwise selection strategy, evaluating each candidate regressor individually and in combination using AIC and BIC. GDP growth emerged as the most robust explanatory variable and was retained in the final specification. This approach aligns with best practices in UCM modeling, where empirical fit guides specification (Durbin and Koopman, 2012; Harvey, 1990; Pelagatti, 2015). This process ensures parsimony in the final specification while preserving its explanatory power. The specified UCM form now can be expressed as:

where regression coefficients $δt$ are assumed to be time varying with zero mean and variance $σν2$⁠.

The irregular component, $εt$⁠, is used to capture short-term, unpredictable shocks. It represents the variations in the remaining residual of the observed time series and is modeled through a suitable selection of structural components. In our case, the irregular component is assumed to be simply Gaussian white noise.

The UCM applied in this study will be formulated as a State Space Model (SSM) form. SSM describes the dynamics of the system at each timestep as a function of interpretable model parameters. It allows unobserved components to be estimated through implementing the Kalman Filter for maximum likelihood estimation of the parameters and components. However, because the SSM in the existing literature is described in different ways and with varying levels of generality (SAS Institute Inc. 2025), we shall use the below general form which includes nonstationary SSMs with time varying system matrices and state variables with a diffuse initial setup. The observation equation is expressed as:

and the state transition equation:

with the initial state:

where $αt$ is called the state vector containing each time varying component, Z is the system matrix and $Zαt$ in equation (7) will be rewritten into the matrix form, T is the transition matrix and it is used to update the state vector $αt$ for the next timestep, random noise $ζt$ consists of independent, zero-mean, Gaussian vectors with covariance matrices Q. Since we do not have any known information about the initial state vector $α1$⁠, the covariance of the initial state, P, is assumed to be set up as follows

Where k is assumed to be an extreme large constant. $P∗$ and $P∞$ are both diagonal, non-negative matrices, $P∞$ consists of zeros and ones, and, if a particular diagonal element of $P∞$ is one, then the corresponding row and column in $P∗$ are zeros.

Thus, the system matrices are set up as follows:

Where $σψ2=σκ2/(1−ρ2)$ with constraints $0<λ<π$⁠, $0≤ρ<1$⁠, $σε2,ση2,σξ2,σκ2,σν2>0$

Subsequently, the Kalman filter is applied to estimate the parameters. The Kalman filter consists of two phases: prediction and update. In the prediction phase, the estimate of the state from the prior timestep is used to calculate an estimated state for the current timestep. During the update phase, the innovation, i.e. the difference between the predicted and observed current state, is multiplied by the Kalman gain matrix and then combined with the previous state estimate to improve the state estimate.

The prediction steps can be expressed as follows:

where $α^t|t−1$ is the predicted state estimate and $Pt|t−1$ is the predicted state covariance.

The update steps can be expressed as follows

where $vt$ is the innovation, $Ft$ is the innovation covariance, $Kt$ is the optimal Kalman gain, $α^t|t$ is the updated state estimate, $Pt|t$ is the updated state covariance.

Finally, the log likelihood function can be calculated explicitly as follows:

where $Ft$ and $vt$ are quantities calculated routinely from the above Kalman Filter process.

For model diagnostics, the chi-square tests the null hypothesis that the corresponding component is not statistically significant. In other words, it checks if a certain component should be included in the model. As shown in Table 1, in our case, the level, cycle and regressor components are statistically significant and should be retained in the model. The slope component is not statistically significant and thus can be removed from the model. Note that although the irregular component is also not significant, we are unable to remove it because it is a stochastic component (Harvey, 1990).

Table 2 presents the estimated variances for the disturbance terms associated with updating each stochastic component. The t-test here is used to determine whether these estimates are statistically significant, namely, whether the corresponding component behaves stochastically or deterministically. Our result indicates that only the cycle variance is at the significant level, which means cycle component $ct$ remains stochastic. In contrast, the level and regression components will be set up as deterministic since their time varying variances are not statistically significant. Therefore, the trend component $μt$ in equation (2) now only consists of a deterministic level $μ$ and regression coefficients will be treated as fixed as well.

