THE IMPLICATIONS OF THE COMPREHENSIVE SPENDING REVIEW FOR THE LONG-RUN GROWTH RATE: A VIEW FROM THE LITERATURE.

Kneller, Richard

Richard Kneller [*]

In 1998 the Government set out its expenditure plans for the remainder of the current Parliament in the Comprehensive Spending Review. Announced within this were large increases in expenditure on education, health and capital spending with the objective of meeting the Government's manifesto pledges. Yet as the recent report by the Treasury on the UK's trend rate of growth states, the expenditure plans of the CSR may also help to raise the growth potential of the economy, although no quantitative assessment of this was made. Using evidence from the empirical growth literature, this article examines the possible effects of these policies on the long-run growth rate of the economy. In general the results from the empirical literature are non-robust, but by conducting a very different style of review we are able to identify several studies from which to determine what these effects might be. Using a stylised version of the CSR we estimate that it may raise the long-run growth rate by as much as 0.1 of a percentag e point per annum, although there is some sensitivity to the underlying assumptions. This appears to confirm the likelihood of modest upside risk to the Treasury's estimate of trend growth.

Introduction

In July 1998 the Chancellor set out in the Comprehensive Spending Review (CSR) the government's expenditure plans for the next three years. Central within this review were large increases in expenditure on education and health, by around [pounds]4Obn. in total, and on infrastructure, by around [pound]6bn, over the next three years.

The aim of the CSR is to target expenditure at Labour's priorities of education and health and principally at its election pledges to reduce waiting lists in hospitals and class sizes in schools. Yet, as the Treasury [1] identifies, these policies may also raise the long-run growth potential of the economy. This article attempts to provide some quantitative assessment of the possible effect on long-run growth.

According to National Institute estimates (July 1998) the CSR will contribute approximately 1 percentage point to the growth rate of GDP in both 1999 and 2000. While such short-run impacts on the economy are reasonably easy to model, the potential impact on the long-run growth rate of the economy is less so. This can be attributed largely to conflicting evidence on the relationship between government spending and long-run growth.

We base our estimates of the growth effects of the CSR on the findings from a review of the empirical literature. Despite the size of the literature, finding a set of consistent results is difficult (Slemrod, 1995; Tanzi and Zee, 1997). In part this can be explained by a failure in most studies to account adequately for the statistical bias that plagues this area of research (Folster and Henrekson, 1997). However, as we show below, even if we compare studies that claim to correct for such bias and are based on similar data sets, non-robustness still abounds. Given this, we review the literature but take a different focus from previous summaries. While accepting that the effect of statistical bias is very important, we argue that the relationship between policy and growth within the model is more complex than that usually assumed when applying empirical tests. A failure to provide a clear theoretical foundation at the outset will mean that few conclusions about the empirical relationship between policy and gro wth can be drawn. At this point in time there are no studies that satisfy all of the issues we raise here but there is evidence to suggest that all play an important role in explaining the inconsistency of previous results.

The review of the literature steers our attention to two studies in particular. These are used to analyse the likely growth effects of the CSR. In order to perform this exercise it is necessary to stylise the CSR somewhat to concentrate on the three main changes to expenditure already mentioned above. Once this is done we find the effect on the long-run growth rate of the economy to be around +0.1 of a percentage point per annum. This might appear small, but such a change in the growth rate can make substantial differences to real GDP over time. In order to give a structure to this empirical review we begin with a brief description of a growth model in which public policy plays a central role.

A simple model of public expenditure and economic growth

The model which the government appears to have in mind when forming policies to raise the long-run growth of the economy has technical progress as the driving force behind growth. We make the distinction between the type of policies that might raise the rate of technical progress from the way in which the expenditure plans of the CSR may be thought to affect growth very clear in this article, by assuming that there is no technical progress in the economy. The government's policies of encouraging technical progress through tax breaks for R&D and increased research in basic science amongst others are therefore not operative in the model.

Although in reality government policy is likely to affect the long-run growth rate of the economy through a number of channels, this simplification consolidates these to affect growth by only one route. This helps to both simplify the structure of the model and allow us to include the three main expenditure plans of the CSR in the model in an identical manner. We assume here that government expenditures are included as one of the inputs into the production function of the representative firm. The most common interpretation of this input is public capital, although if a broader interpretation of capital is allowed to include human capital it might also be thought to include education and health expenditure. [2] The possibility of raising the growth rate by increasing expenditures on education, health and infrastructure therefore follows very neatly from this model.

A second advantage to this simplification is that it allows us to describe models in which government policy affects the growth rate, which we label endogenous growth models, as a special case of the neoclassical model, in which growth is independent of government policy. [3] That is, the effects of policy on growth can be very easily switched on and off in the model through a simple restriction to the parameters. Finally, it should be noted that this set of assumptions is common in the literature and the same model is described in much greater detail by Barro and Sala-i-Martin (1995).

