An Analysis of the Output and Employment Conversion Matrices of Australia ’ s Economy

Based on two snapshots taken from the Australian economy, this study quantifies the impacts of final demand aggregates on output and employment in various sectors using the 1989 and 1997 conversion matrices. The sectoral output and employment are linked with final demand deliveries in such a way that one can measure the impacts on changes in each component of aggregate demand, other components remaining unchanged, on output and employment. A comparison of the aggregate output and employment multipliers in 1989 to 1997 indicates that while the output multipliers have increased, the employment multipliers have declined. This means that through time, due to rising labour productivity, the various components of aggregate demand would need to grow at a faster rate in order to achieve a certain employment growth. It was also found that almost all employment generated between 1989 to 1997 was in three service industries, namely Community, Social & Personal Services; Wholesale Retail, and Restaurants; and Property and Business Services. These are industries that are least likely to have benefited from the productivity gains that resulted from the microeconomic reforms that characterised the Australian economy during this period. On a relative basis, a rise in various components of aggregate final demand can lead to a higher employment generation in these three industries. JEL classification numbers: E12; E24; C67


Introduction
The linking of the demand and production sides of the economy is relevant for effective coordination of stabilisation policies and development strategies which are of paramount importance for policy makers. In macroeconometric modelling there are several ways to deal with the production block by using various types of production functions. In this study, using the 1989 and 1997 input-output (IO) tables, two conversion matrices are computed which translate final demand aggregates into sectoral output and employment. This link is important particularly in Australia, where intermediate demands among various sectors are of significant magnitudes. One should recognise that, by using an IO table in a model, the supply side has not been neglected since both intermediate and final demand encompass demand for capital goods and other factors of production (Klein, 1965, p. 323).
The structure of the rest of the paper is as follows: Section 2 specifies the theoretical and analytical framework of the model. Section 3 discusses the issues associated with the data used in the paper. Section 4 presents the empirical results and some illustrative policy implications of the study which aims to measure the impact of increases in each component of the aggregate demand on the sectoral output and employment using the corresponding the 1989 and 1997 conversion matrices. Section 5 provides some concluding remarks.

Theoretical Framework
The incorporation and implementation of a demand-side IO model in macroeconometric modelling have been examined by many applied economists. The main objective of the integration of an IO system to a macroeconometric model (MEM) is to obtain a "conversion (transition) matrix" by using a base year IO table. Using various versions of the Brookings model, Fisher, Klein and Shinkai (1965) and Kresge (1969) pioneered the use of the conversion matrix to link a national income determination model and an IO system. Some other economists who have also discussed IO analysis in a MEM framework are Klein (1965Klein ( , 1978Klein ( , 1983Klein ( , 1989), Behrman and Klein (1970), Morishima et al. (1972), Preston (1972), Chalmers (1972), Bodkin (1976, Marzouk (1975), Seguy and Ramirez (1975), Sapir (1976), Hebden (1983), Chowdhury (1984, Oshikoya (1990) and Bon and Bing (1993).
According to Klein (1983), the conversion matrix is the vehicle of transformation and has two important applications. First, by multiplying the aggregate demand components in each row of the conversion matrix, the model-builder can compute sectoral output or value added and employment. Second, by multiplying the sectoral price deflators by each column of this matrix, the aggregate final demand price deflators can be estimated. See Bodkin (1976) and Klein (1983) for a detailed discussion of these applications. In this study only the first application has been utilised.
To obtain the conversion matrix one may begin with the following Leontief relation: where I is an identity matrix, X is a (n x 1) vector of total gross output, F indicates the (n x 1) vector of sectoral final demand, and A is the (n x n) square matrix of the Leontief domestic direct coefficients. This means that imports are assumed to be non-competitive and completely exogenous to the IO system. In order to measure the impacts of aggregate final demand components on the sectoral output or employment some assumptions have to be invoked.
Let us assume that C=private consumption, G=government consumption, I=gross fixed capital formation, S=changes in stocks (capital inventory), E=exports of goods and services. If these aggregates, i.e. C, G, I, S and E, shape the λ λ λ λ (column) vector and also if one accepts proportionality and constancy of the (n x m) matrix of the sectoral distribution of final demand components (D), (where n and m denote the number of sectors and aggregate final demand components, respectively) the column vector of sectoral final demand can be written as By substituting (2) into (1), it is clear that Since all elements of (I-A) -1 and D in equation (3) are given by a base year IO table, H or the output conversion matrix can be computed as follows.
Regarding the first application of the conversion matrix (H) in equation (4), given the ex ante or ex post time series data of aggregate final demand components for any given time period, the sectoral output can be accordingly obtained in factor prices. In this respect, one should note that there is no constraint on these computed sectoral output. Therefore, it is necessary for the modeller to bear in mind the extent to which an increase in each component of final demand can be converted to output in various sectors. In other words, an infinite increase in each component of aggregate demand does not imply an infinite increase in output in various sectors. Equation (3) can also be written as Further, the H matrix can be regarded as a comprehensive sectoral output multiplier matrix. For example, h ij shows, if the j th component of aggregate demand changes by one unit, how much gross output in sector i will be changed. That is.
If R is a diagonal matrix which shows the ratio of employment to output (l i /x i ) in sector i, then the sectoral employment can be computed using the following relation: Where Ω Ω Ω Ω=RH is the employment conversion matrix. Similar to relation (6), Ω Ω Ω Ω can quantify the impacts of various components of aggregate demand on the sectoral employment. That is:

