International Trade and Institutions
International Trade and the Size of the Government
Rajat Acharyya
Abstract This paper examines the relationship between trade openness and size of the government. Under homothetic taste, and thus without the real income effect, a more open (small) economy may indeed have a larger size of the government even when the public good that it produces is not traded. When the public good is the most labour intensive good, the absolute size of the government expands with a tariff reduction under a reasonable assumption regarding employment shares of the export good. An additional condition requiring a sufficiently small, although not necessarily less than unity, value of the price elasticity of demand for the public good ensures that the relative size of the government expands as well.
Keywords Government size Openness Tariff reduction Non-traded good
Externality
JEL Classification F11 H11 H42
1 Introduction
Growing concerns over huge budgetary and fiscal deficits in a large number of countries have inspired quite a few researchers in recent times to investigate the determinants of the size of the government. External risks and political instability are the two major explanations that are put forward for larger size of the govern- ment measured by the share of government expenditure in gross domestic product.
Rodrik (1998) argues quite convincingly that government spending provides social insurance in open economies that are subject to external shocks and risks due to
R. Acharyya (&)
Department of Economics, Jadavpur University, Calcutta 700032, India e-mail: rajat.acharyya@gmail.com
©Springer India 2016
M. Roy and S. Sinha Roy (eds.),International Trade and International Finance, DOI 10.1007/978-81-322-2797-7_5
77
terms of trade volatility. This is the reason we observe larger governments in more open economies.1Annett (2001), on the other hand, argues that higher ethnolin- guistic and religious fractionalization within an economy increases the political risk for an incumbent government. This induces the government to pacify the excluded interest groups by increasing the level of government consumption.2Thus, whereas Rodrik finds government expenditure as means of lowering external risks for an open economy, Annettfinds it as means of lowering political risk and instability.
Measuring the size of the government by the share of expenditure on public good in the total expenditure on the private and public goods, Anwar and Zheng (2004) show that the size of the government is determined by the availability of the primary factors of production. In their two-sector, two-factor general equilibrium model of a closed economy, the public good is essentially a private good produced by the government and sold at the marginal cost. In such a framework, they show that an increase in the supply of capital (for example, through an inflow of foreign capital) lowers the size of the government sector (or the share of expenditure on the public good) if the production of the public good is relatively labour intensive.
An interesting implication of this result that the size of the government sector depends on factor endowments is similar to the Heckscher-Ohlin-Samuelson (hereafter HOS) pattern of relative size of different sectors and, therefore, of the comparative advantage of the economies endowed with different amounts of the primary factors. Their analysis thus creates scope for free international trade to have a similar impact on the size of the government sector as the international factor mobility when both the private and the public goods are traded in a standard HOS structure. This is a simple logical derivation from the celebrated Factor Price Equalization theorem. International trade by freeing up resources from the import-competing sectors allows production of exports to increase. If the public good is exportable, then it is straightforward to argue that the size of the govern- ment sector, both the absolute size and the share of expenditure, should increase with the opening up of trade. Thus the observed larger government size in open economies may be due to changes in effective factor supplies that free international trade brings in, provided, of course, the public good is exportable.
But such a result does not follow immediately in a standard HOS framework of an economy if the public good isnota traded good. It is thus non-trivial to examine the relationship between openness to external trade and the size of the government.
This is the primary concern of this paper. More precisely, I examine how freer international trade affects the size of the government through changes in the effective supplies of the primary factors of production, when the private good that the government produces is a non-traded good. In an extended HOS framework of a small open economy, I consider two privately produced traded goods and one government produced non-traded good (henceforth loosely called public good to
1Alesina and Wacziarg (1998) also have found that the government size is larger in smaller economies and the smaller economies are the ones usually more open to the external trade.
2Similar logic can be found in Blomberg (1996) and Velasco (1997).
differentiate it with the two goods produced in the private sectors), all using the same resources—labour and capital. A tariff reduction in such a context is shown to expand the absolute size of the government (defined as the expenditure on the public good), under a set of fairly general conditions. For example, if the export good is labour intensive relative to the import-competing good, by the standard price-magnification effect, a tariff reduction raises the money wage relative to the rate of return to capital. This change in relative wage raises the price of the non-traded public good if it, in turn, is labour intensive relative to the export good.
