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Wealth effects and fiscal policy in the National Institute global econometric model.


This paper analyses the role of wealth in the National Institute model of the World Economy (NIGEM). It also addresses the issues of fiscal solvency and the role of the government budget constraint. We start with a brief theoretical and empirical overview of wealth and consumption functions. We then describe the introduction of public sector blocks into the model and summarise our approach to the determination of wealth. The paper then reports on a set of diagnostic simulations using NIGEM. We analyse the effects of a permanent fiscal expansion and its implications. We also discuss the importance of solvency constraints on the government in the solution of a forward looking model without Ricardian equivalence. We then analyse the effects of a change in equity prices in one country relative to those in the rest of the world.

Consumption and wealth effects

In our analysis we have assumed that individual or representative consumers maximise their utility over time and choose the optimal paths for consumption (C) and net financial wealth (W):(1)
C(t) = f(Y(t),W(t),t) (1)(a)
 W(t) = Y(t) - C(t) (1)(b)

where a dot denotes a time derivative. This is a simple representation of the real balance effect, which states that the value of (net financial) wealth affects consumers'expenditure. We would expect that in a sustainable steady state the personal wealth income ratio should stabilise. This can arise for a number of reasons, including a marginal rate of substitution between consumption and wealth that depends only upon the wealth consumption ratio and not upon time or the level of net financial wealth. We have assumed that in the long run the wealth and income elasticities sum to one, and that they are independent of time and the level of wealth. If all these features hold then both the consumption income ratio and the wealth income ratio must be constant in the long run. However, departures from the long run may persist for considerable time.

Wealth effects are central to any macro model. In the construction of an empirical model we have to consider the implications of variables that are important in a theoretical context. The omission of such variables may distort both individual equations and overall model properties. In estimation, the omission of wealth is likely to have two consequences for our regression if it is not orthogonal to the rest of the regressors in the equation. First, other coefficients are likely to be biased, and this will affect model properties. Barrell, Gurney and In't Veld (1991) reports both our new and old equations for consumption. We discovered that the effects of the omission of wealth from the regression varies between countries. For instance, in our Italian consumption function without net financial wealth the coefficient on interest rates was exceptionally large, and we think that this results from the omission of a significant variable. The second effect of the omission of wealth may be that the estimated dynamics of the equation are biased, and this will often show up in exceptionally long mean lags.

The omission of net financial wealth has been recognised as significant for some time, and it is commonly included in single country models. However, it is not so common in large multicountry models, and some attempt to compensate for this by introducing inflation effects into consumer behaviour. (2) These effects may pick up the initial impact effect of a fall in real net financial wealth that results from a rise in the price level (the real balance effect). They therefore model wealth effects in the short run, but they fail to do so in the long run. Once inflation has subsided then there will be no further effects on consumption. However, if the shock in question has raised the price level, real wealth will be below its desired level and consumption should be below base until real net financial wealth is back to its equilibrium. The defect can only be remedied by the explicit introduction of a relevant real stock variable. This also allows us to undertake coherent policy analyses using our model.

The time series properties of consumption, income and wealth

It is instructive to examine first whether or not consumption (C) and disposable income (Y) (and possibly net financial wealth (W)) form a cointegrating set. We have tested for cointegration between consumption, income and net financial wealth for each of the six major economies. Results for the European economies are reported in Barrell and In't Veld (1992(a)) and Barrell and In't Veld (1992(b)) contains a more extensive analysis.

Table 1 summarises the conclusions from Barrell and In't Veld (1992(b)). For theoretical and policy analysis purposes it is desirable to impose linear homogeneity on the consumption equations in our model. Homogeneity implies that the ratio of consumption to income must be stationary. Although consumption and income cointegrate for the US and Italy, when linear homogeneity is imposed this conclusion no longer holds. For Japan, France and the UK no cointegrating regression could be found. For Germany, on the other hand, cointegration could be accepted in all cases. When net financial wealth is included in the cointegrating regressions, the results are dramatically different. Cointegration between consumption, income and wealth can be accepted for almost all countries, with the only exception being Japan.131 Our results show that the inclusion of net financial wealth is crucial for explaining consumers' expenditure and its omission would be a serious shortcoming in our model. We have reestimated our consumption equations and added wealth effects in the US, Japan, France, Germany and Italy. The UK section of the model already contained wealth effects, but we have replaced the old equation, and we have a more sophisticated wealth accumulation system in place. The properties of the consumption equations and their mean lags are reported in Barrell, Gurney and In't Veld (1991).

