1

Introduction

The ability to accurately forecast commodities prices is a quest that many economists have attempted to undertake. One such commodity that is especially relevant to Canadian economists is softwood lumber. Canada’s forestry sector employs approximately 280,000 Canadians (Government Canada) and as Bonshor and Fazio (2015) outline, “in 2013, Canada’s forestry industry generated a staggering $57.8 billion in revenue and accounted for 1.2% of total Gross Domestic Product (Forestry Canada)”. From policy makers in Canada and the United States negotiating trade agreements to individual builders deciding when to purchase lumber, understanding the driving forces behind softwood lumber prices is vital. As Zhang and Sun (2001) demonstrate, the price of softwood lumber is difficult to forecast due to the synergy of a number of structural factors including inelastic supply and demand and political interference which create volatility. Finally, with the Softwood Lumber Agreement of 2006 set to expire in October 2015, understanding the drivers of the monthly U.S. price is of paramount importance to key stakeholders.

Several past attempts have been made to model the price of U.S. softwood lumber. Bonshor and Fazio (2015) tackle this question utilizing a univariate time series approach. Babula et al. (2012) employ a multivariate cointegrated vector autoregression model, incorporating trade measures, housing starts and futures prices. To the best of our knowledge, this paper employs several new approaches: a) it incorporates a novel supply side variable by utilizing the number of trainloads transporting U.S. softwood lumber b) it incorporates a softwood lumber inventory variable into our model that acts as a proxy for future market expectations, instead of using futures prices and c) it tests two models against each other, the first treating United States Gross Domestic Product and United States housing starts as exogenous and the second treating them as endogenous.

This paper uses data on the monthly prevailing price of softwood lumber measured in $U.S. taken from IFTSTSUB database. As a proxy for demand we collected data on U.S. housing starts taken from the Economic Research Database at the Federal Reserve Bank of St. Louis. As a proxy for future expectations of softwood lumber demand, we collect data on the number of new private housing units authorized by building permits in the U.S. which is also taken from the St. Louis FRED. Supply of softwood lumber as measured in thousands of trainloads was taken from the Bloomberg RAILLUMB index. Real U.S. Gross Domestic Product was also taken from the St. Louis FRED1. Data on the monthly prevailing price of Canadian softwood lumber was taken from the Cansim database. All data is monthly and ranges from January 1993 to October 2013. Further, dummy variables were created to capture the Softwood Lumber Agreements of 2006 and 1996 between Canada and the United States and the recession following the financial crisis in November 2007.

Ultimately, our analysis concludes that a model which treats U.S. housing starts and U.S. GDP as exogenous is superior to the model that treats both variables endogenous based on fit and ability to forecast on both short and long term horizons. However, both lag far behind in their predictive success of a univariate ARIMA (0,1,1) model (Bonshor and Fazio, 2015)

1 Figure 1 graphs the initial untransformed data, Figure 2 provides summary statistics

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Section I - Identification, Estimation, Diagnostic Testing

Section 1.1 - Achieving Stationarity An integral component of proper model identification is ensuring that the data is stationary and has no

significant seasonal trends. As shown in figure 1 of the appendix the untreated data appears to be non-stationary with strong deterministic trends and in many cases appear seasonal. In order to achieve stationarity two methods were tested. The first method was to difference all the data and, in the case of GDP, to apply a Cristiano-Fitzgerald time series filter. Although this method yielded stationary results, significant variation in the data was lost in the differencing process. The inevitable result of this was the construction of VAR models which produced suboptimal results and showed little Granger causality between key variables. As a result, differencing and time series filters were not used.

