Key sectors in the Moroccan economy: an application of input-output analysis

The exploration of the structural features and sectoral interdependences of and in an economy is fundamental for the understanding of its modes of functioning and of its transformations over time. Input-output analysis is largely used to fulfill this objective. Furthermore, information provided by the Leontief inverse matrix is useful for the identification of key sectors. This identification may guide policy makers in setting an adequate industrial strategy. In this paper, the classification of productive sectors is performed by using the Unweighted Rassmussen Approach. The ordering of sectors depends on the intensity of their links with other sectors. Two results ought to be highlighted. First, key sectors of the Moroccan economy (sectors that are classified in category II) reduced to two sectors in 2007 instead of four sectors in 1998. Second, the ordering of sectors is highly sensitive to the precision of the data and to the year in which the classification is realized.


Introduction
orocco is a developing economy classified by the World Bank as a lower medium income country (World Bank 2010 and2011). The Moroccan economy is less diversified than developed countries, but compared to the Middle East and North Africa (MENA) economies, it is relatively more diversified and continues to improve its diversification (OCDE, 2008, p. 460).
Since 1998, Moroccan authorities introduced important legal and institutional reforms to increase the competitiveness and the flexibility of the economy. In this same period, many structural projects have been undertaken to promote investment, employment, and growth. These reforms are designed to meet the major challenges of the Moroccan economy which are: dependence of agriculture on rainfall, high rate of unemployment, and insufficient and volatile growth.
In this paper, we will adopt an aggregate view of the Moroccan economy with the objective to identify some of its structural features using input-output analysis (IOA). The discussion will be completed by providing an identification of the key sectors of the economy using some well established criteria.
The IOA is one of the earlier applications of linear programming in the area of economics (Gass 1975). It is adapted to the objective of exploring the interdependencies of the different sectors of the economy and to the running of simulations to gauge the impact of increases in final demand on the output of different sectors. New uses of IOA recently emerged such as the decomposition of growth into the parts attributable to changes in expenditures and the parts due to change in the productive technology captured by the matrix of technical coefficients 1 A. This paper is organized as follows. In the second section, we introduce the inputoutput framework and the Leontief inverse matrix used to estimate the backward and the forward linkages according to the Unweighted Rasmussen Approach. The third section is reserved to the discussion of the overall structure of the Moroccan economy and to the 1 For an example of these applications see (Voyvoda, 2008). M presentation of some results provided by the intersectoral matrix of flows. In the fourth section, we identify the key sectors of the Moroccan economy. The last section serves to conclude.

Input-output analysis and the methodology of identifying key sectors
We present IOA in the first subsection. In the second subsection we present the Leontief inverse matrix and the backward and forward linkages indices that will be used to establish an ordering of productive sectors in Morocco.

Input-output analysis
Input-output analysis (IOA) describes the flows of services and products in the economy. The refinement of the analysis depends on the available data and the objectives of the study. The validity and the use of IOA in forecasting stand on some hypotheses.
First the technology used in production is supposed to be linear and homogeneous of degree 1; that means that returns to scale are constant. Second, the supply of factors for production is supposed to be fully elastic.
The Input Output Table ( x 11 x 12 … x 1n y 1 X 1 S 2 x 21 x 22 … x 2n y 2 X 2 : : quantity of locally produced output of sector i used by sector j x d ij is proportional to x j . The coefficients of proportion are a ij . These elements are called domestic technical coefficients and provide the structure of local production of the economy. They are computed as follows.
The matrix A d of domestic technical coefficients d ij a describes the flows of products between the sectors of the economy. These coefficients quantify the inter-industries transactions. Otherwise A d is describing the technology of local production of the economy which will be considered constant over a certain period of time in order to make simulations. The second part of the local production of each sector is dedicated to final consumptionY formulated by households, foreigners, firms, and the government. We must signal that total final demand Y is satisfied by the part produced locally Y d and by the part imported Y m So we will have: Remark also that the output of any sector j is used to buy inputs x ij (for i=1, 2, .., n) from other sectors, to buy imported inputs m ij x , and to make payments to primary factors of production such as labor, capital, and so on. These payments are wages, dividends, and interests; and constitute the value added generated by the j th sector. It is expressed as: If we focus on the uses of local production, we will find that for a sector i there is equilibrium between its production and the quantity of this production used by productive sectors plus the quantity used as final demand d i y .
Equation (3) may be written in matrix form by considering the vector X of the outputs of the n sectors, the n n  matrix of domestic technical coefficients A d , and the vector of final consumption of the outputs of the n sectors Y d . So we will have: Let M be the (n, 1) vector of importations of the n sectors from abroad and Y m the vector of consumed importations by final users. In matrix terms, this can be written as follow: M=A m X+Y m . This equation states that the total importations M are used as inputs by the n productive sectors and the remaining part is consumed by final users (households, governments, reexport …). The overall equilibrium between available resources and their uses may be written when we add the two sides of the above equations as follows: Importations constitute leakages that reduce the productions multipliers (Reis and Rua, 2006). This is especially true because domestically produced goods and imported goods are generally not substitutable. We must remark that initial works, undertaken to apply IOA, assumed that domestically produced and imported goods are " equivalent so that any demand or want can be satisfied by either the one or the other kind of goods" (Johansen 1960, p. 16). In the following, we will not distinguish between locally and imported production. The objective is to present a general view about the linkages between sectors. In the application (section 4) we will use A d which is the matrix of domestic technical coefficients.

