ࡱ > T g " bjbjVV ( r< r< V* V* 7 " 7 7 7 7 4 8 8 8 h 8 : 8 A T B H ( H I I I P +N \ O G i 7 R I I R R 7 7 I I Z Z Z R 7 I 7 I Z R Z Z i k I S 0 j " 0 A k g T l g D k k g 7 Hl 7P v P T Z Q D EQ 7P 7P 7P .Y ~ 7P 7P 7P A R R R R g 7P 7P 7P 7P 7P 7P 7P 7P 7P V* r6 :
On The Intertemporal Stability of Bridge Matrix Coefficients
Tobias Kronenberg
Abstract
An increasing number of input-output analysts use micro data from household surveys in order to model the consumption patterns of households as a function of other variables like prices, income, and socio-demographic factors. These surveys usually adopt a different classification (COICOP) than the input-output tables (CPA/NACE). A bridge matrix is required to convert the data from COICOP to CPA/NACE (and vice versa).
This procedure is unproblematic when a bridge matrix is available for the year(s) to which the model refers. If a model is used to construct forecasts or scenarios of the future a problem arises, because the coefficients relating consumption purposes and commodity groups may change over time. This problem has not been adequately addressed in the literature.
The present paper examines a time series of annual bridge matrices from 1991 to 2006 for Germany. It uses descriptive statistics, visualisations, and econometric techniques to identify trends and patterns in the development of coefficients over time. It concludes that modellers may treat many coefficients as (approximately) constant over time, but certain key coefficients are not constant and should receive more attention.
Keywords
Input-output model, consumption expenditure, household sector, bridge matrix
JEL Codes
C67
Contents TOC \o "1-3" \h \z \u
HYPERLINK \l "_Toc289678849" 1 Introduction PAGEREF _Toc289678849 \h 1
HYPERLINK \l "_Toc289678850" 2 Computing the Bridge Matrices PAGEREF _Toc289678850 \h 2
HYPERLINK \l "_Toc289678851" 3 The Bridge Matrix for 2006 PAGEREF _Toc289678851 \h 4
HYPERLINK \l "_Toc289678852" 4 Evolution of the Bridge Matrix Coefficients PAGEREF _Toc289678852 \h 6
HYPERLINK \l "_Toc289678853" 5 Identification of Trends PAGEREF _Toc289678853 \h 8
HYPERLINK \l "_Toc289678854" 6 Conclusion PAGEREF _Toc289678854 \h 10
HYPERLINK \l "_Toc289678855" References PAGEREF _Toc289678855 \h 12
HYPERLINK \l "_Toc289678856" Appendix PAGEREF _Toc289678856 \h 13
Figures
TOC \h \z \c "Figure" HYPERLINK \l "_Toc289677006" Figure 1: Evolution of coefficients for food (COICOP 011) PAGEREF _Toc289677006 \h 7
HYPERLINK \l "_Toc289677007" Figure 2: Evolution of coefficients for transport services (COICOP 073) PAGEREF _Toc289677007 \h 8
Tables
TOC \h \z \c "Table" HYPERLINK \l "_Toc289678859" Table 1: The consumption allocation table for 2006 PAGEREF _Toc289678859 \h 3
HYPERLINK \l "_Toc289678860" Table 2: Concentration of bridge matrix coefficients PAGEREF _Toc289678860 \h 5
HYPERLINK \l "_Toc289678861" Table 3: Estimation of time trends in the coefficients for food PAGEREF _Toc289678861 \h 9
HYPERLINK \l "_Toc289678862" Table 4: Estimation of time trends in the coefficients for transport services PAGEREF _Toc289678862 \h 10
HYPERLINK \l "_Toc289678863" Table 5: Commodity classification PAGEREF _Toc289678863 \h 13
HYPERLINK \l "_Toc289678864" Table 6: Consumption purpose classification PAGEREF _Toc289678864 \h 15
Introduction
Input-output tables tend to focus heavily on the intermediate consumption of products by firms or industries and give little attention to the final consumption of products by households or government. This slightly lopsided perspective has become embodied in the open input-output model, where final demand is fully exogenous and the household sector is only a passive absorber of value added. Adjusting supply to demand, the statistical offices of most countries now produce input-output tables which describe in great detail the transactions between industries while offering very little detail on the transactions of the household sector. Usually there is only one column describing the final consumption expenditure by households and two rows that show the amount of wages and profits earned in each industry. Given this information it is possible to build models with a partly endogenous household sector, but only under the assumption of a representative household.
Lately, however, a number of studies have highlighted the importance of differentiating the household sector, as notable differences between household groups have been observed. As the common input-output tables do not provide much information on the household sector, these studies have to find the required data elsewhere. The most important source of household information is, of course, a household survey.
Household surveys are performed routinely by public agencies in many countries. Using questionnaires and interviews, they collect information on the economic background (income, wealth, employment status etc.), various socio-demographic characteristics (age, gender, nationality of household members) and the consumption expenditure of households. This information makes it possible, for example, to estimate the saving rate and consumption patterns of households from different economic and socio-demographic backgrounds.
Using the information from household surveys in input-output models, however, can be more difficult than it seems, because the survey data are usually compiled according to the COICOP classification, which is different from the CPA/NACE classification underlying most input-output tables. Therefore, a bridge matrix is required to convert data from COICOP into CPA or NACE. Such bridge matrices have been used in a number of recent papers, including Kronenberg ADDIN EN.CITE Kronenberg2010320(2009; 2010)32032017Kronenberg, TobiasErstellung einer Input-Output-Tabelle fr Mecklenburg-VorpommernAStA Wirtschafts- und Sozialstatistisches ArchivAStA Wirtschafts- und Sozialstatistisches Archiv223-248432010Kronenberg200931831831817Kronenberg, TobiasThe impact of demographic change on energy use and greenhouse gas emissions in GermanyEcological EconomicsEcological Economics2637264568102009( HYPERLINK \l "_ENREF_5" \o "Kronenberg, 2009 #318" 2009; HYPERLINK \l "_ENREF_6" \o "Kronenberg, 2010 #320" 2010), Washizu and Nakano ADDIN EN.CITE Washizu2010308(2010)30830817Washizu, AyuNakano, SatoshiOn the environmental impact of consumer lifestyles - using a Japanese environmental input-output table and the linear expenditure system demand functionEconomic Systems ResearchEconomic Systems Research181-1922222010( HYPERLINK \l "_ENREF_9" \o "Washizu, 2010 #308" 2010), Druckman and Jackson ADDIN EN.CITE Druckman2010309(2010)30930917Druckman, AngelaJackson, TimThe bare necessities: How much household carbon do we really need?Ecological EconomicsEcological Economics1794-18046992010( HYPERLINK \l "_ENREF_3" \o "Druckman, 2010 #309" 2010), and Mongelli et al. ADDIN EN.CITE Mongelli2010321(2010)32132117Mongelli, IgnazioNeuwahl, FrederikRueda-Cantuche, Jos M.Integrating a Household Demand System in the Input-Output Framework. Methodological Aspects and Modelling ImplicationsEconomic Systems ResearchEconomic Systems Research201-2222232010( HYPERLINK \l "_ENREF_7" \o "Mongelli, 2010 #321" 2010).
