0084-A1

Testing Reliability of Stumpage Prices as Indicators of the Scarcity of National Forest Resources

Anni Huhtala, Anne Toppinen^[1] and Mattias Boman

Abstract

In resource accounting, the shadow prices of natural resources and environmental effects should be used for correcting market prices to correspond to the social marginal value of goods. Since it is difficult to measure shadow prices in practice, market prices are often used as proxies for the shadow prices of natural assets. However, a prerequisite for the use of these proxies is that there is an established relationship between the size of the natural resource stock of interest and its market price. In this paper we analyse whether changes in stumpage prices in Finland and Sweden have actually reflected changes in the stocks during the past 70 years. Cointegration and unit root tests are used in the empirical analysis. Interestingly, the results indicate that no long-term equilibrium relationships exist between timber prices and stocks.

1. Introduction

According to the theory of natural resources, there should be a relationship between the physical size (volume) of a valuable resource stock and its shadow price (rent) over time. The scarcity of a resource should be reflected in shadow prices, or user costs: when a renewable resource stock increases, the corresponding shadow price of the stock decreases, and vice versa. Unfortunately, there are at least two practical problems related to the optimal shadow pricing of (net changes in) natural resource assets.

First, since we normally do not have observations on the shadow prices of natural resources, market prices have to be used as proxies for resource rents in accounting. This shortcut may be problematic, however, if there is reason to suspect that the market prices are not optimal from the point of view of natural resource management. Externalities and lack of property rights often lead to pricing failures. Second, the theory of natural resources indicates that not only physical changes in the stock of capital but also changes reflected in the shadow price of a natural capital stock are of importance (Asheim, 2000). Consequently, the total monetary value of a resource stock derived by using correct shadow prices does not necessarily reflect physical change, since the ‘volume effect’ and ‘rent (price) effect’ may cancel each other out. In the resource accounting literature, this problem has been acknowledged as an argument against using monetary indicators of sustainability (e.g., Hanley et al (1999), p.59). Even if market prices were optimal from a social point of view, we still would have a problem when using these prices in accounting because important information about physical resource scarcity can be lost in the aggregation.

Recent empirical analyses using modern time series econometric methods to study natural resource rents are Berck and Roberts (1996) and Ahrens and Sharma (1997), who tested price trends of certain nonrenewable natural resources. Similarly, the work of Hotelling (1931) has been applied to the “mining” of the renewable forest resources by Barnett and Morse (1963), Brown and Field (1978), Lyon (1981), and more recently Hultkrantz (1995) and Seroa da Motta and Ferraz do Amaral (2000), who have analyzed time paths of timber prices and depreciation of stocks both theoretically and empirically. None of these studies include resource stocks in the analyses. Nevertheless, as Hyde and Amacher (1996) note, prices are believed to reflect the development of resource stocks over time: “upward price adjustments are the natural and expected results of drawing down natural forest stocks, and we expect continued upward price adjustments until the new price is sufficient to justify investments in long-term forest management.”

Up to date, forests are the most extensively studied renewable resource in green accounting framework (see, e.g., Vincent and Hartwick, 1997 and Vincent 1999). The main purpose of the present article is to investigate whether changes in the forest resource stock are in fact reflected in market prices. This is of interest, since the resource accountant wants to measure the value of the change in volume of standing timber; Eurostat (2000) suggests stumpage prices for this valuation. We therefore use annual data on timber stocks and stumpage prices in Finland and Sweden from the last seventy years. Forestry has been important for economic development in both of these countries, and a systematic resource inventory was started already in the beginning of the 20^th century. The stumpage prices should capture the raw material value of forest biomass, or the resource rent, relatively well, because the property rights have been clearly defined.

2. The model

When adjusting the national accounts for the use of natural resources, it is recommended that, if possible, market prices should be used in the first place in the valuation. To show rigorously why the use of market prices (stumpage prices here, see Eurostat 2000) as proxies for shadow prices of renewable resource stocks (forests) has important consequences for welfare interpretations of extended national green accounts, we use a simple dynamic model. We consider forests as a source of renewable, but potentially depletable, timber harvested for use as raw material, and develop a forestry accounting framework for annual timber production, which is allocated to annual consumption (harvest) and annual investment (change in forest assets).

