# COVID-19 and the Mystery of Lumber Price Movements

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Modeling Price Volatility as a Stochastic Process

_{1}), …, P(t

_{n}) is identical to the joint distribution of P(t

_{1}+ t), …, P(t

_{n}+ t) for any t. For the stationary process, ${\mu}_{P}=E\left[P\left(t\right)\right]$ and ${\sigma}_{P}^{2}=Var\left[P\left(t\right)\right]$ are independent of time and ${\rho}_{P}\left(k\right)=\frac{\mathrm{Cov}\left[P\left(t\right),P\left(t+k\right)\right]}{{\sigma}_{P}^{2}}$. Some processes are stationary, but some are non-stationary, such as the value of an oil company’s stock. The expected value of price might grow without bound, while variance grows as a function of time. We assume the price of lumber does not grow over time, thus we have a mean-reverting stochastic process, the simplest of which is known as an Ornstein-Uhlenbeck process [13].

#### 2.2. Price Impact Model Specification

_{t}and PNF

_{t}were used to represent the COVID-19 pandemic, and the PNF respectively; and ${X}_{it}$ represent the subsequent control variables described in Table 3.

_{t}, a variable constructed to represent the actual value of the AD plus CVD placed on Canadian softwood lumber by the United States. The implementation of AD and CVD policies is a point of contention between Canada and the U.S., as noted in the previous section. Our rationale for including regressions run with and without ADCVD

_{t}is motivated by the lack of clear and consistent data on the monthly rates of AD and CVD tariffs over time. The data we collected and report for this variable have been collected from a variety of sources, as no single source has kept track of this information over time. Additionally, four major companies—Canfor Corporation, Resolute Forest Products, West Fraser Mills, and J.D. Irving—had varying rates of CVD and AD imposed on them because of their size and influence within the softwood lumber industry. In addition, a single rate was set for all other companies, which is a function (often a weighted average) of the rates imposed on the large companies and is used for the construction of this variable. Because of the innate uncertainty and variation due to the nature the of AD and CVD rates, we chose to present the regression output for both time periods with and without this variable. The second model is given below:

_{t}contained in ${X}_{it}$. A detailed description of the variables included in each of the four models can be found in Table 3.

_{t}as we expect that the COVID-19 pandemic caused lumber prices to rise significantly [2]. Based on our initial data exploration (and seen below in Figure 4), there is a sharp increase in both the raw lumber price and the variation of price following the COVID-19 pandemic. By incorporating the event regressors, we expect to be able to attribute more of this variation in price to the pandemic, and not simply just a random walk. Although our variable of interest is the COVID-19 pandemic, we also expect positive coefficients on the other event variables in the model. Similar to the results found by Zhang [9] for example, we expect HS

_{t}and W

_{t}to have positive coefficients, as increases in the number of housing starts can be attributed to an increase in demand, and an increase in wage rates can reduce supply and thus increase price. Additionally, we expect the coefficients on Exch

_{t}to be negative as demonstrated by Adams et al. [18], and Zhang [15], and we expect the coefficients on PNF

_{t}to be positive as an interruption in the supply chain amounts to a suppression of supply which then drives up prices.

## 3. Results

_{t}variable, while the second and fourth the results when it is included. As seen in the table, the majority of the events that we identified are positive and highly statistically significance; most importantly, the central variable of interest in the study, Covid

_{t}, is statistically significant in all regressions—the COVID-19 pandemic had a positive impact on softwood lumber prices. When the entire dataset from 1981–2022 was employed in the regression, the price of softwood lumber increased by 42.1% at the 1% significance level during the pandemic months. With the addition of the ADCVD variable, the significance of Covid

_{t}does not change, although there is a slight reduction in the price impact (38.5%). Additionally, when using the condensed dataset (from 2001–2022), the significance of Covid

_{t}remains, but its impact is reduced somewhat further (32.7% at the p < 0.01 significance level). Now with the addition of the ADCVD

_{t}variable, the coefficient estimate is slightly higher at 33.1%.

_{t}(col 1 in Table 4), the COVID-19 pandemic price impact was 12 percentage points higher than that of the Great Financial Crisis of 2008 (42.1% vs. 30.1%). With the inclusion of ADCVD

_{t}(col 2), the impact is even more pronounced at 20 percentage points (38.5% vs. 18.5%). Across all four regressions Covid

_{t}remains extremely significant, with estimated price impacts ranging from 32% to 42%. Clearly, the pandemic had a sizeable impact on the softwood lumber industry.