The second method to be tested was a quarter-over-quarter transformation of the data. This transformation was used in every data set and unanimously produced stationary results. Stationarity was formally tested through first identifying the optimal number of lags and then conducting an augmented Dickey-Fuller unit root test based off the previously specified number of lags. The ideal number of lags to use in the Dickey-Fuller test were determined through applying a selection-order test and ultimately chosen based on the optimal Akaike Information Criterion. A Phillips-Perron unit root test was conducted on each variable as a final test. In both the Dickey-Fuller and Phillips-Perron unit root tests the null hypothesis is that a unit root exists within the data being tested. With respect to the Dickey-Fuller test on each variable, the null hypothesis was rejected beyond the 5% level except for US Gross Domestic Product (GDP) and Softwood Lumber Inventory. With respect to GDP and Inventory, the respective p-values of the Dickey-Fuller test were p=0.1401 and p=0.1259; very close to being able to reject the null hypothesis of a unit root at the 10% level. Despite being unable to reject the null hypothesis of a unit root in the Dickey-Fuller test, both variables passed the Phillips-Perron test and visually appear to be stationary. For these reasons, GDP and inventory were viewed as stationary and were not manipulated further.

Section 1.2 Adjusting For Seasonality The second issue with the data which required attention was seasonality. As determined by the

autocorrelation function charts for each variable, U.S. housing starts and softwood lumber supply both required seasonal-adjustment, as these two variables move concurrently with one another and both exhibit significant autocorrelation with lags at similar intervals. The source of this seasonality is likely a result of the seasonality underlying U.S. housing starts. The rationale is that, on account of the good weather, there are far more housing starts in the spring and summer months (Ngai and Tenreyro, 2013). In turn, the demand for softwood lumber will be greater in the summer and spring months. Accordingly, in order to meet the rising demand, supply will mimic the seasonal pattern of housing starts. In order to adjust for seasonality a dummy-variable methodology is implemented. Both variables are regressed on dummy-variables associated with each month and the residuals for each regression are stored as the seasonally-adjusted data. As the regression output shows, the coefficients associated with summer and spring months are far greater than in winter months. As a result, when the residuals

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are predicted a disproportionate amount of seasonal demand is removed for summer months in comparison to winter months. The overall effect is a smoothing of U.S. housing starts and softwood lumber supply over the calendar year. In addition, the autocorrelation function graphs for the seasonally-adjusted data confirms the effectiveness of the transformation2.

Section 1.3 - Model Identification The first component of identifying a prospective model for U.S. softwood lumber prices is establishing

which variables are exogenous and which are endogenous. Fundamental economic theory suggests that the price, supply and inventory levels of softwood lumber are determined within the model. The causal links between these three variables are heavily intertwined, thus establishing that they are endogenously determined. However, the demand components of the softwood lumber market are not endogenously determined.

As aforementioned, the proxy used to model softwood lumber demand is monthly U.S. housing starts and U.S. GDP. It is immediately apparent why U.S. housing starts effectively models U.S. softwood lumber demand; the primary use of softwood lumber is in housing construction (Baek, 2011). The inclusion of GDP is meant to model the demand for softwood lumber which is positively influenced by income effects. As income rises there is increased consumer demand for home improvements; many of which (i.e building a deck) make use of softwood lumber (Baek, 2011). Although these two variables are effective in modelling demand for softwood lumber, these variables are theoretically exogenous to the softwood lumber model. The softwood lumber price, quantity and inventory cannot significantly determine the number of U.S. housing starts due to their small relative importance. Kearl et al. (1977) demonstrate that the main drivers of housing starts in the United States is access to credit and monetary policy, specifically short and long-term mortgage rates. As a result U.S. housing starts are considered an exogenous source of demand. For analogous reasons, GDP is considered to be an exogenous source of demand. In order to reflect that there is no Granger Causality emanating from softwood lumber unto U.S. housing starts or GDP this paper tests two candidate models, Model 1 that treats these as exogenous variables and Model 2 that treats them as endogenous.

In order to test the sentiment that U.S housing starts and GDP are exogenously determined a Vector Autoregression is performed with the two aforementioned variables treated as endogenous. Granger causality Wald tests are then used in each equation, testing the null that there is no Granger causation versus the alternative hypothesis that there is Granger causation. Including these two variables as endogenous to our model the results provide evidence in favour of Granger causation between Housing, GDP and the remaining variables of the model. This outcome is in opposition to both the fundamental theory discussed and relevant literature (e.g. Kearl et al. or Babula et al.). On account of the merit underlying the Granger causality test and because this model produced strong AIC statistics, relative to other models tested, it will be included as a prospective model. Section III will test the forecasting of both models and the results of this will ultimately decide which model will be selected.