As in Barro and Sala-i-Martin (1995), we assume a decentralised economy, closed to international trade, which has an equal number of identical households and identical firms and a labour force of constant size. The production function of firm i, written as a ratio to per person employed, is given by,

[Y.sub.i] = [[AK.sup.[alpha]].sub.i][[G.sup.[beta]].sub.Y] (1)

f'(x)[greater than]0, f"(x)[less than]0, where x = K,[G.sub.Y]

[Y.sub.i] is the output of firm i, A is a technology parameter, [K.sub.i] is the capital input of firm i and [G.sub.Y] is the public input (which we assume to be non-rival, non-excludable and produced using identical technology to aggregate output). Given the assumed properties of the public input aggregating across all producers allows us to retain the form of equation (1) and simply suppress the i subscripts.

The different policy implications of the endogenous and neoclassical growth models rest on a restriction to the parameters in the production function, the as and the [beta]s. In both models the reproducible inputs, K and [G.sub.Y] are subject to diminishing marginal returns, but where the endogenous growth model assumes constant returns across these inputs, [beta] = 1 - [alpha], the neoclassical model assumes there are decreasing returns, [beta] [less than] 1 - [alpha]. As in all models of this type, for sustained growth in the steady state the equation describing the evolution of capital must be 'linear' (Jones, 1998). There must be constant returns across the reproducible inputs. In the neoclassical model the equation is less than linear so the rate of growth falls asymptotically over time until it is zero. The importance of the constant returns condition will, it is hoped, become clearer below.

The accumulation of physical capital in the model is determined by the firm's investment decision, the level of technology is determined by nature (which we assume for simplicity to be constant) and the level of public input is determined through the government budget constraint. The government has in its control only one form of expenditure, the productive input [G.sub.Y] which must be financed by revenues from a flat rate tax on output, [[tau].sub.Y]. For simplicity we assume that there are no problems of time inconsistency and that the government must balance its budget at every point in time. The government budget constraint is therefore given by,

[G.sub.Y] = [[tau]sub.Y]Y (2)

To derive the steady state growth rate we maximise the utility of the infinitely-lived representative household which chooses consumption and saving so as to maximise its dynastic utility. We assume that households have an isoelastic utility function (Ramsey, 1928). [4] This yields the following growth path for consumption.

[[gamma].sub.c] = 1/[sigma][[alpha](1 - [[tau].sub.Y])[AK.sup.[alpha]-1][[G.sup.[beta]].sub.Y] - [delta] - [rho]] (3)

where [[gamma].sub.c] is the growth rate of consumption, [delta] is the rate of depreciation of capital and [sigma] and [rho] are parameters from the utility function.

The steady state interest rate (and therefore the growth rate) is constant in equation (3) if the all of the terms in (3) are constant. For this to hold the ratio of productive expenditures to capital, [G.sub.y]/K, must be constant, that is [G.sub.y] and K must grow at identical rates. Differentiating the production function and the government budget constraint with respect to time yields y/y = [alpha]k/k + [beta][G.sub.y]/[G.sub.y] and y/y = [G.sub.y]/[G.sub.y] respectively. From this it should be clear that [G.sub.Y], y and K will grow at identical positive rates only if [beta] = 1 - [alpha]. If [beta][less than]1-[alpha] the steady state growth rate of output per capita in the economy is zero, Y/Y = [G.sub.y]/[G.sub.y] = 0, as in the neoclassical model, whereas if [beta] [greater than] 1 - [alpha] then the growth rate is explosive, Y/Y = [G.sub.y]/[G.sub.y] = [infinity]. Hence the importance of the constant returns to scale assumption to the results of the endogenous growth model.

Despite the simplicity of the model we are provided with a clear distinction between the effect of public investment on output growth in the neoclassical and endogenous growth models. In the neoclassical model the effect on the growth rate of increases in public inputs is temporary, as private capital and public capital are not close enough substitutes, whereas in the Barro endogenous growth model the returns to public investment are so large that the diminishing marginal returns to capital, which otherwise limit growth, are permanently offset.

Using this constant returns assumption and the government budget constraint allows us to re-write (3) as,

[[gamma].sub.c] = 1/[sigma][[alpha](1 - [[tau].sub.y])A[[[tau].sup.1-[alpha]].sub.y] - [delta] - [rho]] (4)

The double [[tau].sub.y] term in (4) highlights the dual effect of government in the model. Increases in government expenditures raise growth, subject to diminishing marginal returns, through the term [[[tau].sup.1-[alpha]].sub.y]. Yet increased expenditure requires increased funding which lowers the after tax return on investment lowering growth, captured through the term (1- [[tau].sub.y]). Barro (1990) demonstrates that the positive effects of government dominate at small sizes of government but the distortionary tax effects dominate if government becomes too large. Using a diagram borrowed from Barro (1990) this relationship is shown in Chart 1. It should be noted that public policy will affect the level of output in the economy in both versions of the model. Even in the neoclassical model increases in public investment raise the marginal product of capital encouraging faster capital investment and growth in the short run, in much the same way as increase in the savings rate (see Peacock and Shaw, 1971, f or details).