_{t}variable is included as a regressor, the positive impact is only slightly reduced to 81.1%. In the model where only the data from 2001–2022 are employed in the regression, the PNF event remains statistically significant (p < 0.01), with its impact respectively ranging from 60.3% to 55.7% depending on whether or not the ADCVD

_{t}variable is included. The severity of this natural disaster on the softwood lumber prices was roughly 2.5 times higher than the impact of COVID-19 pandemic, even though the PNF event lasted only about one-third as long as the pandemic. Both events indicate that disruptions to the lumber supply chain can lead to significant impacts on industry prices.

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Explaining North American Lumber Price Movements: Dependent Variable Logarithm of Spruce-Pine-Fir (SPF) Price Index.

Regressor | (1981) | (1981) | (2001) | (2001) |
---|---|---|---|---|

Exch_{t} | 0.444 *** | 0.246 *** | 0.131 | 0.133 |

(0.093) | (0.080) | (0.119) | (0.113) | |

HS_{t} | 0.0002 *** | 0.0002 *** | 0.0003 *** | 0.0003 *** |

(0.00003) | (0.00003) | (0.0001) | (0.0001) | |

ADCVD_{t} | −0.014 *** | −0.007 *** | ||

(0.001) | (0.002) | |||

PRE_{t} | −0.478 *** | −0.546 *** | ||

(0.035) | (0.030) | |||

MOU_{t} | −0.327 *** | −0.191 *** | ||

(0.037) | (0.034) | |||

L2_{t} | 0.007 | 0.055 | ||

(0.048) | (0.041) | |||

W_{t} | 0.033 *** | 0.024 *** | ||

(0.006) | (0.006) | |||

TRQ_{t} | 0.086 ** | 0.152 *** | 0.173 *** | 0.195 *** |

(0.035) | (0.030) | (0.063) | (0.061) | |

SLA06_{t} | −0.016 | 0.011 | 0.043 | 0.010 |

(0.041) | (0.035) | (0.079) | (0.076) | |

POST_{t} | 0.380 *** | 0.622 *** | 0.352 *** | 0.457 *** |

(0.041) | (0.039) | (0.081) | (0.084) | |

FC_{t} | −0.335 *** | −0.233 *** | −0.192 *** | −0.182 *** |

(0.046) | (0.040) | (0.054) | (0.051) | |

Covid_{t} | 0.345 *** | 0.321 *** | 0.267 *** | 0.268 *** |

(0.048) | (0.040) | (0.050) | (0.048) | |

PNF_{t} | 0.659 *** | 0.614 *** | 0.427 *** | 0.463 *** |

(0.071) | (0.060) | (0.080) | (0.077) | |

Constant | 5.059 *** | 5.343 *** | 4.403 *** | 4.770 *** |

(0.125) | (0.108) | (0.192) | (0.214) | |

Observations | 501 | 501 | 255 | 255 |

## References

- Van Kooten, G.C.; Nelson, H.; Mokhtarzadeh, F. Canada-U.S. Softwood Lumber Dispute: Background. Chapter 2 in International Trade in Forest Products: Lumber Trade Disputes, Models and Examples; van Kooten, G.C., Voss, L., Eds.; CAB International: Wallingford, UK, 2021; pp. 10–26. [Google Scholar]
- Van Kooten, G.C.; Schmitz, A. COVID-19 Impacts on U.S. Lumber Markets. For. Policy Econ.
**2022**, 135, 102665. [Google Scholar] [CrossRef] - Van Kooten, G.C.; Zanello, R.; Schmitz, A. Explaining Post-Pandemic Lumber Price Volatility and its Welfare Effects. J. Agric. Food Ind. Organ.
**2022**, 18. [Google Scholar] [CrossRef] - Statista. Monthly Price of Lumber in the United States from January 2019 to March 2022. 2022. Available online: https://www.statista.com/statistics/1239728/monthly-lumber-price-usa/ (accessed on 25 November 2022).
- Anderson, J.; West, N.; Fitzgerald, A.; Guzman, D. Random Lengths. Various Issues. Forest Product Market Prices and Statistics Yearbook; Random Lengths Publications Ltd.: Eugene, OR, USA, 2021. [Google Scholar]
