The Export Base Theory of Regional Development: A Brief …



The Export Base and Input-output Models of Regional Development

Background to the classroom presentation and discussion

©David M. Nowlan 2006

Among practitioners of regional development policy, the export-base model of development is a favorite tool. You will probably recognize it as the “multiplier” model from Keynesian economics, and indeed that is its origin. Unlike the regional models that we’ll turn to next, this model is demand-driven, as is appropriate for one with Keynesian origins.[1]

The Simple Multiplier

We start from the Keynesian supply and demand aggregate model of an economy, regional or national. On the left-hand side of the Keynesian model, Y represents the flow of output or supply (this also equals regional income). On the right-hand side are the flow demand elements: C for consumption, I for investment, X for exports, less M for imports (M could also be put as a positive supply input on the left-hand side).[2]

[pic] equation 1

Government spending and taxes are not included, in order to simplify the presentation.[3]

Introduce a standard consumption function, with consumption a function of output or income:

[pic]

Similarly, we can relate imports to the level of output or income:

[pic]

I and X we’ll take as exogenous:

[pic] and [pic].

Putting these relationships into equation 1, we get

[pic] equation 2

or

[pic] equation 3

Suppose now that exports,[pic], change by some increment. Then we have, from 3,

[pic] equation 4

The right-hand side in equation 4 is known as the “multiplier”. In this case it shows the increase (or decrease) in the equilibrium income or output in a region as a proportion of the increase (or decrease) in the exogenous export demand.

“c” is the marginal propensity to consume out of income, which we can take to be less than 1. “m” measures the extent to which this consumption is met by imports rather than domestic production, so presumably [pic].

Application of the Multiplier

Suppose that the marginal propensity to consume in some economy is 0.8 and that all of this consumption is met by domestic production, so that m=0. Then the multiplier, [pic] , is 5. This says that for every extra Euro of exports, regional output rises by 5 Euros. The idea basically is this: the “first round” of the extra Euro in exports raises Y by €1. This extra income then creates a “second round” of consumption expenditure of €1x0.8=€0.8. This in turn creates a “third round of expenditure equal to €0.8x0.8=€0.64; and so on. When these “rounds” get added up, they result in a total increase in Y of €5.

In this example, the region has what might be called strong internal linkages. All consumption is directed to local products; at the margin, no consumption goods are imported.[4] The smaller the region and the less developed it is, the less realistic is this assumption.

In this example, c-m, which is the proportion of incremental income that is provided for from local production, is 0.8. A number of studies, even of highly developed regions put this value at between 0.2 and 0.4. For example, a study of U.S. regions based on family expenditure data came up with an average estimate for c-m of 0.23. A study in the 1990s of the impact of Nottingham University, in Britain, on the Nottingham regional economy reckoned that the value of c-m for students was about 0.43 and for staff about 0.22.[5]

If c-m, the marginal propensity to consume locally, were, say, 0.25, then the multiplier would be only 1.33.

Internal Linkages and the Import Content of Exports

Clearly, the extent to which a local, regional economy can produce the goods that consumers want, so they don’t have to be imported, has an enormous effect on the value of the export multiplier. I generally think of this ability as related to the strength of internal linkages in the regional economy, or one might think of it as a measure of the degree of development or maturity of the regional economy. For example, suppose we think of a poor, resource-based region that has some mining operations but little else. Then, consumption based on income earned from mining-sector exports will be spent heavily if not entirely on imports. If consumption is entirely of imports, then c = m and the multiplier is 1 (see equation 4). I.e., the regional income and output is increased by only the increase in exports; there is no second or third round of increases due to internal consumption spending.

Aside from the common practice of using average propensities in place of the correct marginal propensities (because average propensities are more easily measurable), there are other difficulties with using the export-base model as a model of regional development, especially for underdeveloped regions, which is often where one is tempted to use it. Consider an underdeveloped region with perhaps some foreign owned mining, or agriculture or even manufacturing activity; or think of the Greek islands or Sicily with heavy dependencies on tourism, an export industry, using foreign-owned hotels.

Suppose these foreign owned sectors produce most of the exports from the region – a not uncommon situation – and we want to estimate the regional impact of an increase in exports. So, exports, perhaps tourism, rise by, say, €100,000 a year. Now some of this value will probably include the importation of goods and services needed to produce the export products or services. We can call this the marginal propensity to import with respect to exports,[pic]. This changes the import function to

[pic] . We can call [pic] net exports.

