Jérôme Creel

Francesco Saraceno

WEALTH EFFECTS AND PUBLIC DEBT IN AN ENDOGENOUS GROWTH MODEL

The debate on public finances' sustainability has long focused on the conditions for the accumulation of debt. This implied that, empirically, the analyses revolved around estimations of dynamic versions of the debt accumulation equation, through unit root tests and cointegration tests between e.g. revenues and primary expenditures, or debt and deficit. Bohn (2007, Journal of Monetary Economics), has forcefully argued in favour of a stronger focus on theory. The model of this paper shows to which extent and under which conditions earlier results considering fiscal policy in an endogenous growth setting are modified if government spending is not entirely tax-financed. Therefore the model uses Barro's (1990, Journal of Political Economy) production function and Blanchard (1985, Journal of Political Economy)-type consumers to assess fiscal sustainability and the determinants of long-run (or potential) growth, in presence of productive capital services. The main conclusion is that, provided public spending is not too high, it will be growth-enhancing. This feature does not hurt fiscal sustainability if taxes are adjusted appropriately. We also calibrate the model to show that the current level of public capital is low in France, the UK and the USA.

Introduction

The issue of fiscal sustainability is the source of a vast literature since the seminal empirical investigation of [START_REF] Hamilton | On the Limitations of Government Borrowing: A Framework for Empirical Testing[END_REF] on US public debt. Broadly speaking, the empirical literature has followed five approaches. First, time-series properties can be investigated and their consistency with the intertemporal budget constraint (IBC) checked. According to [START_REF] Hamilton | On the Limitations of Government Borrowing: A Framework for Empirical Testing[END_REF], stationarity of the debt time series was required for sustainability. [START_REF] Trehan | Common Trends, the Government Budget Constraint, and Revenue Smoothing[END_REF] and [START_REF] Quintos | Sustainability of the Deficit Process with Structural Shifts[END_REF] respectively advocated that total deficit should be stationary and difference-stationary. Second, Blanchard (1993) and Blanchard et al. (1999) proposed to compute a medium run tax rate or a primary surplus which would be consistent with sustainability, i.e. that would fulfil the IBC. Fiscal policies can be assessed in terms of their sustainability depending on expected future tax rates and surpluses being above or below the computed thresholds. Third, reliance on fiscal rules has been used to check the interactions between flow variables like public spending or taxes and public debt: a sufficiently low (high) response of spending (taxes) to a positive shock on public debt is required for sustainability. Barro (1986) and [START_REF] Bohn | The Behaviour of US Public Debt and Deficits[END_REF] assessed the sustainability of US public finances following this methodology. Fourth, [START_REF] Canzoneri | Is the Price Level Determined by the Needs of Fiscal Solvency?[END_REF] studied the interactions between primary (net of interest) deficit and public debt within a VAR approach, and concluded that US public finances were on a sustainable path. [START_REF] Creel | Using Structural Balance Data to Test the Fiscal Theory of the Price Level: Some International Evidence[END_REF] extended their methodology to European countries and reached the same conclusion. Fifth, the generational accounting approach, originally proposed by Auerbach, Gokhale andKotlikoff (1992, 1994), computes for each generation the costs and benefits of projected trends in public finances, thus allowing potential conflicts to emerge.

In a recent contribution, Bohn has cast serious doubts on the appropriateness of empirical investigations relying on the first broad methodology. His paper proves that if the relevant debt variable is stationary after any finite number of differencing operations, then the IBC is satisfied. The IBC is also satisfied if revenues and with-interest spending are difference-stationary of arbitrary order, and this without cointegration requirement. (Bohn, 2007(Bohn, , p. 1838)). Bohn shows that fiscal sustainability is no longer a time-series properties' issue, even if he acknowledges that in some cases, sustainability may be labelled absurdly weak.

As a consequence, a return to economic thinking (Bohn, 2007(Bohn, , p. 1845) is largely encouraged. In this respect, the other empirical methodologies also need to devote attention to the long-run properties of the underlying economic model. Blanchard (1993)'s computation, for example takes for granted that, at least the rate of growth and the rate of interest are constant and not correlated, whereas fiscal rules and VAR approaches have generally been embedded in short-run specifications. Last, the generational accounting framework is a-theoretical.

In fact, long after [START_REF] Arrow | Public Investment, the Rate of Return and Optimal Fiscal Policy[END_REF] emphasized the importance of fiscal policy as a determinant of long-run growth, a substantial literature has used the features of endogenous growth models to reinvestigate this issue. Most papers belonging to this literature extended the seminal model by Barro (1990) in which tax-financed government services affect balanced-growth along a hump-shaped curve: increases in government services are associated with higher long-run growth rates up to a certain threshold. Barro (1990) uses a constant returns to scale production function incorporating the public sector. Assuming a role for public services as an input to private production, the production function takes the following form:

Y  K G K
where Y is output per worker, K is capital per worker, G is the per capita quantity of government purchases of goods and services, and  satisfies the usual conditions for positive and diminishing marginal products (  ′  0 and  ′′  0 ).

With a Cobb-Douglas production function, equation (1) becomes:

Y K  A G K 
where A > 0 is the constant net marginal product of capital and 0 < α < 1.

Under the assumption of tax-financed public services (i.e., of a balanced government budget), different sizes of governments have two effects on the steady-state growth rate. The increase in taxes reduces investment and growth, whereas the increase in public services raises it through capital productivity increases. The second force dominates when government size is small, whereas for increasing levels of public spending the negative effect of taxes on investment and growth eventually becomes more important.

In the vein of [START_REF] Arrow | Public Investment, the Rate of Return and Optimal Fiscal Policy[END_REF], [START_REF] Futagami | Dynamic Analysis of Endogenous Growth Model with Public Capital[END_REF] assumed that public capital, rather than the flow of public services, enters in the production function. Contrary to Barro (1990), they showed that the economy has a transitional dynamics and, consequently, the tax rate which maximises welfare is lower than the tax rate which maximises the growth rate of the economy. As a corollary, the level of public capital in the economy may be suboptimal if households pay insufficient attention to its productive features. [START_REF] Brauninger | The Budget Deficit, Public Debt, and Endogenous Growth[END_REF] and [START_REF] Yakita | Sustainability of Public Debt, Public Capital Formation, and Endogenous Growth in an Overlapping Generations Setting[END_REF] extended the model to the case of unbalanced budget, encompassing therefore debt dynamics. [START_REF] Brauninger | The Budget Deficit, Public Debt, and Endogenous Growth[END_REF] assumed an AK production function and concluded on the existence of a threshold public deficit ratio. If the ratio stays below the threshold,