Public sector

Public sector debt is an important element of net financial wealth of the private sector. In order to forecast wealth it is necessary for us to model the evolution of public sector debt. This requires that we model public sectors in the countries where we have introduced wealth effects. NIGEM already contained detailed public sector blocks of equations for the United States and Germany. We have now also introduced smaller public sector blocks for Japan, France, Italy and the UK. Full details are given in the NIGEM model manual (1992). The government budget identity is embedded in the models of each of the individual countries. It can be summarised as:

G - T + rB = [delta]B + AMO (1)

where G is total government expenditure and transfers, T is government revenues, B the debt stock, MO the stock of base money and r the interest rate. In every country we distinguish at least three components of expenditure: government consumption, investment and transfers. In all cases both direct and indirect taxes are modelled, whilst the public sector blocks for the United States and Germany disaggregate further so that they separate out profit taxes and contributions to social security. Government interest payments on the stock of outstanding debt are modelled as a return on a perpetual inventory. The change in the debt stock each period pays the long rate in the issue period until it is replaced. These government interest payments flow onto personal sector income to the extent that the debt is held domestically. Any complete model needs a financing rule and we assume that deficits are basically bond financed. However, in each period the stock of high powered money is likely to rise, and hence some of any deficit is likely to be financed by issuing MO. If we operate the model with a narrow money target, then the bond issue is the residual in the government budget identity. If we target interest rates in some other way the demand for high powered money will alter and the bond issue will differ. If the deficit is smaller than the increase in high powered money then the authorities will be making net redemptions of bonds.

Personal sector financial wealth

The evolution of gross financial assets and liabilities is represented in the wealth blocks of the model. NIGEM is a large model and we have chosen not to expand it further with large unmanageable financial sectors for each of the G6. We have followed common modelling practice such as that adopted by Masson et al (1990) and assume that the personal sector has ultimate ownership of all domestically held financial assets. Private sector financial assets are held directly by companies and financial institutions such as pension funds as well as by individuals. However, the personal sector is the ultimate owner of all domestically and privately owned companies and financial institutions. Individuals may not realise the size and structure of their assets because of the complex structure of institutions involved. We could model all institutions and also individuals' perceptions of their assets. We have adopted the simpler approach and discarded (or broken) this corporate veil. The value of personal sector financial assets is, at least in simulations, presumed to grow in line with private sector financial assets.

We distinguish four different financial assets and one liability and define net financial wealth as:

NW = Dp + OA + MO + MASC - LIAB (2)

where Dp is the value of the government debt stock held domestically, OA is the stock of overseas net assets, MO is the stock of non interest bearing money, IIASC is the residual miscellaneous assets category, which is largely the value of equities, and LIAB are the financial liabilities of the personal sector.(4) We have to model the process of asset accumulation in the economy and hence various identities have to be embedded into the model. Total private saving minus investment equals the acquisition of net financial wealth, and by national accounting identity this is equal to the sum of the current account surplus and the public sector's deficit: - Acquisition of net wealth = CB V - BUD (3)

where CB V is the balance on the current account and BUD the public sector surplus.

Net saving has to be allocated amongst acquisitions of new financial assets and borrowing, and hence one of these variables has to be a residual. Given our assumptions about the financing of the government budget deficit, detailed above, the flow of bonds and of base money is fixed. This leaves us three variables that may be a residual: borrowing, the accumulation of overseas assets and our miscellaneous category. In the short term we see the net acquisition of overseas assets (CBV) as being determined elsewhere, and hence only liabilities or miscellaneous assets can be the residual. We have chosen the latter category as the residual. Each category is modelled separately and is discussed briefly below. The change in each component of gross wealth is determined by the revaluation of last period's stock and by the acquisition of new assets.


We have assumed that the existing bond stock is revalued each period in line with changes in the long interest rate.(5) We have tried to take account of the different maturity structure of public debt. Italian debt, for instance, is mainly very short term and hence is not so subject to long rate induced revaluation. The flow of government debt is given by the government financing constraint. The direct and indirect acquisition of new government bonds by the personal sector is assumed to be a fixed proportion of their total portfolio, allowing for a varying proportion of government debt to be held abroad.(6)

Overseas assets

Overseas net assets can change either because the current account is not in balance, or because overseas assets and liabilities are revalued. Valuation methods for, for instance, direct investment abroad are notoriously diverse among countries and early estimates of a country's international position are often substantially revised. However, despite the obvious problems in modelling them, revaluations are important for some shocks and hence they have to be taken into account. The size of overseas assets and liabilities also affects the divergence of GNP and GDP.

