Journal of Economic Structures

The Official Journal of the Pan-Pacific Association of Input-Output Studies (PAPAIOS)

Key Sectors of the Namibian Economy

  • Michael N Humavindu1, 3 and

    Affiliated with

    • Jesper Stage2Email author

      Affiliated with

      Journal of Economic StructuresThe Official Journal of the Pan-Pacific Association of Input-Output Studies (PAPAIOS)20132:1

      DOI: 10.1186/2193-2409-2-1

      Received: 26 March 2012

      Accepted: 10 December 2012

      Published: 4 January 2013

      Abstract

      The present paper presents key sector research for the Namibian economy, based on input–output and Social Accounting Matrix (SAM) analyzes. The analyses were derived from a Namibian SAM for the 2004 period, using 28 economic sectors. We find that mining and government services are currently key sectors. Some manufacturing and services sectors have important linkages in terms of output effects, whilst for employment and income effects, the agriculture sector is paramount. The results obtained are useful for policy purposes in terms of identifying those sectors where interventions are likely to have the greatest impact on the Namibian economy.

      JEL Classification:C67, L16, O21, O55.

      1 Introduction

      The purpose of this paper is to determine the key productive sectors for the Namibian economy. The principal concern with a key sector analysis is the identification of economic activities that exhibit the largest amount of interdependence with the rest of the economy. Such interdependence is usually measured through either backward or forward linkages. Backward linkages pertain to the dependence of a given economic activity on inputs produced from other activities, whilst forward linkages relate to a given economic sector’s role in supplying inputs to other sectors.

      The overall concern with the identification of key sectors is their usefulness in economic development strategy. Since key sectors have high backward and forward linkages with the rest of the economy, investment in these sectors is expected to enhance economic development prospects [6, 7, 14].

      Despite the usefulness of identifying key sectors, especially for development planning, key sector analysis has not been widely used in developing countries in recent years. Indeed, most recent studies have been in developed countries. Part of the reason for this low level of use is perhaps the considerable data requirements: even a basic key sector analysis requires an input–output table, which is only compiled every ten years or so (if at all) by most developing countries. In addition, more extensive analyzes such as the one presented here require employment data, which are often lacking in developing countries. Moreover, many developing countries are capital scarce and cannot easily support investment in key sectors even if such sectors are identified, making them less interesting from a policy perspective. However, key sector analysis remains a useful tool in those countries where the necessary data and the necessary funding are available. This study presents the first set of key sector analyzes for the Namibian economy.

      Namibia is located in southern Africa. It has 2.1 million inhabitants and a gross domestic product (GDP) of approximately US$12.5 billion, with per capita annual income registered at almost US$6,000. It is classified as a lower-middle-income country [2, 17]. Yet Namibia has one of the most unequal income distributions on the African continent, with a Gini coefficient of 0.63. Unemployment (estimated at 36.7 % and 52 % of the labor force in 2004 and 2008, respectively), poverty (56 % of the population live on less than US$2 a day) and household food security are major challenges faced by the country. The Namibian economy is dualistic in character as it comprises a modern market sector based on capital-intensive industry and farming, producing most of the country’s wealth, and a traditional subsistence farming sector.

      The Namibian economy has a high degree of openness as the sum of exports and imports equates to more than 90 % of GDP. Most raw material commodities are exported in unprocessed or semi-processed form, and many consumer goods are imported. Agriculture has a small contribution to GDP (around 5 %), but it employs about 30 % of the total labor force. The largest part of the economic contribution from agriculture is from relatively large, commercial farms, but traditional subsistence farming remains crucial for supporting a large share of the population. About 70 % of the population depend directly or indirectly on agriculture for their livelihood.

      An important structural feature of the economy is the positive current account balance offset by a deficit on the capital and financial account. This reflects a chronic excess of savings over investment in the economy, thereby making Namibia a net exporter of capital. This means that, unlike the situation in many other developing countries, Namibia is not capital-scarce per se; if interesting investment opportunities are available, the country has funding available through its own domestic savings. This means that there is scope for policies to support the development of key sectors once these have been identified.

      Namibia’s new development policy frameworks (the Industrial Policy 2012 and the Fourth National Development Plan) are premised on a targeted sectoral approach. Unlike in the past, where the government attempted to develop all sectors, sector identification and selection is now paramount. The sectors selected for the new growth strategy are manufacturing, transport, logistics and mineral processing. These are perceived to be sectors in which the country has a comparative advantage as well as growth potential. The selection of sectors for development also has a direct bearing on the deployment or direction of flow of instruments such as economic incentives as well as government research and development (R&D). The country is also busy finalizing an Investment Bill that aims to help attract both foreign and domestic investment in key economic sectors. However, these sectors were mainly singled out as important for economic development based on consultations with stakeholders; no major assessment has been undertaken thus far in terms of a key sector analysis. Thus, an analytical exercise in identifying key sectors for the Namibian economy could help ensure that the new development approach to be adopted is grounded in economic reality.

      2 Methodology

      Key sector analysis of linkages in the economy began in the late 1950s, with seminal contributions by Nørregaard Rasmussen [16], Chenery and Watanabe [3], Hirschman [7], Augustinovics [1], Laumas [911], and Lenzen [12], among others. By way of an input–output table, backward linkages can be identified using a standard Leontief inverse [13] while forward linkages can be identified using a Ghosh inverse [5] or, alternatively, using the Leontief inverse as well. There is some debate among practitioners about which approach to use for forward linkages (see e.g. [4, 12, 1820]). Lenzen [12] provides a useful overview of the pros and cons of the various approaches; we follow the approach that Lenzen actually uses in that paper for his own analysis, but note that his discussion can also be interpreted in favor of using other approaches.