The Data
Our aim is to compare the resulting conversion matrices from a earlier Australian IO Accounts 1993, which is the latest international standard for compiling IO tables and national accounts statistics.
All transactions recorded in both tables are expressed at basic prices in million Australian dollars. While structural change in Australia has involved both the shift to service based activities and the emergence of new industries, which is reflected in the use of ISIC rev3, rather than ISIC rev2, we decided to facilitate comparisons by collapsing both classifications to a common 17 sector classification. In other words, the original 1989 and 1997 IO tables were compiled with 35 and 106 industry sectors, respectively, but for the sake of simplicity and consistency of the results, the aggregated version of these tables is employed in this paper. It should be noted both IO tables are at current prices, because unlike the 1989 table, the 1997 table is not available at constant prices. We used the Microsoft Excel and the GRIMP software package to undertake the IO calculations (see West, 1993).

Empirical Results and Policy Implications
The first step in the empirical work is related to the computation of the output and employment conversion matrices. Using the 1989 and 1997 IO tables and equations (5) and (7), the H and Ω Ω Ω Ω matrices are presented in Tables 1 and 2. However, prior to undertaking any empirical analysis it is crucial to check the accuracy of the computed conversion matrices. To this end, after substituting the five components of aggregate demand (C, G, I, S and E) in 1989 and 1997 into the equations (5) and (7), the corresponding sectoral output and employment have been computed. It was observed that the computed sectoral output and employment data were exactly equal to the actual data.
Before looking at the detail of the tables and figures, it is important to point to some Microeconomic reform has been described as involving "the implementation of government policies designed to deregulate or re-regulate product, service and factor markets in such a way as to promote competition and efficiency in relation to both domestic and international markets" (Robinson 1994, p.384). It has been argued that microeconomic reform will give a significant boost to Australian productivity, although the question as to whether this would be a one-off increase or a permanent rise in the rate of productivity growth is open to question (Otto, 1997).
The period under review here was one in which some of the most important outcomes of the microeconomic reform agenda were experienced. These included: • reform of the labour market involving initial restructuring of the ubiquitous centralized wage fixing process to make it more flexible, and the eventual introduction of enterprise bargaining; • significant decreases in import tariffs which had been amongst the highest in the developed world; • changes to the tax system, with reductions in both company and personal income tax rates; • the effects of the deregulation of Australia's highly regulated financial sector which was overhauled as a result of a series of enquiries carried out in the 1980s; and • the efficiency gains that accompanied privatization and corporatization of government owned enterprises.
As might be expected, these reforms had the potential to affect some sectors of the economy in terms of productivity rises to a much greater extent than others (see Figure 3 later in this section).
In the light of this background to developments in the Australian economy, we now turn to some illustrative examples of the inferences that can be drawn from the data contained in the conversion matrices.