In all these papers, a common assumption is implicitly taken for granted: The coefficients of the bridge matrix are assumed to be constant. This may not be entirely realistic if, for example, the relative prices of some goods change drastically or the analysis is conducted over a period of many years. It is possible that substitution effects and technological change (which may in reality be impossible to disentangle) lead to changes in these coefficients. For example, a bridge matrix that allocated expenditure on energy (COICOP code 045) over commodity categories such as gas (CPA code 11) and heating oil (CPA code 23), may be subject to change when the relative prices of gas and oil change, or when technological change (e.g. the installation of gas distribution grids) opens up new consumption possibilities. Therefore, one may wonder whether it is appropriate to assume constancy of the bridge matrix coefficients over time.
This question is related to the intertemporal stability of input-output coefficients, which has been studied by a number of authors ADDIN EN.CITE ADDIN EN.CITE.DATA ( HYPERLINK \l "_ENREF_2" \o "Dietzenbacher, 2006 #324" Dietzenbacher and Hoen, 2006; HYPERLINK \l "_ENREF_4" \o "Gaiha, 1980 #325" Gaiha, 1980; HYPERLINK \l "_ENREF_8" \o "Sevaldson, 1969 #323" Sevaldson, 1969). The intertemporal stability of bridge matrix coefficients, by contrast, has not been studied extensively. Alcal et al. ADDIN EN.CITE Alcal1999326(1999)32632617Alcal, RolandoAntille, GabrielleFontela, EmilioTechnical Change in the Private Consumption ConverterEconomic Systems ResearchEconomic Systems Research389-4001141999( HYPERLINK \l "_ENREF_1" \o "Alcal, 1999 #326" 1999) have shown that such matrices can be subject to change over time, but they did not discuss the question whether these changes are statistically significant. The aim of the present paper is to determine whether the bridge matrix coefficients can be considered from a practical viewpoint as stable over time, and whether the failure to control for changes in bridge matrix coefficients in input-output models is likely to cause biased results. To this end the paper uses a time series of consumption allocation tables for Germany provided by the Federal Statistical Office (Destatis). The paper contributes to the literature on input-output modelling in general, and to that on forecasting and future scenario construction in particular.
In the following section, the series of consumption allocation tables for Germany is described, and the corresponding bridge matrix coefficients are defined and interpreted. In section 3, the bridge matrix for 2006 is described in some detail. Section 4 reports on the evolution of certain bridge matrix coefficients by plotting them graphically over the time period from 1991 to 2006. Section 5 presents the results of a time series regression analysis and shows the some trends are indeed statistically significant. Finally, Section 6 concludes.
Computing the Bridge Matrices
The bridge matrices that form the foundation of the present study were computed from data provided by Destatis in the framework of the German National Accounts. Destatis publishes input-output tables for Germany on an annual basis. The earliest of these tables refers to 1991, the year after German reunification. Older tables were published before that, but since 1990/1 marks a significant turning point in the economic history of Germany, it seems appropriate to use only tables from 1991 on. The most recent table refers to 2007. The national input-output tables always come with a set of additional information, including supply and use tables and a sectoral breakdown of employment. Most importantly for the context of the present paper, each input-output table is accompanied by a consumption allocation table (Konsumverflechtungstabelle, henceforth CAT) for the same year. However, since the CAT is published somewhat later than the corresponding input-output table, a CAT for 2007 is presently not (yet) available. This means that we have access to a series of 16 CATs for the period from 1991 to 2006.
Using these CATs, a corresponding series of bridge matrices can be computed, which offers the opportunity to study the evolution of the bridge matrix coefficients over a period of 16 years. During this period the German economy experienced a number of shocks caused by major political events, such as the consequences of reunification (which was completed formally on 3rd October 1990 but led to a restructuring of the East German economy that would take many years), the introduction of the Euro, and the successive enlargement from EU-12 to EU-27. In the meantime, substantial changes could be observed in the household sector: the population grew from 80 millions to 82 millions, the number of households grew from 35 millions to 39 millions, and the mean age increased from 39.4 years to 42.6 years. The cumulative effect of these political and social developments could have had a significant effect on the coefficients of the CAT. In the following, the structure of the CATs and the bridge matrices is discussed in some detail.
Table SEQ Table \* ARABIC 1: The consumption allocation table for 2006
Consumption expenditure (MEUR)Consumption purpose (COICOP Code)FoodNon-alcoholicbeveragesOthersTotalCPA CodeCommodity group01101201Products of agriculture and hunting13,2342210,97624,23202Products of forestry and logging0091991905Fish and other fishing products4370043710Coal and lignite; peat0053853811Crude petroleum and natural gas0016,81016,81012Uranium and thorium ores000013Metal ores000014Other mining and quarrying products8904213115.1 - 15.8Food products110,2556,7299,126126,11015.9Beverages711,06919,80230,87824Chemical products8016,99517,003Others001,071,8221,071,822Total124,03017,8201,147,0301,288,880Source: Destatis, authors calculations
Since the CATs published by Destatis distinguish 41 consumption purposes and 71 commodity groups, it is not sensible to reproduce the entire table in this article. REF _Ref277946122 \h Table 1 instead presents an aggregated version of the 2006 table which is sufficient for the purpose of illustrating the layout and some interesting features of a CAT.