      In this study, we use a 28-sector input–output table developed from a recent social accounting matrix (SAM; see the discussion in Sect. 3, “Data”, below). We use the Z matrix, showing those monetary flows between sectors that are considered endogenous to the model, to determine the Leontief matrix of input coefficients A, given by A i j = Z i j / X i http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq1_HTML.gif, where X i http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq2_HTML.gif is the total expenditure of sector i, Z i j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq3_HTML.gif is its spending on inputs from sector j, and A i j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq4_HTML.gif is spending on inputs from sector j as a share of its overall expenditure.

      We then determine the Leontief inverse B = [ I A ] 1 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq5_HTML.gif, which gives the backward and forward linkages from different sectors in the economy (I is the identity matrix). The average backward multiplier of sector j is given by B j = i b i j / n http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq6_HTML.gif, where n is the number of sectors. We normalize the backward multipliers by dividing the multiplier of each sector j by the average multiplier for all sectors in the economy, B ¯ = i , j b i j / n 2 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq7_HTML.gif, in order to get B j N = B j / B ¯ http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq8_HTML.gif. In similar fashion, we calculate average forward multipliers as B i = j b i j / n http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq9_HTML.gif and normalized forward multipliers as B i N = B i / B ¯ http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq10_HTML.gif. Sectors with B j N > 1 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq11_HTML.gif have higher-than-average backward linkages, and sectors with B i N > 1 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq12_HTML.gif have higher-than-average forward linkages. Sectors for which both these indicators are greater than 1 are referred to as key sectors: they have higher-than-average linkages both backward and forward, and thus have greater effects on the rest of the economy than most other sectors.

      However, it is also of interest to know whether or not these effects on the surrounding economy are widely dispersed among other sectors. If the effects are concentrated in one or a few sectors, there is a risk that bottlenecks in those sectors might reduce the impact of such effects, so that changes in the key sectors do not have the anticipated overall effect on the economy. Lenzen [12] discusses a case where a sector delivers a large share of some other sector’s overall inputs and is, therefore, identified as a key sector, even though it has no linkages to other sectors in the economy. In order to assess the degree to which multiplier effects are dispersed among other sectors, one can calculate the backward and forward coefficients of variation, defined as V j = 1 n 1 i ( b i j B j ) 2 / B j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq13_HTML.gif and V i = 1 n 1 j ( b i j B i ) 2 / B i http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq14_HTML.gif. These measure the degrees of sectoral skewness in input procurement and output delivery, respectively; the lower these coefficients are for a specific sector, the more evenly that sector’s input purchases and output sales are dispersed among the different sectors of the economy. We can normalize these coefficients by dividing by the economy-wide averages and calculating V j N = n V j / k V k http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq15_HTML.gif and V i N = n V i / k V k http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq16_HTML.gif. If a sector has normalized coefficients that are lower than 1, it means that its backward and forward linkages, respectively, are more widely dispersed in the economy than those that pertain on average. High values, on the other hand, indicate that the sector interacts with only a few other sectors in the economy.

      Thus, key sectors with widely dispersed effects are those with higher-than-average forward and backward linkages which are also dispersed more widely than average. Rueda-Cantuche et al. [21] provide a useful means of visualizing the different possible outcomes from a key sector analysis (Table 1). The upper left corner of Table 1 contains key sectors with widely dispersed backward and forward linkages throughout the rest of the economy. Moving downward in the table, we find sectors with less widely dispersed backward linkage effects on the rest of the economy and, at the bottom, sectors with no or limited overall backward impacts. Similarly, moving to the right, we first find sectors with less widely dispersed forward linkage effects, and then sectors with no (or limited) forward linkage effects. Notably, these definitions identify sectors with higher- or lower-than-average linkages and diffusion. In a highly trade-dependent economy such as Namibia’s, where many of the linkages are to foreign trade rather than to domestic firms, even sectors with higher-than-average linkages may have relatively limited impacts compared with their counterparts in other, less trade-dependent countries.
      Table 1

      Identification of key sectors

       

      Strong forward linkages

      B i N > 1 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq17_HTML.gif

      Limited forward linkages

      B i N < 1 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq18_HTML.gif

      Dispersed forward linkages

      V i N < 1 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq19_HTML.gif

      Concentrated forward linkages

      V i N > 1 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq20_HTML.gif

      Strong backward linkages

      B j N > 1 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq11_HTML.gif

      Dispersed backward linkages

      V j N < 1 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq21_HTML.gif

      Key sectors with widely dispersed effects in the economy

      Key sectors but with forward linkages concentrated

      Sectors with strong, widely dispersed backward linkages but with weak forward linkages

      Concentrated backward linkages

      V j N > 1 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq22_HTML.gif

      Key sectors but with backward linkages concentrated

      Key sectors without widely dispersed linkages

      Sectors with strong but concentrated backward linkages and with weak forward linkages

      Limited backward linkages

      B j N < 1 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq23_HTML.gif

      Sectors with strong, widely dispersed forward linkages but with weak backward linkages

      Sectors with strong but concentrated forward linkages and with weak backward linkages

      Sectors with weak linkages

      In order to provide a picture of the current state of the economy, we also weight the coefficients in the Leontief inverse, based on their current shares σ i http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq24_HTML.gif and δ j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq25_HTML.gif of overall factor income and net final demand, respectively. This allows us to determine weighted backward and forward linkages B j δ = i b i j δ j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq26_HTML.gif and B i σ = j σ i b i j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq27_HTML.gif. This weighting by sectoral size shows the current overall importance of different sectors in terms of providing inputs and/or outputs to other sectors, as opposed to the importance of a marginal change in a sector shown by the unweighted analysis.