We consider an economy, which uses a renewable resource stock, V(t). The stock is increased by natural growth, F(V(t)), and depleted as the resource is used, C(t). Since the natural resource stocks are of particular importance when constructing environmental accounts, the economy's objective is to maximize the social utility (discounted over time by a constant interest rate (> 0)

(1)

subject to the resource constraint dV(t)/dt = F(V(t)) - C(t), which captures the dynamics of the stock variable.^[2] The current value Hamiltonian becomes H(t) =U(C(t)) + j(t) [F(V(t)) - C(t)], where the current value shadow price of the resource stock is j(t). The optimal infinite time solution must satisfy the following conditions:

(2) ¶ H(t)/ ¶ C(t) = U_C(t) - j(t) = 0

(3) = j(t)[d - F_V(t)]

(4) V = F(V(t)) - C(t)

Equation (2) is a social optimality condition; it says that the marginal utility from harvesting one unit of the resource must equal the current value shadow price of a unit of the resource in situ. The shadow price is the current opportunity cost of the standing forest stock and it captures the value of future harvesting benefits and determines the optimal conservation of stock.

In green accounting, the current value Hamiltonian has been interpreted as a theoretical basis for an economy's net national product (NNP). Weitzman (1976) showed that the Hamiltonian along an optimal growth path as comprehensive current NDP (in terms of utility) is a stationary equivalent of future consumption, or "a flow-equivalent proxy for future welfare". Since Weitzman's seminal paper, there has been a growing interest in the theoretical principles of national income accounting. But to derive a hypothesis of a relationship between socially optimal prices and resource stocks for our empirical analysis, we have to elaborate further on the analysis of optimal trajectories towards a steady state equilibrium.

By definition, both the stock and its shadow price are constant in a steady state. However, if the economy does not happen to be in a steady state initially, the shadow prices and, accordingly, the optimal accounting prices will change over time. Taking the time derivative of equation (2) yields which means that C(t) and j(t) change in opposite directions over time. Substituting into (3), and using (2) yields

(5)

Equations (4) and (5) constitute a coupled nonlinear system of differential equations for the optimal control C(t) and the state variable V(t). Now a steady state equilibrium (C_ss,V_ss,j_ss) occurs implying that and C_ss=F(V_ss). For a description of a complete dynamic system, see Huhtala et al. (2001).

According to the derivation above, the socially optimal shadow price should react to different stock levels in order to signal about scarcity. In our econometric analysis, the most obvious proxy for the shadow price in case of timber resources is the stumpage price as suggested, e.g., by Eurostat (2000). Given the welfare interpretation assigned to the Hamiltonian in the green accounting literature, we test whether there is a relationship between stumpage prices and national forest stocks.

3. Econometric issues and data

For relationships including non-stationary time series data, statistical inference based on conventional t and F tests is invalid and the results obtained may be entirely spurious. A time series is denoted I(0) when it is already stationary in levels and non-stationary and integrated of order d (I(d)) when it must be differenced d times in order to achieve (weak covariance) stationarity (see, e.g., Banerjee et al. 1993). Cointegration is essentially based on the idea that there may be co-movement between trending economic time series such that there is a common equilibrium relation which the time series have a tendency to revert to in the long run. Thus, even if certain time series themselves are non-stationary, a linear combination of them may exist that is stationary. In the present case, we are interested in testing whether there is an equilibrium relation in the long run between timber price and timber stock series. Johansen’s (Johansen 1995) full information maximum likelihood method is used here in empirical estimation of cointegration relations.

Finnish and Swedish timber stocks comprise one third of the inventories in the European Union. Although the stumpage prices of roundwood as raw material for the forest products industry are basically determined on the international markets, national markets within Europe do not fully integrate yet (e.g. Toivonen et al. 2002), and therefore analysis by individual countries is called for. A unique set of time series data for Finnish timber prices covering the period from 1911 to 1998 was available in this analysis. The Finnish timber stock data were constructed by adding net growth^[3] to the previous stock level annually. As some inconsistencies were observed in the earliest Finnish timber stock data, only data starting from 1938 were used in the analysis. We used the Swedish timber stock data for the period 1926 to 1998, but coherent Swedish stumpage price series were more difficult to find. Like Hultkrantz (1995), we used a number of different data sources in order to obtain a price time series that covers the whole period 1926-1998 (for a more detailed description of data sources, see Huhtala et al. 2001). The data show that inventories of timber in both countries increased steadily over the period studied (Figure 1). Real stumpage prices, that are used in empirical analysis, show strong business cycle fluctuations and fitted trends in stumpage prices show about 1% annual increase in both countries.

