Identification of the Domains for Reverse Patterns of Forestry Specialization Using a Linear Trade Model that Includes Intermediate Goods

This paper discusses development of a multi-country, multicommodity linear trade model that includes intermediate goods. This new model improves the author’s previous model by rigidly formulating the supply and demand conditions for each good according to the final demand for that good as a linear function of gross domestic product (GDP). Parameter domains of φK (i.e., the level of public benefit in monetary terms provided by the forestry sector in country K, assuming that the forestry sector maintains its present output level) are investigated where the pattern of forestry specialization in each country reverses from its primary state. These domains were identified in three-dimensional φK spaces. Public benefit was assumed to be directly proportionate to the country’s forestry output. Calculations were made using data from the “Asian International Input-Output Table 2000.” Simulations were conducted to examine interactions between Japan, the U.S., and China. Results showed that (1) if the present public benefit from the forestry sector in each country is not considered at all, then forestry output should be decreased in Japan, (2) when public benefit is considered, a “reverse domain” (in which desirable outputs increase) certainly exists within the range of φJ = 0 − 1.0(1010$/year) in the three-dimensional φK spaces, and (3) when the agriculture, forestry, Received September 11, 2009; Accepted January 18, 2010


Introduction
If a country were to attempt to increase the rate of self-sufficiency for its forestry sector or primary industry, the public benefits provided by these sectors should be internalized into trade models. That is, if one were to meaningfully analyze the extent to which evaluation of these public benefits reverses the specialization pattern of these sectors, it would be necessary to construct a trade model with a good command of actual international input-output data.
Although the Ricardian model is simple, it provides a good explanation of the mechanisms of international trade. In recent years, there have been many attempts to augment this model to formulate a multicountry, multi-commodity model or a model including intermediate goods, but none of these efforts have included adequate command of international input-output data (Jones and Kenen, 2002). I devised such a model in a previous study (Ejiri, 2005) to compensate for abandoning price changes. The distinctive feature of this model is that it combines the Ricardian model and input-output data, thus making an analysis that includes intermediate goods possible. However, the model is unable to rigidly formulate the supply and demand conditions for each good in the world market. It allows a gap between supply and demand, and shows the degree of this gap in the parameter values. The disadvantage of this method is that the pattern of specialization suggested by the optimal solution depends largely on the parameter values.
The model presented in this paper addresses the parameter dependence problem. The model's chief advantage is that the supply and demand conditions for each good are rigidly formulated according to the domestic final demand for that good as a linear function of the country's gross domestic product (GDP) (Ejiri, 1997). Naturally, the intermediate demand for a good is determined automatically by the output of that good. The previous model was only applied to Japan and the U.S., but the improved model is also applied to China. As in the previous study, barriers to trade, including transport costs and tariffs, are ignored.

Basic implications of the Ricardian model
The Ricardian model predicts trade profit by looking at the difference in relative labor productivity between sectors across countries (Kimura, 2000, Koizumi and Aihara, 1981, Komiya and Amano, 1979, Watanabe, 1991. Table 1 shows parameter values in a two-country, twocommodity schematic Ricardian model. Table 1(1) and 1(2) indicates the output and allocated labor force at the primary stage. (Values are hypothetical.) Table 1(3) shows the average labor productivity calculated from these values. These labor productivities are assumed to be constant. Table 1(4) shows gains in world output when Japan specializes in the production of cloth and the U.S. in wheat. This table also shows world trade can lead to profit for each country, even when all sectors in one country (here it is Japan) are inferior to another (here it is the U.S.) with respect to absolute labor productivity. Figure 1 illustrates the essential concept of the Ricardian model. Figures 1(1), 1(2), 1(3) show the production possibility frontiers of Japan, the U.S., and the world, respectively, in the case of Table 1 (Ito and Oyama, 1985). Figure 1(3) shows that if the specialization shown in Table 1(4) were achieved, world outputs of wheat and cloth would increase by 15 (10 8 t/year) and 12.5 (10 8 m 2 /year), respectively. Furthermore, if "proper" trade were carried out by each country, it would be pos- Table 1. Parameters for the Ricardian model (1) Output at the primary stage, (2) Allocated labor at the primary stage, (3) Labor productivity, (4) Gains in world outputs from specialization. sible to realize a state of consumption that would bring about higher standards of living (i.e., welfare). To simplify the discussion, I impose the following two assumptions with respect to the utility function: i) If it is inevitable that the feasible domestic consumption of one or more goods decreases after specialization, even if the domestic consumption of other goods increases, then countries will never accept this type of specialization because they will necessarily experience a drop in the Figure 1. Essential concept of the Ricardian model standard of living. ii) In the case that does not contradict assumption i), and if it is possible that the feasible domestic consumption of one or more goods increases after specialization, then countries will pursue this type of specialization because they will necessarily experience an increase in the standard of living.
Given these assumptions, the acceptable domain for each country becomes the upper right region (i.e., the region between the two chained lines) of the primary activity point in Figure 1(1) and 1(2). Moreover, because Japanese wheat imports must be equal to U.S. wheat exports and Japanese cloth exports must be equal to U.S. cloth imports, Japan's possible wheat import has an upper limit, and Japan must export more than its lower limit, by an acceptability condition of the U.S. Given these two restrictions, the Japanese domain of feasible consumption is further limited to the rectangular domain surrounded by both the chained lines and dotted lines in Figure 1(1). Likewise, the U.S. domain of feasible consumption is limited to the rectangular domain surrounded by both chained lines and dotted lines in Figure 1(2). It can easily be proven that if the world output of both goods increases as a consequence of specialization, then these domains necessarily exist for each country.
To identify the amount of trade leading each nation to these rectangular domains, lines of terms of trade are used, each of which has the same terms of trade and starts from each activity point after specialization, i.e., (0,75) for Japan and (200,0) for the U.S. In Figure 1(1) and 1(2), a line with 1:1 terms of trade is drawn as an example. This shows the basic implications of the Ricardian model and reveals the reason behind the increase in the standard of living for each country (i.e., each country specializes in the sector where it has a comparative advantage, rather than an absolute advantage, and then exchanges goods "properly" by trade).

