A World Model of the Demand for

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1 ForestSci., Vol. 33, No. 1, 1987, pp Copyright 1987, by the Society of American Foresters A World Model of the Demand for Paper and Paperboard ANDERS BAUDIN LARS LUNDBERG A STgACT. The objective of this study is to develop and evaluate econometric models describing the long-term development of demand for paper products, which could be used for simulation, policy evaluation, and long-term projections, on a global scale as well as for regions and individual countries. The study is intended to cover a relatively large sample of countries on varying levels of economic development. This means, however, that the availability of data sets rather restrictive limits on the model building. The basic approach in this paper is the same as that by Buongiorno (1978). The final model chosen here for projections and simulations of demand is, however, somewhat different from Buongiorno's model. In addition, a number of alternative model specifications were explored and evaluated. FoR. ScL 33(1): ADDITIONAL KEY words. Econometrics, data sets. THEORETICAL BACKGROUND PAPER AND PAPERBOARD consists of a heterogeneous group of paper grades, mostly used as input into information distribution and packaging of goods. Inspection of input-output tables shows the use of paper to be distributed over most sectors of the economy. The demand for paper may be derived from production theory. Let y = F.(%, v ), (1) be the production function for paper using activity (/), where x/is a vector of inputs of paper grades used in sector j, with typical element xi, and V/a vector of other inputs. Maximizing profits subject to (1) and the given prices, one obtains the demand for paper grade (i) into sector (/) as a function of a vector p* of the relative prices of the output and all inputs (Varian 1978) = (2) Anders Baudin is Associate Professor, Statistical Institute, University of Ume,5, S , Ume,5, Sweden, and Lars Lundberg is with the Trade Union Institute for Economic Research, Wallingam 38, S-11124, Stockholm, Sweden. The work reported in this paper was carried out as a part of the FAO Programme in Outlook Studies for Supply and Demand of Forest Products. We are grateful to the FAO for permission to publish the results, to Philip Wardie and three anonymous referees for valuable comments and criticisms. The authors, of course, bear the full responsibility for the results presented in this paper. Manuscript received November 12, Note: If equation (1) is a Cobb-Douglas production function, with one additional input besides paper, the demand for paper may be written log x o = log a + b log po + log, where b is the elasticity of demand with respecto relative paper price; the elasticity of demand with respect to output equals one. (3') MA CI-I 1987/ 185

2 If the production function (1) is assumed to be linearly homogeneous, the profit function has no maximum. We may instead minimize costs for producing a given output. This implies that paper demand for given output will depend on relative input prices p (Varian 1978). We may write xo = aoy -- fo(p)y, (3) where the input coefficient aii= xo/yj depends only on relative prices of paper and other inputs. Total demand for all paper and paperboard will be x= at y.. (4) Writing the demand for total paper and paperboard as a function of aggregate economic activity, GDP, as is often done in the form x = f(y) = a y, (5) is correct (i.e., a is constant) only if the ao:s are identical, or production in all sectors change in proportion. To avoid instability in the demand relationships caused by structural change, demand for each paper grade should be analzyed separately, using the appropriate end-use indicators. Paper consumption will be determined by supply and demand. However, data limitations made it impossible to estimate a detailed market equilibrium model. First, no internationally comparable data for a sufficient number ofcountdes were available for detailed end-use indicators y, so an aggregate measure of economic activity (GDP) had to be used. This means that structural changes in the economy may shift the demand function. Second, there were no price data for paper substitutes, e.g., competing materials in packaging. Third, no comprehensive cost data were available and thus the supply side could not be modelled. It is well known that estimating the demand function by OLS, disregarding the supply side, may give biased estimates of income and price elasticities of paper demand. Actually, the model used here assumes for each country a horizontal supply curve. However, this may not be too unrealistic for small or medium-sized countfids, strongly depending on exports or imports of paper. THE BASIC ECONOMETRIC MODEL The basic model used in this study is a pooled cross-section time series model, where paper consumption in country i, year t, is assumed to be a log-linear function of GDP, as a measure of aggregateconomic activity, and the real price of paper. 2 in Xit = a + b In Yit q- g In P t q- uit. (6) For a textbook presentation see e.g., Kmenta (1971). 2 Equation (6) may be interpreted as derived by profit maximization subject to a Cobb-Douglas production function, in the same way as equation (3'). However, since (6) refers to a relation between aggregates over product groups and user sectors [cf. Equations (4) and (5)], the elasticity of demand with respect to aggregate output will not necessarily be equal to one if the structure of the economy changes. In addition, there are practical reasons for using this particular functional form; it is likely that the log linear specification reduces the heteroskedasticity of the residuals. The use of the real (i.e., deflated) paper price makes the demand function homogeneous of degree zero in terms of the price level, a property required by economic theory. This price variable is not the same as the relative paper price (i.e., relative to substitutes) in Equation (3). 186 / FOREST SCIENCE