      Given the highly unequal distribution of income and high unemployment in Namibia, it is also of interest to examine whether the forward and backward linkage effects are different when one considers effects on employment or on labor income rather than on output per se. In order to study this, the sectors—in both the size-unweighted and -weighted cases—were weighted using two sets of coefficients q i http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq28_HTML.gif showing the number of people employed per N$ million output and N$ million in labor income per N$ million output, respectively. The size-unweighted and size-weighted linkage measures are then given by B j q = i q i b i j / n http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq29_HTML.gif, B j q δ = i q i b i j δ j / n http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq30_HTML.gif, B i q = j b i j q j / n http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq31_HTML.gif and B i q σ = j σ i b i j q j / n http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq32_HTML.gif, respectively, with corresponding variance measures. In the size-unweighted case, the results show how much impact a marginal change in a sector would have on employment and on labor income, respectively. In the size-weighted case, the results show the current importance of each sector as a whole in terms of overall employment and labor income in the economy, respectively.

      3 Data

      The main source of data for this analysis was the Namibian SAM for 2004 [8] developed by researchers at the Namibian Economic Policy Research Unit (NEPRU). The Namibian SAM has 32 commodity sectors, including three dummy sectors for own real estate services, direct foreign purchases by Namibians, and direct domestic purchases by foreigners. There are 30 activity sectors, including two dummy accounts for own real estate services and for foreign tourism. As regards factor accounts, five exist for income to skilled labor, income to unskilled labor, mixed income to commercial agriculture, mixed income to communal agriculture, and capital income, respectively. There are nine institutions, comprising six household categories, non-profit organizations, enterprises, and government. And finally, there is a Savings/investment category and a Rest-of-world category. A list of the economic sectors in the Namibian SAM is provided in Table 2.
      Table 2

      Namibian economic sectors

      Sectors in the input–output (IO) table

      Activity sectors in the social accounting matrix (SAM)

      Commodity sectors in the SAM

      Other sectors in the SAM

      Commercial agriculture: Cereal crops

      Same as in the IO

      Same as in the IO

      Factors of production

      Skilled labor

      Unskilled labor

      Mixed income—Commercial agriculture

      Mixed income—Traditional agriculture

      Gross operating surplus

      Institutions

      Urban households with wages and salaries as main source of income

      Urban households with business activities as main source of income

      Urban households with other main source of income

      Rural households with wages and salaries as main source of income

      Rural households with business activities as main source of income

      Rural households with other main source of income

      Non-profit institutions serving households

      Enterprises

      Government

      Other sectors

      Savings and investment

      Imports and exports

      Commercial agriculture: Other crops

      Same as in the IO

      Same as in the IO

      Commercial agriculture: Animal products

      Same as in the IO

      Same as in the IO

      Traditional agriculture

      Same as in the IO

      Same as in the IO

      Fishing

      Same as in the IO

      Same as in the IO

      Mining

      Same as in the IO

      Same as in the IO

      Meat processing

      Same as in the IO

      Same as in the IO

      Fish processing

      Same as in the IO

      Same as in the IO

      Grain milling

      Same as in the IO

      Same as in the IO

      Manufacture of beverages and other food processing

      Same as in the IO

      Same as in the IO

      Manufacture of textiles

      Same as in the IO

      Same as in the IO

      Manufacture of wood products and furniture

      Same as in the IO

      Same as in the IO

      Manufacture of paper, printing and publishing

      Same as in the IO

      Same as in the IO

      Manufacture of chemicals, rubber and plastic

      Same as in the IO

      Same as in the IO

      Manufacture of other non-metallic mineral products

      Same as in the IO

      Same as in the IO

      Manufacture of basic metals

      Same as in the IO

      Same as in the IO

      Manufacture of fabricated metal products and machinery

      Same as in the IO

      Same as in the IO

      Electricity

      Same as in the IO

      Same as in the IO

      Water

      Same as in the IO

      Same as in the IO

      Construction

      Same as in the IO

      Same as in the IO

      Trade and repairs

      Same as in the IO

      Same as in the IO

      Hotels and restaurants

      Same as in the IO

      Same as in the IO

      Transport

      Same as in the IO

      Same as in the IO

      Communication

      Same as in the IO

      Same as in the IO

      Finance and insurance

      Same as in the IO

      Same as in the IO

      Market real estate and business services

      Same as in the IO

      Same as in the IO

      Other private social services

      Same as in the IO

      Same as in the IO

      Government services

      Same as in the IO

      Same as in the IO

      Own real estate (Dummy sector)

      Same as in the IO

      Same as in the IO

      Foreign tourism (Dummy sector)

      Same as in the IO

      Same as in the IO

      Petroleum (Dummy sector)

       

      Petroleum

       
        

      Purchases abroad by residents (Dummy sector)

       

      In the Namibian SAM, subsistence agriculture produces a composite own-consumption food product, all of which is provided to people working in that sector. Thus, there are no forward linkages from this sector except through the food recipients’ consumption, and there is no interaction with the other food sectors. This was identified as a limitation by the researchers compiling the SAM (ibid.). There is in fact also some commercial activity in the subsistence farming sector, but it is not captured very well by the current economic statistics. Apart from subsistence agriculture, informal economic activity is not included in the SAM.

