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Analysis of Input (Supply) Multipliers for the Maltese Economy on the Basis of the SIOTs for 2010 and 2015

The goal of this study is to present and assess estimates of input (supply) multipliers within the context of the Maltese economy to identify in which economic sectors it is the most beneficial to allocate primary resources with the aim to support economic growth. Via the application of the Ghoshian Supply-Driven Model, this study presents the first highly disaggregated input (supply) multiplier estimates for the Maltese economy based on the 2010 and 2015 Symmetric Input-Output Tables. This study also includes a comparative analysis between the years 2010 and 2015 to assess changes in the input (supply) multipliers ranking across economic sectors. Based on the 2015 Symmetric Input-Output Table, potential output is mostly increased following the additional allocation of primary inputs to the Manufacturing of other non-metallic mineral products sector following the highest input (supply) multiplier estimate, keeping all else constant. Furthermore, based on the 2010 Symmetric Input-Output Table, the Advertising and market research sector registered the highest input (supply) multiplier. The input (supply) multipliers are subject to the traditional input-output framework and the supply-side modelling assumptions. However, they do provide estimates on the potential change in economy-wide output following exogenous primary input shocks in every sector. In other words, the input (supply) multipliers provide policy makers a guide in which economic sector it is most beneficial to allocate primary inputs, such as labour supply, with the aim of supporting economic growth. The derived input (supply) multipliers may be utilised to aid in the formation of industry specific labour market policies with the aim of supporting overall economic expansion.


Introduction
The goal of this study is to put forward estimates which can help guide policy makers to identify in which Maltese economic sectors it is the most beneficial to allocate primary resources with the sole objective of supporting economic growth. This shall be achieved via the application of the Ghoshian Supply-Driven Model which will be utilised to estimate the input (supply) multipliers based on the Symmetric Input-Output Tables (SIOTs) for the reference years of 2010 and 2015. This is then followed by a comparative analysis of the estimates obtained from both SIOTs with the aim to identify and analyse any changes in the respective ranks of the sectoral input (supply) multipliers. The estimation of input (supply) multipliers provides policy makers with a measure that, utilised together with the conventional Leontief Demand-Driven measures, allows for a deeper level of understanding of the underlying inter-industry linkages of the Maltese economy to thus aid in the formulation of sector specific policies aimed at promoting and supporting economic growth.
Input (supply) multipliers indicate in which economic sector an additional monetary euro worth of primary inputs is the most beneficial in increasing potential economy-wide output. The factors that make up primary inputs are namely Gross Value Added (GVA), imports and net taxes on products 1 . The sub-components of GVA are namely compensation of employees 2 , net operating turnover and net taxes on production 3 . Also, compensation of employees consists of wages application is to be found within the context of linkage analysis (Dietzenbacher and Van der Linden, 1997;Andreosso-O'Callaghan, & Yue 2004;Cardenete Flores and Sancho Pifarré , 2006;Cassar, 2017). Other notable studies which apply this methodology include, for example, Miernyk et al., (1978) in which an assessment of the maximum potential effect for the U.S. economy's output following different primary input constraints, were undertaken. Davis and Salkin (1984) assess the effects on California's economy to identify the importance of water as an input (Davis and Salkin, 1984). A similar study was undertaken by Chen and Rose (1984) to identify the importance of bauxite as an input to the Taiwanese economy (Chen and Rose, 1984). Leung and Pooley (2001) subsequently present an indepth study comparing the input (supply) multipliers to Leontief demand driven based value-added multipliers. It should further be noted that a significant portion of the literature in which the Ghosh supply-side model is put forward focuses primarily on evaluating the model's underlying assumptions and its plausibility when applied to an economic system in the real world. (Oosterhaven 1989(Oosterhaven , 1996Gruver 1989).

