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Pine Sawtimber Severance and Price: A Causality Test for Louisiana

Doleswar Bhandari1, Sun Joseph Chang2, and Michael A. Dunn1

Abstract: Industrial and non-industrial private forests account for about 95 percent of pine sawtimber supply in Louisiana. For these forest landowners, do past prices affect the present supply of timber? On the other hand, can past quantities of timber severed affect the current stumpage price? This study tries to answer these questions with the Granger causality test. According to Granger's causality, stumpage price causes timber quantity severed if we can better predict the current timber quantity severed with both past timber quantities severed and stumpage prices than with just past timber quantities severed alone. Conversely, timber quantity severed causes stumpage price if we can better predict the current stumpage price with both past stumpage prices and timber quantities severed than with just past stumpage prices alone. Granger causality tests were applied to quarterly data from the first quarter of 1984 to the third quarter of 2001 on quantities of pine sawtimber severed and average stumpage prices obtained from the Louisiana Department of Agriculture and Forestry. The ordinary least squares (OLS) procedure was utilized for these analyses. Results showed that past quantities severed caused the current price and past prices caused the current quantity severed. As such a feedback loop exists between quantity severed and price. This result implies that the pine timber market in Louisiana is competitive and efficient. Key Words: Granger causality test, pine sawtimber, stumpage price, timber quantity



Pine sawtimber accounts for about 80 percent of the sawtimber harvest in Louisiana. About 95 percent of the pine sawtimber was harvested from both industrial and non-industrial private forestland. Private forest landowners, acting rationally, take into consideration stumpage prices from the past in making current timber harvest decisions. For the market as a whole, do timber harvests that have occurred in the past affect current stumpage price? Effects of past prices obtained by private forest landowners and past quantities of timber severed on present price and quantity of timber severed in Louisiana have not been studied. In this study we examined the direction of causality between quantity severed and price of pine sawtimber as follows.

Graduate student and associate professor, respectively, Department of Agricultural Economics and Agribusiness, Louisiana State University Agricultural Center. Baton Rouge, LA 70803 2 Professor, School of Renewable Natural Resources, Louisiana State University Agricultural Center, Baton Rouge, LA 70803. [email protected] (225)578-4167. Approved for publication by the Director of Louisiana Agricultural Experiment Station as manuscript 0340-1491



a) Does quantity cause price or b) Does price cause quantity or c) Is there a feedback from both or d) Are both independent?


According to Granger (1969), the time series X is said to "cause" Y relative to the Universe U (U includes both X and Y as components) if and only if the current value of Y can be better predicted with past values of both X and Y than Y alone. Based on this definition, Geweke (1982) developed a direst test for causality by first running the following regression equations

Yt = a 10 + j=1 a 1 j Yt - j + 1t




Yt = a 20 + j=1 a 2 j Yt - j + k =1 b 2 k X t - k + 2 t



where 1t and 2 t are regression residuals; a1j and a2j are parameters relating Yt and its lagged values; and b2k are parameters relating Yt to past values of Xt. Geweke's direct test of Granger's causality involves testing the null hypothesis: b21 = b22 =.... = b2q = 0 which can be effectively carried out with a Chow F test. Granger's causality test was utilized by many people in the past in agricultural economics. Notable literatures on this topic include Zapata and Gil (1999), Zapata and Rambaldi (1997), Milijkovic and Garcia (1996), Bach and Nuppenau (1996), Schimmelpfennig and Thirtle (1994), Weersink, and Tauer (1991), Sarker (1990), and Bessler and Brandt (1982). In forestry, past studies include articles by Chang (1983) and Buongiorno and Brannman (1985).Formulation of theoretical model Rational expectation theory forms the basis for this causality test. This theory postulates that economic variables (in our case quantity harvested and price) are generated by systematic processes. Over time, economic agents learn what the process of determining a variable is, and they will use this knowledge to form expectations of that variable. Buyers and suppliers learn about how much to buy and sell by using available information. Let St be the quantity of pine sawtimber severed, Pt its price and St* the desired quantity of severance (St* = Pt). The partial adjustment model (PAM) says that the actual change in quantity of severance (St ­ St-1) is only a fraction () of the desired change (St* - St-1), that is St ­ St-1 = (St* -St-1) + ut with 0 < < 1 (4) St ­St-1 = (Pt - St-1) + ut (5) St = Pt + (1- ) St-1 + ut (6) St =b1 Pt + b2 St-1 + ut