      The SAM was transformed into a symmetric, 31 × 31 http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq33_HTML.gif, activity-based input–output table with 28 domestic activity sectors and a dummy own real estate services sector, a dummy tourism sector, and a dummy sector for petroleum-based fuels as additional sectors. The transformation was done mathematically (see [22], for the methodology used) rather than by using sector-specific data.

      For the employment multipliers, data from the 2004 labor force survey were used [15]. The Ministry of Labour reports on formal employment only, which means that the informal sector—again, apart from subsistence agriculture—is excluded, both in the SAM and in the labor force data. For the labor income multipliers, the income data from the SAM for unskilled and skilled labor were simply used, as well as the mixed income accruing to people active in traditional subsistence farming.

      4 Results and Discussion

      Tables 3 through 8 depict the results of the key sector analyzes described above. If one looks at the weighted analyzes, which show the current importance of various sectors in the Namibian economy, there are few surprises. Mining, Manufacturing of beverages and other food processing and Government services are crucial for overall output in the economy. Traditional (subsistence) agriculture and Government services are key sectors for both labor income and employment. Mining is a key sector for labor income, while Commercial agriculture: animal products is a key sector for employment. The results partly reflect how large all of these specific sectors are rather than the linkages that they create with the rest of the economy.
      Table 3

      Key sector analysis in terms of output, not weighted by sector size

      Sector

      Backward multiplier

      Backward coefficient of variation

      Forward multiplier

      Forward coefficient of variation

      Commercial agriculture: Cereal crops

      0.8706

      1.0599

      0.8338

      1.0533

      Commercial agriculture: Other crops

      0.8413

      1.1076

      0.7051

      1.1900

      Commercial agriculture: Animal products

      0.8179

      1.0987

      0.9441

      0.9710

      Traditional agriculture

      0.7441

      1.2133

      0.5532

      1.4737

      Fishing

      0.9396

      0.9656

      0.7928

      1.1043

      Mining *

      1.0962

      1.0140

      1.0899

      0.9441

      Meat processing

      1.2438

      0.8098

      0.6347

      1.2825

      Fish processing

      1.0532

      0.9147

      0.5565

      1.4676

      Grain milling

      1.0457

      0.9296

      0.6990

      1.1997

      Manufacture of beverages and other food processing *

      1.0830

      1.0239

      1.0467

      0.9530

      Manufacture of textiles

      0.8796

      1.1908

      0.8785

      1.0693

      Manufacture of wood products and furniture

      1.0380

      0.9926

      0.9527

      0.9646

      Manufacture of paper, printing and publishing *

      1.1542

      1.0886

      1.4062

      0.7862

      Manufacture of chemicals, rubber and plastic *

      1.1182

      1.1277

      1.9316

      0.5722

      Manufacture of other non-metallic mineral products

      1.1019

      0.8611

      0.7308

      1.1654

      Manufacture of basic metals

      1.2289

      0.7660

      0.5772

      1.4113

      Manufacture of fabricated metal products and machinery

      0.9789

      0.9948

      1.8319

      0.4688

      Electricity

      0.7908

      1.3201

      1.0075

      0.9228

      Water

      0.9207

      1.2292

      0.8213

      1.2396

      Construction

      1.2992

      0.7131

      0.6260

      1.3023

      Trade and repairs

      0.4572

      0.4501

      0.3764

      0.2290

      Hotels and restaurants

      1.0343

      0.8767

      0.8770

      0.9950

      Transport *

      1.1233

      0.8795

      2.0323

      0.4306

      Communication

      0.9554

      1.1380

      1.3917

      0.6833

      Finance and insurance *

      1.2883

      0.9243

      1.6721

      0.6102

      Market real estate and business services

      0.9042

      1.1134

      2.3884

      0.3664

      Other private social services

      1.0612

      0.8628

      0.7207

      1.1346

      Government services

      0.8161

      1.1022

      0.5804

      1.4038

      *Key sectors are highlighted in bold

      Table 4

      Key sector analysis in terms of labor income, not weighted by sector size

      Sector

      Backward multiplier

      Backward coefficient of variation

      Forward multiplier

      Forward coefficient of variation

      Commercial agriculture: Cereal crops

      0.5637

      0.9876

      0.1959

      0.9021

      Commercial agriculture: Other crops

      0.6553

      0.9817

      0.4261

      1.2346

      Commercial agriculture: Animal products

      0.4650

      0.8857

      0.3779

      0.9498

      Traditional agriculture *

      2.7414

      1.6357

      2.3457

      1.6503

      Fishing *

      1.2385

      1.2699

      1.0070

      1.3595

      Mining

      0.9947

      1.1247

      0.8695

      1.1102

      Meat processing

      0.6759

      0.6670

      0.1634

      1.1634

      Fish processing

      1.1219

      0.9518

      0.4501

      1.6452

      Grain milling

      0.6514

      0.8256

      0.3049

      1.1881

      Manufacture of beverages and other food processing

      0.7286

      0.8026

      0.4916

      0.6165

      Manufacture of textiles

      0.5955

      0.9134

      0.5331

      0.7805

      Manufacture of wood products and furniture

      1.0698

      0.9306

      0.8651

      0.9100

      Manufacture of paper, printing and publishing *

      1.3708

      1.0902

      1.7301

      0.8848

      Manufacture of chemicals, rubber and plastic

      0.8728

      0.9269

      1.4512

      0.4969

      Manufacture of other non-metallic mineral products

      1.0224

      0.7876

      0.4534

      1.1775

      Manufacture of basic metals

      1.0283

      0.7827

      0.3985

      1.5769

      Manufacture of fabricated metal products and machinery

      0.9280

      1.0414

      1.7488

      0.4787

      Electricity

      0.9304

      1.4891

      1.1905

      1.0177

      Water

      0.9276

      1.3372

      0.8591

      1.2485

      Construction

      0.8914

      0.6208

      0.2963

      1.0943

      Trade and repairs

      1.1747

      1.3051

      0.9902

      1.3309

      Hotels and restaurants

      0.7569

      0.9159

      0.4898

      1.2105

      Transport *

      1.1674

      1.0728

      2.6019

      0.7977

      Communication

      0.9721

      1.2245

      1.9467

      0.8795

      Finance and insurance

      0.8571

      0.7140

      1.9054

      0.8630

      Market real estate and business services

      0.5878

      0.9368

      2.9077

      0.7911

      Other private social services

      1.8576

      1.2998

      1.4129

      1.4757

      Government services *

      2.1877

      1.5479

      1.8195

      1.6083