Figure 2 presents the residual plots for diagnostics. The top two subplots are used to check the normality of residuals. In the residual histogram plot, the kernel density curve and normal density are symmetrically distributed around zero. If the histogram is skewed or has long tails, then the model may not fit the data well. In the Q-Q plot, residuals align fairly with the reference line as well. Therefore, both plots imply that residuals are normally distributed. The bottom two subplots are the autocorrelation function (ACF) plot and partial autocorrelation function (PACF) plot. They are used to check the whiteness of the residuals. The ideal case for both plots is that there are no significant correlations for any lag after lag 0 and all the bars lie within the confidence interval. The ACF and PACF plots here do not exhibit any violation of the whiteness assumption where the correlations are insignificant for all nonzero lags. Thus, the adjusted UCM seems appropriate for modeling the observed production volume.

We have modified the model specification and present the updated results in Table 3. After model calibration, the following parameters are estimated by maximum likelihood using the Kalman filter. These include the damping factor p and the period $2πλ$ of the stochastic cycle, and the regression coefficient of GDP growth. The trend was modeled as deterministic by fixing its variance to zero, and its final state value was derived from the smoothed state estimates. This modeling choice ensures that variation is captured primarily by the cyclical component, rather than by a drifting trend.

The results indicate that the final estimated level of softwood lumber production at the end of the series is 1.487 (log scale), which corresponds to approximately exp (1.487) $≈$ 4.42 billion board feet. This represents the smoothed state estimate of the long-term level at the most recent period in the dataset. For the cycle, the estimated parameter suggests softwood lumber production follows a recurring pattern with a cycle length of approximately 19.6 years. The damping factor of 0.888 indicates that cyclical fluctuations gradually decrease over time. Regarding the regression term, since the dependent variable is in logarithmic form and GDP growth is measured in percentage points, the coefficient reflects the percentage effect of GDP growth on softwood lumber production. Specifically, a 1-percentage-point increase in GDP growth is associated with a 0.595% increase in production, holding other components constant. The summary of model-fit statistics is reported in Table 4. The R-squared is about 0.778, indicating the model fits the data reasonably well.

To visualize the performance of the fitted UCM, we compared the observed production series with simulated curves, as shown in Figure 3. The left panel displays the trend component, which shows a steady upward movement. When regression effects are added, the model can capture some of the short-term variations around that trend, albeit the overall direction remains stable. Subsequently, introducing the cyclical component reveals more significant fluctuations, particularly during periods such as the early 1980s and late 2000s. These cycles align closely with economic shifts, helping to explain deviations from the underlying trend.

Many previous studies have reported the seasonal fluctuations in the lumber industry (Banaś and Kożuch, 2019; Deb et al., 2023; Conrad et al., 2018). Most studies have not explicitly modeled long-term cyclical behavior within a structural time series framework. In contrast, our study integrates GDP growth into the adopted UCM framework and identifies a 19.6-year cyclical pattern in U.S. softwood lumber production. Our results suggest that the industry is influenced not only by seasonal variations but also by broader economic conditions. Accounting for this relationship is essential for understanding structural dynamics in the lumber sector. To ensure long-term profitability and sustainable development, producers may need to adopt adaptive strategies that address both short-term market fluctuations and long-term economic cycles.

Unlike many other studies that apply UCMs, in our application, trend and regression components are assumed to be deterministic components. In the context of UCM, these deterministic components do not introduce significant stochastic variability but instead follow a predictable pattern. As a result, the primary source of variation is attributed to the stochastic cycle rather than to random shocks. In other words, our results imply that structural economic cycles are the dominant forces shaping the production trend, which is aligned with some other international studies (Banaś and Kożuch, 2019; Holma, 2006). This result underscores the importance of public policies that enhance industry resilience and adaptability in response to cyclical market fluctuations. Such policies, including regulatory, fiscal and regional-development interventions, have been shown to improve macroeconomic and sectoral stability during economic cycles (Courvisanos et al., 2016; Duval and Vogel, 2008).

Our findings reveal that softwood lumber production follows a recurring 19.6-year cycle, which may be shaped by various factors. From a biological perspective, the rotation age of many softwood species, such as pine and fir, typically ranges from 20 to 50 years, depending on the desired wood quality and end use (Biblis et al., 1998; Costa et al., 2021). These extended growth periods mean that harvest decisions are often synchronized with biological maturity, which in turn influences when large volumes of lumber enter the market. Forest managers and producers are more likely to plan harvests years in advance, aligning them with expected market conditions, budget and ecological constraints. As a result, the timing of harvest and processing activities is a function not only of short-term demand but also of long-term biological cycles, landowner objectives, and investment horizons. On the economic side, the demand for softwood lumber is closely related to the housing market, which itself follows long-term cycles driven by different factors such as interest rates, population growth, and investment trends (Cunningham and Kolet, 2011; Leamer, 2007; Fischer and Stamos, 2013; Uri and Boyd, 1990). Moreover, some major external shocks, such as the 2008 financial crisis and the COVID-19 pandemic, have induced severe price volatility and supply disruptions that can further reinforce long-term cyclical behavior in production and inventory management (Lamichhane et al., 2025; Zanello et al., 2023).