Data, Methodology and Assumptions
The data required to undertake the application of the Ghosh supply-side model may be directly obtained from an industry-by-industry SIOT. The inter-industry flows of an economy, at a point in time, are recorded and put forward, in monetary terms, across the various elements which make up the SIOT. The Ghoshian Supply-Driven Model is applied on two SIOTs for the reference years of 2010 and 2015 within the context of Malta. The two SIOTs for the years 2010 and 2015 are both disaggregated at a 44 sectoral level. The sectoral classification adopted within the SIOT corresponds to the latest revision of the European Activity (NACE Rev.2, 2008). The SIOTs provide a visualisation of the inputs utilised and output produced by each sector within the Maltese economy for the reference periods of 2010 and 2015. Therefore, the two SIOTs are disaggregated into ‗n' number of sectors representing the different economic sectors that undertake production activity within the Maltese economy.
The derivation of the Ghoshian Supply-Driven Model shall be presented next, and it follows the methodological structure presented in Miller and Blair (2009). It will thereafter be followed by a brief description of the assumptions put forward by the model. The first step towards deriving the input (supply) multipliers is to obtain the Ghoshian Allocation Matrix (B). Leontief in his dual models derived the technical coefficients matrix (A) that is required to derive the Leontief inverse via the division of the intermediate consumption matrix (Z) column with the output of every sector. However, Ghosh's method to derive the allocation matrix B which is required to derive the Ghoshian Inverse is via the division of every row element within matrix Z by the corresponding total output for each sector. Therefore, the computational difference between the two techniques is the -rotation‖ or -transpose‖ within the matrix of domestic inter-industry flows Z (Miller and Blair, 2009).

(1)
The supply of sector i's output for every sector j that purchases the intermediate inputs from sector i is represented by . These elements are referred to as the sales or allocation coefficients (Dietzenbacher, 1997), as opposed to the Leontief technical coefficients (Miller and Blair, 2009). Therefore, the allocation matrix B is derived via the pre-multiplication of the output inverse matrix ̂ with the intermediate consumption matrix , which is denoted in matrix algebra form as: Where Z denotes a square (n x n) dimensional matrix illustrating the domestic inter-industry transactions, ̂ denotes the inverse of the square diagonal (n x n) dimensional matrix ̂ derived from the total production vector x, and B denotes a square (n x n) dimensional matrix that illustrates the total production value created in a sector for each unit of primary input in the other sector (Augustinovics, 1970).
The following relationship may be established from the observation of a SIOT: Where output is a function of domestic inter-industry flows and primary inputs for every sector. Equation 3 may be re-written in matrix algebra notation as: Where denotes a (1 x n) dimensional row vector portraying total output as the summation totals of matrix Z and a row vector of primary inputs . The balance equation of the Ghosh supply-side model is obtained by the substitution of equation 2 into equation 4 and solving, denoted as: Where the solution to the Ghoshian Supply-Driven Model balance equation is denoted via the multiplication of a row vector of primary inputs with the output inverse matrix G.
The Ghosh output inverse matrix G takes the form of a square (n x n) dimensional matrix. The summation of the row elements within the G matrix provides estimates for the input (supply) multipliers for every economic sector shown in equation 7.
The row summation operation of the Ghoshian output inverse matrix (G) for every economic sector provides the input (supply) multipliers in the form of a column vector of dimensions (n x 1). The input (supply) multipliers provide a guide in which economic sector it is most advantageous for primary input resources to be allocated in terms of supporting the increase of potential output. In other words, the multiplier estimates provide a measure that captures the extent to which economy-wide output would change following an exogenous one monetary euro change in a factor of primary inputs of a specific sector. In this regard, this supply-side model is analogous to the Leontief simple output (production) multipliers where output is determined endogenously (Miller and Blair, 2009).
It should also be noted that the column summations of the Ghoshian inverse matrix G provide another interpretation. The column summations may be viewed as reflecting the impact on the output of a sector, following a change in primary inputs of another sector. In other words, the column sums within the output inverse matrix G represent the impact on output of sector j due to a one monetary euro exogenous change in primary inputs for each sector i as depicted in equation 8. Although this type of analysis is not explicitly undertaken in this paper 8 it is interesting to note that although there exists a strict theoretical duality between the Ghosh Supply-Driven model and the Leontief Demand-Driven model, the column sums of matrix G are found to essentially mirror the row sums of the Leontief Inverse Matrix (Miller and Blair, 2009).