(2) an increase of public deficit reduces the economic rate of growth; if the deficit ratio exceeds the threshold, there is no steady state. Yakita assumed a [START_REF] Futagami | Dynamic Analysis of Endogenous Growth Model with Public Capital[END_REF] production function and concluded that the threshold of public finance sustainability is increasing in public capital stock: countries with already high levels of public capital are more prone to sustain their public finances than countries with smaller ones. Moreover, reducing the public investment-to-GDP ratio, while keeping the debt finance ratio constant, raises the threshold of the public debt-to-public capital ratio: the range of sustainable initial public debt is therefore enlarged. In both [START_REF] Brauninger | The Budget Deficit, Public Debt, and Endogenous Growth[END_REF] and [START_REF] Yakita | Sustainability of Public Debt, Public Capital Formation, and Endogenous Growth in an Overlapping Generations Setting[END_REF], increased public investment ratios not only require higher taxes but also increases in bond issuance, which drive interest rates upward. Crowding-out effects are thus prominent in their analyses and it is all the more so that public debt has no direct incidence on the long run steady state. Thus, it is not surprising that their conclusions are relatively weaker for public capital as a growth-engine than Barro (1990) or [START_REF] Futagami | Dynamic Analysis of Endogenous Growth Model with Public Capital[END_REF]. [START_REF] Ghosh | Endogenous Growth, Welfare and Budgetary Regimes[END_REF] also extended [START_REF] Futagami | Dynamic Analysis of Endogenous Growth Model with Public Capital[END_REF] to the case of welfare-maximising fiscal rules, while taking into account government debt. They concluded that under a golden rule of public finance (GRPF), a less strict budgetary stance may lead to lower steady state welfare if public consumption increases and produces crowding-out effects. However, under the GRPF regime, the ratio of public capital to private capital is lower than under other fiscal regimes so that crowding out effects are minimised in this context. [START_REF] Greiner | Human Capital Formation, Public Debt and Economic Growth[END_REF] studied the implication of publicly-financed education in an endogenous growth model with human capital where governments pay attention to fiscal sustainability. All the models described so far, are characterized by infinitely lived consumers. [START_REF] Blanchard | Debt, Deficits and Finite Horizons[END_REF] showed that, after relaxing the assumption of infinite horizons for households, aggregate consumption is a linear function of aggregate financial and human wealth. In his model public bonds are net wealth for households, in contradiction with [START_REF] Barro | Are Government Bonds Net Wealth?[END_REF]. Blanchard also introduced a government which spends on goods but does not affect production directly. Not surprisingly, he concluded on crowding-out effects of fiscal policy.

Blanchard-type consumers and Barro-type production as in equation 1 have already been introduced in endogenous growth models. [START_REF] Mourmouras | Government Spending on Infrastructures in an Endogenous Growth Model with Finite Horizons[END_REF] introduced the production function 2 in the Blanchard model, but they assumed a balanced budget rule in the vein of Barro (1990). They were finally unable to find an analytical solution. [START_REF] Saint-Paul | Fiscal Policy in an Endogenous Growth Model[END_REF] introduced an AK production function in the Blanchard model and showed that higher public debt produced a lower economic rate of growth, even under the assumption that the balanced-growth rate remains above the interest rate: future generations will be harmed by fiscal policy. [START_REF] Reinhart | Death and Taxes: Their Implications for Endogenous Growth[END_REF] used a simplified version of Saint-Paul's model to assess the incidence of higher life expectancy on economic growth and fiscal sustainability. With an AK production, higher debt involves lower public spending at the steady-state, and economic growth rate may rise.

In this paper, we want to show to what extent and under which conditions these results are modified if government services are introduced but are not entirely tax-financed. Therefore the model uses Barro's production function 2 and Blanchard-type consumers to assess fiscal sustainability and the determinants of long-run (or potential) growth, in presence of productive public services. Finally, the model is calibrated using data from national accounts. We assess the degree of optimality of public finances in three large countries that have different fiscal rules (France, the UK and the USA) taking the theoretical model as a benchmark. Finally, we conclude the paper with a discussion of the optimality of public finances' limitations, as well as the quality of public expenditures.

2

The model

Households

Following Blanchard, households maximize a standard lifetime utility function, discounting the probability of death p:

U  E  j  lnc s e pj-s ds
where θ is the subjective rate of time discount. Maximizing, using the budget constraints, and aggregating across consumers, Blanchard obtains:

Ċ  r -C -pp  W W ̇ rW  L -C
The first equation states that consumption grows with the interest rate, and decreases with total wealth. It may be noted that a positive probability of death implies that Ricardian equivalence does not hold, as current wealth affects aggregate consumption. This wealth effect would disappear if households were infinitely lived (i.e. if p = 0). A larger discount rate or probability of death of course increase current consumption for a given wealth, and hence reduces consumption growth. With finite-horizon households (p ≠ 0), both government bonds and capital are part of net wealth: they thus dampen substitution effects. The second equation states that nonhuman wealth increases thanks to interest rate accruals and labour income L, while it is reduced by consumption.

Wealth can take the form of bonds (B) or physical capital (K); furthermore, capital accumulation is a residual from consumption choices and depreciations:

W  K  B K ̇ Y -C -G -K
where G is public spending and δ is the depreciation rate. Public debt dynamics is standard, and depends on interest rate payments and primary surpluses or deficits: Barro (1990), we assume the production function to have constant returns to scale, and to be subject to an externality linked to public spending G, the quantity of public services provided to each household-producer which enters as an input to private production:

B ̇ rB  G -T As in
Y  AK G K 
The marginal product of capital is thus:

∂Y ∂K  1 -A G K 
In equilibrium, the interest rate has to be equal to the net marginal product of capital:

r  ∂Y ∂K -  1 -A G K  -
The complete dynamic system can therefore be written as follows:

Ċ C  1 -A G K  - - -pp   B  K C K K  A G K  -C K -G K - B Ḃ  1 -A G K  -  G B -T B
Define lower case letters as per unit of capital variables: x = X/K. Then, we can rewrite (3) as:

Ċ C  1 -Ag  - - -pp   b  1 c K K  Ag  -c -g - B Ḃ  1 -Ag  -  g b -t b
To derive the steady state values we take as given the stock variables, B, K, and the exogenous decision on the amount of public spending, g = G/K. This implies that we have to determine endogenously two jump variables: the ratio of taxes to capital t = T/K (such that debt increases at the same rate as the other variables), and consumption to capital c = C/K. The solution can be found recursively by imposing equal growth rates in the system above (   Ċ/C  K ̇/K  B ̇/B and eliminating one equation:

c  g  Ag     pp   b  1 c t  gb  1  bc -Ag  
From the first equation we can derive the steady state consumption to capital ratio:

c *  Ag  -g    Ag  -g   2  4pp  b  1 2
(the other root being always negative). Notice that if consumers were infinitely lived, we would have the standard steady state consumption per unit of capital:

p  0  c NC *  Ag  -g  .
A positive probability of death introduces a wealth effect, which is increasing in the ratio of public debt to capital, b. We can now easily prove the following:

Lemma 1 -The effect of g on c * is positive below a threshold g ̄  2 A 1 1- , and negative above it.

Proof -See the Appendix.

In fact, an increase of public spending has two opposite effects on consumption: The first negative, through the increased taxation needed to sustain public spending. The second, positive,

(3) (4a) (4b) (4c)
through the increased productivity of capital. g ̄ denotes the threshold beyond which the former effect dominates.

The effect on the growth rate can be inferred from equation 4b. We can then prove the following:

Proposition 2 -A sufficient condition for the effect of g on σ to be positive is that:

g  g  A2 - 1 1- Proof -See the Appendix.
Equation 5 is not a necessary condition, because the effect on the growth rate could be positive for values of g  g. The threshold for the necessary condition, nevertheless, is impossible to derive analytically. The growth maximizing level of g, that we denote with g * , will have to be found through calibration and numerical simulations.