The aggregated CAT shown in Table 1 reproduces the upper-left part of the full-scale CAT, including the first two COICOP categories (food and non-alcoholic beverages) and a number of CPA commodity groups. Like the familiar IOT, a CAT can be read column-wise or row-wise. Each column refers to a COICOP consumption purpose; each row refers to a CPA commodity group. The first column, for example, shows how the expenditure on the COICOP category food is allocated to the various CPA commodity groups. The bottom row states that consumers spent 124,030 MEUR on this purpose. Naturally, the major part of this (110,255 MEUR) was allocated to the CPA commodity group food products. However, a significant amount (13,234 MEUR) was allocated to products of agriculture and hunting. The difference is that products of agriculture and hunting refer to raw products such as potatoes and tomatoes, whereas food products are processed products such as potato chips and tomato ketchup. Further significant amounts were allocated to fish and fishing products (439 MEUR) and other mining and quarrying products (89 MEUR), and some smaller amounts were allocated to beverages (7 MEUR) and chemical products (8 MEUR). The entire expenditure on food is allocated to these six commodity groups, which means that the other 65 cells in the CATs column for food are equal to zero. In this respect, food is no exception most of the entries in the CAT are equal to zero. Out of the 2,911 cells in the full-scale CAT, only 220 contain nonzero entries. Thus, 92.4% of the CATs cells contain a value of zero.
REF _Ref277946122 \h Table 1 also shows that a CAT may contain some important information which may not be known to all input-output modellers. For example, in the absence of a CAT one might be tempted to allocate the entire expenditure on COICOP category non-alcoholic beverages to the CPA group beverages. According to REF _Ref277946122 \h Table 1, however, this would be a mistake. Only 62.1% of the entire expenditure is allocated this way; the remainder is allocated to food products. The reason for this is that certain products like fruit juice and milk are not assigned to CPA category 15.9 (which is titled beverages) they are assigned to categories 15.3 (processed and preserved fruit and vegetables) and 15.5 (dairy products and ice cream). Even if the analyst is aware of these peculiar rules, she cannot know for certain the share of these products in total expenditure. Therefore, a CAT is absolutely indispensable for models which combine household survey data and input-output data.
While the CAT itself is simply a collection of data, input-output modellers will mostly be interested in the bridge matrix that can be derived from it. Let each element EMBED Equation.3 of the bridge matrix EMBED Equation.3 be defined as
(1) EMBED Equation.3 ,
where EMBED Equation.3 represents element EMBED Equation.3 of the CAT EMBED Equation.3 and EMBED Equation.3 represents the total expenditure on COICOP consumption purpose EMBED Equation.3 . Then, EMBED Equation.3 is the share of EMBED Equation.3 that is allocated to CPA commodity group EMBED Equation.3 . If we know EMBED Equation.3 for all EMBED Equation.3 and EMBED Equation.3 , we can translate the information from the household survey into the CPA classification for use in an input-output model. For example, the data from Table 1 yields a value of 0.107 for EMBED Equation.3 . When translating COICOP into CPA, we would allocate 10.7% of food expenditure to products of agriculture and hunting.
However, the coefficients computed from Table 1 are valid only for the year 2006, the date of the corresponding CAT. In other years, the coefficients may take different values. The aim of this paper is to find out whether the coefficients are stable over time and how many of them are characterised by significant time trends. We begin, however, with a detailed analysis of the bridge matrix for 2006, because this will provide us with the detailed knowledge that is required to understand the intertemporal aspects later on.
The Bridge Matrix for 2006
As it would be impractical to reproduce the entire bridge matrix, which contains 71 rows and 41 columns, this section reports some descriptive statistics and summary measures of the bridge matrix for 2006.
Table SEQ Table \* ARABIC 2: Concentration of bridge matrix coefficients
Consumption purposeNumber ofnonzero entriesCumulative coefficentsCOICOPHeading1st2nd3rd4th5th011Food60.891.001.001.001.00012Non-alcoholic beverages30.621.001.001.001.00021Alcoholic beverages20.951.001.001.001.00022Tobacco21.001.001.001.001.00031Clothing70.810.970.991.001.00032Footwear40.961.001.001.001.00041Actual rentals for housing11.001.001.001.001.00042Imputed rentals for housing11.001.001.001.001.00043Maintenance and repair of the dwelling80.380.620.730.820.89044Water supply and miscellaneous services relating to the dwelling60.470.650.820.950.98045Electricity, gas and other fuels60.470.750.980.991.00051Furniture and furnishings, carpets and other floor coverings100.800.880.920.960.98052Household textiles30.990.991.001.001.00053Household appliances50.890.950.981.001.00054Glassware, tableware and household utensils80.250.490.720.930.96055Tools and equipment for house and garden100.440.770.880.920.95056Goods and services for routine household maintenance120.360.590.680.760.84061Medical products, appliances and equipment70.670.960.970.991.00062Out-patient services20.991.001.001.001.00063Hospital services11.001.001.001.001.00071Purchase of vehicles20.941.001.001.001.00072Operation of personal transport equipment160.540.800.850.890.92073Transport services50.360.680.880.951.00081Postal services11.001.001.001.001.00082Telephone and telefax equipment11.001.001.001.001.00083Telephone and telefax services11.001.001.001.001.00091Audio-visual, photographic and information processing equipment100.390.660.800.880.94092Other major durables for recreation and culture70.450.730.870.950.98093Other recreational items and equipment, gardens and pets150.400.700.830.880.91094Recreational and cultural services70.690.810.880.940.98095Newspapers, books and stationery110.800.900.930.950.97096Package holidays11.001.001.001.001.0010Education20.971.001.001.001.00111Catering services40.880.991.001.001.00112Accommodation services11.001.001.001.001.00121Personal care80.430.810.940.960.98123Personal effects n.e.c.90.470.740.920.950.97124Social protection30.971.001.001.001.00125Insurance11.001.001.001.001.00126Financial services n.e.c.30.900.981.001.001.00122, 127Other services n.e.c.80.380.580.730.860.96Source: authors calculations
REF _Ref279403980 \h Table 2 shows for each of the 41 consumption purposes the number of nonzero coefficients as well as the cumulative size of the fifth largest coefficients. For example, it states that five of the bridge matrix coefficients for transport services (COICOP code 073) are not equal to zero. Furthermore, it states that the largest coefficient is equal to 0.36, the sum of the two largest coefficients is equal to 0.68, the sum of the three largest coefficients is equal to 0.88, the sum of the four largest coefficients is equal to 0.95, and the sum of the five largest coefficients, naturally, is equal to 1.00.
According to REF _Ref279403980 \h Table 2, there are eight consumption purposes which have exactly one nonzero coefficient in the bridge matrix. In other words, these consumption purposes can be allocated to precisely one CPA category. If this were the case for all consumption purposes, the life of an input-output modeller would be a lot easier (but this paper would be a lot shorter). For these consumption purposes, one can safely assume intertemporal stability of the bridge matrix coefficients, because the structure of the CPA and COICOP classifications allows a uniquely determined allocation.