2 Figure 3 Graphs the autocorrelation and partial autocorrelation functions

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A logical point of inquiry for the variable selection of the models tested is the inclusion of the Canadian price of softwood lumber. It is not immediately apparent whether this variable is endogenous to the model, exogenously determined or if it even belongs in the model at all. It is important to note that Canadian softwood lumber and U.S. softwood lumber are closely substitutable (Boyd & Krutilla 1987). Due to the interconnectedness of Canada and the U.S. the prices of softwood lumber between the two countries are rationally theorized to be interdependent. Thus, if Canadian softwood lumber prices were to be left out of the model the results of this paper could only be interpreted as partial-equilibrium results for the softwood lumber market. Rather, upon inclusion of the Canadian price of lumber, the results of the ensuing model can be viewed as asymptotic to general-equilibrium results (see Buongiorno et al. 1988).

To test the theorized interdependence between the Canadian and US price of softwood lumber both variables are included as endogenous and a Granger causality test is performed. Table 1 provides the results of the Granger causality test conducted.

Table 1

As the results show, although the price of Canadian softwood lumber has a distinguishable effect on the quantity of U.S. softwood lumber and future expectations for demand there is no Granger causality from the Canadian price unto the U.S. price. One possible explanation for this stems from the tariffs that Canadian softwood lumber exporters face as a result of the Softwood Lumber Agreement of 2006. In an effort to maintain competitiveness between Canadian suppliers, who are subsidized by the Canadian government, and U.S. suppliers the SLA of 2006 levies tariffs, volume restrictions and several other ‘export measures’ on Canadian lumber when the monthly prevailing price of U.S. lumber falls below $355 (Foreign Affairs, Trade and Development Canada, 2015). Thus, the price of Canadian lumber cannot effectively undercut the U.S. price since the export measures keep it artificially high. The U.S. price certainly has an effect on the Canadian price for exactly the same reasons but in the opposite direction (since a fall in the U.S. price will artificially raise the Canadian price). This,

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perhaps, is the root of the one-way Granger causality effects determined in our model3. As a final safeguard models are tested with and without Canadian softwood lumber prices and there is a noticeable reduction in the maximum likelihood estimates for the model with the inclusion of the Canadian price variable4. Alternatively, the price of Canadian softwood lumber is tested as an exogenous variable. Doing so allows the price of Canadian softwood lumber to remain an explanatory variable for the quantity of U.S. softwood lumber and the future expectations of softwood lumber demand; two variables which were evidenced by the previous Granger causality test to be dependent on Canadian softwood lumber prices5. In addition, the inclusion of Canadian softwood lumber prices as an exogenous variable included the best maximum likelihood estimates thus far6. For these reasons, the price of Canadian softwood lumber is also included as an exogenous variable.

The final variables which merit an explanation are the exogenous dummy variables which reflect the effect of the Softwood Lumber Agreements of 1996 and 2006 respectively, and the 2007 financial crisis7. Following the methodology established by Babula et al. (2012), these dummy variables are included in order to account for large exogenous shocks emanating from each event. The former event, the 2006 softwood lumber agreement, resulted in the application of tariffs to the Canadian price of softwood lumber on the basis that the Canadian government was unfairly subsidizing domestic lumber. As a result of this exogenous political shock, the model shows that the Quantity of U.S. softwood lumber was significantly positively affected. This provides some evidence that the agreement ‘worked’ for U.S. producers since the goal of the agreement was to help U.S. producers maintain a competitive footing in both price and quantity with respect to their Canadian counterparts. The latter dummy variable, accounting for the 2007 financial crisis, is a reflection of the substantial decline in housing starts and an overall deterioration of the U.S. economy. The results of the model reveal that the price of U.S. softwood lumber is significantly negatively affected throughout the duration of this period. Surprisingly, the only binary variable which was not significant within the model was the 1996 Softwood Lumber Agreement. Although there was a great degree of political turmoil surrounding this event the model shows no distinct changes over the period of these agreements8. Lastly, the maximum likelihood estimates are more favourable when including these two exogenous variables9.