According to Tables 1 and 2, from 1989 to 1997 the aggregate output multipliers (i.e. the column sums of the output conversion matrices) for all aggregate demand components have exhibited a meagre increase with the only exception being the gross fixed capital formation, which has shown a very small decline (See also Figure 1). As discussed earlier, each element of these matrices can be regarded as a sector-specific multiplier. For instance, a 100 dollars increase in government consumption in 1997 increased the gross output by about 85 dollars in the Community, social and personal services sector (see row 17 and column 8 in Table 1) and by 14 dollars in the Transport and storage sector (row 13 and column 8 in Table 1).
Among the four reported columns of the output conversion matrices, it appears that an increase in the exports of goods and services has the highest multiplier effect on output in both 1989 and 1997. Overall, it can be stated that in 1997 a one dollar rise in private consumption or government consumption could increase aggregate gross output by 1.5 dollars. A similar increase in exports had an impact of 1.76 dollar on output in the same year. Therefore, on a relative basis, one can argue that policies aimed at promoting exports can precipitate output growth, particularly in the following sectors: Mining; Wholesale retail, and restaurants; Basic metals and fabricated products; Agriculture, forestry and fishing ; Food, beverages and tobacco (See the magnitudes of the penultimate column of Table 1). As a rule of thumb one can expect that, on average, a dollar increase in aggregate final demand can stimulate total gross output by roughly 1.4-1.8 dollars depending on the type of expenditure (see Table 1). It should be noted that the above multipliers are based on a snapshot of the structure of the Australia's economy as captured by the actual IO tables.
[ Table 1 and Figure 1 about here] The next step is to investigate how sectoral employment would change if one of the final demand components increases by one unit. Based on the conversion matrices in Table 2  However, the rise in productivity is more pronounced in more capital-intensive industries such as Mining and quarrying; and Electricity, gas and water. Not only are these industries amenable to productivity enhancing technological change but they are also industries that have reaped the benefits of many aspects of microeconomic reform. These include labour market reform, privatisation and corporatization of state owned enterprises and, for those industries with large export markets, the benefits of a lower Australian dollar that resulted from tariff reductions and deregulation of the foreign exchange market. Figure 4 shows that (1) service industries constitute the bulk of employment in the Australian economy; (2) the number of jobs created by non-service industries is negligible or declining; and (3) almost all the new jobs created between 1989 and 1997 were in the service industries. These employment-generating industries, which are amongst the industries whose productivity is least affected by microeconomic reform, are, in order of importance, as follows: Community, social & personal services; Wholesale retail, and restaurants; and Property and business services. On the other hand, Finance and insurance, which did not change its fourth ranking over the period, did, as Figure 3 indicates, show labour productivity growth which was more akin to that of the previously mentioned capital-intensive industries than to the other service industries. Along with technological change in the area of information technology, this increase can be, at least in part, attributed to deregulation of the finance sector that occurred in the 1980s as part of the microeconomic reform agenda.