Some consumption purposes can be nearly, but not quite, uniquely allocated. For example, a share of 0.95 of expenditure on alcoholic beverages is allocated to one CPA category (beverages), and the remaining share of 0.05 is allocated to another CPA category (products of agriculture and hunting). The example of tobacco is even more striking: Almost all of this expenditure is allocated to tobacco products (CPA code 16), but a very small share (0.4 percent, to be precise) is allocated to articles of paper and paperboard (CPA code 21.2).
Other consumption purposes, by contrast, are much more heterogeneous. The category labelled furniture and furnishings, carpets and other floor coverings (COICOP code 051) includes a variety of different products, which means that the associated column of the bridge matrix contains 10 nonzero entries. However, the five largest coefficients taken together account for 98% of total expenditure in this category. This is more or less true for virtually all consumption purposes. The sum of the five largest coefficients is almost always close to one. This means that only a small number of the bridge matrix coefficients is truly relevant from a practical point of view.
Evolution of the Bridge Matrix Coefficients
In order to study the changes in the bridge matrix between 1991 and 2006, a two-step procedure is most enlightening. The first step consists of comparing results for 1991 and 2006; the second step traces some important developments over the entire period of observation.
The number of nonzero entries has changed. In 2006 there were 220 whereas in 1991 there were only 218. A closer inspection reveals that all the nonzero entries of 1991 where still larger than zero in 2006 and that two cells had, in addition, received nonzero values in the meantime. In quantitative terms, however, these two cells are negligible, and the difference may be due to rounding errors. This means that when we consider the evolution of the bridge matrix over the years, we are practically concerned with the evolution of 220 coefficients, because the other elements of the bridge matrix have always been equal to zero (allowing for rounding errors).
Figure SEQ Figure \* ARABIC 1: Evolution of coefficients for food (COICOP 011)
Source: authors calculations
In order to get a first glimpse at the evolution of bridge matrix coefficients, it is useful to look at some graphs. REF _Ref289670767 \h Figure 1 shows the evolution of the coefficients for food (COICOP 011). The largest coefficient, as evidenced by REF _Ref277946122 \h Table 1, is the one for food products (CPA 15.1-15.8). However, a glance at REF _Ref289670767 \h Figure 1 makes it clear that this coefficient was not constant over time. It started at a value of 0.900 in the table for 1991, then moved up to a peak value of 0.904 in 1993, and subsequently declined to a value of 0.888 in 2005, although in 2006 it had again increased to 0.889. In general, the figure suggests a downward trend in this coefficient. The opposite is true for the coefficient on products of agriculture and hunting (CPA 01), which grew from a value of 0.096 in 1991 to 0.107 in 2006. The coefficients on products of fishing (CPA 05) and other products of mining and quarrying (CPA 14) have also increased between 1991 and 2006. The coefficients of beverages (CPA 15.9) and chemical products (CPA 24 excl. 24.4) have moved up and down without any obvious trend.
Figure SEQ Figure \* ARABIC 2: Evolution of coefficients for transport services (COICOP 073)
Source: authors calculations
REF _Ref289676547 \h Figure 2 shows the evolution of the coefficients for transport services (COICOP 073). The visual representation suggests that there could be significant time trends. Most notably, the coefficient of air transport services (CPA 62) has increased from 0.24 to 0.36, whereas the coefficient of rail transport services (CPA 60.1) has decreased from 0.25 to 0.20 and that of other land transport services (CPA 60.2-60.3) has decreased from 0.40 to 0.32. This suggests that consumers preferences may have shifted from land transport to air transport or that relative prices have shifted in a way which increased the share of air transport in total transport service expenditure.
The visual representations in REF _Ref289670767 \h Figure 1 and REF _Ref289676547 \h Figure 2 make it possible to identify possible trends, but they do not permit statements on the statistical significance of those trends. Therefore, the next section will discuss the identification of significant trends by econometric means.
Identification of Trends
In order to estimate the extent and statist i c a l s i g n i f i c a n c e o f t i m e t r e n d s , o n e w o u l d h a v e t o e s t i m a t e t h e f o l l o w i n g e q u a t i o n f o r e a c h b r i d g e m a t r i x c o e f f i c i e n t :
( 2 ) E M B E D E q u a t i o n . 3 ,
w h e r e b i , j , t a r e t h e 7 1 b r i d g e m a t r i x c o e f f i c i e n t s f o r c o n s u m p t i o n p u r p o s e j o b s e r v e d i n y e a r t a n d i , j , t i s t h e e r r o r t e r m , w h i l e i , j a n d i , j a r e t h e c o e f f i c i e n t s t o b e e s t i m a t e d . T h e i n t e r p r e t a t i o n w o u l d b e t h a t i , j i s t h e i n t e r c e p t , i . e . t h e v a l u e o f b i , j t h a t w e w o u l d e x p e c t t o h a v e o b s e r v e d i n y e a r 0 i f i , j , 0 h a d b e e n e q u a l t o z e r o . T h a t i s , i , j w i l l g e n e r a l l y n o t b e e q u a l t o b i , j , 0 b e c a u s e i , j , 0 w a s p r o b a b l y n o t e q u a l t o z e r o .
T h e m o r e i n t e r e s t i n g c o e f f i c i e n t , h o w e v e r , i s i , j . T h i s i s t h e e s t i m a t e d e f f e c t o f t o n b i , j , t , i n o t h e r w o r d s t h e t i m e t r e n d i n w h i c h w e a r e i n t e r e s t e d . I f i t i s d i f f e r e n t from zero, we have a time trend. This will be the case quite frequently (basically, as soon as there is any change in bi,j,t over time). However, the interesting question is whether the time trend is statistically significant, i.e. significantly different from zero. The results of the econometric estimation can tell us whether this is the case.
However, it would have been quite bothersome to actually estimate an equation for each of the 2911 bridge matrix coefficients. Therefore, a slightly different specification was adopted:
(3) EMBED Equation.3 ,
where di,j is a set of 71 dummy variables for each commodity group. For EMBED Equation.3 , all dummies except d1,j are equal to zero, so (3) collapses to EMBED Equation.3 , which is of course exactly the same as equation (2). The adoption of (3) just made it easier to implement the estimations using the EViews software; it does not affect the interpretation of the results.