On the basis of the aforementioned theory and experimentation this paper has arrived at two candidate models. The primary distinction between these two models relies on the assumption of whether or not GDP and

3 The Prevailing Monthly Price is the most recent 4 week average of the weekly Framing Lumber Composite Price published by Random Lengths Publications Inc, Oregon, U.S.A, available 21 days before the beginning of the month to which it applies. Thus, it is the U.S. price of lumber, not the Canadian price expressed in $US, lending support to our hypothesis (source: Monthly Report on Softwood Lumber Prices and Consumption, April 2015) 4 The noticeable reduction in the Akaike Information Criterion was from 17.928 to 17.328 5 This was shown in the Granger causality test for the initial model 6 Upon adding Canadian softwood lumber prices the Akaike Information criterion decreased from 17.328 to 17.27 7 The softwood lumber agreement extends from October 2006 to May 2012 and the 2007 financial crisis dummy extends from November 2007 to June 2009. 8 As an interesting side note, the 1996 Softwood Lumber Agreement had strong significant effects on the Canadian price of softwood lumber 9 The AIC criterion without the dummy variables is 21.56 and with the binary variables it is 17.328

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U.S. housing starts are endogenously determined within the model or exogenously determined. Model 1 will henceforth be in reference to the model which includes the price, quantity and future expectations of US softwood lumber as endogenous variables and specifies the U.S. housing starts, U.S. GDP, price of Canadian softwood lumber and the previously specified binary variables as exogenous. The distinguishing property of Model 2 is that U.S. housing starts and U.S. GDP are considered endogenous to the model, while the event dates and price of Canadian lumber are still treated as exogenous. As previously mentioned, Model 1 produced the best maximum likelihood estimates10. Conversely, Model 2 provided evidence, through the Granger causality test, that GDP and U.S. housing starts are endogenously determined. The next step in the analysis is ensuring that the residuals of the candidate models satisfy the expectations of residual normality.

Table 2

Section 1.4 - Diagnostic Testing To begin, it is essential to determine whether or not the dynamic process specified in each model is

stable. In order to test this the eigenvalues associated with the predicted model will be analyzed. The eigenvalue stability condition is that all eigenvalues remain within the unit circle. Both Model 1 and 2 passed the eigenvalue stability condition. The Granger causality tests for each model were previously discussed in detail. One noteworthy change in the Granger causality tests from Model 1 to 2 is that by including U.S. GDP and housing starts as endogenous, U.S. softwood lumber quantity and price have no significant effect on future softwood lumber use as measured by the building permits proxy. Rather, it is U.S. housing starts and GDP which appear to jointly determine the future expected use of softwood lumber. Nonetheless, the remainder of the variables show signs of significant Granger causality.

Section 1.5 - Testing Residuals The consensus of the post-estimation diagnostic tests for model 1 are positive; it appears that the residuals of both models are asymptotic to the necessary normality conditions. To begin, the residuals of each model resemble white noise from both a visual and statistical standpoint. Upon conducting a Lagrange Multiplier

10 The AIC for model 1 is 17.328, for model 2 the AIC is 26.44

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test for residual autocorrelation, we fail to reject the null hypothesis of white noise for any number of lags. Moreover, further tests for autocorrelation within the residual unanimously return negative results. Such tests include the Portmanteau white noise test, a simple regression of the residual on lagged terms as well as a Lag-order selection test. In addition to ensuring that the residuals of the models resemble white noise, tests for heteroscedasticity also returned negative results. More specifically, the residuals are normally distributed around a mean value of zero. Lastly, tests concerning skewness and kurtosis in addition to the Shapiro-Wilk test for normality all retain the null hypothesis of normality within the residuals.

Section II - Analysis of Results, IRF, SVD, Testing

The pinnacle source of judgment on the efficiency of the models constructed depends on the behaviour in which the variables included respond to one another. More specifically, an effective model will produce impulse response functions that coincide with economic theory. A constraint of this paper is that when categorizing a variable as exogenous it is not possible to derive impulse response functions with respect to exogenous shocks. As a result, the impulse response functions for Model 2 will be considered within this section of the paper.