(7) With =b1 and 1- = b2, equation 7 can be estimated econometrically as St =b0 + b1 Pt + b2 St-1 + ut (8) The rational expectation of St in period t is its mathematical expectation given the available information. This theoretical model is generalized using Granger's causality definition. Geweke's ordinary least squares regression is a specific causality test based on Granger's definition. There are four kinds of causal relationships between price and quantity severed. One of the directions is that price causes quantity severed as suggested by economic theory. Another direction is that quantity severed might cause price. We cannot ignore this possibility because quantity severed plays a vital role in determining price. Another possibility is that a feedback loop exists between price and quantity severed. If this is the case, we need to develop a simultaneous equation model to describe the relationship. Another possibility might be that price and quantity severed act independently. Since this is a strictly empirical test for causality, the Granger's test used in this study is based on ordinary least squares estimation as proposed by Geweke (1982). Let St be the quantity of pine sawtimber severed in period t and Pt be its price. n and m are the number of lags used for quantity severed and their prices respectively. Then P does not cause S if and only if the (minimum mean square error) linear predictor of St based on St-1, .. St-i Pt-1, ....Pt-j , is identical to the linear predictor based on St-1 .. St-n alone. That means knowledge of past prices of pine sawtimber does not help to predict the quantity severed. Given

S t = b10 + i =1 b1i S t -i + u1t


(9) n m S t = b20 + i =1 b2i S t -i + j =1 c2 j Pt - j + u 2t (10) m Pt = c30 + j =1 c3 j Pt - j + u3t (11) m n Pt = c40 + j =1 c4 j Pt - j + i =1 b4i S t -i + u 4t (12) where u1t , u2t, u3t , and u4t are the error terms for equations (9) to (12) respectively and are assumed to be white noise with zero mean and constant variance, in equation (10) c2j= 0 for j=1 to m means past prices do not cause current period quantity severed. Similarly, in equation (12) b4is =0 for i=1 to n means quantities severed in the past do not cause the current period price. The expected sign of c2j is positive because higher past prices stimulate larger harvests. The actual sign of the coefficient is empirically determined. Similarly, the expected sign of b4i is negative, because with higher supplies in the past current prices are expected to decline. Again, the sign of the coefficient is also empirically determined. If both c2j and b4i are insignificant, we can say that price and quantity are working independently. Conversely, if both c2j and b4i are significant then we 13

can say there is a feedback loop between price and quantity severed. If a feed backloop exists, simultaneous equations will be required to model the timber market (in the present context this would be beyond the scope of this work). The test of the hypothesis that Pt-j does not cause S2t is a test that c2j =0 for j= 1, 2, 3, ..... m. The test statistic is an F-test obtained by estimating equation (10) as the unconstrained model and equation (9) as the constrained model and conducting an F-test as follows: ( SSEc - SSEu ) m F= SSEu (T - k ) (13) where SSEc and SSEu are constrained and unconstrained sum of squares of errors, respectively. m is the number of constraints imposed for the number of lags for the prices. T is total number of sample observations; k is the number of parameters in the unconstrained model. If the calculated F-value is greater than the 5% critical value with m, T-k, degrees of freedom, then the null hypothesis is rejected. That means past prices cause the current period quantity severed (equations 9 and 10). Similarly past severances cause the current price (equations 11 and 12).

Data sources and description Price and quantity severed data for pine sawtimber were obtained from the Office of Forestry, Louisiana Department of Agriculture and Forestry. Quantity severed of pine sawtimber was available monthly, whereas price data were reported quarterly. Although high, low, and average prices were available quarterly, average prices were selected for this study. Monthly severance data were compiled into quarterly data expressed in 1000 board feet to match with price data. The nominal stumpage prices were converted into real prices by dividing the nominal price with CPI for all United States urban consumers, with the base period 1982-1984 =100. The sample data were available from the first quarter of 1984 to the third quarter of 2001 for 71 quarterly observations. Descriptive analysis The mean quantity severed per quarter was 298.184 million board-feet, with a maximum severance of 543.316 million board-feet and a minimum of 180,570 thousand board-feet. Overall quantity severed over time was more or less constant.

Table 1. Variability of quantity severed and price of pine sawtimber Variable Observations Mean Std Dev Minimum Price ($) 71 178.8 50.85 87.16 Quantity of Severance 71 298,184 55,873 180,570 (1000 board-feet)

Maximum 283.87 543,316


Quantity severed and price over time

Quantity (1000 Board-feet)

550000 450000 350000

300 250 200 150

250000 150000 1 11 21 31 41 51 61

Price ($)

100 50 71

Quarter (1994 - 1 To 2001 -3) Price ($)

Formatted: Font: (Default) Arial, 9 pt, Bold, Font color: Black Formatted: Font: 10 pt

quantity (1000 Board-feet)

The mean price per thousand board-feet for the 71 quarters was $178.80 with a minimum of $87.16 and a maximum of $283.87. The coefficient of variation for quantity severed was higher (28.73%) then that for price (18.73%). Data also show that there was low correlation between price and quantity severed as evidenced by the very low correlation coefficient 0.014.