Leontief inverse Matrix and the methodology of ordering sectors
Input-output analysis provides a demand driven view of the economy. The links between final demand Y and the sectors' outputs X can be more explicitly presented by the relationship: The matrix I is a n n  unit matrix. We pose (I-A) -1 =B. B is the Leontief inverse matrix 2 with generic element b ij . By the IO model, we can depict the impact of an increase of final demand addressed to a sector j on the output of other productive sectors.
The Leontief inverse matrix B provides the direct and indirect necessary materials to produce a supplementary unit by a given sector to respond to an increase of final demand. To get a thorough view about the functioning of the economy and evaluate the indirect effects we will study sectoral multipliers. Two cases are distinguished. The first is a unitary increase of the final demand addressed to a specified sector j. The second case is the uniform unitary increase of final demand addressed to all productive sectors.
The backward linkages of a sector are measured by the intensity of its links with sectors providing inputs. The strength of these relationships is gauged by output multipliers. The demand addressed to sector j increase its output by one unit; this is a direct effect. To produce an extra unit by sector j, the output of sector i must increase by a quantity Δ x i . The induced effect in the i th sector will have an effect on the output of the k th sector and so on.
If we are interested by the effect of an increase by one unit in the final demand addressed to the j th sector we will suppose that the elements of Δ Y are zeros except the j th element where we have 1. The output multiplier is "defined as the change in gross output resulting from unit change in final demand in a given sector" (Matallah 2006, p. 288). By its definition the output multiplier of the j th sector is equal to 3 : Remark that the output multiplier of a sector j "can be decomposed between the effects occurring within the sector (intra-sector effects) and those that spread to all other sectors (inter-sector effects)" (Kweka et al. 2001, p. 7).
3 In this paper, we note a one unit increase of the final demand for the output of the j th sector by . This is an indicative function which is equal to 1 if i=j and 0 otherwise. Now we are interested by the impact of a uniform unit increase 4 of final demand addressed to all productive sectors. In this case, the increase in final demand is represented by a unitary vector Δ Y l =(1 1 ... 1) T . Remark that because we discuss in terms of MAD 5 the increase in final demand Y is equal to n MAD. The induced increases in the output of all sectors are given by this equation: We will use the indices of linkages identified accordingly to the approaches of Rasmussen (1956) and Hirschman (1958) to classify the aggregate sectors of the Moroccan economy into those with above average effect on the remaining sectors and those with below average effect. For this, we define the average element b of the Leontief inverse matrix B=(I-A) -1 as follows: We use these indices even if they have limits as observed by Sonis et al. (1995).
Indeed, "one of the criticisms of above indices (BL j and FL i ) is that they do not take into consideration the different levels of production in each sector of the economy" (Sonis et al., 1995, p. 235).
To compare sectors according to their backward and forward effects we must normalize by 1 (Shuja et al., 2008). According to the values BL j and FL i , the productive sectors are classified into four categories (Boucher 1976, p. 456-7). If both BL j and FL i of a sector are above 1 then the sector is of category II. These sectors are considered by Hirschman (1958) as key sectors. Backward linkages are judged more interesting, for this reason category III is composed of sectors with BL j above 1 and below 1 FL i . Sectors with BL j low (below 1) and FL i above 1 are classified in category I. Sectors having neither BL j or FL i above 1 are classified in category IV. 6 "Backward linkages are the relationships of a sector with the sectors providing inputs. Forward linkages are the relationships between the activity in a sector and its sales" (Matallah, 2006, p. 290). 7 During the period 1998-07 the real GDP increased by an average annual rate of 4.1% (HCP 2009, p. 29).  Aside the structural dependence on oil and natural gas, the Moroccan economy depends heavily on imports of equipments, machines, and other sophisticated products. 8 It is important to scrutinize the shift in the importance of agriculture in an economy since the experience of economic development is characterized by a strong decline in the part of agriculture in GDP and in employment. See for a discussion (Alvarez-Cuadrado and Poschke 2009). 9 During the period 1998-2007, agricultural production recorded negative growth rates in 1999, 2000, and 2007(HCP 2009). 10 It is important to compare with the data in (HCP 2009, p. 33).