      *Key sectors are highlighted in bold

      Table 5

      Key sector analysis in terms of employment, not weighted by sector size

      Sector

      Backward multiplier

      Backward coefficient of variation

      Forward multiplier

      Forward coefficient of variation

      Commercial agriculture: Cereal crops *

      3.2270

      1.4408

      2.8142

      1.5707

      Commercial agriculture: Other crops *

      3.0944

      1.5084

      2.7570

      1.6132

      Commercial agriculture: Animal products *

      3.0798

      1.4688

      2.7692

      1.5568

      Traditional agriculture *

      3.0264

      1.4939

      2.5800

      1.6718

      Fishing

      0.6739

      1.0451

      0.4292

      1.4909

      Mining

      0.3461

      0.7048

      0.2437

      0.6628

      Meat processing

      2.0295

      1.2449

      0.1635

      1.1028

      Fish processing

      0.4672

      0.7652

      0.1068

      1.6427

      Grain milling

      1.4342

      1.1961

      0.3719

      1.0087

      Manufacture of beverages and other food processing

      0.6414

      0.7150

      0.4343

      0.6388

      Manufacture of textiles

      0.4369

      0.8062

      0.4736

      0.6431

      Manufacture of wood products and furniture

      0.7928

      0.8047

      0.5346

      0.6109

      Manufacture of paper, printing and publishing

      0.6086

      0.9439

      1.0412

      0.8876

      Manufacture of chemicals, rubber and plastic

      0.6380

      0.9526

      1.4410

      0.5253

      Manufacture of other non-metallic mineral products

      0.5466

      0.8230

      0.2444

      0.8374

      Manufacture of basic metals

      0.4370

      0.6266

      0.1249

      1.4031

      Manufacture of fabricated metal products and machinery

      0.7191

      1.0582

      1.4880

      0.5281

      Electricity

      0.4347

      1.2661

      0.7141

      0.7971

      Water

      0.5030

      1.1890

      0.5693

      1.0186

      Construction

      0.8525

      0.8577

      0.4596

      1.3932

      Trade and repairs

      0.8987

      1.3361

      0.9173

      1.2477

      Hotels and restaurants

      1.0384

      1.0394

      0.7331

      1.3966

      Transport

      0.6175

      0.8208

      2.2011

      0.7732

      Communication

      0.4944

      1.0095

      1.5338

      0.8519

      Finance and insurance

      0.6344

      0.8503

      1.7314

      0.8413

      Market real estate and business services

      0.3843

      0.8830

      2.4098

      0.8247

      Other private social services

      0.7958

      1.0144

      0.5749

      1.3212

      Government services

      0.5439

      1.1627

      0.3851

      1.5680

      *Key sectors are highlighted in bold

      Table 6

      Key sector analysis in terms of output, weighted by sector size

      Sector

      Backward multiplier

      Backward coefficient of variation

      Forward multiplier

      Forward coefficient of variation

      Commercial agriculture: Cereal crops

      −0.0779

      −1.9610

      0.1613

      0.6902

      Commercial agriculture: Other crops

      0.2195

      2.0492

      0.2734

      0.6726

      Commercial agriculture: Animal products

      0.3853

      2.0328

      0.5832

      0.7113

      Traditional agriculture

      0.6389

      2.2449

      0.4330

      1.3379

      Fishing

      1.4230

      1.7865

      0.9525

      1.1278

      Mining *

      5.3910

      1.8762

      2.5952

      1.5683

      Meat processing

      0.9256

      1.4983

      0.1429

      3.5210

      Fish processing

      1.3446

      1.6925

      0.3853

      2.2398

      Grain milling

      0.3535

      1.7199

      0.2783

      0.8580

      Manufacture of beverages and other food processing *

      3.1360

      1.8945

      1.5432

      1.5595

      Manufacture of textiles

      0.4927

      2.2032

      0.6717

      0.6519

      Manufacture of wood products and furniture

      −0.0673

      −1.8366

      0.4719

      0.2961

      Manufacture of paper, printing and publishing

      −0.5111

      −2.0141

      0.7941

      0.6106

      Manufacture of chemicals, rubber and plastic

      −0.6374

      −2.0864

      1.3392

      0.5429

      Manufacture of other non-metallic mineral products

      −0.2109

      −1.5932

      0.2461

      1.2574

      Manufacture of basic metals

      0.8858

      1.4173

      0.2048

      2.3811

      Manufacture of fabricated metal products and machinery

      0.0910

      1.8405

      1.9085

      0.3600

      Electricity

      0.0459

      2.4425

      0.8567

      0.2503

      Water

      0.2020

      2.2744

      0.4332

      0.4780

      Construction

      3.9418

      1.3194

      0.6655

      3.0845

      Trade and repairs

      0.0823

      0.8329

      0.4104

      0.2207

      Hotels and restaurants

      0.2296

      1.6221

      0.5556

      1.1606

      Transport

      −0.3152

      −1.6273

      2.2309

      0.3593

      Communication

      0.3741

      2.1056

      1.5293

      0.2501

      Finance and insurance

      0.5182

      1.7103

      1.6564

      0.2856

      Market real estate and business services

      −0.1008

      −2.0601

      3.5852

      0.2327

      Other private social services

      1.4711

      1.5964

      0.6918

      1.3642

      Government services *

      6.2754

      2.0394

      3.6344

      1.4282

      *Key sectors are highlighted in bold

      Table 7

      Key sector analysis in terms of labor income, weighted by sector size

      Sector

      Backward multiplier

      Backward coefficient of variation

      Forward multiplier

      Forward coefficient of variation

      Commercial agriculture: Cereal crops

      −0.0402

      0.9876

      0.0121

      0.9021

      Commercial agriculture: Other crops

      0.1364

      0.9817

      0.0952

      1.2346

      Commercial agriculture: Animal products

      0.1747

      0.8857

      0.2210

      0.9498

      Traditional agriculture *

      1.8780

      1.6357

      1.2677

      1.6503

      Fishing

      1.4964

      1.2699

      0.9886

      1.3595

      Mining *

      3.9025

      1.1247

      2.1179

      1.1102

      Meat processing

      0.4013

      0.6670

      0.0191

      1.1634

      Fish processing

      1.1427

      0.9518

      0.2151

      1.6452

      Grain milling

      0.1757

      0.8256

      0.0612

      1.1881

      Manufacture of beverages and other food processing

      1.6830

      0.8026

      0.6192

      0.6165

      Manufacture of textiles

      0.2661

      0.9134

      0.2509

      0.7805

      Manufacture of wood products and furniture

      −0.0553

      0.9306

      0.1244

      0.9100

      Manufacture of paper, printing and publishing

      −0.4842

      1.0902

      0.1585

      0.8848

      Manufacture of chemicals, rubber and plastic

      −0.3969

      0.9269

      0.3874

      0.4969

      Manufacture of other non-metallic

      −0.1561

      0.7876

      0.0427

      1.1775

      mineral products

          