We have gone some way toward modelling the full capital account. We assume that gross overseas assets are revalued by a weighted average of the change in equity prices in the rest of the G7 and overseas liabilities by the change in the domestic equity price. Equity prices are modelled in each of the G7 countries and we presume that in the long run they grow in line with world nominal GDP expressed in a common currency and are negatively related with long-term interest rates. The long rate in NIGEM is determined as a forward looking 10 year average of short-term interest rates, so this also makes the equity price index forward looking. These equity price equations are discussed further in Barrell, Gurney and In't Veld (1992b), and are reported in the current model manual. However, we have taken account of the fact that not all overseas assets are revalued, as for all major economies short-term banking flows play a significant role and these are not affected by changes in equity prices and exchange rates. Government debt is also held by overseas residents, and its value is not affected by equity prices.

The balance on the current account is the net acquisition of overseas assets whilst the accumulation of gross assets and liabilities also includes gross capital flows. We assume that half the current account balance flows onto overseas assets and half flows off overseas liabilities. The current account is, however, only a small proportion of gross capital flows. We do not wish at this stage to construct a full model of all capital flows, but we have to take account of the effects of gross capital flows. We have therefore assumed that portfolio equilibrium requires constant asset stock to income ratios and hence overseas asset and liability stocks grow in line with nominal GNP in the rest of the world. Revaluations therefore apply to a growing stock of gross assets.(7)

Miscellaneous assets and non interest bearing money

The miscellaneous assets category contains equities and other interest bearing liquid assets. As with other assets, the change in the total can be decomposed into a revaluation of the existing stock and the net acquisition of assets. We assume that liquid assets are not reva~ued whilst all other miscellaneous assets are revalued in line with equity prices. The change in base money is determined by the deficit financing rule and the monetary policy regime. Because our accounting identities (2) and (3) have to hold, one variable has to be a residual and the miscellaneous category is the obvious candidate. Total net private savings, the sum of current account imbalance and the government deficit, are assumed to flow onto this component of wealth. After eliminating terms, the change in this category can be expressed as the change in the debt stock held abroad plus the change in the personal sector's financial liabilities.(8)


The most significant component of the financial liabilities of the personal sector in most countries is loans for house purchases. Given the size and scope of our model, we do not want to build a large model of the housing markets in each of the G6. We therefore assume that in portfolio equilibrium household borrowing grows in line with personal disposable income. The forecast chapter in this Review discusses the ratio of liabilities to personal disposable income for the G6 countries.

Fiscal policy and solvency constraints

This section analyses the effects of a fiscal expansion in each of the major economies in turn. We first discuss the issue of fiscal solvency and then we analyse the effects of a permanent change in government spending with a strong solvency constraint on government behaviour.

The issue of government solvency has come to the fore in political and academic debate in the recent past. The Maastricht Treaty imposes both debt and deficit rules on potential members of a European monetary union. There has been much debate in Europe about the need for such fiscal constraints, but in the longer run it is clear that governments have to remain solvent. This important issue is discussed at length in Blanchard et al. (1990). These authors distinguish two solvency concepts, and three ways of assessing them. The stronger requirement is that governments are assumed to be solvent if the discounted value of future deficits and surpluses inclusive of interest payments, as a percentage of GDP, sums to zero. This requires that the government eventually returns to its current debt to GDP ratio, however arbitrary that starting value. The weaker solvency requirement is that the debt income ratio eventually settles at some constant value. This requires that the government deficit also stabilises as a per cent of GDP, preferably at a sufficiently low level that the implied long-run debt to income ratio is not implausibly high.191 Governments will ultimately be bound by a fiscal solvency constraint, and if markets are forward looking then that constraint will bind immediately if it appears that the government has embarked on an unsustainable policy.

The analysis of fiscal solvency questions using a large scale model requires that the model contains complete public sectors along with overseas and government debt stocks. The income from asset stocks has to flow to individuals either at home or abroad. It is possible to proceed along the lines advocated by Masson et al. (1990) and assume that consumers are fully forward looking.(10) We think that this is both a rather difficult assumption to justify empirically and unnecessary for our purposes.(11) The existence of wealth effects in consumption should be sufficient to embed an asset stock equilibrium into a model and hence make it adequate to assess issues of fiscal solvency.

In Anderton, Barrell and In't Veld (1992) we report fiscal expansions in each of the European economies in turn. The fiscal expansion involves a permanent increase in government spending financed by issuing bonds with exchange rates kept fixed. We have assumed that the monetary authorities target a combination of real GDP and inflation, with inflation having five times the weight of GDP. This rule is also used by Masson and Symansky (1992) and the European Commission in 'One Market, One Money', and in the multi-country model comparisons discussed by Whitley (1992). This rule will accommodate step changes in the price level, although it will not accommodate permanent inflation, and it is not as strict as a monetary targeting rule. As a result of the effects of cumulating interest payments the debt stock is put on an explosive path. We can therefore regard the outturn as economically unsustainable. At some point the authorities would have to reverse their fiscal stance.