Chart 1. The growth effects of distortionary tax financing of productive government expenditures in the Barro growth model

The difference between the results of these two models is clearly important if the growth effects of the government's expenditure plans are to be analysed, as in this article. Put simply, the neoclassical growth model predicts that the CSR will raise the level of output in the economy, whereas the endogenous growth model predicts that the CSR will raise both the level of output and the growth rate of the economy. Determining which model to follow can be made only from considering the empirical evidence.

A review of the empirical literature

Despite the size of the literature and the number of different ways expenditure variables have been studied, in contrast to the theoretical literature the empirical literature is less clear about the effects of fiscal policy on growth. There emerges only weak evidence of a negative relationship between government consumption expenditure and growth and slightly stronger evidence of a positive relationship between transport and communication expenditure and growth. This lack of a clear set of results has been attributed in previous summaries to the problem of estimating growth regressions in general and using fiscal variables within these in particular (see amongst others Slemrod, 1995; Folster and Henrekson, 1997; and Temple, 1999). [5] Perhaps the principal source of any bias is the simultaneity of fiscal expenditures and growth, that is, the direction of causality is unclear. For example, if period averages of the data are used and these are too short in length then it is likely that any correlation between expenditures and growth will in part reflect the use of fiscal policy as an automatic stabiliser to the economy over the business cycle. If period averages are too long in length it is possible that any statistical relationship includes the general finding (known as Wagner's law) that larger economies tend also to have larger governments. This has led some to dismiss the use of fiscal policy as an explanatory variable of growth, inferring that it reflects symptoms rather than causes of growth (Sala-i-Martin, 1997).

Yet, while accepting that the statistical problems identified by Folster and Henrekson (1997), Slemrod (1995) and others are important, it is possible that an additional part of this lack of a consistent set of results from the literature can be explained by the predictions of growth models themselves. Indeed it is possible to show that simply accounting for the likely sources of statistical bias, and principally simultaneity, is still insufficient to provide a consistent answer as to whether fiscal policy affects growth or not. This is because the relationship between fiscal expenditure and growth that the empirical literature claims to test is consistent with the theory only under certain conditions and it is important to control for these predictions first. These are: a) for a given method of financing expenditures; b) if the economy is in the steady state; c) if expenditures are homogeneous in their effect on output; and d) if fiscal expenditure is an adequate representation of the economic benefits from government policy. [6]

To demonstrate that controlling for statistical bias is not sufficient, we follow Folster and Henrekson and compare studies that correct for statistical bias but we ignore for now those that closely follow the predictions of the model. We therefore consider only studies that use a sample of developed nations (in order to reduce problems of collinearity along with possible parameter heterogeneity and simultaneity): that are estimated from panel data techniques (to allow for possible heterogeneity across the intercept terms); that use data that have been averaged across time (to remove possible simultaneity from business cycle effects - but not too long in case of simultaneity from Wagner's law) [7]; and that use instrumental variable estimation (in case of simultaneity) at least to check the robustness of the results. Once this is done we are left with two studies, Cashin (1995) and Fuente (1997). Using the results for public investment expenditure as an example (although it is possible to find others), Cashin finds a robust statistically significant relationship (albeit on occasion at the 10 per cent level) between public investment and growth, both when controlling and not controlling for human capital investment. Fuente finds the same result only if measures of taxation and the budget deficit are excluded from the regression. For further examples of this problem see Kneller et al. (1999) and KBG. It would appear therefore that the problems of estimating growth effects of fiscal policy run deeper than the standard statistical explanations. We review the four possible explanations highlighted above in turn.

The government budget constraint

Jones (1995) provides the basis for a somewhat compelling argument that a robust statistical relationship is never likely to be found between fiscal policy and growth. Time series data of the rate of output growth within OECD countries have displayed either no persistent increase over the postwar period in some and signs of having slowed down in others. In contrast, government policy has been subject to the sort of shifts announced in the CSR that have ratcheted it on a generally upward trend. In the endogenous growth model shifts in policy lead to permanent changes in the growth rate, yet there is no evidence that such shifts matter within the data. This argument is further strengthened by the finding that capital investment rates, R&D and human capital accumulation also display positive trends over time. This would suggest that policy is irrelevant whether it affects growth directly, as in the model described above, or indirectly via input accumulation or technological change, as current government policies assume.

Jones does concede, however, that two positively trended series such as taxation and expenditure may be correlated with and un-trended (or negatively trended) series such as growth if their effects are broadly offsetting (more than offsetting in the direction of taxation). Jones dismisses this as the miracle case (although in fairness he does not consider government policy explicitly). Yet this is already one of the predictions of the simple growth model presented above. As Chart 1 shows, the positive effects of government expenditure are, at least in part and possibly completely, offset by the negative effects of the taxes used to fund them. Miller and Russek (1997) provide the general framework of a methodology to deal with this issue empirically and this is developed for the growth literature by Kneller, Bleaney and Gemmell (1999).