      Manufacture of basic metals

      0.5913

      0.7827

      0.0886

      1.5769

      Manufacture of fabricated metal products and machinery

      0.0688

      1.0414

      1.1153

      0.4787

      Electricity

      0.0431

      1.4891

      0.5741

      1.0177

      Water

      0.1623

      1.3372

      0.2354

      1.2485

      Construction

      2.1575

      0.6208

      0.2059

      1.0943

      Trade and repairs

      0.1687

      1.3051

      2.5012

      1.3309

      Hotels and restaurants

      0.1340

      0.9159

      0.2688

      1.2105

      Transport

      −0.2613

      1.0728

      2.4608

      0.7977

      Communication

      0.3037

      1.2245

      1.4423

      0.8795

      Finance and insurance

      0.2750

      0.7140

      0.9858

      0.8630

      Market real estate and business services

      −0.0523

      0.9368

      5.2666

      0.7911

      Other private social services

      2.0543

      1.2998

      0.9526

      1.4757

      Government services *

      13.4203

      1.5479

      8.1868

      1.6083

      *Key sectors are highlighted in bold

      Table 8

      Key sector analysis in terms of employment, weighted by sector size

      Sector

      Backward multiplier

      Backward coefficient of variation

      Forward multiplier

      Forward coefficient of variation

      Commercial agriculture: Cereal crops

      −0.4037

      1.4408

      0.2490

      1.5707

      Commercial agriculture: Other crops

      1.1289

      1.5084

      0.8860

      1.6132

      Commercial agriculture: Animal products *

      2.0290

      1.4688

      2.3287

      1.5568

      Traditional agriculture *

      3.6345

      1.4939

      2.0048

      1.6718

      Fishing

      1.4276

      1.0451

      0.6058

      1.4909

      Mining

      2.3803

      0.7048

      0.8534

      0.6628

      Meat processing

      2.1122

      1.2449

      0.0275

      1.1028

      Fish processing

      0.8343

      0.7652

      0.0734

      1.6427

      Grain milling

      0.6782

      1.1961

      0.1073

      1.0087

      Manufacture of beverages and other food processing

      2.5973

      0.7150

      0.7865

      0.6388

      Manufacture of textiles

      0.3423

      0.8062

      0.3205

      0.6431

      Manufacture of wood products and furniture

      −0.0719

      0.8047

      0.1105

      0.6109

      Manufacture of paper, printing and publishing

      −0.3769

      0.9439

      0.1372

      0.8876

      Manufacture of chemicals, rubber and plastic

      −0.5086

      0.9526

      0.5531

      0.5253

      Manufacture of other non-metallic mineral products

      −0.1463

      0.8230

      0.0331

      0.8374

      Manufacture of basic metals

      0.4405

      0.6266

      0.0399

      1.4031

      Manufacture of fabricated metal products and machinery

      0.0934

      1.0582

      1.3645

      0.5281

      Electricity

      0.0353

      1.2661

      0.4951

      0.7971

      Water

      0.1543

      1.1890

      0.2243

      1.0186

      Construction

      3.6174

      0.8577

      0.4591

      1.3932

      Trade and repairs

      0.2262

      1.3361

      3.3318

      1.2477

      Hotels and restaurants

      0.3224

      1.0394

      0.5785

      1.3966

      Transport

      −0.2424

      0.8208

      2.9932

      0.7732

      Communication

      0.2708

      1.0095

      1.6340

      0.8519

      Finance and insurance

      0.3569

      0.8503

      1.2880

      0.8413

      Market real estate and business services

      −0.0599

      0.8830

      6.2758

      0.8247

      Other private social services

      1.5428

      1.0144

      0.5573

      1.3212

      Government services *

      5.8493

      1.1627

      2.4914

      1.5680

      *Key sectors are highlighted in bold

      The unweighted analysis, which shows the effect that marginal changes in sectors would have on the overall economy, exhibits a more complicated picture. Not surprisingly, given the dualistic nature of the Namibian economy, the choice of metric is important for those sectors identified as key in the unweighted analysis. When a traditional output metric is used, a range of manufacturing sectors (and a few service sectors) are identified as key, with both backward and forward linkages, and many of the remaining manufacturing and service sectors are identified as having strong linkages in at least one direction. On the other hand, when labor income is used as a metric, the subsistence agriculture sector (where any change in production will, by definition, translate almost completely into a change in income and consumption for the people involved in the sector), fishing, and a few highly-paid, labor-intensive manufacturing and service sectors are the only ones identified as key sectors with large linkage effects on the economy. Finally, when employment is used as a metric, the low-wage, labor-intensive agricultural sectors come out as the only key sectors.