3 The model is estimated on annual data for paper consumption for all major consuming countries for the period Consumption is measured as production plus imports minus exports, i.e., changes in stocks are included. The source of paper consumption data, the FAO Yearbook of Forest Products, permits a subdivision of total paper into three groups: newsprint, printing and writing paper, and other paper and paperboard. In order to reduce measurement errors, which may be expected to be proportionately larger for small figures, countries with consumption in 1981 less than 20,000 MT for newsprint, 50,000 MT for printing and writing, and 100,000 MT for other paper and paperboard, are deleted. The number of countries included are 56 for newsprint, 44 for printing and writing, and 53 for other paper and paperboard. The measure of economic activity is GDP in 1980 prices and in USD at 1980 exchange rates; the source is FAO Compendium of Macro-Economic Indicators. 3 The measure of relative paper price is a trade unit value (in USD) for exports or imports, depending on which trade flow is the largest for the country in question, divided by the deflator of GDP in USD in that country. 4 The basic demand function is assumed to be identical for all countries and constant over time. The estimation results are given in Table 1. The GDP and price elasticities are highly significant in all three cases. For all groups, the GDP elasticity is around 1, which is somewhat lower than the results obtained by Buongiorno (1978) using similar methods on data for In studies of paper demand it is customary to estimate the regression of per capita consumption per capita income (Buongiorno 1977, 1978; fkberg 1968). This practice seems to be based on the theory of demand for consumer goods, based on utility maximization, despite the fact that paper is mainly used as an input. For consumer goods the per capita approach may be relevant: if the elasticity of per capita consumption with respect to per capita income is different from one, the effect on total demand will obviously be different if total income increases by increasing population or per capita income? Table 2 shows that the income and price elasticities obtained when estimating on per capita data are only marginally different from the same elasticities obtained For several reasons GDP in a common currency may fail to reflect correctly cross-country differences in economic activity. For instance, exchange rates may not reflect actual purchasing power parity; i.e., currencies may be over- or undervalued. Our method in fact assumes purchasing power parity to hold in 1980; the strong fluctuations of the dollar exchange rate does not influence our measure of economic activity, since the rate used for converting the GDP data into USD is kept constant. 4 The reasoning behind this is that on perfectly competitive markets for homogeneous goods, the export price f.o.b. will be identical to the domestic market price in exporting countries; in importing countries import price c.i.f. equals the market price. The deflator was computed as GDP in USD at current prices and exchange rates D = GDP in USD at 1980 prices and exchange rates 5 It may be noted that the elasticity of paper demand (x/ ) with respecto end-use activity y in (3') is equal to one. In terms of (4) and (5), therefore, an estimated GDP elasticity greater than one may indicate a shift of the composition of GDP in favor of paper-using sectors. 6 If we have where n is population, then so that d log x d log. n + b d log(y/n) dt dt dt M CH 1987 / 187