Overall structure of the Moroccan economy
Four indicators will be used to characterize the degree of openness of different sectors. The first is the rate of exportation which is the part of the i th sector's exportation z i in the production generated by this sector (rex i =z i /x i ). The second indicator is the rate of penetration which is calculated as the part of the importation of a product in its apparent consumption defined as production and importation (demand of products) minus exportations (rp i =m i /(x i +m i -z i ). The third indicator is the rate of exposedness also known as the rate of internationalization, calculated from the rate of exportation and the rate of penetration (rexp i = rex i +(1-rex i )rp i ). The last indicator is the rate of coverage which measures the part of importations financed by exportations (rc i =z i /m i ). The following table summarizes these data.   (Dobrescu et al. 2010, p. 179-180). The quantities 1-Sc for j=1,…,n provide an idea about the proportion of the production of each sector that is distributed as income to domestic and foreign factors. 1-Sr provides the part of final consumption in the supply of each sector. The following table provides the Sr and Sc of each sector.  Table 4 shows that 63% of the production of the sector of food and tobacco industry is used to purchase domestically produced intermediate items. The sector of real estate, rental and services to companies and the sector of education, health and social action are the sectors that use less of domestic materials as intermediate consumption.
Production of the sector of refined petroleum and other energy products and the sector of real estate, rental and services to companies cover respectively 91.2% and 62.5% of intermediate consumption.

Ordering of sectors in the case of Morocco
We will use the BL j and FL i to identify the key sectors in the Morocco economy.
We must remark that to refine and precise the ordering of productive sectors other investigations must be undertaken to take into account employment, income, and taxes impacts. The proposed classification is based on production/output multipliers. The average element b of B is equal to 0.07. The following table provides the BL j and the FL i , the category of each sector and its rank.  Nihou and Khellaf (2005) for the year 1998. Concerning the intensity of forward linkages of the sector of agriculture, forestry, hunting, and exploitation, it is equal to 1.449. The results let us suppose that agriculture is more linked to other sectors as provider of inputs comparatively to its integration to the productive sectors as user of inputs. This is highly plausible because Moroccan agriculture uses intensively imported products such as equipments and selected seeds. It is paradoxical to observe that even if Morocco is the first producer and exporter of phosphates, the quantity of this product used by farmers is very low and ironically small ones don't find the derivatives of this product in the market.
The results show that the sector of fishing and aquaculture has backward and forward linkage indices under unity. That means that the links of this sector as purchaser of outputs from productive sectors are low and its impact as provider of inputs to other sectors is low. This result is concordant with the findings of Boudhar and Belaid (2009) who found that "… the fishery products system remains poorly integrated into the  When the final demand addressed to each of the n productive sectors increase by one unit the total final demand increases by n units. In our case, we have 20 sectors. This means that the uniform unit increase in the demand addressed to all productive sectors is equal to 20. The impact of this uniform increase of one unit is given by equation (11). The effect is equal to 27.42 MAD. Thus, on average each unit increase in final demand induces 1.37 increase in the production of sectors. That means that globally, an extra MAD in final demand produces approximately 1.37 MAD. This value of general multiplier is almost the same found by Nihou and Khallaf for the year 1998 (Nihou and Khallaf 2005, p. 12).

Conclusion
The discussion in this paper has attempted to determine the structural patterns of the Moroccan economy. Furthermore, we tried to detect whether there are any structural shifts in the Moroccan economy during the period 1998-2007. Indeed in such a period, it is likely to witness structural transformations especially for a country that introduced reforms and adopted policies in order to facilitate its integration to the world economy and modernize its economic structures. The available data does not reveal any structural change of the Moroccan economy.
In this paper, an ordering of sectors is performed using measures of the intensity of their links, as suppliers and users with other sectors. The results show some change of the ordering between 1998 and 2007. The sector of food and tobacco industries is ranked at the top of the key sectors in the two years.
The specialization of the Moroccan economy is a vertical integration with the world economy. This form of specialization rarely leads to the development of a web of dense domestic links between productive sectors. What is needed for Morocco is not just a passive integration with other economies but a strategic integration that is conducive to the development of a horizontal specialization that will lead to a strengthening of links between productive sectors.