Kneller et a!. (1999) demonstrate that the inclusion and exclusion of different fiscal variables within the regression equation changes the implicit method of financing fiscal expenditures. This leads to the same sort of variability in the parameter estimates noted above when comparing results from the Fuente and Cashin studies.

To demonstrate this point, suppose that growth, [g.sub.it], in country i at time t is a function of conditioning (non-fiscal) variables, [Y.sub.it], and a vector of fiscal variables, [X.sub.jt].

[g.sub.it] = [alpha] + [[[sigma].sup.k].sub.i=1][[beta].sub.i][Y.sub.it] + [[[sigma].sup.m].sub.j=1][[gamma].sub.j][X.sub.jt] + [u.sub.it] (5)

Assuming that all elements of the government's budget (including the deficit/surplus) are included, so that

[[[sigma].sup.m].sub.j=1] [X.sub.jt] = 0,

then one element of X must be omitted in the estimation of equation (5) in order to avoid perfect collinearity. The omitted variable is effectively the assumed compensating element within the government's budget constraint. Thus, if we rewrite (5) as:

[g.sub.it] = [alpha] + [[[sigma].sup.k].sub.i=1][[beta].sub.i][Y.sub.it] + [[[sigma].sup.m-1].sub.j=1][[gamma].sub.i][X.sub.jt] + [[gamma].sub.m][X.sub.mt] + [u.sub.it] (6)

and then omit [X.sub.mt] to avoid multicollinearity, the identity:

[[[sigma].sup.m].sub.j=1][X.sub.jt] = 0

implies that the equation actually being estimated is

[g.sub.it] = [alpha] + [[[sigma].sup.k].sub.i=1][[beta].sub.i][Y.sub.it] + [[[sigma].sup.m-1].sub.j=1]([[gamma].sub.i] - [[gamma].sub.m])[X.sub.it] + [u.sub.it] (7)

It follows that the correct interpretation of the coefficient on each fiscal category is the effect of a unit change in the relevant variable offset by a unit change in the omitted category, which is the implicit financing element. An omitted variable bias and non-robust results are introduced if formal testing that the omitted fiscal variable can be safely excluded from the regression is not carried out.

Using a data sample and estimation technique that closely matches those common in the literature, the authors show that once the implications of the government budget constraint are accounted for there is strong support for the idea that public investment has a positive effect on growth and distortionary taxation a negative effect. These results are also found to be robust to a number of tests including estimation by instrumental variables.

The long run

As also noted above the differences in the growth effects of fiscal policy between the endogenous and neoclassical growth models are restricted to their predictions about the long run or steady state. Government policy variables do not feature in the steady state solution for the neoclassical model whereas certain types of policy do feature in the steady state for the endogenous growth models. In both models public policy helps to determine the rate of transition to this steady state, as government policy does affect the level of income. In empirical tests a further problem is that fiscal policy is often used to stabilise cyclical fluctuations in growth. Changes in expenditure and revenues may therefore be caused by growth rather than the other way round. In order to remove evidence of the business cycle and the transition most studies use some form of period averaging. [8] The choice of the length of the period average is clearly crucial in this process and it is perhaps surprising that little formal testing is often done to determine an appropriate choice. Five-year periods appear to have become standard in the literature but Bleaney et a;. (2000) (hereafter BGK) demonstrate that they are insufficient to remove evidence of transitional effects from the data.

In order satisfactorily to identify the steady state, long time series of data on individual countries is required. In practice finding data series of a suitable length is difficult and in the fiscal policy literature Kocherlakota and Yi (1997) is the only example where this has been successfully done. Using public capital stock and income tax rate data from the UK and US for 150 and 100 years respectively they find that the public capital stock raises the growth rate whereas growth is lowered by increases in income taxation. [9] These are similar findings to Kneller et al. (1999) and BGK (2000). These results are robust to various choices over the lag structure of the regression equation.

The homogeneity assumption

In the model described above the three policies announcements of the CSR are assumed to affect the growth rate in a homogeneous manner. In reality it is unlikely that [pounds]1 of any two productive goods or services has an identical impact on growth (and economists do not always agree on what constitutes productive and unproductive expenditures in the national accounts). Devarajan, Swaroop and Zou (1996) (hereafter DSZ) make a simple extension to equation (1) in the model to allow for two differentiated forms of non-rival, non-excludable public goods [G.sub.Y1], and [G.sub.Y2] to affect firm production.