Table SEQ Table \* ARABIC 3: Estimation of time trends in the coefficients for food
Dependent Variable: S011Method: Panel Least SquaresDate: 07/02/10 Time: 11:34Sample: 1991 2006Periods included: 16Cross-sections included: 71Total panel (balanced) observations: 1136VariableCoefficientStd. Errort-StatisticProb.AGRIC0.0955250.000198482.47480.0000BEVERA5.28E-050.0001980.2665800.7898CHEMIC6.40E-050.0001980.3233630.7465FISH0.0030080.00019815.191020.0000FOOD0.9007620.0001984549.5300.0000MINQUA0.0005880.0001982.9685800.0031AGRIC_TREND0.0008742.25E-0538.841820.0000BEVERA_TREND4.10E-072.25E-050.0182350.9855CHEMIC_TREND1.24E-062.25E-050.0550820.9561FISH_TREND3.20E-052.25E-051.4233570.1549FOOD_TREND-0.0009172.25E-05-40.790670.0000MINQUA_TREND1.02E-052.25E-050.4521780.6512R-squared0.999987Mean dependent var0.014085Adjusted R-squared0.999985S.D. dependent var0.105891S.E. of regression0.000415Akaike info criterion-12.62157Sum squared resid0.000171Schwarz criterion-11.99216Log likelihood7311.053Hannan-Quinn criter.-12.38384Durbin-Watson stat1.005740Source: authors calculations
REF _Ref289415406 \h Table 3 shows the results of this estimation for the consumption purpose food (COICOP 011). As shown in REF _Ref277946122 \h Table 1 and REF _Ref279403980 \h Table 2, there are six nonzero coefficients. The largest is of course the coefficient on food products (FOOD, CPA 15.1-15.8) . T h e e s t i m a t e d i n t e r c e p t ( ) i s 0 . 9 0 , w h i c h m e a n s t h a t t h e s h a r e o f f o o d p r o d u c t s i n t o t a l c o n s u m p t i o n e x p e n d i t u r e f o r f o o d w o u l d h a v e b e e n e x a c t l y 9 0 p e r c e n t i n 1 9 9 1 i f t h e e r r o r t e r m h a d b e e n e q u a l t o z e r o . T h e s e c o n d l a r g e s t c o e f f i c i e n t i s t h a t o n p roducts of agriculture and hunting (AGRIC, CPA 01), which amounts to 9.6 percent. The other coefficients are relatively small.
Concerning the time trends, REF _Ref289415406 \h Table 3 allows for some interesting observations. With regard to AGRIC and FOOD, we can observe highly significant time trends with very low p-values. The time trend of AGRIC is positive, while that of FOOD is negative. In other words, consumers seem to have substituted products of agriculture and hunting for (processed) food products. This might reflect changed attitudes toward healthy diets, for example buying fresh vegetables on the market to prepare a real meal rather than buying convenience food and simply putting it into the microwave oven. However, it should be noted that the trend, though significant, is very small. All else being equal, the share of AGRIC in food expenditure rises by a mere 0.09 percentage points per year, while that of FOOD falls by a similar magnitude. Thus, we have here an example of a significant time trend, but since its magnitude is so small, its inclusion in a model may not be strictly necessary. The other time trends are statistically not significant. Thus, with respect to food expenditure, it may be permissible to assume constant bridge matrix coefficients.
Table SEQ Table \* ARABIC 4: Estimation of time trends in the coefficients for transport services
Dependent Variable: S073Method: Panel Least SquaresDate: 07/02/10 Time: 14:20Sample: 1991 2006Periods included: 16Cross-sections included: 71Total panel (balanced) observations: 1136VariableCoefficientStd. Errort-StatisticProb.AIRTRA0.2685850.001130237.73830.0000LANTRA0.3958510.001130350.38780.0000RAITRA0.2381210.001130210.77320.0000SUPTRA0.0769000.00113068.068120.0000WATTRA0.0205420.00113018.182840.0000AIRTRA_TREND0.0055670.00012843.378420.0000LANTRA_TREND-0.0045020.000128-35.084250.0000RAITRA_TREND-0.0019570.000128-15.246500.0000SUPTRA_TREND-0.0006120.000128-4.7709550.0000WATTRA_TREND0.0015040.00012811.723290.0000R-squared0.998717Mean dependent var0.014085Adjusted R-squared0.998535S.D. dependent var0.061817S.E. of regression0.002366Akaike info criterion-9.138502Sum squared resid0.005566Schwarz criterion-8.509093Log likelihood5332.669Hannan-Quinn criter.-8.900768Durbin-Watson stat1.337091Source: authors calculations
REF _Ref289421679 \h Table 4, by contrast, shows a case where time trends are not only statistically significant but also of considerable magnitude. It refers to the consumption purpose transport services, which is characterised by five nonzero coefficients in the bridge matrix: for air transport (AIRTRA), transport by rail (RAITRA), land transport other than rail (LANTRA), water transport (WATTRA), and supporting services (SUPTRA, e.g. travel agencies). Interestingly, all of these coefficients exhibit statistically significant time trends. The time trend of air transport is estimated to be 0.005567, which means that the share of air transport in total expenditure on transport services rises by 0.56 percentage points per year. Conversely, the time trends for land transport are negative. The share of rail transport falls by 0.20 percentage points per year, while that of land transport other than rail falls by 0.45 percentage points per year. These time trends can have a significant influence on model results over a period of, say, ten or twenty years. If we were to construct a model that does not take them into account, we might seriously underestimate the future demand for air travel and overestimate the future demand for land travel. The other time trends (on SUPTRA and WATTRA), are also statistically significant.
Conclusion
The results presented above clearly indicate that the conversion coefficients between CPA and COICOP may be subject to statistically significant trends. A very interesting example is the case of transport services, where the share of air transport has significantly increased at the expense of land transport over the time period between 1991 and 2006. The presence of such trends means that models which use a bridge matrix to convert data from COICOP into CPA (and vice versa) might produce misleading results if the trends in the conversion coefficients are not taken into account.
The present study, still being at an early working paper stage, has not dealt with the question how trends in the conversion coefficients can be captured in a model. As a first step, it might be a good idea to identify time trends econometrically (as in section 5) and extrapolate the trends into the future. However, a simple extrapolation ignores the fact that changes in conversion coefficients can be driven by various factors which may persist in the future or not. As a next step, it would be good idea to look at the influence of price changes on conversion coefficients and to model them explicitly.
References
ADDIN EN.REFLIST Alcal, R., G. Antille and E. Fontela (1999). 'Technical Change in the Private Consumption Converter', Economic Systems Research, vol. 11(4), pp. 389-400.
Dietzenbacher, E. and A. R. Hoen (2006). 'Coefficient stability and predictability in input-output models: a comparative analysis for the Netherlands', Construction Management and Economics, vol. 24(7), pp. 671-680.
Druckman, A. and T. Jackson (2010). 'The bare necessities: How much household carbon do we really need?', Ecological Economics, vol. 69(9), pp. 1794-1804.