Production of the public good, on the other hand, falls by the consequent decline in itsrelativedemand, but increases because tariff reduction raises, for certain values of the employment shares in the export sector, the output of the import-competing good which necessitates a proportionate increase in the production of the public good under homothetic tastes to clear the domestic market. This market-clearing expansionary effect appears to be stronger than the contractionary demand effect so that the production of the public good increases at the end. Accordingly, with both the price and the output of the non-traded good increasing following a tariff reduction, the absolute size of the government increases. The relative size of the government, defined as the share of total expenditure spent on the public good, on the other hand, increases when the ratio of the share of export production to that of the import-competing production in national income exceeds the ratio employment shares of the private traded sectors. Otherwise, the expansion of the relative size of the government depends on the value of the price elasticity of demand for the public good. However, if the public good is price-inelastic, the government size increases regardless of whether the share of export production is large or small. Since lower levels of tariffs essentially make an economy more open to the external world, these results should mean that, ceteris paribus, more open economies have larger gov- ernments as is in fact observed by Alesina and Wacziarg (1998) and Rodrik (1998).
The production of the non-traded public good may generate positive externality effects in the rest of the economy. If the public good is in the nature of physical and/or social infrastructure (such as hospitals or health care, building of paved roads and the like), such externality effects may be in the nature of improvement in productivity of labour and capital. When such productivity effects of the production of the public good are taken into account, a tariff reduction still may increase the size of the government sector but now under more stringent conditions.
The rest of the paper is organized as follows. In Sect.2we discuss the frame- work of our small open economy. Section3works out the effects of tariff reduction on the production of the public good and the size of the government and Sect.4 considers the positive externality effect of the production of the public good.
Finally, concluding remarks are provided in Sect.5.
2 The Framework of a Small Open Economy
Consider a small open economy with two traded goods,XandY, produced in the private competitive sectors and a non-traded public good G produced by the government. Though we label G as a public good, following Anwar and Zheng (2004), we assume that it has the same characteristics as the private goods.3The only difference lies in the pricing of these goods. Whereas the marginal cost pricing for the two private goods are outcomes of perfect competition, the marginal cost pricing for the public good is the outcome of no-profit-no-loss motive of the government. Given the nature of the good produced by the government, we abstract from any positive externality that such production may generate. However, if instead the good under consideration had been in the nature of a semi or pure public good, we would have expected it to generate a positive externality in production. In a later section, we will explore whether and how such a dimension of the good produced by the government determines the size of the government sector.
All the three goods are produced by labour (L) and domestic capital (K) under constant returns-to-scale technology. The world prices of the traded goods are given to our small open economy and there is an initial ad-valorem tariffton the import good Y. Suppose, the export good X is not domestically consumed, and that the consumers allocating their budget on goodsYandGhave homothetic taste. Thus, the optimal consumption ratio,GYdd, depends only on the relative price of the public good. This assumption helps us ignore the income effects of a tariff reduction. Note that the tariff reduction that we consider here will raise the real income of our small open economy by reducing the distortion that a tariff introduces. As long as the public good is normal in consumption, such a real income increase will raise the demand for it and, therefore, its production and the size of the government. Thus by assuming homothetic taste we rule out this favourable effect to examine whether greater openness can still lead to a larger size of the government.
Competition in the private sector means prices equal average (and marginal) cost of production for the traded goods
PX ẳaLXWỵaKXr ð1ị
ð1ỵtịPYẳaLYWỵaKYr ð2ị where prices with asterisk denote the world prices.
3In mixed economies like India, the government is not only the provider of pure and semi public goods, but also of many private goods which cannot even be justified on grounds of positive externalities as, for example, in cases like public transport, public education, or health care. It is the size of this component of the government activities that really is a concern for many. This is one reason why we confine ourselves with only a publicly provided private good instead of a pure public good.