Y = [AK.sup.[alpha]] [[G.sup.[beta]].sub.Y1] [[G.sup.[lambda]].sub.Y2] (8)

The elasticity parameters of separate expenditure terms are therefore no longer constrained to be identical, [beta] [not equal to] [lambda]. If [beta] + [lambda] = 1- [alpha] the results from the endogenous growth hold, whereas if [beta] + [lambda] [less than] 1 - [alpha] then we have the neoclassical model in which expenditures affect the level but not the growth of output. [10]

Using [G.sub.Y1] = [phi][G.sub.Y] and [G.sub.Y2] = (1 - [phi])[G.sub.Y] in equation (8) (where [phi] equals the proportion of productive expenditure in the government budget), [phi] + (1 - [phi]) = 1, and assuming household utility is of an isoelastic form allows us to express the steady state growth rate as,

[gamma] = 1/[sigma][(1-[[tau].sub.Y])[alpha][AK.sup.[alpha]-1][[[phi][G.sub.y]] .sup.[beta]][[(1-[phi])[G.sub.Y]].sup.[lambda]] - [rho]] (9)

In the endogenous growth model, growth now depends on the mix as well as the level of expenditures. This mix effect depends upon a combination of the relative productivity of [G.sub.Y1] and [G.sub.Y2], given by the elasticity parameters, and the relative budget shares. [G.sub.Y1] can be thought of as having a greater relative productivity than [G.sub.Y2] if the change in the rate of growth from a change in [G.sub.Y1], [delta][gamma] / [delta][G.sub.Y1] is greater than the change in the rate of growth from a change in [G.sub.Y2], [delta][gamma] / [delta][G.sub.Y2], holding total government expenditure constant. For the Cobb-Douglas production function used here this can be shown to be the case when: [11]

[lambda]/1 - [phi] [less than] [beta]/[phi]. (10)

Chart 2 shows the effect of changes in the mix of productive expenditures on the growth rate in this model. The maximum of the line corresponds to the point where

[phi]/1 - [phi] [less than] [beta]/[lambda].

If [G.sub.Y1] has a greater elasticity value than [G.sub.Y2]([beta] [greater than [lambda]), then the rate of growth may still not be increased if the expenditure share of [G.sub.Y1] to [G.sub.Y2] is currently too high. This suggests that changing the mix of expenditures is as important for the growth rate as changes to the level of expenditure.

Chart 2. Growth effects of changes in the mix of productive government expenditures

DSZ provide some empirical support for this model using a sample of 21 developed countries from 1970-90. DSZ regress the 5-year moving average of the growth rate against four expenditure variables (health, education, defence and transport and communication) expressed as a ratio to total expenditures. [12] Expenditure data have been used in this form previously in the literature but DSZ explicitly account for possible level effects of the policy by also including the ratio of total expenditure to GDP in the regression. It is not clear how well this corrects for the omitted variable bias discussed in KBG (1999). Certainly their parameters (in table 2 on p.102) suggest that increased overall spending has a mildly beneficial effect on the growth rate despite the implicit effect of the taxes needed to pay for it.

When the four expenditure variables are included within the same regression only transport and communication expenditure is statistically significant. Yet when education and health expenditure data is further disaggregated they find 'other education', hospital and 'other health' to have significant positive effects on the growth rate; while primary and secondary schooling and universities have negative growth effects. In these disaggregated regressions the coefficient on the transport and communication variable becomes statistically insignificant.

The characteristics of government

Empirical studies of the growth effects of government expenditure make the implicit assumption that the data on fiscal expenditures are an adequate proxy for the policies that underlie these expenditures. It is somewhat easy to think of reasons why this might not be the case. We use here the example of differences in corruption and efficiency of governments. Put formally, estimation of an equation of the form of (7) assumes that the [gamma]s reflect the benefits [13] from the expenditure policy rather than simply their cost. If instead the estimated parameters contain the effects of say inefficiency and corruption, as in equation (11) below, then the estimated parameters can no longer be interpreted as the effect of fiscal expenditure on growth (Pritchett, 1996). [14] This may cause further problems if this leads to the false conclusion that the [gamma]s, the part that empirical studies are trying to estimate, are different across countries when they are not.

[g.sub.it] = [alpha] + [[[sigma].sup.k].sub.i=1][[beta].sub.i][Y.sub.it] + [[[sigma].sup.m-1].sub.j=1]([[psi].sub.j][[gamma].sub.j] - [[psi].sub.m][[gamma].sub.m])[X.sub.jt] + [u.su.it] (11)

where [psi] measures the degree of inefficiency/corruption etc. of each expenditure type.

Evidence relating corrected government expenditure data and growth does not at this time exist but evidence that the degree of corruption and inefficiency is important for growth does. Indeed the idea that institutional differences matter for growth has a rather long pedigree within the literature. Mauro (1995) uses a series of subjective [15] indices measuring the degree of corruption, efficiency (of several types) and political stability within government for a sample of 68 countries. He finds reasonably robust evidence of a negative relationship between corruption and bureaucracy and private investment or capital equipment investment, but a less robust relationship for growth. This leads Mauro to conclude that the likely relationship is from bureaucracy and corruption to affect growth via investment. This relationship is robust to the use of instrumental variables.

Conclusions and growth effects of the CSR

To summarise: an inability to find robust evidence of a relationship between government expenditure and growth appears to be due in part to the statistical problems that dog this entire area of research, such as simultaneity, and in part from a failure to use the predictions of growth models closely enough when forming empirical tests. Currently there are no studies that account for all of the predictions of the model although there does appear to be some evidence suggesting their importance.