The Ghoshian Supply-Driven model follows the assumption that the distribution patterns of output supply is fixed. In contrast to the Leontief Demand-Driven model with fixed input coefficients, the Ghosh Supply-Driven model assumes fixed output coefficients. The proportion of output supplied and sold by sector i to each sector j is identical. This also invokes the assumption that the Ghoshian Supply-Driven Model follows a production function with perfectly substitutable inputs 9 , meaning that no input is essential (Gruver, 1989).
Another assumption invoked by the Ghoshian Supply-Driven model is that resources within an economy are assumed to be infinite. Therefore, any exogenous change in a factor of primary inputs on total output can be estimated as long as the other factors that make up primary inputs remain unchanged. This implies that any level of potential output may be attained from the model since the modelling technique does not take into account the resource limitations of the economy under study. Therefore, the input (supply) multiplier estimates should be utilised with caution. However, they do provide first cut estimates to assess the change in the potential economy-wide output following exogenous primary input shocks in every economic sector.

Results
The input (supply) multipliers capture the resultant impact on economy-wide output following a one monetary euro exogenous shock in primary inputs for every economic sector. Therefore, the input (supply) multiplier estimates are of great importance for policy makers because they indicate in which economic sectors it is most beneficial for primary inputs to be allocated in terms of supporting economic growth. Similarly, the input (supply) multipliers can also be utilised to assess the consequent effects on total output following adverse shocks on primary inputs. Table 1 provides the ranking of the input (supply) multiplier estimates for the years ending 2010 and 2015. In Table 1, the top ten sectors are ranked based on the highest input (supply) multipliers for the year ending 2015. The description of each economic sector is found within Appendix A, which follows the NACE Rev.2 (2008) classification. The input (supply) multipliers and their rankings have been estimated for all economic sectors within the context of the Maltese economy, which are collectively found within Appendix B. The estimates from Table 1 were calculated following equation 7 in the methodology chapter via the row summation of the Ghoshian output inverse matrix ( ) for every sector. Furthermore, the derivation of the Ghoshian output inverse matrix ( ) was possible following the solution of the Ghoshian Supply-Driven Model balance equation in equation 5 that is presented within the methodology chapter.
From Table 1, for the year ending 2015, the top-ranking sector with the highest input (supply) multiplier of 2.62 euro is the Manufacture of other non-metallic mineral products (8) sector, followed by the Electricity (13) sector amounting to 2.61 euro. Therefore, based on the 2015 SIOT, a one monetary euro increase in the availability of primary inputs towards the Manufacture of other non-metallic mineral products (8) and the Electricity (13) sectors would lead to an increase in economy-wide output of 2.62 and 2.61 euro respectively. Similarly, from Appendix B and for the year ending 2010, the top-ranking sector with the highest input (supply) multiplier of 2.56 euro is the Advertising and market research (28) sector, followed by the Electricity (13) sector amounting to 2.52 euro. Therefore, based on the 2010 SIOT, a one monetary euro increase in the availability of primary inputs towards the Advertising and market research (28) and Electricity (13) sectors would lead to an increase in economy-wide output of 2.56 and 2.52 euro respectively. The input (supply) multipliers are also justified to assess the impact on economy-wide output following adverse exogenous shocks in a factor of primary inputs. From Table 1 and for the year ending 2015, one monetary euro less availability of primary inputs to the Manufacture of other non-metallic mineral products (8) sector would result in economy-wide output to decline by 2.62 euro. Similarly, for the year ending 2010, one monetary euro less availability of primary inputs to the Advertising and market research (28) sector would result in economy-wide output to decline by 2.23 euro. The reduction in the total output originates from the fewer primary inputs available for output production in the sector in which the shock originates, which in turn supplies its output to other economic sectors in the form of inputs required for their production processes to produce output. In this case, based on the 2015 SIOT, the less availability of primary inputs, for example labour, in the production process of the Manufacture of other non-metallic mineral products (8) sector would lead to a reduction in the output of the sector itself and in turn the output of the other economic sectors that depend on Manufacture of other non-metallic mineral products (8) sector.  For the year ending 2010, had the availability of primary inputs of any of these sectors increased by one monetary euro, total output would only increase by a unitary amount since their input (supply) multiplier estimates amount to one euro, respectively. However, for the year ending 2015, the input (supply) multiplier for the Households activities as employers (43) sector slightly increased to 1.01 euro. Therefore, although the same unitary effect on total output occurs following a one monetary euro increase in primary inputs of sectors 25 and 44, sector 43 slightly increases the overall economy-wide output. However, the increase is negligible and would not maximise the increase in potential output had the same primary inputs been allocated to the top-ranking sectors, keeping all else constant.