- Federal Reserve Bank of St. Louis (FRED). U.S. Census Bureau and U.S. Department of Housing and Urban Development, New Privately-Owned Housing Units Started: Total Units [HOUST]. 2022. Available online: https://fred.stlouisfed.org/series/HOUST (accessed on 29 November 2022).
- World Trade Organization (WTO). (n.d.). Anti-Dumping, Subsidies, Safeguards: Contingenties, etc. Available online: https://www.wto.org/english/thewto_e/whatis_e/tif_e/agrm8_e.htm (accessed on 25 November 2022).
- Global Affairs Canada. Softwood Lumber. 2022. Available online: https://www.international.gc.ca/controls-controles/softwood-bois_oeuvre/index.aspx?lang=eng (accessed on 25 November 2022).
- Zhang, D. The Softwood Lumber War: Politics, Economics, and the Long U.S.-Canadian Trade Dispute, 1st ed.; Routledge: London, UK, 2007. [Google Scholar]
- Insurance Bureau of Canada (IBC). Insured Losses of 2021 Floods Now $675 Million. 2022. Available online: http://www.ibc.ca/bc/resources/media-centre/media-releases/insured-losses-from-2021-floods-in-bc-now-675-million (accessed on 11 November 2022).
- COFI; BC Council of Forest Industries, Vancouver, BC, Canada. Personal Communication, 20 September 2022.
- Lawler, G.F. Introduction to Stochastic Processes, 2nd ed.; Taylor & Francis Group: Boca Raton, FL, USA, 2006. [Google Scholar]
- Dixit, R.K.; Pindyck, R.S. Investment under Uncertainty; Princeton University Press: Princeton, NJ, USA, 1994; p. 74. [Google Scholar]
- Dias, M.A.G. Stochastic Processes with Focus in Petroleum Applications. April 2008. Available online: http://marcoagd.usuarios.rdc.puc-rio.br/stochast.html (accessed on 20 May 2022).
- Zhang, D. Welfare impacts of the 1996 United States—Canada Softwood Lumber (trade) Agreement. Can. J. For. Res.
**2001**, 31, 1958–1967. [Google Scholar] [CrossRef] - Zhang, D. Welfare impacts of the 1996 United States—Canada softwood lumber agreement: An update. Can. J. For. Res.
**2006**, 36, 255–261. [Google Scholar] [CrossRef] - Statistics Canada. Table 14100306: Average Hourly Earnings for Employees Paid by the Hour, by Industry. Monthly, Unadjusted for Seasonality. 2022. Available online: http://dc.chass.utoronto.ca.ezproxy.library.uvic.ca/cansimdim/English/ (accessed on 25 November 2022).
- Adams, D.M.; McCarl, B.A.; Homayounfarrokh, L. The role of exchange rates in Canadian—United States lumber trade. For. Sci.
**1986**, 32, 973–988. [Google Scholar]

**Figure 3.**Potential paths of composite and U.S. lumber prices based on Ornstein–Uhlenbeck Stochastic Mean-Reversion processes with means indicated by straight lines.

**Figure 4.**Composite framing price index in CAD January 1980 through July 2022 Source: Statista (2022) and Random Lengths (various issues).

Year ^{a} | Average of AD or CVD (%) |
---|---|

1987–1991 | 15.00 |

1992 | 9.92 |

1993–1994 | 6.51 |

2001 | 25.60 |

2002 | 22.42 |

2003 | 13.92 |

2004–2005 | 10.81 |

2006 | 11.86 |

2007–2009 | 15.00 |

2010 | 14.09 |

2011 | 15.00 |

2012 | 11.25 |

2013 | 6.67 |

2015 | 8.57 |

2017 | 22.85 |

2018–2020 | 20.23 |

2021 | 19.84 |

2022 | 17.91 |

Item | Composite Price | U.S. Price |
---|---|---|

Intercept α | 57.6332 | 78.0546 |

(1.851) | (2.198) | |

Slope β | 0.9072 | 0.8658 |

(17.300) | (14.013) | |

Residual standard error | 123.1 | 142.5 |

Monthly σ | 13.41 | 16.00 |

R^{2} | 0.8039 | 0.7317 |

F-statistic | 299.3 | 196.4 |

Number of observations | 75 | 74 |

^{a}t-statistics provided in parentheses.