Model estimation and hypothesis testing Choosing the length of lag represents a common problem in time series analysis. Because of the immediate availability of existing timber stands, it is assumed that if there is any response of price to quantity severed or vice versa, it should occur within two years. However for better results, lag lengths were further scrutinized by using AIC criteria. For the quantity model, explanatory variables St-4, St-6, St-8, Pt-1and Pt-4 yielded the minimum AIC values. Similarly, for the price model explanatory variables Pt-1, Pt-4, Pt-8, St-2, St-5 and St-6 gave the minimum AIC values. We did not eliminate insignificant lag variables that preceded significant ones. All lag variables up to the point of the last significant lag variable were included because their inclusions do not affect the outcome of our estimations. Results of these models are as follows:

1. Quantity model: Based on equation (10), the null hypothesis was that there is no relationship between current quantity severed and past prices. The estimated model is as given below: St = 258903 + 0.04314 St-1 ­ 0.09354 St-2 ­ 0.12977 St-3 + 0.22765 St-4 (2.88) (0.32) (-0.74) (-0.95) (1.67) + 0.07767 St-5- 0.14506 St-6 + 0.0018 St-7 + 0.25924 St-8 (0.57) (-1.12) (0.01) (1.98) + 648.1Pt-1 + 140.6 Pt-2 ­ 599.7 Pt-3 - 347 Pt-4 (1.36) (0.22) (-0.95) (-0.74) (14) Adj. R square= 0.3654 MSE= 1818621980 DF= 50 F= 3.97 p=0.0003 15

In equation (14), St is the current period quantity of pine sawtimber severed in thousand board-feet. Numbers in parentheses are t-ratios of the estimated coefficients. The model was significant, which is evident from the p-value of the F test. Lag quantities and lag prices explained only about 37 percent of variation in the current quantity St of pine sawtimber severance between the first quarter of 1984 and the third quarter of 2001. The impact of past quantities on current quantity varied considerably, as evidenced by the positive coefficients of St-1, St-4, St-5, St-7 and St-8 and the negative coefficients of St-2, St-3 and St-6. Furthermore, comparatively higher t-ratios for St-4, and St-8 indicate that quantity severed follows a seasonal pattern. Joint impact of past prices was tested by using an F-test. SSEs were obtained from constrained and unconstrained models to calculate the F value. ( SSEc - SSEu ) / m (1.077669 *1011 - 90931099024) / 4 F= = = 9.072 SSEu /(T - k ) 90931099024 /(63 - 13) where the number of constraints m is 4 and the number of total parameters k in the unconstrained model is 13. The calculated F = 9.072 is higher than the 5% significant F value of 2.557 with 4 and 50 degrees of freedom. We reject the null hypothesis of no influence of past prices (C1= C2= C3= C4=0) on the current quantity severed. Although each individual coefficient was insignificant, they were significant jointly. We conclude that past prices cause the quantity severed. 2. Price model: in this model the current price is the dependent variable and past quantities and past prices are the independent variables. Lag length was identified by using AIC criteria where minimum value was obtained from lag prices up to Pt-8 and lag quantities up to St-6. The estimated model is presented below; Pt = -94.18 + 0.79027 Pt-1 + 0.02256 Pt-2 + 0.03393 Pt-3 -0.0931 Pt-4 ­ 0.14375 Pt-5 (-2.81) (5.81) (0.13) (0.20) (-0.55) (-0.87) + 0.1935 Pt-6 -0.1867 Pt-7 + 0.3226 Pt-8 + 0.000033 St-1 + 0.000101 St-2 (1.17) (-1.14) (2.58) (0.87) (2.66) + 0.00003 St-3 + 0.0000036 St-4 + 0.000113 St-5 + 0.000075 St-6. (15) (0.69) (0.08) (2.71) (1.95) Adj. R-square=0.94 MSE= 144.7 DF=48 F=73.27 In equation (15), Pt is the current price of pine sawtimber in dollars per thousand board-feet. The numbers in parentheses are t-ratios of the coefficients. The overall model was highly significant. It is interesting to note that past quantities severed and past prices explained about 94 percent of the variation in current price. Coefficients Pt-1 and Pt-8 were positive and highly significant. This is evidence that price also shows patterns of seasonality. Similarly, past quantities positively contributed to price changes and it is evident from the sign of coefficients for the past quantities St-1, St-2, St-3, St-4, St-5 and St-6. Among these coefficients, St-2 and St-5 were highly significant.