Gaiha, R. (1980). 'On testing the stability of input-output relationships in the Indian economy', Journal of Development Economics, vol. 7(2), pp. 273-282.
Kronenberg, T. (2009). 'The impact of demographic change on energy use and greenhouse gas emissions in Germany', Ecological Economics, vol. 68(10), pp. 26372645.
Kronenberg, T. (2010). 'Erstellung einer Input-Output-Tabelle fr Mecklenburg-Vorpommern', AStA Wirtschafts- und Sozialstatistisches Archiv, vol. 4(3), pp. 223-248.
Mongelli, I., F. Neuwahl and J. M. Rueda-Cantuche (2010). 'Integrating a Household Demand System in the Input-Output Framework. Methodological Aspects and Modelling Implications', Economic Systems Research, vol. 22(3), pp. 201-222.
Sevaldson, P. (1969). 'The stability of input-output coefficients', in (Carter, A. P. and A. Brody Eds.), Applications of Input-Output Analysis, Amsterdam and London: North-Holland Publishing Company.
Washizu, A. and S. Nakano (2010). 'On the environmental impact of consumer lifestyles - using a Japanese environmental input-output table and the linear expenditure system demand function', Economic Systems Research, vol. 22(2), pp. 181-192.
Appendix
Table SEQ Table \* ARABIC 5: Commodity classification
No.CodeFull nameCPA1AGRICProducts of agriculture, hunting and related services012AIRTRAAir transport services623ARTPAPArticles of paper and paperboard21.24BASFERBasic ferrous metals27.1. - 27.35BASPREBasic precious metals and other non-ferrous metals 27.46BEVERABeverages15.97BUILDIBuilding installation, completion and other construction services45.3 - 45.58CERAMIOther non-metallic mineral products26.2 - 26.89CHEMICChemical products excl. pharmaceutical products24 (excl. 24.4)10CLOTHIWearing apparel; furs1811COALCoal and lignite; peat1012COMPUTComputer and related services7213COMSOCCompulsory social security services75.314EDUCATEducation services8015ELECTRElectricity, steam and hot water40.1, 40.316ELEMACElectrical machinery and apparatus n.e.c.3117FABMETFabricated metal products, except machinery and equipment2818FININTFinancial intermediation services, except insurance and pension funding services6519FISHFish and other fishing products; services incidental of fishing0520FOODFood products15.1 - 15.821FORESTProducts of forestry, logging and related services0222FOUNDRYFoundry work services27.523FURNITFurniture; other manufactured goods n.e.c.3624GASESGas40.225GLASSGlass and glass products26.126HEALSOCHealth and social work services8527HOTRESHotel and restaurant services5528HOUSERPrivate households with employed persons9529INSPENInsurance and pension funding services, except compulsory social security services6630LANTRAOther land transportation services60.2 - 60.331LEATHELeather and leather products1932MACHINMachinery and equipment n.e.c.2933MEDPREMedical, precision and optical instruments, watches and clocks3334MEMORGMembership organisation services n.e.c.9135METOREMetal ores1336MINQUAOther mining and quarrying products1437MOTVEHMotor vehicles, trailers and semi-trailers3438OFFMACOffice machinery and computers3039OILGASCrude petroleum and natural gas; services incidental to oil and gas extraction excluding surveying1140OTHBUSOther business services7441OTHSEROther services9342OTHTRAOther transport equipment3543PHARMAPharmaceutical products24.444PLASTIPlastic products25.245POSTELPost and telecommunication services6446PRIMEDPrinted media22.147PRIRECPrinting services and recorded media22.2 - 22.348PUBADMPublic administration and defence75.1 - 75.249PULPAPPulp, paper and paperboard21.150RAITRARailway transportation services60.151RANDDResearch and development services7352REALESReal estate services7053RECCULRecreational, cultural and sporting services9254REFPETCoke, refined petroleum products and nuclear fuels2355RENTINRenting services of machinery and equipment without operator and of personal and household goods7156RETTRARetail trade services, except of motor vehicles and motorcycles; repair services of personal and household goods5257RTVCOMRadio, television and communication equipment and apparatus3258RUBBERRubber products25.159SATFINServices auxiliary to financial intermediation6760SECRAWSecondary raw materials3761SEWWASSewage and refuse disposal services, sanitation and similar services9062SITPRESite preparation, construction, civil engineering45.1 - 45.263SUPTRASupporting and auxiliary transport services; travel agency services6364TEXTILTextiles1765TOBACCTobacco products1666TRAMOTTrade, maintenance and repair services of motor vehicles and motorcycles; retail sale of automotive fuel5067URANUranium and thorium ores1268WATERWater4169WATTRAWater transport services6170WHOTRAWholesale trade and commission trade services, except of motor vehicles and motorcycles5171WOODWood and products of wood and cork (except furniture); articles of straw and plaiting materials20
Table SEQ Table \* ARABIC 6: Consumption purpose classification
No.COICOPDescription1011Food2012Non-alcoholic beverages3021Alcoholic beverages4022Tobacco5031Clothing6032Footwear7041Actual rentals for housing8042Imputed rentals for housing9043Maintenance and repair of the dwelling10044Water supply and miscellaneous services relating to the dwelling11045Electricity, gas and other fuels12051Furniture and furnishings, carpets and other floor coverings13052Household textiles14053Household appliances15054Glassware, tableware and household utensils16055Tools and equipment for house and garden17056Goods and services for routine household maintenance18061Medical products, appliances and equipment19062Out-patient services20063Hospital services21071Purchase of vehicles22072Operation of personal transport equipment23073Transport services24081Postal services25082Telephone and telefax equipment26083Telephone and telefax services27091Audio-visual, photographic and information processing equipment28092Other major durables for recreation and culture29093Other recreational items and equipment, gardens and pets30094Recreational and cultural services31095Newspapers, books and stationery32096Package holidays3310Education34111Catering services35112Accommodation services36121Personal care37123Personal effects n.e.c.38124Social protection39125Insurance40126Financial services n.e.c.41122, 127Other services n.e.c.
Forschungszentrum Jlich, D-52425 Jlich, Germany. Tel.: 02461-61-1721. E-mail: HYPERLINK "mailto:t.kronenberg@fz-juelich.de" t.kronenberg@fz-juelich.de
This would be mostly salt.