Variable | Description | Unit | Source | Model 1 | Model 2 | Model 3 | Model 4 |
---|---|---|---|---|---|---|---|

${P}_{t}$ | Composite Lumber Price | $CAD | Random Lengths | X | X | X | X |

Exch_{t} | $CAD to $USD Exchange Rate | C$/US$ | FRED Economic Data | X | X | X | X |

HS_{t} | New Privately Owned Housing Units Started in the United States | 1000s | FRED Economic Data | X | X | X | X |

ADCVD_{t}^{a} | Anti-Dumping and Countervailing Duty Rates by the USA on Canadian Softwood Lumber | % | Various sources | X | X | ||

W_{t} | Average Hourly Wage of Canadian’s Employed in Forestry and Logging | $CAD | Statistics Canada | X | X | ||

PRE_{t} | Pre—Softwood Lumber Agreements | 0 or 1 | January 1981–December 1986 | X | X | ||

MOU_{t} | Memorandum of Understanding | 0 or 1 | January 1987–September 1991 | X | X | ||

L2_{t} | Period in between MOU and TRQ | 0 or 1 | January 1992–December 1993 | X | X | ||

TRQ_{t} | Tariff Rate Quota Periods | 0 or 1 | April 1996–March 2005 | X | X | X ^{b} | X ^{b} |

SLA06_{t} | Softwood Lumber Agreement of 2006 | 0 or 1 | October 2006–December 2015 | X | X | X | X |

POST_{t} | Post Softwood Lumber Agreement of 2006 | 0 or 1 | January 2017–July 2022 | X | X | X | X |

FC_{t} | Great Financial Crisis | 0 or 1 | December 2007–June 2009 | X | X | X | X |

Covid_{t} | COVID-19 Pandemic | 0 or 1 | January 2020–January 2022 | X | X | X | X |

PNF_{t} | Pacific Northwest Floods | 0 or 1 | November 2022–June 2022 | X | X | X | X |

**Table 4.**Explaining North American lumber price movements: dependent variable logarithm of composite price index.

Regressor | (1981) | (1981) | (2001) | (2001) |
---|---|---|---|---|

Exch_{t} | 0.647 *** | 0.486 *** | 0.438 *** | 0.435 *** |

(0.079) | (0.066) | (0.095) | (0.087) | |

HS_{t} | 0.0002 *** | 0.0002 *** | 0.0003 *** | 0.0002 *** |

(0.00003) | (0.00002) | (0.00004) | (0.00004) | |

ADCVD_{t} | −0.013 *** | −0.008 *** | ||

(0.001) | (0.002) | |||

(0.030) | (0.025) | |||

MOU_{t} | −0.349 *** | −0.223 *** | ||

(0.032) | (0.028) | |||

L2_{t} | −0.014 | 0.040 | ||

(0.041) | (0.034) | |||

W_{t} | 0.028 *** | 0.018 *** | ||

(0.004) | (0.005) | |||

TRQ_{t} | 0.003 | 0.066 *** | 0.081 | 0.108 ** |

(0.030) | (0.025) | (0.051) | (0.046) | |

SLA06_{t} | −0.031 | −0.002 | 0.045 | 0.010 |

(0.035) | (0.029) | (0.063) | (0.058) | |

POST_{t} | 0.216 *** | 0.436 *** | 0.201 *** | 0.324 *** |

(0.035) | (0.033) | (0.065) | (0.064) | |

FC_{t} | −0.263 *** | −0.170 *** | −0.146 *** | −0.133 *** |

(0.040) | (0.033) | (0.043) | (0.039) | |

Covid_{t} | 0.351 *** | 0.326 *** | 0.283 *** | 0.286 *** |

(0.041) | (0.033) | (0.040) | (0.036) | |

PNF_{t} | 0.626 *** | 0.594 *** | 0.443 *** | 0.472 *** |

(0.061) | (0.050) | (0.065) | (0.059) | |

Constant | 4.983 *** | 5.220 *** | 4.345 *** | 4.755 *** |

(0.107) | (0.089) | (0.154) | (0.164) | |

Observations | 501 | 501 | 255 | 255 |

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**MDPI and ACS Style**

Zanello, R.; Shi, Y.; Zeinolebadi, A.; Kooten, G.C.v. COVID-19 and the Mystery of Lumber Price Movements. *Forests* **2023**, *14*, 152.
https://doi.org/10.3390/f14010152

**AMA Style**

Zanello R, Shi Y, Zeinolebadi A, Kooten GCv. COVID-19 and the Mystery of Lumber Price Movements. *Forests*. 2023; 14(1):152.
https://doi.org/10.3390/f14010152

**Chicago/Turabian Style**

Zanello, Rebecca, Yin Shi, Atefeh Zeinolebadi, and G. Cornelis van Kooten. 2023. "COVID-19 and the Mystery of Lumber Price Movements" *Forests* 14, no. 1: 152.
https://doi.org/10.3390/f14010152