Brief positive analysis of the Ricardian model
"Positive analysis" is an empirical analysis that analyzes the structure and function of an actual economic system. "Normative analysis" is a critical analysis intended to design an ideal economic system, regardless of the actual economies. Figure 2 shows the weighted correlation between q r (Japan/U.S. labor productivity) and Δe (the ratio of <Japanese excess exports to U.S.>/<outputs of Japan>) with respect to 24 goods (sectors) listed in Table 4 described below (Krugman and Obstfeld, 2003). Table 2 shows the same correlation coefficients, weighted in the same way, between each pair of countries in the table. Because pairs of countries with significant correlations were limited, one should be careful when applying the Ricardian model for positive analysis among the countries. However, the present study remains valid because its goal is a normative analysis of the impact of the internalization of public benefits from the forestry sector, not a positive analysis of the present pattern of trade. Anyway, Figure 2 shows the applicability of the Ricardian Table 2. Correlation coefficient between q r and Δe model for positive analysis of actual trade between Japan and the U.S., and this fact reinforces the applicability of this model for normative analysis between other countries.

Variables
Terms and variables used in this study are defined as follows. "World market": countries economically affected by the specialization of any country in the group and whose outputs, exports, imports, and so on may change as a result of this specialization. "Countries outside the world market" or "rest of the world": countries unaffected by specialization. : Variables with this superscript may change their value during the process of specialization. Variables without this superscript always retain their primary value. o : primary or initial value of a variable with a superscript. K: index of countries within the world market (K = 1, . . . , m). (In the following analysis, instead of K, the subscripts J, A, and C may be used to denote Japan, the U.S., or China, respec- of outputs in country K. A K : matrix of input coefficients for country K, which is given by total domestic demand for each good in country K (D K = A K X K + F K ). E K : exports of each good from country K. M K : imports of each good to country K. E KR : export of each good from country K to countries outside the world market. ("R"="rest of the world") M KR : import of each good from countries outside the world market : total labor force of country K. (L o K , the total labor force of each country, is assumed to have been endowed and is therefore sum of the GDPs of all countries within the world market.

Restrictions
Restrictions used in this linear trade model are as follows: 1) Restriction on the labor force: The total amount of labor in all sectors in each country cannot exceed the total labor endowment of the economy.
2) Restriction on GDP: The GDP of each country cannot fall below its primary level (the level before specialization) subsequent to specializa-tion.
3) Restriction on supply and demand: i) The supply of each good must be equal to the demand for that good within the world market.
(S W : supply of each good within the world market, D W : demand for each good within the world market) ii) Domestic final demand for each good is linearly dependent on the GDP of the country. .
(β K = 0 is assumed. However, tests with random numbers show that almost all realistically meaningful β K values other than β K = 0 also lead to feasible solutions of this linear programming problem.) 4) Restriction on the output of each sector: The output of each sector cannot fall below its minimum limit and cannot exceed the maximum potential output of the sector. [12] γ 5) Restriction on non-tradable goods: The absolute value of excess exports of each non-tradable good in each country cannot exceed its absolute value at the primary stage. [13] The goods of three sectors, i.e., "20. Electricity etc.," "21. Construction," and "24. Public administration," are treated as non-tradable goods here. . .