Section 2.1 - Analyzing the Impulse Response Functions For the purposes of this analysis the assumption that U.S. housing starts and GDP are exogenous

variables will be relaxed. In order to generate proper orthogonalized impulse response functions these two variables must be considered endogenous. However, due to the exogeneity previously theorized, the impulse response functions from impulses in price, quantity and future expectations unto GDP and housing starts will not be considered. With that being said, the impulse response functions generated by Model 2 are shown in figure 3 of the appendix. An important aspect of this component of the analysis is identifying the ordering the variables for the orthogonalized impulse response functions. Thus far only an unrestricted vector autoregression has been considered. However, when creating an orthogonalized impulse response function a recursive vector autoregression is being assumed. Accordingly, the ordering in which the variables are included is of substantial significance. The ordering used within this paper agrees with the common practice of implementing a proposed channel of causality moving upwards from quantity, to demand and finally ending with price. In alternative wording, shocks to quantity (production) should have a contemporaneous effect on demand and price. Conversely, with a shock to price or production, the current order assumes there is no contemporaneous effect from these variables unto quantity (production). Zhang and Sun (2001) outline the inelasticity of supply and demand that characterize the softwood lumber market, thus assuming to contemporaneous effect within a one-month horizon is not unrealistic. The ordering for the recursive version of model 2 begins with quantity, then moving rightwards to GDP, Housing starts, future expected lumber usage and finally ending with price.

As shown in figure 3, when impulsing the first demand variables, U.S. GDP, the respective softwood lumber variables responds in an interesting fashion. With an impulse to GDP there is no discernable increase in the US price of softwood lumber. This result is in opposition to the income effects theorized by Baek (2011).

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Baek’s view is that with an increase in GDP the associated income effects will increase consumer demand for house remodelling and thereby increase demand for softwood lumber and causing prices to rise. Nonetheless, this relationship has not materialized within the results of the model. Perhaps, as theorized by Kearl et al. (1977), mortgage rates are far more important in determining housing starts, the main driver of softwood lumber, than an income effect from a small increase in GDP. When impulsing GDP similar results are yielded with respect to the response of the quantity of softwood lumber (Q) and the expected future usage (spec). Surprisingly, the model predicts that quantity will have a slight negative response to an increase in GDP approximately 3 months after the initial impulse. Moreover, expected future use of softwood lumber has a significant negative response 6 months later. This result could be an area for future research, but is beyond the scope of this paper.

The responses to the latter demand variable, U.S. housing starts are more indicative of what theory predicts. With an impulse to U.S. housing starts there is a significant increase in the quantity of softwood lumber being produced; this effect lasts approximately 4 months and then diminishes. The rationale behind this behaviour is that with more housing starts there is a subsequent increase in the demand for US softwood lumber and quantity responds in the short run. Lastly, the expected future use of softwood lumber is not responsive to impulses to U.S. housing starts. This was an expected result as the expectation for future use of softwood lumber should be a leading indicator to current demand and thereby remain unreactive to contemporaneous impulses in demand.

Given the structure of the recursive vector auto regression that was implemented, with price being the lattermost variable, it is expected that the endogenous variables are relatively unreactive to impulses in price. Upon an impulse in price there is no significant response in quantity (production); this result is in agreement with the supposition that supply is inelastic to price in the short run. With respect to the expected future use of softwood lumber, an impulse to the price generates a slightly negative response which persists for 3 months. This is a sensible result which follows basic economic theory; when the price of a normal good rises it is expected that future demand is decreased.

When impulsing the quantity of lumber supplied, the results produced by the model are unexpected. The initial response of the price of softwood lumber is positive and diminishes within the first 2 months. Economic theory would predict that an increase to supply would lower the price of a good. Nonetheless, the effect is minimal and persists for only a very short horizon. The reaction of the future expected demand for softwood lumber follows the same pattern. There is an initial positive reaction that quickly dissipates within the first 3 months. The reaction in the expected future demand for softwood lumber is consistent with economic theory. An increase in the supply (production) of softwood lumber is likely a result of an expected increase to demand in the near future. As a result, it is sensible for the expected future demand of softwood lumber to increase in response.