This review suggests that the conclusion of Jones (1995), that no statistical relationship between policy and long-run growth can ever be found, may be premature. If the effects of changes in policy are broadly offsetting then even if policy is subject to large persistent shifts of the kind announced in the CSR, growth rates may not. BGK (2000) and Kocherlakota and Yi (1997) use the simple examples of the negative effects of taxation offsetting the positive effects from government expenditure and find it to have empirical support.

The effects of policy may also fail to appear in the data if the expenditure categories used are too aggregated, if the methodology fails to deal adequately with the transitional effects of policy, and if policy is misdirected or ineffective because of inefficiency and corruption. This is a clear agenda for future research, although obtaining time series data of sufficient length is not easy and made more difficult if disaggregated data is required. A further problem is the difficulty of separating the available expenditure data into productive and non-productive types a priori, as required if the methodology of KBG (1999) is to be implemented. It could be argued from this that using expenditure data is not the best means to study the economic benefits of government policy. However this is often the only measure available at the macroeconomic level and with careful and innovative use of the data this section of the literature may have much to offer.

Growth effects of the CSR

The limitations of the empirical literature mean we are unable to replicate fully the likely growth effects of the CSR in any great detail. In order to overcome this problem we stylise the CSR somewhat and concentrate on the three main tenets of the Chancellor's speech, the increased expenditure on education, health and public infrastructure.

All calculations are based on the parameter estimates from the DSZ (1996) and BGK (2000) studies. These are chosen in preference to Kocherlakota and Yi (1997), as the variables used in Kocherlakota and Yi do not translate easily to the expenditure plans of the CSR. Both DSZ and BGK studies have parameter estimates for education and health expenditure but neither has parameter estimates for public capital. To proxy for this we use the parameter value for transport and communication for DSZ and 'other productive-expenditure' from BGK. Parameter estimates and standard errors from these studies are given in the second column of Table 2. In order to control for the negative effects of taxation we assume that the government balances its budget. When using the BGK study we assume that 30 per cent of the change in expenditure on the CSR is financed by non-distortionary taxes which corresponds approximately to its share of revenues in the national accounts [16] and when using DSZ we control for the level effects of ex penditure through the total expenditure to GDP term. It should be remembered throughout that the estimates from the two studies are based on a sample of OECD countries rather than just the UK. All results should therefore be seen as indicative rather than precise.

Expenditure data are taken from the ONS and we express them both as a ratio to GDP and to total expenditure in accordance with the needs of KBG and DSZ studies respectively. Forecasts of GDP are taken from the National Institute forecasts (October 1999). It is likely that there will be some sensitivity of the results to this choice when the parameters from BGK are used and it should be remembered that these GDP estimates have their own set of error bounds. We decide against testing for the sensitivity to this however.

Once this is done, then by our estimates health expenditure as a ratio to GDP rises from 6.20 per cent in 1998 to 6.62 per cent in 2001, education expenditures from 5.10 per cent in 1998 to 5.51 per cent in 2001 and capital investment from 1.04 in 1998 to 1.51 per cent in 2001. As a ratio to total expenditure the rises are from 10.90 to 11.87 for health, 13.38 to 14.28 for education and 2.54 to 3.25 for capital investment.

Table 1 shows that the level of education and health spending in the UK compare reasonably well with corresponding figures for other OECD countries, but the level of capital spending less so. Over the past 30 years or so most governments from industrialised nations have cut back spending on public investment. The political sensitivity of social security and health expenditures and the need to finance increasing national debt has meant that public investment has been targeted as the easy political option (De Haan et al., 1996). It can also be seen that in this sample of OECD countries the UK currently spends, as a percentage of its GDP, the lowest level on capital expenditure, 1.3 per cent in 1987-92. The CSR reverses some of this decline but the figure remains comparatively low.

The estimated effects using the parameters from DSZ are that the long-term growth rate is increased by 0.1 per cent per annum. The table shows the two-standard error ranges associated with individual components in order to provide confidence intervals for these. The covariance matrix of the parameters is not published and this makes it impossible to estimate the standard error of the overall impact. While the figures confirm the upside risk mentioned by the Treasury, we are unable to say with what degree of precision the overall figure is estimated.

The figures using the parameters estimated by BGK are calculated assuming that 70 per cent of the tax needed to pay for the extra spending is raised through distortionary taxation (see footnote 16). This proportion corresponds to the actual pattern of tax revenues in 1998. With this assumption this study also suggests that the growth rate will be increased by about 0.1 per cent per annum. Table 2 shows that this number is the outcome of much larger but imprecise impacts from spending offset by the consequences of taxation. The two-standard error range is calculated using the parameter covariance matrix. The confidence interval this provides is -0.125 to 0.327.

The aim of this exercise has been to use the parameter estimates from the empirical literature in order to estimate the likely effect on the long-run growth rate of the changes in government spending announced in the CSR. The fact that both studies lead to a similar conclusion that the CSR will add about 0.1 per cent per annum to the growth rate might seem reassuring, but the different magnitudes of the component parts, seen in combination with the error ranges, indicate how imprecise the exercise at present is. It is to be hoped that developments in the literature over time will both improve the precision of these estimates and widen the range of the policy questions which can be addressed. In the mean time, any claim that any particular spending policy has had a clear impact on the growth rate plainly needs to be interpreted with caution.