Objective function
The "objective function" is defined as the total amount of each country's GDP within the world market, and the maximization of this function is planned.
3.4. Internalization of the public benefits from the forestry sector in the linear programming model "True GDP" is defined as the sum of the GDP and public benefit, in monetary terms, provided by the forestry sector in the country, and this index denotes the true welfare of the nation (Ejiri, 1996(Ejiri, , 1999a.
This study recognizes that many forestry operations, such as thinning (not clear cutting), may result in a simultaneous impact -producing timber and benefiting the public, for example (Ohta, I., 2005, Ohta, T., 2005, Yoshimoto et al., 2005. The forestry sector's support of local communities and the forests they depend on is also considered a public benefit. Therefore, public benefits, in monetary terms, provided by the forestry sector are collectively handled as follows. No matter whether "zoning" is done or not, public benefits (in monetary terms) provided by the forestry sector in the country can be attributed to a) public benefits that are independent of output, b) public benefits that are considered part of the increasing function of relevant forestry output, or c) public benefits that are considered part of the decreasing function of relevant forestry output. That is to say, where ϕ K is the amount of public benefit, in monetary terms, provided by the forestry sector in country K (unit: 10 10 $/year), c K is constant that is independent of the values of X KF A or X KF B (unit: 10 10 is decreasing function of X KF B , X KF is output of the forestry sector or primary industry in country K, ( F : the sector number of forestry or primary industry. Unit: 10 10 $/year), X KF A , X KF B are the portion of X KF that can be categorized into a variable of ϕ KA and ϕ KB , respectively (unit: 10 10 $/year).
This study adopts the following linear approximation: where c KA , d KA , c KB , d KB are constants(> 0). Therefore equation [18] can be transformed as follows.
This study assumes the following relations: are the present value of X KF , X KF A and X KF B , respectively. Under this assumption, equation [20] can be transformed as follows.
is redefined as ϕ K , it can be rewritten as follows.
where G ϕW is the sum of the true GDP of each country within the world market and G ϕK is the true GDP of country K (G ϕK ≡ G K + ϕ K ).
The optimal solution (i.e., the set of optimal outputs of each sector) that maximizes the sum of true GDP in the world is investigated using the simplex method. Table 3 and Figure 3 show the key concepts of the main body of this model (i.e., equations [2]-[12], [17]) using a hypothetical input-output table (Morishima, 1956, Niida, 1978.  Table   3(2) denotes the optimal outputs of each country, i.e., the optimal solutions of this linear programming problem and other derived values.

Key concepts of the model
This optimal solution is denoted by the activity point T. The process of deriving this optimal point can be explained as follows: Equation   Table 3. Input-output table at each activity point in Figure 3 (1) Before specialization, (2) After specialization.
[≡ F D + ΔE; ΔE ≡ E − M ]; X: output of the country). Then, the world's final demand possibility frontier is identified as P'Q'R'S' using the two frontiers of each country.
Because the equation G DP K = n i=1 F Ki holds for each country, the next equation also holds: Figure 3. Combination of Recardian model and input-output table In this case, n = 2, and therefore the set (F W 1 , F W 2 ) that brings out equal G DP W forms lines with slopes of −45 degrees, e.g., line l. The

Data
The "Asian International Input-Output Table 2000" (Institute of De-veloping Economies, Japan External Trade Organization, 2006) provided the basic data. Table 4 shows output and employment data for each sector in Japan, the U.S., and China. Table 5 indicates how each sector may be aggregated for the purpose of investigating the effects of aggregation.

Results
In what follows, 10 10 $ is the monetary unit and 10 4 workers is the labor force unit. Furthermore, the degree X Ki /X o Ki to which the output of each sector increases subsequent to specialization is referred to as the "rate of output increase." Additionally, I denote the rate of output increase for the forestry sector (or primary industry output in cases in which the forestry sector is aggregated) in country K by f K . This is explicitly defined as f K ≡ X KF /X o KF . Table 6 shows the impact of public benefits from the forestry sector on patterns of specialization. Table 6(a) shows that when public benefits from the forestry sector are not taken into account, it is desirable for Japan to reduce its level of forestry output (and level of "Agriculture & Fishery" output as well) and increase its level of transport equipment output. In contrast, it is desirable for the U.S. to increase the former and reduce the latter.   Table 7. q GK is defined as the value of the rate of gross value-added increase in the forestry sectors. That is, q GK is calculated as      Figure 4 shows the reverse domains of forestry in each country calculated using the data of 15 aggregated sectors. Figure 5 shows the reverse domains calculated using the data of 14 aggregated sectors. Figure 6 shows the reverse domains for three aggregated sectors, but these results were calculated without the restriction on non-tradable goods (i.e., equation [16]). The reason for removing this restriction was that it is unnatural to impose such restrictions on all tertiary sectors.

Conclusions
This paper pointed out the following. When the public benefit pro- The model presented here succeeds in formulating the supply and demand conditions for each good in the world market using a combination of the Ricardian model and input-output data. That is to say, this model has a good command of international input-output data and succeeds in identifying the reverse domain.
Arbitrary factors inevitably affect the evaluation of public benefits and therefore lessen the value of this model for practical use. However, this model is an effective tool for evaluating the extent to which labor productivity must be increased to increase the self-sufficiency of forestry or other primary industries in the context of policy change (Ejiri, 1999b, 1997, Min, 2008. This method is also useful for econometrically analyzing the trade of forest products within a global market (Yukutake et al., 2003, Yukutake et al., 2006, Yukutake et al., 2007, Yoshimoto et al., 2002, especially when the proposed model is evaluated in terms of the general equilibrium theory. It could also be useful for evaluating the construction of a spatial equilibrium model (Shimamoto, 2002).