4 TABLE 1. Estimated income and price elasticities, basic pooled cross-section time series model. Printing Other paper Newsprint and writing and paperboard GDP 0.950*** 1.035*** 0.992*** Price *** *** *** / SE *** = significant at 1% level. ** = significant at 5% level. * = significant at 10% level. on aggregate data, and that the per capita GDP elasticities are fairly dose to one, so that the choice of per capita or aggregate data does not really matter. In the rest of the paper, aggregate data have been used. EXTENSIONS OF THE MODEL: DYNAMICS OF DEMAND ADJUSTMENT Adjustment of paper demand to changes in income or price may not be instantaneous; lags in adjustment may occur because of inertia in consumer habits (cf. berg 1968) or, for intermediate goods, because substitution induced by relative price changes requires time. According to models of partial adjustment or habit persistence, a dynamic specification of the demand for paper can be written (Kmenta 1971): In x t = a + b ln Yt q- g ln Pt q- boln xt_ 1 " u t. (7) The coefficients bl and g in this model give the short run or impact GDP and price elasticities. The long-run income elasticity of paper demand can be calculated as b b* - -- (8) 1-bo' According to the results in Table 3, there are indeed adjustment lags in the paper demand function, since the coefficients bo for In xt_ are strongly significant (if bo = 0 the adjustment would be instantaneous), and the impact elasticities are dearly lower than the elasticities of the static model. 7 This means that a shortrun analysis would have to take the dynamics into account. The choice between a static or dynamic model is not only a question of long- 7 Note also that the bo's are all clearly less than 1, which is required for stability of the model (7) (cf. Kmenta 1971). TABLE 2. Estimated income and price elasticities, basic model on per capita data. Newsprint Printing and writing GDP per capita 1.120*** 1.033*** Price *** *** / SE / FOREST SCIENCE

5 TABLE 3. Estimated income and price elasticities, dynamic model. Impact elasticity Printing Other paper Newsprint and writing and paperboard GDP 0.537*** 0.652*** 0.660*** Cons{t_ ) 0.434*** 0.365*** 0.328*** Price *** '** '** Long-run elasticity Price GDP / SE term versus short-term analysis, but also of correct model specification and should be evaluated by a model control. However, since there are no methods available for evaluating different model specifications with respect to the behavior of residuals in pooled time series cross-section models, we cannot discriminate between them on these grounds. Since the long-run GDP and price elasticities obtained from the dynamic model are almost identical to the elasticities from the static model, we may conclude that for the purpose of long-run analysis, we may retain the simpler static model specification. COUNTRY-SPECIFIC DETERMINANTS OF PAPER DEMAND It is well known that countfids on the same income level may have different levels of paper consumption, depending on differences in level of education, reading habits, population structure, etc. That the variation in paper consumption across countfids cannot be explained by differences in GDP and prices alone is stressed by the fact that the residuals from Equation (6) show a very distinct and systematic country pattern; i.e., for many countfids all residuals are of the same sign. This indicates that the model is misspecified, i.e., that some important variables explaining intercountry differences are missing. A very simple way of allowing for intercountry differences in consumption levels is to introduce a set of countryspecific intercept dummy variables Di, where Di = 1 for country k Di = 0 for all other countfids (cf. Buongiorno 1978). The regression equation then becomes In xit ' ao + aidi + b In Yit + g In Pit -Jr uit, (9) i=l TABLE 4. Estimated income and price elasticities. Cross-section time series model with country-specific shift variables. Printing Other paper Newsprint and writing and paperboard GDP 0.808*** 1.095'** 1.214'** Price '** '** '** Number of significant dummy variables (***) / SE MARCH 1987 / 189

6 TABLE 5. Estimated income and price elasticities. Inclusion of a time variable. Printing Other paper Newsprint and writing and paperboard GDP 0.945*** 0.816*** 1.514*** Price '** *** *** Time '** *** *** / SE The estimation technique used in Equation (9) is a covariance technique that is proved to be asymptotically equivalent to generalized least squares (GLS) and asymptotically as efficient as GLS (Wallace and Hussian 1969). The results are given in Table 4. Most dummy variables are strongly significant. A comparison with the basic model in Table 1 shows that the standard error of the residuals is substantially reduced. The GDP elasticities do not change much, but the price elasticities are clearly reduced by introducing the country dummies. A property of Equation (9) is that the means of the residuals for individual countries are zero. EFFECTS OF CHANGES IN OTHER DETERMINANTS OF PAPER DEMAND Another question for the analysis concerns the effects of trends in other determinants of paper demand than economic activity and prices. Demand for paper may change, for example, because of substitution of electronic media for printed media and other packaging materials for paper, even if GDP and price remain constant. If such changes are correlated with y and p in Equation (9) the estimated elasticities will be biased. Since no appropriate data were available, an attempt to capture these effects was made by including time as an additional variable. The equation then becomes lnx.=ao+ aidi + bln y, + glnpit + hot+ u.. (10) The coefficient ho will reflect long-run trends in reading habits, structure of advertising, share of paper-intensive sectors in GDP, structure of retail distribution, packaging technology, and surface weight of paper, for example. A declining share of printed media on the market for advertising, or a decrease in surface weight, would be revealed in a negative value of ho. Estimation of demand functions including a linear time variable for the main paper groups in Table 5 gives a positive value of ho for printing and writing, and a negative value for newsprint and for other paper and paperboard. An interpretation is that the factors mentioned above have on balance, had a positive effect on the demand for printing and writing and a negative effect on the demand for the other product groups during the 1960s and 1970s. For printing and writing and for other paper and paperboard, these effects are substantial; they amount to an annual increase of 1.7O/o for the first group, and an annual decrease of - 1.8O/o for the second. The inclusion of the time variable changes the estimated GDP elasticities somewhat. According to Table 5, the demand for newsprint and for other paper and 190 / FOREST SCIENCE