Equation 2 then becomes

[pic] equation 5

From this,

[pic], and the export multiplier becomes

[pic] equation 6

If, in order to increase exports, 60% of the value of the exports has to be imported to serve as inputs to the export good or service, then the multiplier becomes only 40% of the value it would have if exports could be increased without the need for a direct increase in imports, i.e. in equation 6, the numerator [pic]. If (c-m) is 0.25, as before, then the multiplier, previously 1.33, is reduced to 0.53. An increase in export value of €100,000 will increase regional income and output by €53,000.

Again in this case, the magnitude of [pic]says something about the maturity or development level of the regional economy. A more mature economy will be able to supply a higher percentage of the goods and services needed to increase exports.

Foreign Ownership and Use of Foreign Capital and Labour

The story may not end here. Let’s look at another complication. Again suppose the export sector is heavily foreign owned. The value of exports then, less the imports needed to produce those exports, will represent income to the region. Suppose a certain percentage of that income accrues to the foreign owners either as payments for the services of foreign nationals or as profits to the foreign owners. Suppose further that none of this foreign income is spent in the region; only payments to local factors of production are spent in the region, in the proportion (c-m). This foreign income again represents a “leakage” from the export value; call this leakage proportion [pic] of the net exports, i.e. of [pic].

Then, equation 5 becomes

[pic] equation 7

From this,

[pic], and export multiplier becomes

[pic] equation 8

Equation 8 is our new export multiplier, with a further reduced numerator. To see the effect of this on the regional multiplier, assume again that [pic] and that [pic]. The numerator in equation 8 is therefore 0.2. In other words, with a 60% import component of incremental exports and a 50% payout of net exports to foreign workers and owners, the regional export multiplier is only one-fifth of its value without these leakages. If we assume again that (c-m) is 0.25, an additional export flow of €100,000 a year will increase the annual output and income in this region by only €27,000.

For poor regions with exports heavily dependent on foreign investment, one can see that the multiplier effect on the region of increased exports could be quite small. The more developed the region is, the more it can export from locally owned enterprises, the higher will be the multiplier effect of improved export performance.[6]

Application to Investment Flows

Notice that this multiplier analysis could also be applied to an increase in exogenous investment,[pic]. Suppose the government of some region introduces policies that lead to an increase in investment in, say, tourist facilities of €1 million a year for the foreseeable future. Regional equilibrium output or income would be expected to rise by €1 million times the multiplier. If there were no complications related to import needs of the new investment or foreign earnings, then the simple multiplier of equation 4 would be appropriate.

But, if new investment had an import component, and if earnings generated by the investment went in part to foreign workers or foreign construction companies who spent outside the region, then the more complicated multiplier of equation 8 would apply, with [pic] and [pic] suitably interpreted in terms of investment activity rather than export activity. Once again, this multiplier could well be below 1, especially in a underdeveloped region with poor internal linkages. Notice as well, that incremental investment in a particular project will have a finite life, maybe only a few years. In this case the impact on regional income will be short-lived; the effect will not be a permanent increase in the income or output level.

Separate Equations for Separate Sectors

One way to handle the fact that changing exports from different sectors may have dramatically different multiplier effects on the regional economy is to estimate a separate multiplier relationship for each of the different sectors. Thus, one might segregate and estimate separately those export sectors that rely relatively heavily on imports as inputs to the exports, and also those that are foreign owned or otherwise rely heavily on foreign factors of production. Multipliers for these sectors may be relatively small. Domestically owned sectors using a high proportion of local goods and services as inputs could then have an equation and multiplier of their own. This procedure of course requires more data, but the gains may well justify the greater effort.

A separation of different sectors in this way presages in some ways the input-output approach discussed below.

Issue of Supply Constraints

As noted at the outset, these multiplier models of regional development are demand driven. Nothing is said about the availability of productive factors, especially labour, to meet any increments in demand. As in Keynesian models generally, there is an implicit assumption that the economy has idle factors that can be brought into use if demand rises.