The intuition for this result is the following. For values of g  g ̄, an increase of public spending induces an increase of consumption, with negative effects on the growth rate. The direct effect of increasing productivity nevertheless dominates. For intermediate values ( g ̄ g  ĝ as defined in the Appendix) the two effects push in the same direction, as increasing g both increases productivity and savings. Finally, above ĝ the effect of further increases of g on productivity is negative. This effect is initially dominated by the effect on savings, but as g goes beyond the threshold g the loss of productivity grows larger, and the effect of increases of g on the growth rate eventually becomes negative.

Calibration on National Accounting Data

We took data from the French, British and US national accounts 1 to calibrate the model and find the optimal rate of public spending to capital, g * . The comparison between these three countries is interesting because they have quite different fiscal frameworks: France and the UK are constrained by the Stability and Growth Pact; nevertheless, the latter has adopted a specific framework, the Golden rule of public finances which gives more fiscal leeway to finance public investment. Finally, US public finances face no rule at all.

The technology parameters for the three countries can be estimated from equation 2. Thanks to the Cobb Douglas formulation, the value of α can be approximated by the share of public capital services on GDP. The level of public capital services is computed as general government gross capital formation plus acquisitions of produced non financial assets, less disposals of non produced non financial assets. Once estimated α, we computed A  YG  K 1-  -1 for each country.

We assumed the discounting and preference parameters to be equal for the three countries, and we took the values commonly found in the current literature. Table 1 summarizes the calibration parameters.

-----1 French data were taken from the web site of French National Institute (INSEE), UK data were taken from the Blue Book 2007 and US data were taken from the web site of the Bureau of Economic Analysis (BEA).

(5) Using these parameters, we computed for each country the different thresholds and the growth maximizing level of public spending, g * . Table 2 reports the computed values, and the difference between actual and optimal levels of public spending (both as a ratio to capital and as a ratio to GDP). Notice that while the first two thresholds ( g ̄ and g ) only depend on technological factors, the last one depends on the level of indebtenness of the country. Thus, the growth maximizing level of public expenditure cannot be computed independently of the debt conditions.

Figure 1 shows the relationship between consumption, the growth rate, and the level of public services g in France. As in Barro (1990), we have a hump shaped curve both for consumption and for the growth rate (the other countries have similar patterns). The first immediate consideration related to the results of Table 2 is the fact that the three countries are below their optimal level of public expenditure. Comparing g with the computed optimal level leads to conclude that budgetary efforts are necessary to bridge the gap. For example, the actual level of public capital services is 0.018 in France (with a historical peak of 0.022 in 1991 and an astonishingly low variance of 1.6•10 -6 since 1978), well below the optimal value g *  0. 0489. Even discountiong for the roughness of the calibration, the gap between optimal and actual g -3 per cent of the total value of gross private capital in France, i.e. almost 10 per cent of GDP -is sufficiently high to question the relevance of public finances limitations in the case of France. As a matter of fact, the UK with its Golden rule of public finances is the country that comes closest to the optimal level of public capital services: the gap between optimal and actual g is less than 1 per cent, i.e. around 3 per cent of the British GDP. The USA perform relatively well also with a gap of around 5 per cent of GDP. These difference are of course influenced by technology, capital and so on, but the institutional setting plays a crucial role (public investment in France declined dramatically in the 1990s, as reported in Figure 2).

Our rough calibration exercise also allows to pursue the analysis one step further. The assumption that g * is a benchmark for the economy allows to infer the quality of public spending in each of the three countries. The quality of public spending has generally been assessed with respect to a given level of output. Most studies related to that issue take as given the production frontier (see, e.g., [START_REF] Afonso | Public Sector Efficiency: An International Comparison[END_REF], using one country (or a group of countries) as a benchmark, and computing distance from the benchmark for the other countries. Within the present framework, it is possible to evaluate the efficiency or quality of public spending when the production frontier is moving, thanks to the endogenous growth setting. Then, the model can serve as a normative instrument to gauge the efficiency of all public spending. As a matter of fact, one can assess this efficiency from three different, although related, perspectives. First, one can compare the actual level of public capital services with its optimum level. Above, we concluded that the gap was worth 5 per cent of GDP for the USA, or equivalently, that the ratio g/g * is equal to 40 per cent. This, can be interpreted as saying that in the US public capital services have reached 40 per cent of the full capacity (for which their efficiency would be 100 per cent). The corresponding figures for France and the UK are 37 per cent and 36 per cent respectively (see Table 3, column 3).

Second, one can compare all public spending (g Tot ) with the optimal level for the economy, g * . Take for example France, where g Tot (equal to 0.137) largely exceeds the optimal value of 0.0489. If following our model the latter is interpreted as the proportion of total spending which is efficient, and if we assume that France could reach this optimal level, taking the levels of public debt and private capital at their actual levels, only g * /g Tot ≃ 36% of total public spending can be labelled as "productive". The corresponding values for the US and the UK are respectively 23 per cent and 12 per cent (see Table 3, column 4). The differences can be explained by a standard decreasing marginal productivity argument, public spending in these two countries having been shown to be already closer to their optimum. 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Table 3 Efficiency Scores (column 2 taken from Table 3 in [START_REF] Afonso | Public Sector Efficiency: An International Comparison[END_REF] Third, we can go a step further and gauge the efficiency of current expenditures. Taking as given the former efficiency assessment of total spending (g * /g Tot ), we can assume that a composition effect between current and capital expenditures does exist. The latter, approximated by public capital services, are assumed to be a 100 per cent productive. Then the corresponding efficiency of current expenditures x can be computed from a simple formula:

g * g Tot  1. g g Tot  x. g Tot -g g Tot
If we apply that formula, we find that 26 per cent of French current expenditures are productive in the sense of Barro (1990). The corresponding values for the US and the UK are respectively 16 per cent and 8 per cent (Table 3, column 5).

As we said above, our approach allows to compare the quality of public spending without assuming a constant production frontier nor giving some countries more weight than others in the estimations. [START_REF] Afonso | Public Sector Efficiency: An International Comparison[END_REF], for instance, use a non-parametric production frontier technique, and their results are used to rank countries according to the distance of their efficiency score vis-à-vis a benchmark. It is obvious that it is impossible to evaluate the score of those countries which form the benchmark, i.e. which are somewhat arbitrarily assumed to be on the production possibility frontier. Thanks to the use of an underlying model, we don't have such a limitation in our framework.

Table 3 reports the estimations by [START_REF] Afonso | Public Sector Efficiency: An International Comparison[END_REF] for our three countries and compares them with ours. It is clear that for non benchmark countries like France and the UK, efficiency "scores" are high when one assumes a constant production frontier. In the case of France, for instance, Afonso et al. find that total output in 2000 could have been reached with only two thirds of actual public spending, i.e. 66 per cent of French public spending were "productive". In sharp contrast, we report a score of 36 per cent for all expenditures after we take into account the fact that public services endogenously cause an increase in steady-state production. We can also report a score of 26 per cent for French current expenditures. We can further compute the difference in efficiency betwen capital and current spending, as the percentage decrease between column 3 and 4 of Table 3. This is largest in the UK, 33 per cent (compared with 30 and 28 per cent in the US and France respectively). We can interpret this as an indicator of the more pronounced preference of UK authorities for public capital services. It can also be interpreted as reflecting the cost of the UK It is also interesting to see how our results compare with the original Barro (1990) model. In Figure 3 we plot consumption and the growth rate in our case (p = 0.05) and in the case of infinitely lived households (p = 0), that corresponds to the Ricardian equivalence case. We only report figures with French parameters and values, as plots are similar whatever the country. As the figure shows, the introduction of a wealth effect increases consumption for each level of public services, but it also decreases the growth rate (as is intuitive from equation 4b). The lower savings, the lower economic growth in this neoclassical context. In comparison with the infinitely-lived agents' case, the value-added of our results can be twofold: First, they stem from a realistic assumption, a finite horizon; second, growth-maximising consumption at the steady-state is positive and not nil as in the infinite horizon case.