7 paperboard appears to be somewhat more sensitive to income, and the demand for printing and writing less than in Table 4. 8 The effect on the rate of growth of paper demand of such factors as changes in economic structure or packaging technology may not have been constant during the 20-year period covered by the analysis. A number of alternative nonlinear trend functions have been estimated, but the nonlinear effects were not significant. One possibility is that there may have been a downward trend break, in connection with the first oil crisis and the subsequent recession, in the development of the structural and technological factors. This was tested by introducing a time dummy into the equation; the terms hid + h2dt were added to Equation (10), where D -- 0 for , D -- 1 for There is a significant indication of a negative trend shift for other paper and paperboard, but not for the other products. VARIATION OF GDP ELASTICITY WITH INCOME LEVEL It has been argued ( berg 1968, Buongiorno 1978) that the incomelasticity of paper demand does not need to be constant, as in models (9) and (10), but may decrease with income level, so that the growth of paper demand for a given rate of economic growth is higher in low income countries. A test of this hypothesis was made by splitting the sample of countries into four groups by level of per capital GDP in USS in For each group a dummy variable D s was created such that D s -- 1 for countries in group j, D s = 0 for other countries. The equation becomes n--1 4 In xit ao + aid i + boln Yit + bsd ln Yit + g In P t i l j l + hot + hid + h2dt + u,. (11) In this model, the GDP elasticity (bo + b s) is assumed to be the same within each group, but may differ among groups. In addition to the income groups, the USA is treated separately as a fifth group, since it accounts for a large share of world paper consumption. 9 According to the estimation results in Table 6, the GDP elasticity clearly declines with per capita income for other paper and paperboard; the differences are statistically significant and quite large. For the two other product groups there appears to be no such clear pattern of a continuous decline of income elasticity; in fact, the sensitivity of paper demand to income seems to be lowest in the middle income range (4,000 to 9,000 USS). The model gives a very low value for priming and writing in the USA. In most cases, except other paper and paperboard, and for the middle income group, the elasticity differences are not significant. MODELCONTROL On the basis of the evaluation of alternative models, Equation 11 was chosen as the main alternative. A model control was performed by inspecting the residuals of Equation (11). There is no clear sign of heteroskedasticity; plots of residuals One might expect multicollinearity to arise when y and t are both included in the regression, since for any single country the y variable typically contains a strong trend. However, since our data consist of pooled time series, the correlation between y and t is not particularly high, since there is a crosssectional effect on the time series of GDP. 9 It is also possible to allow the price elasticity to be different between income groups. This was tested for newsprint, but no significant differences were found. MARCH

8 TABLE 6. Estimated income and price elasticities. Income elasticity differences by income group. Printing Other paper Elasticity Newsprint and writing and paperboard GDP per capita income <2,000 USD 0.975*** 0.856*** 2,000-4, ,000-9, (*) 0.713(**) > 9, USA (*) Price *** '** Trend '** '** 1.310(**) 1.027(***) 0.775(***) 0.811(*) *** ' (***) against In y show a slightly elliptic form. No overall trends were found, although there are positive or negative trends in the residuals for some individual countries. (See, e.g., Figure 5). For these countries the residuals are obviously serially correlated, which is an indication of model specification error. The effect of serial correlation in residuals is loss of efficiency in estimation, but the estimates are still unbiased. To solve this problem in a pooled time series cross-section context, there remains some methodological problems to be solved, namely: ' observed ---estimated YEAR 1981 FIGURE 1. Actual and predicted world consumption of newsprint / FOREST SCIENCE