      If one focuses on the output-oriented analysis, the results indicate several key sectors where increased activity could have important linkage effects on the economy. Of those identified as key sectors with widely dispersed effects, two are service sectors. One is transportation which is important for the economy not only because it draws on a wide range of other sectors for its inputs, but also because such services are a vital input to almost all economic activity in this sparsely populated country. The second service sector with widely dispersed effects is financial services. Like transportation, financial services are a key input to many economic activities. However, perhaps more unexpectedly, the latter services constitute a sector that uses inputs from many other sectors.

      As regards the manufacturing sectors identified as key sectors, those with widely dispersed effects—both forward and backward—draw on raw material inputs from the domestic economy. The goods produced are then used both as intermediate inputs and as consumer goods.

      Key manufacturing sectors with less widely dispersed backward effects are those that sell their products to a broad range of other sectors—hence the widely dispersed forward effects—but whose main input from the domestic economy is the use of transportation and retail services to distribute their products. Sectors with widely dispersed backward effects but with limited or no forward effects are mostly those that draw widely on domestic inputs but sell mainly to export markets or to tourists visiting Namibia. Thus, transport and communications, identified as a sector for policy support, is indeed a key sector, according to our analysis.

      Manufacturing has also been identified for policy support. Our analysis indicates that there is scope for more selectivity and targeting of individual manufacturing sectors rather than the entire range of manufacturing activities.

      The special role given to mineral processing in policy documents is, however, not supported by our analysis. On the other hand, traditional agriculture, which comes out as a key sector according to most of our analyzes, has not been identified for policy support.

      A few cautionary notes are in order at this point. The Namibian economy is highly trade-dependent, and even those sectors which are identified as having stronger-than-average linkages to the rest of the economy may be relatively weakly linked in absolute terms. In addition to this, since the Namibian economy is fairly small, and several of the key sectors identified here are small subsets of it, many sectors consist of only a few companies. This means that the entry of a single new company or the exit of an old one could change the structure of a sector enough to shift it from one category in the analysis to another. It also means that if a sector were to expand rapidly, it is uncertain whether the domestic markets would be sufficient to provide the additional inputs needed, or to absorb the additional output. In practice, constraints in other sectors might create problems—especially for those sectors identified as having multiplier effects, albeit only on a few other sectors.

      Nonetheless, as long as one is contemplating interventions that are either relatively limited in scope or that will unfold over extended periods of time, key sector analysis can help identify interventions that are likely to have the greatest knock-on effects in respect of other sectors in the Namibian economy. Even in an economy as trade-dependent as Namibia’s, for policy purposes it is useful to identify the specific sectors where interventions are likely to have the greatest overall effect on the economy. Key sector analysis can contribute to that goal.

      Appendix:  Notation Used in the Paper

      A Leontief matrix of input coefficients

      A i j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq4_HTML.gif
      Spending on inputs from sector j as share of sector i’s overall expenditure

      B Leontief inverse

      b i j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq34_HTML.gif
      Coefficient of Leontief inverse
      B ¯ http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq35_HTML.gif
      Average multiplier
      B i http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq36_HTML.gif
      Average forward multiplier of sector i
      B i N http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq37_HTML.gif
      Normalized forward multiplier of sector i
      B i σ http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq38_HTML.gif
      Forward multiplier of sector i, weighted by its share of overall factor income
      B i q http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq39_HTML.gif
      Forward multiplier of sector i, weighted by employment or labor income
      B i q σ http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq40_HTML.gif
      Forward multiplier of sector i, weighted by employment or labor income and by share of overall factor income
      B j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq41_HTML.gif
      Average backward multiplier of sector j
      B j N http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq42_HTML.gif
      Normalized backward multiplier of sector j
      B j δ http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq43_HTML.gif
      Backward multiplier of sector j, weighted by its share of overall net final demand
      B j q http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq44_HTML.gif
      Backward multiplier of sector j, weighted by employment or labor income
      B j q δ http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq45_HTML.gif
      Backward multiplier of sector j, weighted by employment or labor income and by share of overall net final demand