Country

Finally, we investigated how the growth rate and optimal taxation react to different level of initial indebdtedness. In Figure 4 we plotted for different levels of b = B/K the growth maximizing level of public services, and the corresponding growth rate and level of taxation. It can be observed that, in spite of the positive effect on the wealth of the households, an increasing level of debt causes an increase in the tax burden, and a decrease in the optimal level of public services. The maximum attainable growth rate is also decreasing in b. Only countries with low initial public debt level can afford high levels of public capital services and low taxes. In this respect, no "one-size-fits-all" fiscal strategy can exist: the optimal strategy must be conditional on the initial level of debt. Although our results abstract from important issues like a sustainable growth respectful of the environmental issue, they show that in some cases, increasing public spending will be growth-improving, without hurting the sustainability of public finances. Moreover, the theoretical model has been used as a benchmark for assessing the efficiency of public spending. In the cases of France, UK and US, it has first been shown that the actual level of general government gross fixed capital formation was below its optimal level. Second, total public spending lacks efficiency and a reallocation in favour of productive public expenditures would be beneficial for all economies, although the UK has performed better in terms of productive expenditures. It has also been shown that such a result has been reached at the expense of current expenditures: whereas the UK has been performing the best for productive expenditures, its current expenditures have proven to be far less productive than in the other two countries.

Possible extensions of the model are manifold. First, we need to control empirically that the threshold public spending is compatible with a sustainable tax rate, in a Blanchard (1993) manner. Then, the sensitiveness of the results to the constant probability of death could be analysed. Finally, we could extend the model to incorporate nominal rigidities in the mid-run and of fiscal and monetary rules in the vein of new Keynesian models. , and negative above it.

Proof -The derivative of c *

with respect to g is:

∂c * ∂g  Ag  -g    Ag  -g   2  4pp  b  1 2 Ag  -g   2  4pp  b  1  2 Ag -1 -1  c *  2 Ag -1 -1 Ag  -g   2  4pp  b  1
This implies that: ∂ ∂g  Ag -1 -1 -∂c * ∂g We can notice that ∂ ∂g  0 in one of the following three cases:

 Ag -1 -1 - c *  2 Ag -1 -1 Ag  -g   2  4pp  b  1  ∂ ∂g  0  LHS Ag -1 -1  RHS c *  2 Ag -1 -1 Ag  -g   2  4pp  b  1
1) LHS  0  RHS 2) LHS  RHS  0 3) 0  RHS  LHS Denote ĝ  A 1 1-
as the threshold below which LHS  0 (cases 1 and 1). For g ̄ g  ĝ , RHS  0 and the proposition is trivially proven (case 1).

For g  g ̄ , RHS  0. , but we can prove that LHS > RHS. With some manipulation, we have that:

∂ ∂g  0  X Ag -1 -1  2 Ag -1 -1 - Z c * Ag  -g   2  4pp  b  1  0
The proposition is proved if X > Z.   1 implies that X > 1. Then, to prove the proposition we just need to prove that Z < 1. Substituting c * , we have:

Ag  -g    Ag  -g   2  4pp  b  1 2 Ag  -g   2  4pp  b  1  1  Ag  -g   2  4pp  b  1  Ag  -g  
which is always true provided g  g ̄.

We are left with case 3, in which g  ĝ , and both LHS and RHS are negative.

Multiplying both sides of equation 6 for -1 we obtain:

∂ ∂g  0  1 -Ag -1   c * 1 - 2 Ag -1  Ag  -g   2  4pp  b  1
The threshold g can be found analytically. Rewriting steady-state consumption like:

c *  c NC *  Ag  -g   2  4pp  b  1
2 one needs to demonstrate that:

X  Ag -1 -1  2 Ag -1 -1  c NC * 2 Ag  -g   2  4pp  b  1  1 2
Since the first element on the RHS is always positive, a sufficient condition for ∂ ∂g  0 is: X  1/2 . With trivial algebra, we can show that this is always true as long as g  g where:

g  A2 - 1 1-

Figure 1 Steady

 1 Figure 1 Steady State Consumption (c * ) and Growth (σ) as a Function of g (Right Panel) The Left Panel is a Zoom of the Right Panel for c *

  Figure 2

  Government Spending (left axis) percent of GDP (right axis)

  Figure 3

  Figure 4

  The effect of g on c * is positive below a threshold g ̄  2 A 1 1-

  A sufficient condition for the effect of g on σ to be positive is that: g  g  A2 -

  Thus, we have to study under what conditions LHS > RHS.

Table 1

 1

		Calibration Parameters
		US	FR	UK
	b = B/K	0.182	0.187	0.084
	K/Y	2.41	3.20	4.72
	g = G/K	0.014	0.018	0.004
	α	0.033	0.070	0.018
	A	0.478	0.383	0.234
	δ	0.1	0.1	0.1
	θ	0.05	0.05	0.05
	p	0.05	0.05	0.05

Table 2 Thresholds of Optimal Public Spending Ratios for the Calibrated Model

 2

		US	FR	UK
	g ̄	0.0004	0.0012	0.0001
	g	0.0276	0.0414	0.0076
	g *	0.0342	0.0489	0.0106
	g	0.014	0.018	0.004
	g * -g	0.0206	0.0309	0.0068
	(G/Y) * -G/Y	0.049	0.099	0.032

  , column 3 to 5: our computations)

		Input efficiency	Public Capital Services' efficiency (percent)
		(percent)	g/g *	g * /g Tot	x	=	Tot -g g -*	g g
	US	100	40	23			16
	France	64	37	36			26
	UK	84	36	12			8


B E Lear

Ned From

Recen T His

E Cre

Introduction

The financial crisis which began in 2007 in the United States has piqued interest in its causes and consequences for the domestic economy and for the rest of the world as well. Contagion effects are expected to arise not only in the financial markets but also in the fields of goods and services. The ongoing crisis may be worldwide.

Although globalization has long been associated with competitiveness and its resulting lower prices, this crisis has arrived at a moment when inflation has reappeared. Nevertheless, determinants for the return of inflation are not similar to those of the early 1970s where external factors-e.g., the oil shocks-were associated with internal ones-e.g., sharply declining productivity and rising wages. In the mid-2000s, external factors have been prominent determinants of inflation in the so-called rich countries. Despite a recent rising trend, core inflation reflecting domestic factors and therefore corrected for the incidence of volatile prices for items such as raw materials remains at relatively low levels, for example, below 2% per year in the Euro area. Globalization seems to be associated with rising inflation because of the growth of emerging economies and related high overall demand.