The final impulse variable, the expected future demand for softwood lumber (spec), provides the most convincing and significant impulse response functions. Upon impulsing the expected future demand there is a significant increase in the price of U.S. softwood lumber approximately 6 months later. Such a response is expected as the impulse variable is a measure of future expected demand Thus, as the expected future demand

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materializes into an actual increase in demand, in this case 6 months later, prices respond concurrently. Similarly, the response of softwood lumber quantity (production) is significantly positive at 2 and 4 months after the initial impulse. Thus, softwood lumber production leads the expected increase in demand; providing further evidence that softwood lumber production is inelastic in the short run but can be elastic in response to future expectations.

Section 2.2 - Forecast Error Variance Decomposition of US Softwood Lumber Prices Insofar, the primary purpose of this paper has been to effectively model the U.S. price of softwood

lumber. In accordance to this motive, it is of utmost importance to establish the most substantial determinants of the variation in the price of U.S. softwood lumber. A tool that can be used to conduct this analysis is founded in a Cholesky Forecast Error Variance Decomposition test. This test is performed by forecasting the variable being analysed s-steps ahead and accounting for the resulting forecast error with shocks to the endogenous variables of the model. Thus, the results provided in table X2 represent the proportion of the variation in the forecast error of US softwood lumber prices that can be accounted for by “innovation shocks” to the endogenous variables in the model. The test is conducted with forecasts of up to 13 steps ahead in order to account for the optimal lag-order selection of the model. Moreover, in keeping with the previous impulse response function analysis, U.S. housing starts and GDP will be treated as endogenous in order to identify the influence these variables have on U.S softwood lumber prices.

Table 3

As the results of the variance decomposition analysis shows, the most significant explanatory variable in the forecast error variance of U.S. softwood lumber prices is the price itself. Thus, with a unitary innovation shock to each variable, the response to the shock emanating from the price of U.S. softwood lumber accounts for over 80% of its own total forecast error variance. This holds for forecasting up to 8 months ahead. A significant takeaway of this is result is that it highlights the very autoregressive nature of the price of U.S. softwood lumber and provides evidence that past prices are the driving explanatory factor of variation in future prices. An

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interesting trend within the results is that the greater the time horizon is for the forecasts the lower the proportion of total forecast variance is explained by the U.S. softwood lumber prices. It is particularly interesting that the future expected demand (spec) variable only begins to have any explanatory power until approximately 6 months ahead. This result coincides with both the previous impulse response functions and the theorized method in which future expectations are internalized within the model. In terms of short run variation, apart from price, U.S. housing starts (H) accounts for the greatest proportion of forecast variation. Although the magnitude of U.S. housing starts explanatory power is small, it is reassuring that demand in the short run and long run has a discernable effect on the price of U.S. softwood lumber. Lastly, the shock variance decomposition test has provided evidence that forecasting with a simpler autoregressive process may be superior to the forecasting abilities of the model constructed.

Section III - Forecasting

Both Model 1 and Model 2 were used to forecast the price of U.S softwood lumber. Additionally, as a point of reference for the performance of each model the price of U.S softwood lumber is forecasted through a random walk process. As reflected in Table 3, Model 1 was more effective in forecasting than Model 2. With respect to both short term and long term forecasting horizons Model 1 produced mean squared prediction errors that were far lower than those of Model 2. Moreover, the success ratios of Model 1 are unambiguously larger than those of Model 2 over all tested forecasting horizons. This result coincides with the previous hypothesis that GDP and U.S housing starts should be treated as exogenous. Overall, neither Model 1 nor Model 2 were proficient at forecasting the price of softwood lumber logs in comparison to Bonshor and Fazio’s (2015) univariate ARIMA (0,1,1) model. Throughout all forecasting horizons the univariate ARIMA (0,1,1) model produced superior MSPE statistics and success ratios. This result is testament to the difficulty in constructing a well behaved general-equilibrium model and the essential inclusion of a moving average term in modelling U.S softwood lumber prices.