Government, on the other hand, though is the sole producer of the public good, charges the price which covers the average cost under the no-profit-no-loss motive:
PGẳaLGWỵaKGr ð3ị
There are also the least-cost choices of input coefficients aij, which under the constant returns-to-scale technology depends only on the factor prices
aijẳaijðW=rị; iẳL;K;jẳX; Y;G ð4ị Since the public good is a non-traded good, its market must clear domestically.
Given homothetic taste, we must have then the following market-clearing condition Gd
Yd ẳf PG PY
ẳG
Y ð5ị
where, G and Y are the levels of output of the public good and the import-competing good respectively. We close the model with the following full employment conditions
LẳaLXXỵaLYYỵaLGG ð6ị KẳaKXXỵaKYYỵaKGG ð7ị The determination of equilibrium configuration of factor prices, price and output of the non-traded public good, and the output of the traded private goods is fairly standard as in a typical HOS model. By the competitive conditions (1) and (2) and the least-cost choices (4), the money wage and the rate of return to capital are uniquely determined by the given world prices of the two private traded goods, for any given rate of the ad-valorem tariff. By the marginal cost pricing rule for the public good as described in (3), the average cost then determines the price of the public good. Finally, given the least-cost input choices, the market-clearing con- dition (5) together with the full employment conditions (6) and (7) determine the three output levels.
In the rest of our analysis, we assume that the export goodGis the most labour intensive and the import-competing good is the least labour intensive. That is,
aLG
aKG [aLX
aKX [ aLY
aKY 8W
r ð8ị
The implication of this assumption will be made clear later. This intensity ranking is not too unrealistic in the context of the nature of exports and imports of the developing countries in general. On the other hand, most of the production in the government sector is labour intensive with a view of generating employment opportunities.
3 Openness and the Size of the Government
In this framework, the level of tariff indicates the extent to which our small economy is open to the external trade. The lower the tariff on imports, more open the economy is. Thus if a ceteris paribus tariff reduction can be shown to raise the share of the public good in total expenditure of the economy, we can conclude that more open economies have larger governments. This is the thought experiment we carry out in this section.
Since we have assumed in (8) that imports are capital intensive relative to exports, by the price-magnification effect, a tariff reduction raises the money wage and lowers the rate of return to capital
Wb ẳ hKX j jhXY
Tb; ^rẳ hLX j jhXY
Tb ð9ị
where hat over a variable denote the proportional change; hij is the cost share of input-iin sector-j;j jhXYẳhLXhKYhLYhKX[0; and Tbdðð11ỵỵttịị.
The price of the public good, on the other hand, rises with the tariff reduction by our assumption that the public good is the most labour intensive or least capital intensive (so thathKX[hKG)
bPGẳ hKXhKG
j jhXY
Tb ð10ị
With the domestic price of imports falling, this means a switch in the domestic demand in favour of the import good Y and away from the public good. Since output of the public good is demand-determined by virtue of it being a non-traded good, its production must therefore contract on account of this demand effect of a tariff reduction. There will be, in addition, a market-clearing effect on the pro- duction of the public good necessitated by the homothetic taste assumption. As evident from (5),
Gb ẳðhKYhKGịeG
j jhXY
TbỵYb ð11ị
where, eGẳ bGbY
bPGbPY
is the (absolute) value of the price elasticity of (relative) demand for the non-traded good.
Thefirst term captures the demand effect induced by the change in the relative price of the public good following the tariff reduction. The second term captures the market-clearing effect under the assumption of homothetic taste. Under such an assumption, the relative demand for the public good can change only when the relative price of it changes. Thus, if a tariff reduction raises the output of the import-competing good, then for any given relative price, the production of the public good must also increase proportionately to match the (relative) demand for the public
good and, therefore, to clear the domestic market for the non-traded good.4Note by the assumption that our economy is small, any change in production of the traded goods cannot affect the world prices and hence the price of the public good relative to the (domestic) price of imports.