In this context of financial crisis and soaring inflation, central bankers are facing a trade-off: should they cushion the crisis at the risk of pushing inflation upwards or of creating another financial bubble; or should they curb inflation at the risk of deepening the crisis? Surely, the trade-off is not so simple. Curbing inflation may retain competitiveness and low interest rates, helping firms and the financial sector to avoid the crisis, whereas cushioning the crisis may remove the threat of depression and boost production above demand, pushing inflation downwards.

The specificity of the current inflation is its external origin, as far as rich countries are concerned. Therefore, central banks' reactions may be useless insofar as they are set unilaterally. Depressing domestic activity with a restrictive monetary stance may not depress the emerging economies' insatiable demands. Central banks should therefore implement coordinated policies that would put an end to inflation pressures worldwide. However, coordination is not an easy task and central banks are generally left with a single possible strategy: doing it on their own. Nash equilibria, to introduce some economics jargon, are the rule and coordination the exception.

Taking this general-though still debatable-principle as a given, one has to answer the following question: in the present context, what is the best strategy? I will endeavor to address only the cases of the Federal Reserve (Fed) and the European Central Bank (ECB), though the reactions of all other important central banks such as the Bank of Japan, the Bank of England, the Bank of Canada, the Bank of China and the Bank of Switzerland are important in that they may dampen or deepen the crisis through interest rate and exchange rate channels. Many theories compete as to which policy is optimal given the context. I will briefly mention three, from the old Keynesian-Monetarist controversy to the new Inflation Targeting (IT) framework. It seems rather obvious that the ECB is influenced by Monetarism and its sequel, the so-called New Keynesian framework, whereas the Fed embraces the IT framework. Although not a novelty in itself, it should be kept in mind because it can be used as an anchor for expectations. Ben Bernanke is not only the chairman of the Fed, he is also among the top economists who have long promoted IT. Remembering his academic work should help forecast his actions. Jean-Claude Trichet, the ECB's chairman, is in a different position as far as predicting his future actions is concerned: he must fulfill the primary objective laid down in the Maastricht Treaty, i.e., price stability. In addition, his institution relies on monetary aggregates, although not exclusively.

Recalling the theoretical backgrounds of US-and euro-area monetary policies has another advantage: the different theories have been assessed empirically, and it is possible to see whether Monetarism and/or IT deliver efficient strategies and to what extent.

Some theoretical background

The nomination of Bernanke as the US Fed Chairman has relaunched the debate on the benefit of adopting an official Inflation Targeting (IT) framework in that country, since he was an early promoter of this kind of monetary strategy.

Recently, the US financial turmoil has sparked a debate about the optimal monetary strategy, the sharp decline in the US monetary policy rate being interpreted as a step backward in the struggle against inflation.

It is straightforward to show (Figure 1) that in the recent past, and after intervention rates had risen from a low 1%-level in May, 2004, to a peak of 5.25% in August, 2006, key short-run interest rates, in nominal terms, have sharply decreased in the US between the beginning of the crisis and mid-2008. After a 25-basispoint decrease on April 30, 2008, interest rates in the US have been decreased on the whole by more than 300 basis points, and it has happened over a short horizon of three quarters. In contrast, the key interest rate of the ECB has remained flat.

It is argued that these contrasting strategies stem from contrasting theoretical frameworks regarding the management and efficiency of monetary policy. They are briefly sketched below.

Unsurprisingly, the Monetarist revolution appears as the first important strand in the literature. This is largely due to Monetarism being a historical prerequisite to that which followed. Monetarism arose as a response to the Keynesian revolution of the mid-nineteenth century, along two different time horizons. In the short run, the Monetarists claimed the dominance of monetary policy over fiscal policy as a stabilization tool, although they admitted that monetary policy was plagued with "long and variable lags." On the question of the reliable monetary policy instrument, they favored monetary aggregates over a short-term nominal interest rate. Therefore, in the long run, they claimed that the Quantity theory was valid.

The Quantity theory is usually presented under the following form:

(1) M∆V=P∆Y where M is a monetary aggregate (whether M0, M1 or M3), V is money velocity, P is the general price index and Y is GDP at constant price.

The Quantity theory views money as a means of payment and does not give much attention to another prominent money function: savings or reserve of value for intertemporal transactions. Thus, the theory argues that all present transactions, assessed through nominal GDP, must be settled up with money, taking into account its availability and the many transactions for which a given amount of money can pay.

It has been possible to infer an optimal monetary rule from this logical setting. Under the following three assumptions-inflation is costly, V is constant in the long run and Y is at a steady state (i.e., non-voluntary employment has disappeared)-targeting a zero-inflation rate seems optimal. In order to attain such a target, it is necessary to limit money growth gradually until it reaches zero. Differentiating equation (1) leads to the well-known expression:

(2) ∆M /M=∆P/P Finally, a zero-money-growth rate is an optimal monetary rule in so far as inflation is always a monetary phenomenon, a strong assumption in itself as it is also well-known that inflation can be attributable to demand factors, to shocks on productivity and to external determinants like the price of oil.

Beyond this optimal monetary rule, [START_REF] Friedman | The Optimum Quantity of Money[END_REF] also promoted deflation, building upon two different ideas. First, liquidity preference is a costless device, in comparison with the issuance of bonds and stocks which give rise to the payments of yields or dividends. Promoting money demand is crucial in this respect as it minimizes welfare costs. In order to do so, fixing the short-run nominal interest rate at zero is optimal. Second, a positive Wicksellian real interest rate is also optimal, unless investment is too high and fuels inflation expectations. Using the usual Fisher equation, the consistency between these two ideas makes it necessary that prices always decrease or that a constant deflation occurs in the economy.

These two monetary strategies-declining money growth rates or the achievement of deflation-were complemented by another macroeconomic revolution: the rational expectations (RE). After [START_REF] Phelps | Phillips Curves, Expectations of Inflation and Optimal Unemployment over Time[END_REF] and [START_REF] Friedman | The Role of Monetary Policy[END_REF] criticized the downward sloping Phillips curve on expectations grounds, the conclusion that no trade-off was possible between inflation and unemployment even in the short run led to the dismissal of economic policies.

After the consecutive re-emergence of general equilibrium in macroeconomics, within the so-called new classical framework, increasing importance has been attributed to stability and expectations, to be opposed with the stabilization issue of the 1950s and 1960s. The necessity of achieving a stable economic environment for firms and households was concomitant to the idea that governments were destabilizing private behaviors, notably because their objectives were alleged to go beyond the steady state (lower unemployment than the NAIRU; higher economic growth than potential growth) for electoral reasons.

The emergence of the notion of stability and the conditions needed for reaching it, led to the emergence of new concepts in the macroeconomic literature: discipline, commitment, credibility, reputation, delegation and conservatism became the master words of the profession. All these words originated in the introduction of RE in all behaviors. As Robert [START_REF] Lucas | Econometric policy evaluation: a critique[END_REF] stated with regard to control theory: unlike rockets, people try to understand and predict the actions of their controllers. Control theory therefore had to be replaced with time consistency and credibility issues in economics. Tying the hands of governments with rules was advocated as a good solution to the time inconsistency of policy management. Delegating monetary policy to conservative central bankers was another solution.