* National Institute of Economic and Social Research.

Notes

(1.) 'Trend Growth -- Prospects and Implications for Policy', Her Majesty's Treasury, November 1999

(2.) A model that does exactly this can be found in Capolupo (1996).

(3.) Government policy can affect the long-run growth rate in the neoclassical model if it affects the sources of growth, technological change or population growth (see Peacock and Shaw, 1971, for details).

(4.) Further details on this utility function and the solution to this model can be found in Barro and Sala-i-Martin (1995) Ch.2-4.

(5.) We do not review the relevant biases associated with these statistical problems here and instead refer the reader to the general review offered by Temple (1999).

(6.) To demonstrate this non-robustness we group past studies according to the type of variable used in estimation and list the main results from each in Tables Al to A3.

(7.) Wagner's law is the idea that some forms of government expenditure such as health have an income elasticity greater than one. As income rises then so will the demand for these services. If the period average is too long, it is believed that any correlation will reflect causation from growth to expenditure in much the same way if expenditure is used as an automatic stabiliser over the business cycle.

(8.) Recent work by Jones (1998) suggests that the US economy has been in a succession of transitions for the last 150 years casting doubt on whether period averaging of any length will be sufficient.

(9.) Interestingly they find that these results hold only when both fiscal variables are included in the regression. The authors recognise from this the importance of the government budget constraint when performing empirical tests but do not set it up explicitly.

(10.) If [beta] + [lambda] [greater than] 1- [alpha] then the growth rate explodes towards infinity. As is typical in these types of model the results rest on a knife-edge.

(11.) DSZ note the problem with using the Cobb-Douglas production function is that neither form of expenditure, [phi] cannot be allowed to be equal to 0 or 1 because of the effect that this has on total output. While this is obviously a restriction on the use of the Cobb-Douglas production function we retain it for the purposes of demonstration and refer the reader to the original text for an alternative treatment.

(12.) DSZ provide empirical support for their model using data from a sample of developing countries. However they do also report some results for developed countries to test for robustness and it is those we refer to here. The results we discuss correspond to those in table 2 of the original article.

(13.) Pritchett (1996) describes this as the economic cost.

(14.) We assume in equation (II) that the benefits to each expenditure form are a multiplicative combination of their economic cost and the degree of inefficiency, corruption etc. It is possible to think of other possible relationships between efficiency and economic cost.

(15.) These indices are subjective to network of analysts and correspondents of Business International (a private institution for whom the data are taken) based within the country rather than subjective to the author.

(16.) Distortionary taxes include taxes on income and profit, social security contributions, taxation on payroll and manpower, taxation on property. Non-distortionary taxation includes taxation on domestic goods and services.

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 Comparative government spending across countries, percentage
 ratio to GDP
 France Germany Italy UK US
Education 5.29 3.51 3.84 5.10 7.39
Health 10.47 7.06 5.24 6.20 7.72
Capital 5.05 5.22 5.21 1.04 2.47

Source: Government Financial Statistics, IMF (1998). UK ONS -- Datastrearm.

Note: Figures are for last available data point. France 1993, Germany 1991, Italy 1988, UK 1998, US 1996.