From Appendix B, noticeable differences in the ranking of the input (supply) multipliers for the years ending 2010 and 2015 were observed across all Maltese economic sectors. From Table 1, when focusing the comparison of the input (supply) multipliers for the top ten highest ranking sectors based on the 2010 and 2015 SIOTs, the Electricity (13) sector was the only domestic sector that managed to maintain the same ranking. The highest input (supply) multiplier for the year ending 2010 is attributed to the Advertising and market research (28) sector, which according to the 2010 SIOT, only 4 per cent of its output takes the form of imports. However, from Appendix B and for the year ending 2015, in terms of input (supply) multiplier, the same sector ranked 26, with 46 per cent of its total output attributed to imports.
In the SIOTs for the years 2010 and 2015, the sector with the highest share of imports is the financial services (21) sector. Based on the 2010 SIOT, the financial services (21) sector accounted to around 90 per cent of its total output as imports. Similarly, based on the 2015 SIOT, the financial services (21) sector accounts to around 87 per cent of its total output as imports. The high import content stems from the inclusion of Special Purpose Entities (SPEs) within the NACE sectoral classification as directed under the latest NACE REV.2 (2008) during the construction of the SIOTs. From Appendix B, it can also be observed that the input (supply) multipliers of the financial services (21) sector for the years ending 2010 and 2015 exhibit low multiplier magnitudes relative to the other domestic economic sectors, amounting to 1.18 and 1.13 euro respectively.

Conclusion and Discussion
The input (supply) multiplier estimates capture the extent to which the allocation of an extra monetary euro worth of primary inputs to an economic sector would increase overall potential output throughout the entire economy in terms of supporting economic growth. Therefore, this measure can be utilised to assess the potential increase on economy-wide output following one monetary euro exogenous shock in a factor of primary inputs. In the context of a the domestic SIOTs employed for this study, primary inputs pertain to all the components of GVA together with the imports of goods and services component.
The multipliers derived in this paper can be of use for policymakers for the formulation of sector specific labour market policy formation as they illustrate how a potential change in sectoral labour supply, which is captured via compensation of employees (a sub-component of GVA) could influence production activities not only in that sector, but across all sectors in the economy. In other words, the input (supply) multipliers may indicate in which economic sector, operating within the Maltese economy, it would be most advantageous to increase the labour supply with the aim of supporting higher economic growth. The relevance of the results presented in this paper for policy makers should be evaluated within the context of the significant labour supply shortage present within various sectors of the Maltese economy. This notwithstanding the negative impact that the COVID-19 pandemic has had on the economy (NPB, 2020). The Malta Employers' Association wage inflation survey carried out in 2019 concluded that more than half of the Maltese companies surveyed employ foreign workers. Increasing female participation rates and pension workers also contributed to the rise in the labour force. Maltese-based companies face strong competition to meet their required personnel demand (Vistage, 2021). Amongst others, the Malta Financial Services Authority (MFSA, 2015) and the Malta Gaming Authority (MGA, 2018) had already presented publications on the challenges faced by the skills gap to meet labour demand. Therefore, Maltese-based companies recruit foreign workers to fill in the excess labour demand, leading to the influx of foreign nationals (The Malta Chamber, 2018). The hospitality sector also faces the challenge of skills shortage, reinforced with the lack of foreign workers available locally due to the pandemic (Cefai, 2021). The influx of foreign workers and increased female participation in the labour force drives upwards the supply of labour which in turn positively shocks total output. The input (supply) multipliers could thus be utilised by policy makers to indicate in which sector it is most beneficial to allocate primary resources, such as labour supply, with the aim of supporting economic expansion. Furthermore, it should be noted that, all else equal, in a situation where labour supply does not keep up with increased labour demand, market pressures would also lead to an upward pressure on wage inflation. The resulting effects of excess labour demand could be assessed via the Leontief Cost-Push Price Model, where the consequence of increasing wage costs reflect in higher prices across all Maltese economic sectors because of their interlinkages (Theuma, 2018).