Thus, to determine how the production of the public good changes with a tariff reduction, we need to know how the outputs of the traded private goods change. First of all, these output levels would change by the factor substitution effect. The increase in the wage level relative the rate of return to capital makes all lines of production relatively more capital intensive. With labour and capital fully employed, the output levels must, therefore, adjust. Had all the three goods been traded, the output levels would have changed only by these factor substitution effects. But with the public good being non-traded, there will be further changes in the output of the traded private goods. As spelled out above, for any given output level of the import-competing good, the production of the public good falls with the tariff reduction. The consequent release of some labour and capital previously employed in the government sector, therefore, increases thenetendowment of these factors for the private sub-economy. This triggers the output magnification effects. However, given the three goods, the direction of change in the output levels triggered by the factor substitution and net endowment changes will not follow directly from the particular intensity ranking assumed in (8). Formally, as shown in the appendix
Yb ẳ gkKXj jkXGðhKYhKGịeG
ðkKXkLXịj jhXY
Tb ð12ị
bXẳ kKXdðkKXkLXị ỵ ð1kKXịg
ðkKXkLXịkKXj jhXY ỵ ð1kKXịj jkXGỵ ðkKXkLXịkKGkKX
hKGhKY
ð ịeG
ðkKXkLXịk2KXj jhXY
" #
bT
ð13ị Gb ẳ gkKXỵðhKYhKGịj jkXGeG
ðkKXkLXịj jhXY
bT ð14ị
where; gkLXrXþ kLXkKY
kKXhLYþkLYhKY
rYþ kLXkKG
kKXhLGþkLGhKG
rG[0;
d 1
kKXẵkKXhLXrXỵkKYhLYrYỵkKGhLGrG[0;
rjẳ^aKj^aLj
ðWb ^rị; jẳX; Y; G; is the factor substitution elasticity in sector-j;
j jkXGẳkLXkKGkLGkKX\0
4In case of non-homothetic tastes, this market-clearing effect would not have been there. Instead, the output of the public good would have been determined, in addition to the demand effect induced by change in price, by the demand effect consequent upon change in the real income.
The first term in the parenthesis of each of the expressions in (12) and (13) captures the factor substitution effect whereas the second term captures the demand-induced net endowment-change effect as spelled out above. First of all, given the intensity ranking in (8), the output of the import-competing good rises, bY[0, if,
kKX[kLX ð15ị
Given (15), both the factor substitution effect and the net endowment-change effect are favourable for the import-competing sector.5 The factor substitution effect, on the other hand, lowers the output of the export goodXwhereas the other effect is ambiguous.
In rest of our analysis, we shall assume (15) in addition to (8) to reduce the multiplicity of cases. Thus, given these assumptions, a tariff reduction raises the production of the import-competing good whereas that of the export good may fall.6 Finally, since the output of the import-competing good increases, Yb[0, from (11) it appears that the market-clearing effect raises the production of the public good and thus works in the opposite direction of the demand effect.
Therefore,
Proposition 1 By (8) and (15), a tariff reduction ðTb\0ị raises the volume of production of good G and the absolute size of the government.
Proof By (8) and (15),j jhXY[0 andhKG\hKY. Then, it is immediate from (14) that Gb[0. This completes thefirst part of the proof.
For the second part, define the expenditure on goodGas the absolute size of the government
SẳPGG ð16ị
Thus, by (8),bSẳbPGỵGb[0.
Hence the claim. □
A tariff reduction affects the absolute size of the government in three ways. First is the price effect. Tariff reduction raises the price of the public good and thus the expenditure on it for any given consumption and output levels. The other two effects
5This result that a fall in tariff actually raises the domestic production of the import-competing good is similar to the well-known Metzler Paradox in the literature on international trade. This, however, arises due to the existence of a non-traded good which uses the same factors of pro- duction as do the traded goods.
6The imports,M, can still increase. SinceM=Yd–Y, we can writeYbdẳqbYỵ ð1qịM, whereb qẳYYd. SinceYdincreases, even if the outputYincreases faster, by the property of weighted average, we haveYb[Ybd[M. Thusb Mb may still be positive.