It should be noted, however, that the entries in the CATs > P Q S T \ ] )
7
0 1
k
w
z
{
|
}
øti^ h/) hj mH sH h/) hu mH sH h/) hCB mH sH h/) h+h mH sH h/) hd NH mH sH h/) h mH sH h/) hd mH sH h/) hV mH sH h/) h mH sH h/) h{ mH sH h/) h
* mH sH !j h/) h1W 0J UmH sH h/) h% mH sH h/) h^t~ mH sH " ? R S T ]
j
l
m
w
{
|
}
R !
f#
*$gdk_ - *$gd>+ *$gd>+ , *$gd>+ * *$gd>+ ( *$gd>+ $*$a$gd>+ }
ʶoQoB. &j h>+ h 5UmH nH u h>+ h 5mH nH u;h>+ h 56CJ OJ QJ \]aJ mH nH sH tH u"h>+ h 0J 5mH nH sH u -j h>+ h 0J 5UmH nH uh>+ h 5mH nH u h>+ h 0J 5mH nH u 'j h>+ h 0J 5UmH nH uh mH nH uh/) hVv mH sH j h/) hVv UmH sH h/) mH sH h/) h/) mH sH
0 1 2 L ŹťwiwR@@ "h>+ h 0J 5mH nH sH u -j h>+ h 0J 5UmH nH uh>+ h 5mH nH u h>+ h 0J 5mH nH u ;h>+ h 56CJ OJ QJ \]aJ mH nH sH tH u'j h>+ h 0J 5UmH nH uhnj 5mH nH u&j h>+ h 5UmH nH u ,j} h>+ h 5UmH nH u h>+ h 5mH nH u L M N O P Q R S T p q r s t u յybPPAA h>+ h 5mH nH u"h>+ h 0J 5mH nH sH u -j h>+ h 0J 5UmH nH uh>+ h 5mH nH u h>+ h 0J 5mH nH u ;h>+ h 56CJ OJ QJ \]aJ mH nH sH tH u'j h>+ h 0J 5UmH nH uhnj 5mH nH u&j h>+ h 5UmH nH u ,jw h>+ h 5UmH nH u յybPPAA h>+ h 5mH nH u"h>+ h 0J 5mH nH sH u -j h>+ h 0J 5UmH nH uh>+ h 5mH nH u h>+ h 0J 5mH nH u ;h>+ h 56CJ OJ QJ \]aJ mH nH sH tH u'j h>+ h 0J 5UmH nH uhnj 5mH nH u&j h>+ h 5UmH nH u ,jq h>+ h 5UmH nH u ! " # ? @ A B C D \ ] ^ x յybPPAA h>+ h 5mH nH u"h>+ h 0J 5mH nH sH u -j h>+ h 0J 5UmH nH uh>+ h 5mH nH u h>+ h 0J 5mH nH u ;h>+ h 56CJ OJ QJ \]aJ mH nH sH tH u'j h>+ h 0J 5UmH nH uhnj 5mH nH u&j h>+ h 5UmH nH u ,jk h>+ h 5UmH nH ux y z { | } ~ յybPPAA h>+ h 5mH nH u"h>+ h 0J 5mH nH sH u -j h>+ h 0J 5UmH nH uh>+ h 5mH nH u h>+ h 0J 5mH nH u ;h>+ h 56CJ OJ QJ \]aJ mH nH sH tH u'j h>+ h 0J 5UmH nH uhnj 5mH nH u&j h>+ h 5UmH nH u ,je h>+ h 5UmH nH u! ~ h j r + & l *$gd>+
%
f#
*$gd>+ - *$gd>+ *$gd>+
f#
*$gdk_
f#
*$gdk_ յybPAA h>+ h 5mH nH u"h>+ h 0J 5mH nH sH u -j h>+ h 0J 5UmH nH uh>+ h 5mH nH u h>+ h 0J 5mH nH u ;h>+ h 56CJ OJ QJ \]aJ mH nH sH tH u'j h>+ h 0J 5UmH nH uhnj 5mH nH u&j h>+ h 5UmH nH u ,j_ h>+ h 5UmH nH u : ; < = E F G a յybPAA h>+ h 5mH nH u"h>+ h 0J 5mH nH sH u -j h>+ h 0J 5UmH nH uh>+ h 5mH nH u h>+ h 0J 5mH nH u ;h>+ h 56CJ OJ QJ \]aJ mH nH sH tH u'j h>+ h 0J 5UmH nH uhnj 5mH nH u&j h>+ h 5UmH nH u ,jY h>+ h 5UmH nH ua b c e f g h i j p q r s յung`I6I $h>+ h]=# CJ OJ QJ aJ mH sH -j h>+ h]=# CJ OJ QJ UaJ mH sH hW: hSW hW: hW: hW: h/) h/) h;b OJ QJ mH sH %j h/) hVv OJ QJ UmH sH ;h>+ h 56CJ OJ QJ \]aJ mH nH sH tH u'j h>+ h 0J 5UmH nH uhnj 5mH nH u&j h>+ h 5UmH nH u ,jS h>+ h 5UmH nH u שeHe5e $hnj CJ OJ QJ aJ mH nH u 9jM h>+ h]=# CJ OJ QJ UaJ mH nH u3j h>+ h]=# CJ OJ QJ UaJ mH nH u*h>+ h]=# CJ OJ QJ aJ mH nH u 'h>+ h]=# 0J CJ aJ mH nH sH u2j h>+ h]=# 0J CJ UaJ mH nH u 'h>+ h]=# CJ OJ QJ aJ mH nH u#h>+ h]=# 0J CJ aJ mH nH u,j h>+ h]=# 0J CJ UaJ mH nH u
' ( ) * s t u ͻycIc,I 9jG h>+ h]=# CJ OJ QJ UaJ mH nH u3j h>+ h]=# CJ OJ QJ UaJ mH nH u*h>+ h]=# CJ OJ QJ aJ mH nH u 'h>+ h]=# 0J CJ aJ mH nH sH u2j h>+ h]=# 0J CJ UaJ mH nH u 'h>+ h]=# CJ OJ QJ aJ mH nH u#h>+ h]=# 0J CJ aJ mH nH u,j h>+ h]=# 0J CJ UaJ mH nH u 5h>+ h]=# 6CJ OJ QJ ]aJ mH nH sH tH u
Ӽ}yfWf@. #h>+ h 0J CJ aJ mH nH u,j h>+ h 0J CJ UaJ mH nH u h>+ hW: CJ OJ QJ aJ %j h>+ hW: CJ OJ QJ UaJ h. hW: h/) hW: hr h/) h;b j h>+ h]=# UmH sH 5h>+ h]=# 6CJ OJ QJ ]aJ mH nH sH tH u,j h>+ h]=# 0J CJ UaJ mH nH u 3j h>+ h]=# CJ OJ QJ UaJ mH nH u$hnj CJ OJ QJ aJ mH nH u