Figure 1a. Timber inventory and real stumpage price in Sweden (1926-98)

Figure 1b. Timber inventory and real stumpage price in Finland (1938-98)

4. Results

Prior to cointegration analysis, Augmented Dickey Fuller (ADF) (Dickey and Fuller 1979) unit tests were performed for individual time series. The results in Table 1 indicate that the null hypothesis of non-stationarity could not be rejected for inventory series in Sweden or Finland, although it could be rejected for their first differences at the 1% and 5% level, respectively. For stumpage price in Finland, non-stationarity could be rejected at the 5% level. For Swedish stumpage price, the null-hypothesis of non-stationarity was not rejected. The testing points out that since Finnish stumpage prices can be regarded as stationary at the 5 % level and we have to be extremely careful when proceeding to test for cointegration in the Finnish case.

Using Johansen’s cointegration method, a two-variable VAR-model was estimated for each country. Since inventory data for both countries are trending, a specification allowing for an unrestricted constant in cointegration regression was chosen. A two-lag model was found to be sufficient to remove residual price autocorrelation in the Swedish model, while a model with three lags proved more suitable for Finland. The chosen VAR-models were tested to be acceptable statistical formulations regarding residual autocorrelation, normality and heteroscedasticity.

Table 1. ADF-test results for timber price and inventory series. T indicates the inclusion of a trend in test equation and number i, k=i the number of lagged differences in the equation. *(**) denotes the rejection of null hypothesis of non-stationarity at 5 % (1 %) level (see e.g. Dickey and Fuller 1979)

The existence of long-run equilibrium relationships between timber price and inventory were tested using the Johansen’s trace test, and the results are reported in Table 2. For Sweden, no co-integration could be detected irrespective of the different model specifications. It can be concluded that, in the long run, no tendency for timber prices and inventories to reach a steady state equilibrium was found for Sweden.

As reported in Table 2, no cointegration could be detected for Finland either. However, in the Finnish time series there is an interesting period starting in the mid 1950s when the timber stock decreases as can be seen from the data plot for Finland in Figure 1. Annual harvesting exceeded the natural growth of forests, and for several years the net growth of the forest stock was negative. One would expect that market prices would have reacted to the intense harvests and the decline of the stock. If the prices did not react to increased harvests, as our tests above seem to indicate, one explanation could be that a relatively large timber stock as a variable does not capture such net changes in the stock, or relative scarcity, quickly enough.

Table 2. Results from Johansen’s tests for cointegration rank, r, between timber price and inventory. The null hypothesis is no cointegration.

Due to the above concerns, we went on to test whether there would be cointegration between Finnish stumpage prices and the net growth of forests. The idea was that the timber prices would perhaps be more sensitive to the negative net growth figures than only occasionally declining, but constantly positive, timber stock figures. Finnish data on the annual net growth of forests are available from 1911. A testing procedure similar to that used above with timber stocks was applied. The results of Johansen’s cointegration test (Table 3) also failed to support the hypothesis that cointegration existed between market prices and the net growth of forest stock in Finland. The test result of no cointegration for the Finnish net growth model was more definite than that for the timber stock. Finally, we tested for cointegration between real stumpage prices in Finland and Sweden and found no evidence of cointegration there either.

Table 3. Results from Johansen’s tests for cointegration rank, r, between stumpage price and net growth of forests in Finland. The null hypothesis is no cointegration and * (**) denotes rejection of hypothesis at 5 (1) % level

5. Conclusions

Our empirical analysis suggests that market prices for timber are not cointegrated with the size of forest resource stocks in a theoretically consistent way. In the case of Scandinavian forests, it appears as if resource accountants currently have access to data that are wrong measures of shadow price or physical stock, or both. The last century has brought considerable technological progress, which certainly should be reflected in timber price changes. However, the lack of cointegration between the Finnish and Swedish stumpage prices would indicate that price development on the roundwood markets is affected by factors other than technological changes that cross national borders.

When no market prices are related to any stock of forest services of interest, studies of the demand for non-market priced goods and services are required. Based on our empirical analysis, we conclude that there may be a market price that proxies the shadow price of the timber resource. However, stumpage prices will not automatically do the job. The minimum requirement that environmental accountants should always establish is a relationship between market prices and the scarcity of the resource, before using these market prices as proxies for the shadow value of the stock.

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