It seems reasonable to assume that, if export or investment demand rises, capital will flow into the region to provide for investment needs, since capital in today’s world is relatively mobile (although for a variety of reasons associated mainly with riskiness, the returns to capital required in some regions to generate this inflow may be well above the international average). But labour is, in general and especially in Europe, not so mobile. With sticky international or inter-regional migration of labour, an upsurge in export or investment demand in the region may simply result in higher wages and no real growth, if labour markets are tight, with low unemployment levels.[7]

Even within regions of high unemployment, the mix of skills, education and talent among the unemployed may not be the mix required to allow the expansion of demand. In today’s world, skilled labour is likely to be scarce particularly in the poor regions that might otherwise benefit from increased demand. Thus, even with high unemployment among the uneducated or unskilled, the Keynesian conditions of surplus factors may not exist in such a way that additional export or investment demand will lead to additional regional output or income.

Further Caveats

Two final comments on the export-base model of regional development: 1) Except in the case of a new-found resource and a subsequent resource boom (which, as we’ve seen, may not have much of a multiplier effect), a region that succeeds in increasing its exports is likely to be a region that has a strong internal economy. Think of the growth in exports from the industrial districts we looked at – all of them depended upon the successful growth and development of the sectors from which the exports came, including those industries supplying machinery to the original industry on which the district was based. Thus, the export-base model in an important sense puts the cart before the horse. Exports are built upon a successful regional economy, they don’t create it. 2) The export-base model is most at home when applied to smaller regions which are likely to be more open than larger regions and therefore to have a relatively more important export sector. In particular, the export-base model logically cannot be complete as a model of economic development since it cannot, for example, be applied to the whole-world economy, which has no exports.

The Input-Output Regional Model

The input-output regional model is basically an expansion of the aggregate, single-equation export base model to include a richer array of economic sectors in the economy. It focuses on the interdependencies among producing sectors, but, unlike the simple multiplier model, does not usually incorporate the feedback from higher income levels to higher consumption or household demand.

Here, I will look only at the basics of an input-output regional model by introducing two sectors, a manufacturing sector and a service sector. The basic idea is that each sector provides inputs to itself and to the other sector, in amounts that depend on the output of those sectors. In addition, there is a final demand for each sector consisting of the demand for sector output from consumers (households), from exports, from investment and from government (basically the same ingredients as the right-hand side in equation 1, except that imports in some input output models need not be deducted[8]).

Input-output analysis begins with the construction of a “transactions” table, based on surveys of the regional or national economy. The following table, Table 1, shows outputs in the rows and inputs or final demand in the columns. There are two sectors, manufacturing and services. Begin by assuming that the value of output in the manufacturing sector is €100 and in the services sector €50.

Table 1

| | INPUT VALUES | | |

| | |manufacturing |services |FINAL DEMAND |TOTAL OUPUT |

| | | | | | |

|OUTPUT VALUES | | | | | |

| |manufacturing |10 |5 |85 |100 |

|COLUMN TOTALS | |100 |50 | | |

To produce €100 of manufacturing output, €10 units of input from the same sector is needed along with €20 of input from the services sector. These required inputs are based on the technology within each sector (and clearly on the mix of activities, manufacturing and services, within each sector, although this mix is generally assumed to be constant). These values, shown in the shaded region of Table 1, constitute the core of the input-output table, sometimes called the transactions matrix.

The rest of the input column consists of the value added in the sector, essentially wages, returns to capital and profit, plus the value of imports.[9] Thus, in this example, the amount of value added plus imports is €70 in the manufacturing sector and €25 in the services sector.

The final demands for the output of each sector consist of consumption final demand, exports and investment demand, plus government demand, if government is included. Notice that the sum of the outputs, added along a sector row, equals in value the sum of the sector inputs, as it should.

Within the shaded area, the proportion of total input value that is required as input from each sector is the input-output coefficient associated with that particular transaction. Thus, of inputs to the manufacturing sector, 10% is required as manufacturing input and 20% is required as services input. Thus, these two coefficients are therefore 0.1 and 0.2 respectively. Similarly, the corresponding input coefficients in the services sector are 0.1 and 0.4. The core matrix of the input-output model thus becomes

[pic].

Using these coefficients, we may write:

for the manufacturing sector 100 = (0.1)100 + (0.1)50 + 85

and for the services sector 50 = (0.2)100 + (0.4)50 + 10

These equations say that output, on the left-hand side, equals demand, on the right-hand side, much like the single equation export-base model in equation 1.

Now the point of input-output analysis, as a tool of regional development, is to understand how the structure and levels of output in the various sectors is affected by changes in the final demand for the products of each sector, much as we wanted to use the simple export base model to see how the regional economy responded to changes in exports (or investment).