% & ' ( ) * ٿ~d~Gd4d $hnj CJ OJ QJ aJ mH nH u 9jA
h>+ h CJ OJ QJ UaJ mH nH u3j h>+ h CJ OJ QJ UaJ mH nH u*h>+ h CJ OJ QJ aJ mH nH u 'h>+ h 0J CJ aJ mH nH sH u,j h>+ h 0J CJ UaJ mH nH u 2j h>+ h 0J CJ UaJ mH nH u #h>+ h 0J CJ aJ mH nH u'h>+ h CJ OJ QJ aJ mH nH u
* + , - I J K L ͻycIc,I 9j; h>+ h CJ OJ QJ UaJ mH nH u3j h>+ h CJ OJ QJ UaJ mH nH u*h>+ h CJ OJ QJ aJ mH nH u 'h>+ h 0J CJ aJ mH nH sH u2j
h>+ h 0J CJ UaJ mH nH u 'h>+ h CJ OJ QJ aJ mH nH u#h>+ h 0J CJ aJ mH nH u,j h>+ h 0J CJ UaJ mH nH u 5h>+ h 6CJ OJ QJ ]aJ mH nH sH tH u
Ӽ{aM77 *h>+ h CJ OJ QJ aJ mH nH u 'h>+ h 0J CJ aJ mH nH sH u2j h>+ h 0J CJ UaJ mH nH u 'h>+ h CJ OJ QJ aJ mH nH u#h>+ h 0J CJ aJ mH nH u5h>+ h 6CJ OJ QJ ]aJ mH nH sH tH u,j h>+ h 0J CJ UaJ mH nH u 3j h>+ h CJ OJ QJ UaJ mH nH u$hnj CJ OJ QJ aJ mH nH u ! " # $ % & ' ( D E F G ȵȞq]qC/ 'h>+ h 0J CJ aJ mH nH sH u2j h>+ h 0J CJ UaJ mH nH u 'h>+ h CJ OJ QJ aJ mH nH u#h>+ h 0J CJ aJ mH nH u5h>+ h 6CJ OJ QJ ]aJ mH nH sH tH u,j h>+ h 0J CJ UaJ mH nH u $hnj CJ OJ QJ aJ mH nH u 3j h>+ h CJ OJ QJ UaJ mH nH u9j5 h>+ h CJ OJ QJ UaJ mH nH u
РЉn\H\.\ 2j
h>+ h 0J CJ UaJ mH nH u 'h>+ h CJ OJ QJ aJ mH nH u#h>+ h 0J CJ aJ mH nH u5h>+ h 6CJ OJ QJ ]aJ mH nH sH tH u,j h>+ h 0J CJ UaJ mH nH u $hnj CJ OJ QJ aJ mH nH u 9j/
h>+ h CJ OJ QJ UaJ mH nH u3j h>+ h CJ OJ QJ UaJ mH nH u*h>+ h CJ OJ QJ aJ mH nH u < = > ? j k l ϲm[G[-[ 2j h>+ h 0J CJ UaJ mH nH u 'h>+ h CJ OJ QJ aJ mH nH u#h>+ h 0J CJ aJ mH nH u5h>+ h 6CJ OJ QJ ]aJ mH nH sH tH u,j h>+ h 0J CJ UaJ mH nH u $hnj CJ OJ QJ aJ mH nH u 9j) h>+ h CJ OJ QJ UaJ mH nH u*h>+ h CJ OJ QJ aJ mH nH u 3j h>+ h CJ OJ QJ UaJ mH nH u l . 1 ͳnc\QFQ9Q.Q9 h/) hq mH sH h/) hf NH mH sH h/) hx| mH sH h/) hf mH sH h/) hyU j h>+ hW: U5h>+ h 6CJ OJ QJ ]aJ mH nH sH tH u,j h>+ h 0J CJ UaJ mH nH u $hnj CJ OJ QJ aJ mH nH u 3j h>+ h CJ OJ QJ UaJ mH nH u9j# h>+ h CJ OJ QJ UaJ mH nH u*h>+ h CJ OJ QJ aJ mH nH u \ ] e f k l , - 2 @ M h # # # # $ $ $ $ $ $ $ R$ ~k~~ $j h"_ UmH nH sH u h"_ mH nH sH uj h"_ UmH nH sH u h"b mH nH sH uh"b mH sH j h
i UmH sH hdU mH sH h
i mH sH h' h' 6mH sH h' mH sH h/) hf 6mH sH h/) hf NH mH sH h/) hf mH sH $R$ S$ T$ X$ Y$ Z$ [$ \$ o$ p$ q$ ' ' ' ' ( ( ( ( ( ( ( 3( 4( E+ F+ G+ H+ {+ |+ }+ + + + + + + / / / / ǻyf$j h"_ UmH nH sH u $j h"_ UmH nH sH u hw mH nH sH uh"b mH sH j hw UmH sH hw mH sH h
i mH sH j h
i UmH sH h"b mH nH sH uh"_ mH nH sH uj h"_ UmH nH sH u $j h"_ UmH nH sH u(/ L/ M/ N/ R/ S/ T/ U/ V/ W/ 0 j2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 ƺvnbnSbvH h-q mH nH sH uj h-q UmH sH j h-q UmH sH h-q mH sH j h"b UmH sH h"b mH sH h
i mH sH hW: mH sH hGV mH sH hZd{ mH sH h' mH sH hw mH sH j hw UmH sH hw mH nH sH uj h"_ UmH nH sH u $jl h"_ UmH nH sH u h"_ mH nH sH u W/ 2 \; = = A F PF oF F $$$*$If a$gd>+ $$*$If gd>+ $ *$gd>+ $
B Pd, hx *$^`Pa$gd>+ *$gd>+
3 3 3 4 4 4 4 74 84 94 D4 E4 G4 H4 |4 }4 ~4 4 4 4 4 4 4 4 4 4 4
5 5 :8 ;8 <8 =8 n8 ҴҡǕ}uiui j h"_ UmH sH h"_ mH sH hV, mH sH h3/ mH sH hW: mH sH j h"b UmH sH $j h"_ UmH nH sH u $j& h"_ UmH nH sH u h-q mH nH sH uh"_ mH nH sH uj h"_ UmH nH sH u $j h"_ UmH nH sH u!n8 o8 p8 t8 u8 v8 w8 9 9 ,9 N9 \9 9 9 9 9 b: : B; C; ; ; ; ; <