At least this strand of the literature had in common with the Monetarist revolution the assumption that inflation is costly, whatever the level. Unlike this revolution, however, the optimal instrument of monetary policy is the interest rate rather than a monetary aggregate. It has led to the rise and adoption of an interest rate rule, like the Taylor rule, to monitor key macroeconomic indicators: inflation and growth. The rule generally states that the short-run nominal interest rate is set according to three targets: a longrun real equilibrium interest rate, an inflation target and an output growth target. Central banks would be urged to trade off between the two latter targets, generally giving more weight to inflation than to output. Adopting such a rule would improve the transparency and efficiency of monetary policy, minimizing the biases economic policies might produce in the economy. Such a rule would be "expectable" and would help to dampen the economy but not create shocks to it.

Old stories: dealing with Monetarist and Rational Expectations empirical validity

These two monetary revolutions-Monetarism and interest rate rule in an RE environment-have been disputed on many grounds (see [START_REF] Gertler | Financial Structure and Aggregate Economic Activity: An Overview[END_REF] and most certainly on empirical grounds.

The deflation strategy advocated by [START_REF] Friedman | The Optimum Quantity of Money[END_REF] has been largely weakened since the long and devastating deflation era which Japan has gone through from the late 1990s to the 2000s (see [START_REF] Hamada | Policymaking in Long-Run Links among Money, Prices and Output: Worldwide Evidence[END_REF]. It has always been well-known, on microeconomic grounds, that periods of declining prices are self-fulfilling, in the sense that urgency by consumers to wait for lower prices leads to ever higher discrepancy between supply and demand, until supply stocks disappear. Thus, on macroeconomic grounds, deflation produces disincentives to produce until the whole process reaches an end; hence a long recession is expected to occur.

As for the Quantity theory, although some papers still give credit to its reliability to gauge (future) inflation (see, e.g., [START_REF] Morana | Inflation and monetary dynamics in the USA: a quantity-theory approach[END_REF], evidence of proportional relationship and causality between monetary growth and inflation is weak in developed economies where money has been competed against by more sophisticated non-zero-yield financial instruments (see, e.g., De [START_REF] De Grauwe | Is Inflation Always and Everywhere a Monetary Phenomenon?[END_REF]Herwartz and Reimers, 2006). A simple plot of inflation and M2 growth rates in the US between 1970 and 2008 (Figure 2) shows that there has never been an identity between both rates. Moreover, the correlation between both series is extremely low in the whole sample (.05) and even lower in a shorter sample excluding the years prior to the 1990s (.008). Endorsing a monetary strategy that would largely depend on this theoretical setting is doomed to failure. Notwithstanding the fact that actual inflation is not a purely monetary phenomenon, monetary aggregates may not be a good indicator of future inflation. Thus, money cannot be presented as an anchor for future expectations.

The weak reliance on money as an efficient tool for monetary policy is evidenced by a vector auto-regressive (VAR) model performed on U.S. monthly data in the sample taken from 1970:1-2007:6. The model includes real GDP, core price index and M2. All variables have been first-differenced and therefore the variables included in the VAR model are stationary. Optimal lags are equal to 9 according to the Akaike criterion.

Results (Figure 3) show that a shock to monetary growth has absolutely no significant effect on either output growth or core inflation. Monetary policy seems rather impotent in this framework, quite at odds with the abundant empirical literature on monetary VARs (see [START_REF] Christiano | Monetary Policy Shocks: What Have We Learned and to What End?[END_REF]. Replacing M2 with the fed funds rate gives a different picture where monetary policy is potent (Figure 4, optimal lags are equal to 13). Despite a rather usual "price puzzle," it is shown that a shock to the interest rate produces a negative and significant response of output growth at a 6-to-9-month horizon; the response is significantly persistent until two years after the shock. These latter results are at odds not only with the Monetarist revolution, but also with the RE monetary policy recommendations. Shocks to monetary policy are not rapidly embedded in future expectations, provoking only marginal short-run fluctuations to economic activity: they produce long-lasting changes to growth. Thus, monetary policy remains potent.

The interest rate rules which have developed along the RE recommendations, within the "rules vs. discretion" debate launched by [START_REF] Kydland | Rules Rather than Discretion: The Inconsistency of Optimal Plans[END_REF], have also revealed their limits. First, the constant-coefficient specification is cumbersome: it cannot respond to shocks if the rule is applied in a mechanical way, without leaving much leeway for compensating unexpected economic conditions.

Second, the rule is very sensitive to the assemsment of theoutput gap which remains an open issue in a world of rapid technological progress which is likely to modify the production frontier. Moreover, in the short run, potential output depends on the degree to which tensions between actual and maximum use of inputs are accommodated by agents. High inflation aversion, i.e., a low degree of accommodation, may lead to underestimating potential output.

Third, the performance of a Taylor rule in the U.S. economy is poor. [START_REF] Qin | In-sample and out-of-sample properties of linear and nonlinear Taylor rules[END_REF] have recently shown that the out-of-sample forecasting performance of the rule was better than univariate (AR) models only before 1979, though Taylor rules have long been said to characterize the post-1980s rather than the 1970s (see [START_REF] Clarida | Monetary policy rules and macroeconomic stability: evidence and some theory[END_REF]. Thus the relevance of the Taylor rule for anchoring monetary expectations is disputable.

Inflation targeting

A great deal of attention has been paid to Inflation Targeting (IT) in the recent literature devoted to monetary policy. In the words of its promoters, e.g., [START_REF] Bernanke | Inflation targeting, lessons from the international experience[END_REF], (flexible) inflation targeting should be viewed as a "framework" rather than as a recommendation for the adoption of mechanical rules like the Taylor rule. As such, it goes well beyond the monetary recommendations embedded in the two above-mentioned revolutions: in fact, this relatively recent strand of the literature has advocated a general framing of monetary policymaking, encompassing clear targets, accountable policymakers and a flexible strategy.

The essence of IT lies somewhere between rules and discretion, and has been labelled: "constrained discretion. (Bernanke et al., 1999, p.4). Later they add: "By imposing a conceptual framework and its inherent discipline on the central bank, but without eliminating all flexibility, IT combines some of the advantages traditionally ascribed to rules with those ascribed to discretion" (Bernanke et al., 1999, p.4).

" In the words of its promoters: "Inflation targeting is a framework for monetary policy characterized by the public announcement of official quantitative targets (…) for the inflation rate (…); by explicit acknowledgment that low, stable inflation is monetary policy's primary long-run goal; (…) (by) vigorous efforts to communicate with the public about the plans and objectives of the monetary authorities, and (…) mechanisms that strengthen the central bank's accountability for attaining those objectives"

The IT framework can be related to discipline in that it anchors expectations thanks to the publicly announced inflation target range, but it permits some flexibility: deviations from the target do not incur a loss of credibility and reputation provided the reasons for the deviations are explained to the people. This flexibility gives some leeway to monetary policy and gives the IT framework a specific feature that the Taylor rule, for example, cannot fully retain.