For the causality test, the null hypothesis in this model was that coefficients of past quantities (1= 2 = 3= 4= 5= 6 =0) equal zero. This joint test was conducted by an Ftest with constrained and unconstrained models.


( SSEc - SSEu ) / J (10833 - 6945.4) / 6 = = 6.58 SSEu /(T - k ) 6945.4 /(63 - 15)

The calculated F = 6.58 is larger than the 5% significant F value of 2.294 with 6 and 48 degrees of freedom; hence, we rejected the null hypothesis and concluded that past quantities of harvest cause the current price of pine sawtimber in Louisiana. The inclusion of past quantity data increased adjusted R2 from 0.92 to 0.94. These OLS estimates for the price model were slightly affected by the usual statistical problems of multi-collinearity, as evidenced by the high R2 value (0.955) and the few significant variables. Since our purpose in this study was to test joint effect of past quantities on the current price we did not correct for it in our OLS models. Similarly, we also tested for the presence of conditional heteroscedasticity for both models using four lag periods. In both cases p-values of F-ratios were more than 0.40, which was much larger than the critical value of 0.05. This suggests that in both cases the error terms were homoscedastic. An autocorrelation test was conducted by using Durbin's h-test because we were using lagged dependent variables as independent variables. In both models, p-values of Durbin's h-ratios were larger than 0.49, which was much larger than the critical value 0.05. Therefore, both OLS models performed well considering autocorrelation. Ramsey's (1969) RESET specification test was used for both of these models, mainly because of its simplicity of implementation. An F-test was conducted for both models by using the original unconstrained model as the constrained model for the RESET test and the original unconstrained model plus the squares, cubes, and quadruples of the predicted values of the dependent variable as the explanatory variables in the new unconstrained model. Results are given below: Quantity model:


( SSEc - SSEu ) / m (90931099024 - 81374770642) / 3 = 1.800 = 81374770642 /(63 - 16) SSEu /(T - k )

The calculated F-value 1.800 was less than the critical value 2.80 at =0.05 with 3 and 47 degrees of freedom, indicating that these three variables were insignificant to the model. We concluded that there was no misspecification of this model. Price model: ( SSEc - SSEu ) / J (6945.43 - 6443.13) / 3 = = 1.195 6443.13 /(63 - 18) SSEu /(T - k ) The estimated F-value of 1.195 was less than the critical F-value 2.80 at =0.05 with 3 and 45 degrees of freedom. This joint test showed that inclusion of polynomial terms of predicted prices did not contribute to the model. Therefore, there was no misspecification for the price model. 17 F=

SUMMARY AND CONCLUSION Granger's causality test is a strictly empirical test to determine the causal relationship between price obtained and quantity of pine sawtimber severed by private industrial and non-industrial forest landowners in Louisiana. Based on Granger's definition, quantity severed causes price if we are better able to predict price with the quantity data than without them in our analysis. Similarly, price causes quantity if the price information helps predict the quantity severed. The OLS procedure specifically developed by Geweke for this purpose was carried out against both data sets from the first quarter of 1984 to the third quarter of 2001. Results of the statistical analyses indicate that prediction of future price and future quantity is improved if we consider price and quantity data rather than price alone or quantity alone. In other words, we find strong evidence that past quantities helped predict the current price and past prices helped predict the current quantity. As such the results suggest that a simultaneous equation relationship exists between stumpage prices and timber severed. It is also interesting to note that the price model is substantially better explained than the quantity model in our analyses. The result of this study also suggests that timber price is very efficient. Simple past prices and past quantity alone are very good predictors of current price. In this case, the immediate past can tell a lot about current situation, a result that is quite compatible with the timber market where many buyers and many sellers interact. No individual buyer or seller is capable of making "big" money from an information monopoly. Timber suppliers are getting competitive prices and timber buyers are paying competitive prices. This empirical test thus lends support to the hypothesis that a competitive timber market exists. It is also found from this empirical test that a price signal lasts at least two years for the pine sawtimber market. Another very exciting result is that the price from two years prior is a significant predictor of current price. Weak prediction of quantity severed is attributed to many other factors such as seasonality involved in harvesting, forward contracting between sellers and buyers, and sizable volumes of inventory stock for longer periods. The effect of seasonality is observed very strongly in quantity severed, which is expected in the timber market, since timber harvesting depends on weather. The result of this study is quite consistent with what is observed in actual conditions, where changes in quantity cannot be explained by just past prices and volumes.



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