9 , observed --- estimated YEAR Fxoum 2. Actual and predicted world consumption of printing and writing papers / / ' observed / ' ' estimated 4ooool, ' YEAR Fmcrm 3. Actual and predicted world consumption of other paper and paperboard MARCH 1987 / 193

10 o o o 10000, o o 7000 observed... estimated YEAR Fmu œ 4. Actual and predicted consumption of newsprint in the U.S l. 1. The identification of serial correlation in cross-section models. The traditional check of autocorrelation in the residuals by the Durbin-Watson statistic or the auto-correlation function (Box and Jenkins 1971) cannot be meaningfully interpreted, since in a pooled cross-section time series approach it is not invariant with respect to the ordering of the countries, which of course is arbitrary. 2. Development of efficient estimation procedures for such models, for a given nature of autocorrelation. In Figures 1 to 3 the time pattern of actual world paper consumption can be compared with the figures predicted by the model in Equation (11) for the three product groups. The figures indicate that the long-run development of demand is predicted rather well by the model. The short-run fluctuations, on the other hand, are not fully reflected in the model behavior. In Figures 4 and 5, actual and predicted consumption is shown for two large consumers. For some countries, e.g., Germany (Figure 5), not only the short-run behavior but also the long-run trends of actual and predicted figures are different. This may reflect a particular national development of factors such as the competitive position of printed media in advertising. In model terms this means that in order to obtain better forecasts for individual countries, it might be necessary to allow for different time trends (the coefficient h) in individual countries. CONCLUSIONS The variation in paper consumption across countries and over time can be well explained by the variation in GDP and real paper prices. 194 / FOREST SCIENCE

11 ' 1500' 1400, 1300, 1200' 1100, ' / ' observed estimated YEAR FIGUR 5. Actual and predicted consumption of newsprint in Germany FR The choice between per capita or aggregate consumption and income data does not affect the results of the analysis. 3. The fit of the model is improved by including country-specific shift dummy variables, to represent international differences in socioeconomic factors affecting paper demand. 4. There is no indication that a dynamic model specification would perform better in forecasting long-run paper demand than a static model. 5. A possible interpretation of including a time variable in the equation is that the effects on demand by factors other than income and price, such as structural change and developments in information and packaging technology, has on the average been positive for printing and writing paper, and negative for the other groups, in particular for other paper and paperboard. For this group there is an indication of a negative trend shift, i.e., a still more negative development in the 1970s than in the 1960s. 6. The price elasticity of paper demand seems to be low, i.e., in the range from -0.2 to -0.3 [cf. Buongiorno (1978), where price elasticities range from to -0.72]. 7. The income elasticity of paper demand appears to decline with income level MA CH 1987 / 195

12 for other paper and paperboard; for the other groups, no such tendency can be found. 8. On average, the income elasticity of newsprint and printing and writing paper seems to be a little less than 1, i.e., in the interval 0.8 to 1.0; for other paper and paperboard, the GDP elasticity is somewhat higher. 9. The income elasticities and the absolute values of price elasticities are generally lower than in the static model presented by Buongiorno (1978). There is, however, one major difference between the models; namely that in our model a time trend is included to reflect technological and structural change. Thus, the estimated elasticities are not quite comparable. LITERATURE CITED œ1 o, C.J The demand for paper and paperboard in Western Europe Almqvist & Wicksell. Box, G. E. P., and G. M. Jœma s Time series analysis, forecasting and control. Holden-Day. BUONGIORNO, J Long-term forecasting of major forest products consumption in developed and developing countries. For. Sci. 23(1): BUONGIORNO, J Income and price elasticities in the world demand for paper and paperboard. For. Sci. 24(2): FAO. Compendium of macro-economic indicators. FAO. Yearbook of forest products. Rome K œnt^, J Elements of econometrics. MacMillan. V m N, H.R Microeconomic analysis. W. W. Norton. WALLACœ, T. D., and A. HUSS,N The use of error components models in combining crosssection with time series data. Econometrica 37(1). 196 / FOREST SCIENCE

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