In this note we explicitly take this requirement into account and we have imposed strong fiscal solvency. Although the increase in expenditure initially increases the budget deficit, it cannot be allowed to do so in the long run. We have used the personal income tax rate as an instrument that eventually returns the budget deficit to base. Table 2 sets out the associated path for income. Income returns to base (or slightly overshoots) after somewhere between 5 and 12 years. We have chosen to bring the solvency constraint into operation slowly, so that the budget deficit (as a per cent of income) takes around six years to return to base.(12) Table 3 sets out the path of the budget deficit. The deficit is back on base after about seven years, but the economy has not returned to full stock flow equilibrium. Charts 1 and 2 plot the trajectory for the ratio of government debt to income. In all cases this rises until the deficit returns to base, and declines thereafter. The economy has not achieved full stock equilibrium even after twenty years, although in all cases it is approaching equilibrium.

The combination of a wealth/income equilibrium and a strong solvency constraint on the government implies that in the long run the ratio of net overseas assets to income must stabilise back at its base level. Hence in equilibrium the change in net overseas assets as a per cent of income must return to its base level. A strong solvency constraint will leave overseas assets unchanged, and hence the balance of payments will be unaffected. However, if we had imposed a weak solvency constraint and allowed the ratio of government debt to income to rise in long-run equilibrium then our results would have been different. A higher debt stock with an unchanged asset income ratio would require a decline in the ratio of overseas assets to income. In equilibrium this would require a decline in the current account as a per cent of income.(13)

The effects of equity prices

We have undertaken some experiments to analyse the implications of a change in the equity price index. We wish to analyse the implications of a permanent rise in expected profits and hence the rate of return on equities is unchanged. We have implemented a permanent 1.0 per cent increase in the stock market index in one country at a time whilst leaving the index otherwise endogenous. This shock raises the value of domestically held wealth and also increases the value of overseas liabilities. Table 4 details the net overseas assets income ratios. The increase in domestic financial wealth raises consumption and hence imports, and the flow of property income to overseas residents also increases. The balance of payments surplus falls and net overseas assets fail. The adjustment process is lengthy. Table 5 gives the effects on the current account. A higher value of equities raises the value of domestically held wealth, and hence stock equilibrium will require a fall in the ratio of overseas assets to income. The speed at which the economy approaches stock equilibrium is, once again, very slow.

The effects of a rise in equity prices depend in part upon the composition of financial wealth and also upon the estimated consumption equations. Public sector debt is around 100 per cent of GDP in Italy, and most of this is held directly by the personal sector. We would therefore expect equity prices to be less important than in say the UK where government debt represents a much smaller proportion of private sector financial wealth. The very weak wealth effect we have found in Germany produces a very slow response to a shock to wealth.


The construction of a model of the economy that contains both stocks of assets and flows of income from those assets is necessary for proper analysis of policy. The existence of financial stock variables in combination with effective budget constraints on all groups of actors requires that the government face a long-run solvency constraint. The speed at which this constraint bites will effect the properties of our model and hence its use in policy analysis. The fiscal solvency constraints suggested here take between five and eight years to be fully effective, and they reduce the effective public spending multiplier to zero after somewhere between five and twelve years. However, even though output returns to base quickly, the economy cannot be seen as having returned to equilibrium because the stock of government debt relative to income is still above base, albeit declining, after twenty years. The slow dynamics of stock flow adjustment are further illustrated by the effects of a change in real equity prices. When we solve large scale models in forward looking mode we have to impose terminal conditions either on rates of growth of variables such as the price level or on stock variables such as the rate of change in the ratio of overseas assets to income. Although it is clear from our simulations that our model is heading back toward equilibrium after 20 years, we should proceed carefully with the imposition of conditions that are only asymptotically valid.


Anderton, R Barrell, R and In't Veld, J, (1992), 'Forward looking wages, and the analysis of monetary union', paper presented at SPES Warwick Conference, forthcoming in Barrell, R and Whitley, J (eds.) Macroeconomic Policy Coordination in Europe: the ERM and Monetary Union.

Barrell, R Gurney, A and In't Veld, JW, (1991 ), 'The introduction of wealth into a model of the world economy', paper presented at MMB Conference, Warwick, July 1991.

Barrell, R Gurney, A and In't Veld, JW, (1992), 'Real exchange rates, fiscal policy and the role of wealth: an analysis of equilibrium in a monetary union', .lournal of Forecasting, forthcoming.