Table 4

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Conclusion

This paper made a novel attempt to model the prevailing monthly price of U.S. softwood lumber using a multivariate vector autoregression. Several key takeaways stand out. First, what makes the models constructed in this paper divergent from the current stock of literature is the incorporation of the future expected demand for softwood lumber. In order to model the future expected demand for softwood lumber this paper uses the monthly amount of building permits issued in the U.S. As shown, a positive shock to building permits produced a significant increase in the price and quantity demanded of U.S. lumber at a horizon of approximately 6 months. This, to the best of our knowledge, is the first time a link has been empirically demonstrated between these three variables. Utilizing this information in conjunction with futures prices can help guide expectations about the future price and quantity of lumber demanded at approximately a 6 month horizon. Secondly, the model that treated U.S. GDP and U.S. housing starts as exogenous was superior in all aspects to the model that treated these variables as endogenous. However, the forecasting results of both these models lagged far behind a simpler ARIMA (0,1,1) model. This may be a reflection of the difficulties outlined earlier in predicting the price of softwood lumber, due to characteristically inelastic supply and demand and the exposure of price to political forces that can shape the market but appear to happen at random. This paper provides evidence for this conclusion, demonstrating the significant effect of the Softwood Lumber Agreement of 2006 and the 2007 financial crisis on the price of U.S. softwood lumber. In closing, the results of this paper have demonstrated the difficulties in constructing a succinct model for the U.S softwood lumber market and the advantages of using more elementary modelling techniques.

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Bibliography Babula, Ronald A., Daowei Zhang and John Paul Rothenberg, 2012, “A Dynamic Monthly Demand Model of U.S.-Produced Softwood Lumber With a Futures Market Linkage” Journal of International Agricultural Trade and Development ISSN: 1556-8520 Volume 8, Number 2. Baek. J . “Dynamics of the U.S.-Canada Softwood Lumber Trade: Market and Welfare Effects of the 2006 Softwood Lumber Agreement.” Journal of International Law and Trade Policy. 12(2): (2011) 69-81. Bonshor, Matthew and Justin Fazio, 2015, “Forecasting U.S. Softwood Lumber Prices” Queen’s University Economics Department. Boyd, Roy, and Kerry Krutilla. "The Welfare Impacts of U.S. Trade Restrictions against the Canadian Softwood Lumber Industry: A Spatial Equilibrium Analysis." The Canadian Journal of Economics 20, no. 1 (1987): 17-35. Buongiorno, Joseph, Jean-Paul Chavas, and Jussi Uusivuori. "Exchange Rates, Canadian Lumber Imports, and United States Prices: A Time-series Analysis." Canadian Journal of Forest Research, (1988), 1587-594. Foreign Affairs, Trade and Development Canada, 2015, “Softwood Lumber: Key Information Regarding the Agreement” retrieved from: http://www.international.gc.ca/controls-controles/softwood-bois_oeuvre/index.aspx?lang=eng. Foreign Affairs, Trade and Development Canada, 2015, “Monthly Report on Softwood Lumber Prices and Consumption Softwood Lumber Agreement (SLA) 2006”, retrieved from: https://www.eics-scei.gc.ca/report-rapport/SWLSLA_EUSC_201504.html. Kearl, James R.; Mishkin, Frederic S. "Illiquidity, the Demand for Residential Housing and Monetary Policy," The Journal of Finance (1977): 1571-1586. Ngai, Rachel L. and Silvana Tenreyro, 2013, “Hot and Cold Seasons in the Housing Market,” London School of Economics, CEP, and CEPR. Zhang, D., and C. Sun, 2001, “U.S.-Canada trade disputes and softwood lumber price volatility” Forest Products Journal 51(4): 21-27.

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New Private Housing Units Authorized by Building Permits

Appendix

Figure 1 - Untransformed Data

Figure 2 - Summary Statistics

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Figure 3- Autocorrelation and Partial Autocorrelation Functions Figure 4 - Impulse Response Functions