To see how to do this, we generalize the above analysis by letting [pic] stand for manufacturing output, [pic] stand for services output, [pic] stand for manufacturing final demand and [pic] stand for services final demand. Then, recognizing that total input to a sector is equal in value to total output, we see that

[pic] and

[pic]

Rearranging, these become

[pic] and

[pic] equation 9

The final demands,[pic] and [pic], are given. Suppose we want to know the outputs of each sector, given these final demands. In the two equation 9 equations, we have two unknowns, [pic] and [pic], whose values we would like to know. In general we can solve for their values in terms of the givens [pic] and [pic].

Rearranging, we get

[pic] and

[pic]. equation 10

If you plug in the values of [pic] and [pic] from Table 1, you should get the expected result, that [pic]and [pic].

If export demand for manufacturing rose so that the final demand for manufacturing went from 85 to, say 105, you could use the two equations 10 to calculate the effect of such a demand increase on the outputs of the two sectors. You should get [pic] and [pic].

Notice that although the rise in export demand was only for manufacturers, the output of both sectors rose. This is because of the input-output interdependency among the sectors.

The model may be generalized further by designating the core matrix, [pic],

as [pic].

If we apply these coefficients to the output and input values we get

[pic] and

[pic]

Rearranging, these become

[pic] and

[pic]

In matrix form, this is[pic] equation 11

We can use equation 11 to solve for [pic] and [pic] in terms of [pic] and [pic]. Thus,

[pic]. equation 12

The matrix [pic] is called the inverse of the matrix

[pic]. It is the input-output equivalent of the single-equation multiplier, which, you will recall, has a similar inverse form, [pic].

From our example, [pic] . From this, [pic]. The inverse[10] of this matrix is

[pic]. equation 13

Substituting the equation 13 numbers into equation 12, and using our original example with [pic]and [pic], we get, using matrix multiplication, values for [pic] and [pic]:

[pic], as we should.

Using the same “multiplier,” i.e. the inverted matrix of equation 13, but now increasing the final demand for manufacturing output from 85 to 105, as we did before, we once again get [pic] and [pic].

One of the advantages of input-output analysis is that we can explore the significance of internal linkages on regional output. The coefficients in the core matrix give us important information about these linkages. Suppose, for example, that we were able to strengthen the internal linkages in this region in such a way that more local input was used in producing manufactures goods with a corresponding reduction in imports. Let’s say that to produce €100 of manufacturing output now uses €20 rather than €10 from local manufacturers as input. Correspondingly, the value added + import content of inputs will fall from 70 to 60, so Table 1 now becomes

Table 2

| | INPUT VALUES | | |

| | |manufacturing |services |FINAL DEMAND |TOTAL OUPUT |

| | | | | | |

|OUTPUT VALUES | | | | | |

| |manufacturing |20 |5 |85 |100 |

|COLUMN TOTALS | |100 |50 | | |

From this,

[pic] and [pic]. Taking the inverse

(again using Excel), we get

[pic]. Thus, we have, as in equation 12,

[pic].

The strengthening of the internal linkages, with an additional 10% of manufacturing input to the manufacturing sector coming from local rather than imported sources, has raised the output of that sector from €100 to €113, and it has raised the output of the services sector from €50 to a little over €54. Notice that there has been no change in the level of exports or final demand.

This suggests that import substitution can be an important source of regional development. But import substitution must be done smartly and not clumsily. For example, slapping tariffs or other restrictions on imports, for the purpose of encouraging the use of local production, is likely to raise the cost of the affected inputs and thus raise the cost of the exported goods or services. Export demand will fall and the region could very well end up worse off than it was before the clumsy attempt at import substitution.

Smart ways of encouraging import substitution are likely to vary from region to region, but they may include training programs to upgrade the knowledge and quality of labour input to those activities that might provide local inputs, or they might include subsidy programs to help upgrade equipment or encourage investment in a sector with clear import-substitution potential. Another way to encourage import substitution may be the creation of trade associations that improve communication between those firms that need inputs and those firms that provide inputs.

Recall the story of the Sassuolo ceramic tile district discussed in Porter 1990. Tile firms initially imported all of their tile-making equipment. Local firms gradually became proficient at supplying equipment that was particularly suited to the type of clay used in the district; not only was local equipment substituted for imported equipment but the locally produced equipment then became and remains a major source of exports outside the region.