Barrell, R and In't Veld, JW, (1992a), 'Consumption and models of the world economy', DIW Quarterly Review, March 1992.

Barrell, R and In't Veld, JW, (1992b), 'A cross country analysis of consumption and wealth effects', mimeo.

Barro, R and Grossman, H, (1971 ), 'A general disequilibrium model of income and employment', American Economic Review, 61, 82-93.

Blanchard, O, Chouraqui, JC, Hagerman RP, and Sartor N, (1990), 'The sustainability of fiscal policy: new answers to an old question', OECD Economic Studies, 15. . , . .

Currie, D, Levine, P, (1991), 'The solvency constraint and fiscal policy m an open economy. Chapter 3 m External Constraints on Macroeconomic Policy: The European Experience Alogoskoufis, G, Papademos, L, and Portes, R (eds.), CEPR London. Gurley, J and Shaw, E, (1960), Money in a Theory of Finance, Washington, Brookings Institution.

Hall, RE, (1978), 'Stochastic implications of the life cycle-permanent income hypothesis', Journal of Political Economy, Vol 186.

Hey, JD, (1980), 'Optimal Consumption under income uncertainty' Economic Letters, vol 5.

Masson, P, Symansky, S and Meredith, G (1990), 'Multimod Mark II: A Revised and Extended Model', IMF Occasional Paper 71 Washington DC.

Masson, P, Symansky, S, (1992), 'Evaluating policy regimes under imperfect credibility', in Bryant et al (ed.): Evaluating Policy Regimes: New Research in Empirical Macro Economics, Brookings.

NIGEM Model Manual, NIESR, May 1992.

Whitley, J, (1992), 'Common policy simulations', paper presented at SPES Warwick conference March 1992, forthcoming in Barrell, R and Whitley, J (eds.) Macroeconomic Policy Coordination in Europe: the ERM and Monetary Union.


(1) Net financial wealth is often assumed to enter both the budget constraint and the utility function. Hey (1980) demonstrates that optimal consumption depends upon instantaneous net financial wealth in an uncertain world, but it is common to go beyond that and follow Barro and Grossman (1971) and assume that it is an object of utility.

(2) See Barrell and In't Veld (1992a).

(3) Other studies have shown that demographic/actors are significant/or Japan and the omission of this variable could explain the lack of cointegration.

(4) We have not assumed Ricardian equivalence (see Barro, 1974) to hold, and government bonds are considered to be net wealth. However, we have assumed that individuals only look at their 'outside' financial assets. Non-interest bearing government debt is not anybody's liability, and hence does not net out. The distinction between inside and outside assets is drawn from Gurley and Shaw (1960).

(5) The revaluation term on the value of government debt held domestically, Dp, can be approximated by 0.55 (LR(-I)/LR - 1), where LR is the long interest rate, and 11LR is the price of a consol. The long rate in NIGEM is determined as a forward looking ten years average of short-term interest rates. The damping factor 0.55 is used to approximate the revaluation of an eight years bond, rather than a consol.

(6) Percentages of public debt held abroad in 1990 were:
 US Japan Germany France Italy UK
 14 3.5 21 6 3 8

(7) In NIGEM each country has both gross assets and liabilities, and we also have a rest of the world asset stock. World assets equal world liabilities.

(8) If BUD -- [delta]Dp + [delta]Da +- [delta]MO, where [delta]Da is the debt stock held abroad and AMO is the increase in the money base, then it follows from (2) and (3) that A MASC z A Da -1- A LIAB.

(9) If the deficit is a per cent of GDP, and the nominal GDP growth rate is b per cent, then in the long run the debt stock settles at a/b.

(10) This does not however imply full Ricardian equivalence c.f. page 4 of their paper.

(11) Currie and Levine (1991) construct a model for the analysis of solvency in which consumers are myopic, but respond to wealth. Their simple model can be seen as a one country maquette of that discussed here.

(12) Our solvency constraint has the income tax rate responding to the average deviation from base over 12 quarters of the government defidt ratio. This means it takes at least three years for us to hit our target. This seems more realistic than the much more rapid adjustment used in MULTIMOD (see Masson et al (1990)) where in similar experiments income falls significantly below base within three years in all countries. We think this an iraplausible description of government behaviour.

(13) See Currie and Levine (1991). If the equilibrium ratio for the stock of overseas assets fails from A to (A-S) and if the rate of growth of nominal income is x per cent then the equilibrium current account surplus falls from (x/l00)*A to (x/100)*(A-S).
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Author:Barrell, Ray; Veld, Jan Willem in't
Publication:National Institute Economic Review
Date:May 1, 1992
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