and Figures 2, 3 and 4 about here]
A cursory look at Table 2 shows how we can reinforce the creation of employment in these three sectors. With a sector-specific employment multiplier of 13.43, the Community, social & personal services industry is very responsive to an increase in government consumption.
Based on the structure of Australian's economy in 1997, one million dollars increase in government expenditures created at an aggregate level about 18 full-time jobs. Of these 18 jobs, more than 13 were in the Community, social & personal services industry. On the other hand, it seems that a similar increase in private consumption, on a relative basis, can increase employment in the Wholesale retail, and restaurants industry more than the other industries. It should be noted that the above three industries have also the largest employment multipliers in relation to a change in private and government consumption, and to some extent exports. This means that, given the present structure of the economy, if various components of final demand were to increase, the overwhelming majority of the created jobs would be within the above three service industries.
Despite the declining employment multipliers, it is important to note that the aggregate employment multiplier for government consumption has the highest magnitude compared to the other three components of aggregate final demand (i.e. C, I, and E) in both 1989 and 1997. In 1997 a million dollars rise in government consumption could create 18 jobs, suggesting that for approximately each $56,000 spent, one full-time job was created. The same increase in C, I and E could create 13, 11.5 and 12 jobs, respectively in 1997. This suggests that, in times of high unemployment the most effective (but not necessarily the most efficient) way of creating employment is through increased government expenditure.
It should be recognized that purchasing power parity studies indicate that labour-intensive services are often more costly to produce in rich countries than in poor countries (see, inter alia, Dowrick, 2001, andOECD, 2001) and so one might expect that these sectors (like Community, social and personal services; Wholesale retail, restaurants etc; and Property and business services) to be increasing in relative labour cost and employment figures as the country grows.
More broadly, Baumol (1997) also argues that the rising production cost in labour-intensive industries, such as the arts, health care, and education, is inevitable. The rising rate of publicsector price deflator well above the aggregate GDP deflator in recent times can be explained by "the low productivity of labour-intensive government activities compared with the relatively capital-intensive private sector" (Fordham, 2003, p.574). Gundlach and Wöβmann (2001) examined changes in the productivity of schooling for six East Asian countries, supporting the view that the cost of schooling rose by more than the price of other services in 1980 to 1994. It can be argued that increases in employment in service industries may be attributed to declining relative productivity. According to Gundlach and Wöβmann, the relative fading productivity of the education sector in East Asian countries relates to a marked decline in the pupil-teacher ratio. Therefore, it is quite normal that labour-intensive services such as education and community services are highly likely to continue to grow faster in terms of employment and at the same time they will enjoy lower productivities for an advanced country such as Australia. In relation to this issue, using a different sectoral classification, Valadkhani (2003) has found that the following industries are not only the fastest growing (in terms of annual employment growth during the 1985-2000 period) and the largest sectors (in terms of their share in total employment and salary and wages in the year 1996-97), but also possess relatively higher employment elasticities: Retail trade; Construction; Health & community services; Property & business services; and Education. It can be argued that these important industries will play a substantial role in generating employment in the foreseeable future.

Conclusions
This paper has linked the sectoral output and employment to the final demand deliveries for 17 major sectors in 1989 and 1997. It has identified and discussed the expenditure categories and sectors that give large multiplier outcomes with a view to illustrating some of the ways in which policies designed to meet objectives such as increased GDP or employment growth might be framed. This discussion has occurred in the context of the microeconomic reform agenda that has brought significant structural reform to the Australian economy over the period in question.
Nonetheless, this brief discussion of the relevance of a knowledge of sectoral multipliers for policy development has only scratched the surface of the possible interpretations that might be placed on the data.
As discussed by Valadkhani (2003), one should recognize that the use of IO systems for ex ante forecasting is very limited due to the following restrictive assumptions: (1) homogeneity of output; (2) zero rates of substitution between inputs and infinite elasticity of supply of factors of production; (3) fixed proportions between inputs and outputs; (4) absence of economies of scale; (5) linearity in the cyclical impact; and (6) exogeneity of primary inputs and final demand components. IO models cannot capture the importance of major asymmetries that exist over the business cycle and the dynamic and feedback effects on factor prices, the exchange rate, consumption, public expenditure, exports and imports. Therefore, the restrictive assumptions embedded in an IO system make generalisations and forecasting difficult but the objective of this study was to analyse the impacts of various aggregate demand components on the sectoral output and employment as they occurred in an ex post (rather than ex ante) sense. In other words, the elements of the computed conversion matrices have been used in this paper to reveal how the Australian economy actually reacted to such shocks at the time. Thus the findings are, to some extent, indicative of the forces at work. Exports of goods and services λ 5 1989Rank 1997Rank 1989Rank 1997Rank 1989Rank 1997Rank 1989Rank 1997   Source: ABS (2001) andOECD (1994).