The regression component of our model further demonstrates a positive correlation between softwood lumber production and GDP growth. This outcome reflects the key role of lumber in anticipating economic activity, particularly in construction and infrastructure, which tend to expand during periods of economic growth. Rising GDP often coincides with increased investment in residential and commercial building, thereby driving up demand for wood products and stimulating higher production levels. This observed pattern aligns with industry trends and prior modeling efforts that include GDP growth as a key explanatory variable in forest product demand models (Buongiorno, 2015; Turner and Buongiorno, 2004; Michinaka et al., 2011; Prestemon et al., 2018; Skog et al., 1998; Zhang et al., 2015b).

Understanding the cyclical behavior of lumber production is essential to guide forest management. Empirically, we extracted the stochastic cycle and identified peaks and troughs from the smoothed cycles. The intervals between turning points can be defined as contractions (from peak to trough) and expansions (from trough to peak) (Harvey et al., 2007). In the production setting, an expansion simply means output is rising relative to trend. It may reflect demand recovery, supply normalization, or inventory rebuilding. During this period, as production is increasing, investing in and adopting sustainable practices can help reduce ecological pressure (Heilmayr, 2014; Sohngen et al., 1999). In contrast, during contractions and especially at troughs, the efforts can shift toward preventing resource degradation, as these periods offer opportunities for reforestation (Assunção et al., 2015). By identifying turning points from the estimated stochastic cycles, forest managers and policymakers can better time conservation tools and targeted interventions.

At the global level, the lumber industry is closely related through international trade and supply chains. Market fluctuations in the U.S. may have direct implications for other major global players, such as Canada, Northern Europe, and Asia. For instance, the U.S. is a major importer of Canadian softwood lumber, accounting for approximately 69% of Canadian softwood lumber exports in 2015. In Canada, the softwood lumber industry is crucial to the national economy, contributing to about 1.2% of real GDP. Although trade disputes have historically shaped U.S.–Canada lumber relations, recent discussions suggest that the U.S. government is considering an increase in tariffs on softwood lumber imports. If implemented, such measures could affect the U.S. housing and construction sectors by increasing the cost of imported lumber and, in turn, overall construction expenses. While the stated objective is to support domestic producers, these actions may introduce short-term supply disruptions and increased price volatility. Additionally, a shift toward greater reliance on domestic logging could raise important environmental concerns.

However, we also acknowledge several limitations in this study. First, the relatively small number of observations may constrain the scope of our findings, potentially masking location-specific or type-specific heterogeneity in the data. A larger dataset could help capture more subtle regional variations and improve the robustness of the results. Second, the application of UCM requires careful and sophisticated specifications. Different configurations may lead to varying outcomes, which shows the sensitivity of the model to its structural assumptions. Different setups of each component may also significantly influence the models’ behavior and interpretation. Given these challenges, future research could focus more on regional analysis to better understand how local economic and environmental factors influence the dynamics of the system. Incorporating more detailed data could also help us understand regional differences more clearly.

In conclusion, the softwood lumber industry plays a crucial role in the U.S. economy. A thorough understanding of lumber production dynamics is essential for both industry upstream and downstream manufacturers. This study provides a detailed analysis of the long-term industry trends by implementing the UCM framework to decompose and understand the key components over the past 50 years. The findings reveal that the dominant source of variation in lumber production is its internal stochastic cycle, which is identified as a 19.6-year cyclical pattern, slightly longer than previous estimates. Exogenous economic conditions, such as GDP growth, play a secondary role in affecting industry production. By identifying the latent components and their different roles, this study fills the research gap in understanding the cyclical nature of the industry. These insights are valuable for both policymakers and manufacturers seeking to develop strategies that promote greater stability and resilience in the lumber market.

The authors gratefully acknowledge the Hatch funding provided by the USDA National Institute of Food and Agriculture and the financial support from the Alabama Agricultural Experiment Station.