Figure 4. US monetary policy, VAR 2

In the recent past, some OECD countries turned formally to an IT regime: between New Zealand, which did so in 1990, and Spain, which did so in 1995, five others, including Canada, Sweden and the UK, took part. These institutional regime shifts raised questions about their direct incidence on the optimality of implemented monetary policy: for example, have (expected) interest and inflation rates been lower there than in non-IT countries? Empirical literature has been mixed so far, mainly because non-inflation-targeting countries have endorsed relatively similar policies to inflation-targeting countries or have benefited from the overall "Great Moderation" era. Inflation-targeting promoters generally argue that this framework is conducive to low inflation and low inflation expectations, although worldwide inflation has been decreasing since the mid-1980s. They also make a point on the small pass-through in the inflation rate from shocks to the price level in IT countries, although other countries decided to curb inflation and to disinflate in order to gain competitiveness, irrespective of a pure IT framework (e.g., the EMU, where the ECB does not target inflation in the sense given by [START_REF] Bernanke | Inflation targeting, lessons from the international experience[END_REF]. Promoters finally point out that IT is a transparent nominal anchor, likely to improve policy effectiveness regardless of the fact that other possible transparent anchors exist in non-targeting countries: monetary aggregates in the case of the ECB or the nominal exchange rate in the cases of China, Norway, Japan, etc.

In order to disentangle the monetary effects which are specific to IT countries from those pertaining also to non-IT countries, [START_REF] Angeriz | Assessing inflation targeting through intervention analysis[END_REF] use an Unobserved Component Model in the vein of [START_REF] Harvey | Forecasting structural time series models and the Kalman filter[END_REF] to assess the lock-in effects in IT OECD countries in comparison with the US and the EMU which are chosen as the control group. Their conclusion is that non-IT central banks have been as successful as IT central banks in locking in inflation expectations. Creel and Hubert (2008) use a Markov-Switching VAR in the vein of [START_REF] Hamilton | A new approach to the economic analysis of nonstationary time series and the business cycle[END_REF] to gauge regime switches in major IT countries. They escape the control group problem and conclude that switching to an IT regime has permitted countries to improve the effectiveness of monetary policy: better predictability of policy responses and higher monetary leeway, under the form of low real interest rates, are among the characteristics of an IT regime.

Both approaches are complementary. As a matter of fact, conclusions from a mix of these two papers are twofold. On the one hand, according to Angeriz and Arestis (2007), viewing the US as a non-IT country leads to the conclusion that it has succeeded as well as IT countries in curbing inflation and future expectations. This conclusion would apply to the ECB as well.Thus, the Fed and the ECB would be comparable. On the other hand, according to Creel and Hubert (2008), the effectiveness of monetary policy in IT countries is strong and should help to promote its generalization around the world. In this respect, however, the Fed and the ECB are not comparable: the Fed is governed by a promoter of IT, which makes the above-mentioned generalization to the US likely, and the objectives of US monetary policy embed inflation and growth; hence, they pertain to discipline and flexibility. On the contrary, the ECB has a superior objective: price stability, hence, it gives a heavy weight to discipline. Moreover, officials at the ECB have regularly refused to follow an IT strategy, making it unlikely that they change their minds in the near future.

All in all, the closeness of the Fed's monetary strategy with an IT strategy facilitates expectations by the public on the actual and future monetary reactions decided upon at the Federal Open Market Committee (FOMC) as the public knows the overall framework the FOMC is likely to follow. The Monetarist/New Keynesian with RE framework that the ECB is following is also well known to the public. The main difference between the two central banks however is in the empirical potency of their underlying models: whereas IT has proved efficient, the Monetarist world with RE has proved inefficient in that it was unable to reproduce the data (see Figures 3 and4).

Beyond IT: the credit channel

Beyond IT, Bernanke also improved knowledge on the links between monetary policy and banks. In two papers with A. Blinder (Bernanke andBlinder, 1988, 1992), he showed that bank reserves and therefore reserve requirements not only impinge on bank deposits, i.e., money, but also on bank loans; hence, bank credit impinges on aggregate demand and monetary policy has real effects. This view is based on the assumption that bank loans and bonds are not perfect substitutes, at odds with the perfect substitution assumption in the usual IS/LM model. Thus, private agents have to trade off between bonds and credit for financing their investments. During a monetary contraction, the financing composition is changing towards more bonds, at the expense of bank credit. However, smaller firms are more badly hurt than bigger ones because they remain more sensitive to bank credit than to bonds; stated differently, their reliance on bond financing is small.

In this respect, monetary policy is highly potent: through the credit channel, it can produce real effects, either contracting or expansionary. Tight money in this conceptual framework would have more negative effects on the output than in the IS/LM model.

In the following, we have assessed the credit channel in the US. We show that integrating the interest rate on loans in a VAR comprising GDP, inflation and the federal funds rate improves the overall interpretation of the model.

The sample runs from the fourth quarter of 1982 to the second quarter of 2007. Studies dedicated to monetary policy rules usually show that a change in the conduct of US monetary policy occurred under Paul Volcker's chairmanship (see [START_REF] Clarida | Monetary policy rules and macroeconomic stability: evidence and some theory[END_REF]. Volcker was appointed in 1979. However, [START_REF] Boivin | Has US monetary policy changed? Evidence from drifting coefficients and real-time data[END_REF] reports a break in the conduct of monetary policy in October, 1982, and recalls that the fed funds rates between 1979:10 and 1982:10 were not a good measure of monetary policy stance, being replaced during that period by non-borrowed reserves. [START_REF] Clarida | Monetary policy rules and macroeconomic stability: evidence and some theory[END_REF] also mentions this breakpoint. Therefore, our sample begins right after the fed funds rate started being a good measure of the monetary stance. By limiting the sample to the second quarter of 2007, we escape the noise introduced by the management of the "subprime" financial turmoil.

All quarterly data come from the Federal Reserve website except GDP, which comes from the OECD database. Unit-root tests have been performed. All data are I(1). They have been transformed in firstdifference before being introduced in the VAR models.

Three models have been assessed. First, a three-variable VAR was studied, comprising GDP, inflation and the federal funds rate. Using the LM estimator, three lags have been chosen. Responses of the fed funds rate to a shock to production and inflation have the usual features in the short run (Figure 5). However, the fed funds rate decreases three-quarters after the shock to inflation, although not significantly. This decrease can be linked to the decrease in production.

It is also noteworthy that the response of the fed funds rate to a production shock is more substantial and long-lasting than to an inflation shock. It is in contrast with all the above-mentioned literature on US monetary policy rules and points to the fact that the Fed has been able to trade off between its three objectives-low unemployment, low inflation and low long-term interest rates-to the benefit of the former. It remains to be said that the Fed's response to GDP deviations is in sharp contrast with the strategy generally attributed to the ECB.

Following [START_REF] Bernanke | The Federal funds rates and the channels of monetary transmission[END_REF], it can be argued that the responses of the fed funds rate to inflation and GDP deviations show that the Fed follows a reaction function. Finally, Figure 5 shows that a shock to the fed funds rate produces the expected GDP decrease in the mid-run; however, it produces an increase in the inflation rate, hence a so-called "price puzzle."

In the second model (Figure 6), we use the commodity prices as an exogenous variable and the "price puzzle" is no longer statistically significant: consumer prices no longer catch future expectations which are now embedded in commodity prices. The pass-through argument is also confirmed because a shock to prices does not lead to a sharp move in the inflation rate: the inflation rate has returned to its beforeshock level five quarters after the shock.