From Table 1 and based on the 2015 SIOT, the increase in potential output is maximised following the allocation of primary inputs to the Manufacture of other non-metallic mineral products (8) sector. The moment that labour supply lags behind labour demand, market pressures would drive wages upwards that in turns leads to price increases across all Maltese economic sectors, keeping all else constant.
From Table 1 in the results chapter, for the year ending 2015, the highest input (supply) multiplier was attributed to the Manufacture of other non-metallic mineral products (8) sector. In other words, every additional one monetary euro worth of primary inputs allocated to the Manufacture of other non-metallic mineral products (8) sector would significantly increase potential output based on the 2015 SIOT. Similarly, from Appendix B and for the year ending 2010, the highest input (supply) multiplier was attributed to the Advertising and market research (28) sector. Therefore, every additional one monetary euro worth of primary inputs allocated to the Advertising and market research (28) sector would significantly increase potential output based on the 2010 SIOT. These results are based on the reference year in which the SIOTs were constructed, including the assumptions imposed by the standard input-output framework and the supply-side model, keeping all other things constant.
From Appendix B, findings present that the overall ranking of the input (supply) multipliers between the reference years of 2010 and 2015 changed. In fact, Figure 1 shows different rankings of the top ten sectors with the highest input (supply) multiplier estimates, excluding the Electricity (13) sector, which ranked second across both SIOTs for the year ending 2010 and 2015. Following the analogous feature between the input (supply) multipliers and Leontief output (production) multipliers, the magnitude of the input (supply) multipliers also depend on the share of leakages in relation to the amount of inputs utilised during the production of output by every sector. From Appendix B, sectors with high import content such as the Financial services (21) sector experienced low multiplier effects on potential output.
The application of the Ghosh Supply-Driven Model to estimate the input (supply) multipliers is subject to several robust assumptions, presented in detail within the methodology chapter. The input (supply) multiplier estimates should be interpreted with caution following the robust assumptions implied by the input-output modelling framework and the supply-side model. However, the input (supply) multipliers estimated in this study provide a first cut estimate in which economic sector it is most optimal to make primary resources available to support economic growth in the Maltese economy.
A research avenue which would enable significantly further insights on the impact of a further availability of primary inputs on the production process is the formulation of a computable generable equilibrium (CGE) model (Sue Wing, 2004;Boeters and Savard, 2011) within the context of the Maltese economy which could for example be utilised to assess the effects on the labour market following different scenarios of policy implementation. For instance, this would potentially allow for a more in-depth study on the effects on wages and unemployment. Furthermore, depending on the specification of the CGE model, assuming it allows for the disaggregation of the households institution, it could be possible to study the effects on the labour market of different policy scenarios across the different household groups and thus assess also the sector specific impact of such policies on household income distribution.

Appendix B
Input ( Manufacture of wood and of products of wood and cork, except furniture; manufacture of articles of straw and plaiting materials C16 7 Manufacture of paper and paper products, printing and reproduction of recorded media, manufacture of coke and refined petroleum products, chemical products, basic pharmaceutical products and pharmaceutical preparations and rubber and plastic products C17-22 Manufacture of wood and of products of wood and cork, except furniture; manufacture of articles of straw and plaiting materials 1.82 9 2.11 5 7 Manufacture of paper and paper products, printing and reproduction of recorded media, manufacture of coke and refined petroleum products, chemical products, basic pharmaceutical products and pharmaceutical preparations and rubber and plastic products