 Estimated growth effects of UK comprehensive spending
 review, July 1998
Study Parameter (standard error)
Devarajan et al. (1996) Education -0.029 (0.020)
 Health 0.019 (0.013)
 Transport & commun. 0.089 (0.025)
 Total expenditure 0.015 (0.008)
 Total
Bleaney et al. (2000) Education 0.484 (0.087)
 Health 0.333 (0.213)
 Other productive 0.332 (0.124)
 Distort taxes (70%) -0.431 (0.074)
 Total
Study Growth Effect Confidence interval
Devarajan et al. (1996) -0.025 0.010 -
 0.017 -0.006 -
 0.090 0.040 -
 0.019 0.001 -
 0.102 not available
Bleaney et al. (2000) 0.195 0.126 -
 0.139 -0.039 -
 0.156 0.040 -
 -0.391 -0.257 -
 0.101 -0.125 -
Study
Devarajan et al. (1996) -0.060
 0.040
 0.141
 0.040
Bleaney et al. (2000) 0.267
 0.318
 0.273
 -0.525
 0.327
 APPENDIX:
 Estimated relationship between government
 consumption expenditure and growth in previous empirical studies
 Length of
 Econometric period
Author(s) Countries Years method average
Ram (1986) 115 1960-80 Cross-section, 10
 time series
Landau (1986) LDCs Cross-section
Grier, Tullock 115 1950-81 Panel data 5 years
(1989)
Romer (1989a) 94 1960-85 Cross-section 16 years
Romer (1989b) 112 1960-85 Cross-section 16 years
Romer (1990) 90 1960-85 Cross-section 16 years
Alexander (1990) 13 OECD 1959-84 Panel Annual
Barro (1991) 98 1960-85 Cross-section 16 years
Agell, Lindh & 23 OECD 1970-92 Cross-section 21 years
Ohlsson (1997)
Author(s) Main findings
Ram (1986) Size of government produces significant positive
 coefficients
Landau (1986) Government consumption expenditure has a significant
 negative effect
Grier, Tullock Government consumption expenditure has a significant
(1989) negative effect
Romer (1989a) Government consumption expenditure has a significant
 positive effect
Romer (1989b) Government consumption expenditure has a significant
 positive effect
Romer (1990) Government consumption expenditure has a significant
 positive effect
Alexander (1990) Government consumption expenditure has a significant
 negative effect
Barro (1991) Fovernment consumption expenditure has a significant
 negative effect
Agell, Lindh & Expenditure share insignificant
Ohlsson (1997)
 Estimated relationship bebetween transfer
 payments and welfare expenditure and growth in previous empirical studies
 Length of
 Econometric period
Author(s) Countries Years method average
Korpi (1985) OECD 1970-87 Panel 18 years
Landau (1985) 16 OECD 1952-76 Panel/ Annual
 cross-section
Weede (1986) 19 OECD 1960-82 Panel/ 7-years
 cross-section
McCallum, Blais 17 OECD 1960-83 Panel/ 7-years
(1987) cross-section
Castles, Dowrick 18 OECD 1960-85 Panel 6 years
(1990)
Weede (1991) 19 OECD 1960-85 Panel 7-years
Nordstrum 14 OECD 1970-89 Cross-section 20 years
(1992)
Sala-i-Martin 75 Cross-section
(1992)
Persson, Tabellini 14 OECD 1960-85 Cross-section 16 years
(1994)
Hanson, OECD 1970-87 Cross-section 18 years
Henrekson (1994)
Cashin (1995) 23 OECD 1971-88 Panel 5-years
Nazmi, Ramirez Mexico 1950-90 Time-series Annual
(1997)
Author(s) Main findings
Korpi (1985) Transfer payment expenditure has a significant negative
 effect
Landau (1985) Transfer payment expenditure has no significant effect
Weede (1986) Transfer payment expenditure has a significant positive
 effect
McCallum, Blais Transfer payment expenditure has a significant negative
(1987) effect
Castles, Dowrick Transfer payment expenditure has a significant negative
(1990) effect
Weede (1991) Transfer payment expenditure has a significant positive
 effect
Nordstrum Transfer payment expenditure has a significant positive
(1992) effect
Sala-i-Martin Transfer payment expenditure has a significant positive
(1992) effect
Persson, Tabellini Transfer payment expenditure has a significant positive
(1994) effect
Hanson, Transfer payment expenditure has no significant effect
Henrekson (1994)
Cashin (1995) Transfer payment expenditure has a significant positive
 effect
Nazmi, Ramirez Transfer payment expenditure has a significant positive
(1997) effect
 Estimated relationship between public investment expenditure,
 other expenditure categories and growth in previous expirical studies
Author(s) Countries Years Ecnometric Length of
 method period
 average
Landau (1986) LDCs
Barth, Bradley 16 OECD 1971-83 Cross-section 13 years
(1987)
Barro (1989) 72 1960-85 Cross-section 16 years
Barro (1991) 98 1960-85 Cross-section 16 years
Easterly, Rebelo 100 1970-88 Cross-section 19 years
(1993)
Cashin (1995) 23 OECD 1971-88 Panel 5-years
Devarajan, 14 1970-1990 Panel 5-year
Swaroop, Zou developed moving
(1996) average
Kocherlakota & Yi US, UK US 1891- Time-series Annual
(1997) 1991 (10 lags)
 UK 1831-
 1991
Kneller, Bleaney, 21 OECD 1970-94 Panel 5-year aves
Gemmell (1999a)
Bleaney, Gemmell, 21 OECD 1970-94 Panel (static 5-year aves,
Kneller (2000) and dynamic) annual
Author(s) Main findings
Landau (1986) Education, defence, capital expenditure
 insignificant
Barth, Bradley Total public investment insignificant
(1987)
Barro (1989) Total investment significant
Barro (1991) Transport & communication significant,
 total public investment insignificant
Easterly, Rebelo Transport & communication significant,
(1993) total investment, education, health
 insignificant
Cashin (1995) Ratio of public inestment to GDP has a
 significant positive effect
Devarajan, Health, transport & communication
Swaroop, Zou significant positive, defence, education
(1996) significant negative
Kocherlakota & Yi Public investment insignificant when
(1997) included individually, significant when
 included with tax variables
Kneller, Bleaney, Productive expenditure significant
Gemmell (1999a) positive, non-productive expendtirure
 insignificant (when controlling for
 govt. budget constraint).
Bleaney, Gemmell, Productice expenditure, health and
Kneller (2000) education significant positive (when
 controlling for govt. budget constraint)