In a third model, we have introduced the bank prime loan rate among the endogenous variables of the model. Results are striking (Figure 7). A shock to the fed funds rate has no significant effect on GDP; Figure 5. Impulse response functions, 3-variable model, no exogenous variable rather, it produces a significant rise in the interest rate on loans, hence a "credit channel." Moreover, a shock to the bank prime loan rate accompanied by an increase in the fed funds rate produces a GDP decrease in the mid-run, without any effect on the inflation rate that remains at its before-shock level. The assertion that a shock to the bank prime loan rate is "accompanied" by an increase in the fed funds rate is not an assumption: a Granger-causality test leads to the conclusion that causality goes from the fed funds rate to the bank prime rate (Table 1).

This empirical investigation has had two main outcomes. First, it has shown that monetary policy is potent (model 2) in that it has had real and stabilizing effects: the fed funds increase if GDP increases; and a rise in the fed funds rate reduces GDP. Second, within an expanded model incorporating a bank rate, it has shown that the real impact of monetary policy is indirect, in that it has gone through the bank lending rate. Therefore, it can be concluded that the potency of monetary policy in the US is enhanced if the monetary policy stance gives way to a shock to the interest rate on loans.

Conclusion

The Monetarist and RE revolutions led to viewing monetary policy as having a bigger impact on expectations than on actual variables. This view is now shared by the New Keynesian framework. In this paper, we have shown that the ability of well-known monetary rules pertaining to these frameworks and meant to anchor expectations, was weak: the Friedman rule and the Taylor rule have weak out-of-sample forecasting properties.

There are other means of anchoring expectations, and in this paper we have endeavoured to go back to Bernanke's papers. We have found evidence that US monetary policy has been consistent with the views he has expressed in various papers and communications. We have also found evidence that US monetary policy has been potent. Therefore, we claim that reading Bernanke's papers helps not only to understand his past actions but also to forecast his future decisions.

Figure 6. Impulse response functions, 3-variable model, commodity price inflation as an exogenous variable Table 1. Granger causality tests

In contrast, the cautious ECB has stuck to a monetary strategy whose main arguments are related to Monetarism and its sequels. Although this strategy is easily predictable, its efficiency is debatable. The Quantity theory has been shown to be invalid. Moreover, since the beginning of the "subprime" crisis, the ECB has not made a move on the interest rate, remaining tough on inflation, although it has flooded financial markets with easy money. Therefore, long-term interest rates have moved upward, and the ECB has taken the risk of increasing further the risk premium. In the meantime the Fed has tried to lead bank rates downward. A monetary strategy consisting in indirectly modifying interest rates on loans has been shown to have real and stabilizing effects. Fed funds rates increase when GDP is above its before-shock level, and the ensuing increase in the interest rate on loans dampens GDP fluctuations. A symmetric move is expected to produce symmetric effects.

Figure 1 .

 1 Figure 1. Monetary policy stance: US and the euro area

  N.B.: GDPV is GDP at constant prices, INFCORE is core inflation, IRS (or FFR in the following) is the fed funds rate, INF is CPI inflation, LOAN_R is the interest rate on bank loans; variables preceded by "D" are stated in first-difference.

Figure 2 .

 2 Figure 2. The Quantity Theory in the US?

  N.B.: name of the variables given below figure3; DGDPV and INF are expressed in percent.

-24- Creel, J., Hubert, P. (2008), "Has the adoption of inflation targeting represented a regime switch? Empirical evidence from Canada, Sweden and the UK," mimeo, OFCE.


GENDER EQUALITY AND EMPLOYMENT Hélène PÉRIVIER, Researcher, OFCE-Sciences Po

It is always somewhat frustrating to have to discuss such a vast topic in a limited amount of time, but I do thank you for having invited me to take part in this Round Table. My contribution will be structured around three questions:

Is gender inequality a reality on the labour market today?

Is gender inequality fair or effective?

How can we fight those inequalities?

GENDER INEQUALITY ON THE LABOUR MARKET

Gender inequality is obviously a reality today on the labour market, in all countries, though to varying degrees.

In all developed countries, women are less-represented in the active population and are more affected by unemployment when they do come on the market. In France, female unemployment is two to three points higher than that of men. As in other countries, they work most often part-time: 85% of part-time positions are held by women. When they do work full-time, they are less inclined to remain at the office late, as they have other constraints on their schedule, hence lower salary and slower career development. Thus, there is clearly inequality where the quantity and volume of jobs are concerned.

In terms of quality, too, the situation is imbalanced. In France and elsewhere, women tend to be in specific sectors (social work, education) and men in others. Indeed, the labour market appears to reproduce the traditional roles of men and women, with women often employed to perform tasks they already do in their homes. This means that women and men both are not able to enter different areas.

Similarly, in all countries and to a very noticeable extent, the glass ceiling phenomenon is very strong: as one moves up the ladder in terms of responsibility and salary, the percentage of women present declines, often to zero, despite their holding high-level degrees and being present on the labour market. The positions which they do hold are often in the service sector and are unstable. As such, they have less access to vocational training and, thus, fewer opportunities on the labour market than men.

Salary, the indicator of all inequalities on the labour market, tells a story that is no different. There is a difference of approximately 25% between male and female salaries in France, due to a combination of working hours, pure discrimination unexplained by any economic factor (one-fourth of the reason) and the sectors in which women work (one-third of the reason).

INEQUALITIES: FAIR AND EFFECTIVE?

The inequalities I described above are obviously unfair and, like Professor McCrudden, I see that injustice as reason enough, alone, to do everything in our power to fight them. Some people assert that men and women are biologically programmed to play different roles in society, women in the home and men in the workplace. Yet, even assuming this is true, women Hélène PÉRIVIER should receive a salary as mothers, with the social rights and economic freedom that they need. Therein, the current situation can be described as unfair. I believe that there is no biological programming where work is concerned and that each individual should be able to develop, whether in the workplace or at home, as he or she desires. There too, there is injustice, in that women cannot give free rein to a career plan like men do.

FIGHTING INEQUALITIES

In France, no significant advances have been made with regard to gender equality for the last fifteen years. The first causes of this status quo are to be sought in the home: no matter what they have done during the day, women continue to be responsible for the bulk of the housework, taking care of the children, cleaning, doing groceries, etc., without any significant or increasing assistance from their spouse. An INSEE study shows that male participation in housework has increased by only five minutes in the last fifteen years, whereas women are working more and more. There comes a point when the male must become more involved in family life and the overall role-sharing must be adjusted to accommodate two working parents. This obviously requires, from the very early stages of parenthood, public policies that help the working population organise differently.

The laws exist already, as concerns gender equality in the workplace, yet French women fail to mobilise them and, in this respect, are far behind their American counterparts. Only 6% of the complaints lodged with the HALDE involve gender discrimination, and they come primarily from men. Indeed, surprisingly, men who are denied their pensions or family subsidies turn to the HALDE, while a woman who returns from maternity leave to find that her salary has not increased with the overall pay scale does not. This means that it is not enough to devise laws; one must also communicate about them, enforce them and ensure they are used. Also central to equality in the workplace is the question of function. In France, affirmative action does exist, but is difficult to implement. The suggested quota for women on major corporations' Boards of Directors is only 20%, and is even being re-examined as potentially unconstitutional. Meanwhile, the Norwegians have successfully enforced a quota of 40%. Clearly, there and elsewhere, strong-handed action can and will bring progress in addressing the issue of inequalities between men and women on the labour market.