      I Identity matrix

      n Number of sectors

      V i http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq46_HTML.gif
      Forward coefficient of variation of sector i
      V i N http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq47_HTML.gif
      Normalized forward coefficient of variation of sector i
      V j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq48_HTML.gif
      Backward coefficient of variation of sector j
      V j N http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq49_HTML.gif
      Normalized backward coefficient of variation of sector j
      X i http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq2_HTML.gif
      Total revenue and expenditure of sector i

      Z Matrix of monetary flows in the economy

      Z i j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq3_HTML.gif
      Sector i’s spending on inputs from sector j
      δ j http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq25_HTML.gif
      Sector j’s share of overall net final demand
      σ i http://static-content.springer.com/image/art%3A10.1186%2F2193-2409-2-1/MediaObjects/40008_2012_Article_9_IEq24_HTML.gif
      Sector i’s share of overall factor income

      Declarations

      Acknowledgements

      Financial support from Formas through its COMMONS programme, from the Jan Wallander and Tom Hedelius foundation, and from Elforsk is gratefully acknowledged. The authors are also grateful for constructive comments from two anonymous reviewers on an earlier version of this paper. The usual disclaimers apply.

      Authors’ Affiliations

      (1)
      Namibian Competition Commission
      (2)
      Department of Social Sciences, Mid Sweden University
      (3)
      Department of Economics, Umeå University

      References

      1. Augustinovics M: Methods of international and intertemporal comparison of structure. In Contributions to input–output analysis. Edited by: Carter AP, Bródy A. North-Holland, Amsterdam; 1970:249–269.
      2. CBS/Central Bureau of Statistics (2009) Preliminary national accounts 2000–2008. National Planning Commission, Government of the Republic of Namibia, Windhoek
      3. Chenery B, Watanabe T: International comparisons of the structure of production. Econometrica 1958, 26: 487–521. 10.2307/1907514View Article
      4. Dietzenbacher E: In vindication of the Ghosh model: a reinterpretation as a price model. J Reg Sci 1997, 37: 629–651. 10.1111/0022-4146.00073View Article
      5. Ghosh A: Input–output approach in an allocation system. Economica 1958, 25: 58–64. 10.2307/2550694View Article
      6. Hewings GJD: The empirical identification of key sectors in an economy: a regional perspective. Dev Econ 1982, 20: 173–195.View Article
      7. Hirschman A: The strategy of economic development. Yale University Press, New Haven; 1958.
      8. Lange GM, Schade K (2008) A social accounting matrix for Namibia, 2004: a tool for analyzing economic growth, income distribution and poverty. NEPRU Working Paper 112. Namibian Economic Policy Research Unit, Windhoek
      9. Laumas PS: Key sectors in some underdeveloped countries. Kyklos 1975, 28: 62–79. 10.1111/j.1467-6435.1975.tb01934.xView Article
      10. Laumas PS: The weighting problem in testing the linkage hypothesis. Q J Econ 1976, 90: 308–312. 10.2307/1884632View Article
      11. Laumas PS: Key sectors in some underdeveloped countries: a reply. Kyklos 1976, 29: 767–769. 10.1111/j.1467-6435.1976.tb02001.xView Article
      12. Lenzen M: Environmentally important paths, linkages and key sectors in the Australian economy. Struct Chang Econ Dyn 2003, 14: 1–34. 10.1016/S0954-349X(02)00025-5View Article
      13. Leontief W: The structure of the American economy, 1919–1924: an empirical application of equilibrium analysis. Harvard University Press, Cambridge; 1941.
      14. McGilvray J: Linkages, key sectors and development strategy. In Structure, system and economic policy. Edited by: Leontief W. Cambridge University Press, Cambridge; 1977:49–56.
      15. Ministry of Labour (2006) Labour force survey 2004. Ministry of Labour, Government of the Republic of Namibia, Windhoek
      16. Nørregaard Rasmussen P: Studies in inter-sectoral relations. Einar Harks, Copenhagen; 1956.
      17. NPC/National Planning Commission (2008) A review of poverty and inequality in Namibia. Government of the Republic of Namibia, Windhoek
      18. Oosterhaven J: On the plausibility of the supply-driven input–output model. J Reg Sci 1988, 28: 203–217. 10.1111/j.1467-9787.1988.tb01208.xView Article
      19. Oosterhaven J: Leontief versus Ghoshian price and quantity models. South Econ J 1996, 62: 750–759. 10.2307/1060892View Article
      20. Oosterhaven J: Adding supply-driven consumption makes the Ghosh model even more implausible. Econ Syst Res 2012, 24: 101–111. 10.1080/09535314.2011.635137View Article
      21. Rueda-Cantuche JM, Neuwahl F, Delgado L (2009) The adjustment capacity of the European economy examined with an input–output based key sector analysis: towards a review of the European Single Market. Cuaderno 01/09, Cuadernos de Trabajo de SHAIO Serie 1. Sociedad Hispanoamericana de Análisis Input–Output, Oviedo
      22. United Nations Studies in methods: handbook of national accounting, series F 74. In Handbook of input–output table compilation and analysis. United Nations, New York; 1999.

      Copyright

      © M.N. Humavindu, J. Stage; licensee Springer. 2013

      This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://​creativecommons.​org/​licenses/​by/​2.​0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.