Input-output tables vary enormously in size, i.e. in the number of separate sectors included. A typical regional table might have a dozen or more sectors; some national tables reach close to 100 sectors. These large-scale tables are impressive and can be useful, but they like most input-output analysis, are subject to drawbacks. One real problem is that the coefficients of the core matrix are drawn from the overall situation when the underlying survey information was collected, so they not only consist of averages rather than marginal coefficients (recall that this is a common problem with the single-equation export-base model as well) but, if technology is changing rapidly they may be well out-of-date by the time the table is constructed and ready to use. One way that has sometimes been used to overcome that problem is to have a group of industry experts sit down with the input-output table and discuss how the core coefficients are likely to have changed since the original data were collected. Based on this, some corrections can be made and a greater level of confidence may be placed in the analysis (provided the experts know what they’re talking about!).

-----------------------

[1] Remember, Keynes was writing with the great depression of the late twenties and early 30s in mind. Supply constraints, at least for labour, were not an issue.

[2] This relationship is an equilibrium supply=demand equation if investment is taken to be desired investment, which is generally the case. If however, investment is defined simply as output that is not consumed or exported, then equation 1 becomes an identity.

[3] With governments taken into account, government expenditures and taxation “leakages,” [pic],would have to be added to equation 1. G is usually considered exogenous and T is a function of regional income, [pic]. You can work through the multiplier relationships with this addition, if you wish.

[4] You might wonder how the balance of payments will balance if we have an increment of exports but no increment of imports. The answer is that transactions in the capital account provide the necessary balancing items.

If the incremental exporter sold the incremental goods (or services) outside the region and retained the earnings outside, then a capital outflow would exactly match the current account exports and balance would be achieved. However, in this case the incremental export income would not be available for consumption spending within the region. So, given the example above, what must happen is this: the incremental export generates revenue in outside currency or other assets (these would be liabilities of some institution in the outside region or country, right?). These assets (or at least 80% of them) are then sold to the foreigners for the currency of or assets in the original region (i.e., liabilities of some institution in the original region), which can then be used!&',?@n ò ó õ

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úõúõðëãßÛÑßÇÀ߼߸߮ to make consumption purchases within the original region. Foreigners have drawn down their holdings (i.e. their assets) denominated in the liabilities of the original region, so this counts also as a capital outflow from the region and again the balance of payments is seen to retain its balance (as it must).

[5] These c-m values are in fact based on expenditure patterns which yield average values for propensities to consume and import, not marginal values. If these averages were used in export-base models it would be as if [pic]and [pic] were equal to 0, so average and marginal propensities would be the same, an assumption for which there is no justification, but which is nonetheless often used simply because marginal propensities are difficult to estimate.

[6] Sometimes, a regional multiplier is calculated not for regional income and output but for regional employment. The idea is very similar. Total employment,[pic], is divided into employment in the export sector, [pic], and employment in the non-export or local sector, [pic]. Employment in the local sector is assumed to be a function of total employment (just as consumption was assumed to be a function of total income in the Keynesian model):[pic]. Export-sector employment is given exogenously: [pic].

So we have,

[pic] and

[pic]

The employment multiplier in this simple case is [pic]. A higher [pic]entails a higher multiplier, and suggests a more mature, more developed region with stronger internal linkages.

[7] A “booming” export sector may result in what is known in the literature as the “Dutch disease.” This takes its name from the situation in the Netherlands in the 1960s when North Sea natural gas discoveries led to a booming natural gas sector. This had adverse consequences for the emerging manufacturing sector in the country. First, the booming sector needed more workers and was able to pay higher wages to get these workers. This had the effect of raising wages generally in the country’s economy and so making the manufacturing sector less competitive. Magnifying this effect was rising value of the Dutch gilder as a result of the export boom, which further worsened the competitiveness of the manufacturing sector.

[8] This depends on how the input-output matrix is constructed. If the core matrix includes imports as inputs, then they must be deducted from the final demand (this is most like equation 1). But if the core matrix includes only domestic production, then imports do not need to be deducted in the final demand columns.

[9] Here is where the comment in the previous footnote becomes relevant. If imports are similarly divided into manufacturers and services, then they could be included in the values that go into each sector as inputs, in which case they would not be included as part of the value added row below the core matrix, but would have to be subtracted from final demand. Both types of input-output analysis are used, with and without imports in the core matrix. In this example, imports are not included in the core matrix.

[10] Inverting matrices by hand can be a bit of a chore, but nowadays even common spread sheet applications like Excel can do the job for you – at least that’s what I used here.

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