Abstract
In this chapter, the shock examined is an unanticipated, permanent, increase is government spending equivalent to one per cent of GDP in the control solution. This fiscal stimulus is spread evenly across the three exogenous components of public sector expenditure; namely, general government employment EG, public consumption CG and investment IG by general government. The shares of these three items in total exogenous government spending on goods and services are 0.6217, 0.2595 and 0.1188 respectively. (Note that the last item excludes investment by publicly owned business enterprises.)
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This is done in Breece et al. (1994), where a fiscal shock is imposed under alternative situations in which monetary policy does, and does not, contribute towards financing the fiscal expansion.
As we will see below, in the case of the fiscal shock we must extend the definition of significant initial events to include also t = 2 (the quarter after the imposition of the shock).
Because all GNE consists notionally of the domestic good and since the price of the domestic good does not move at all at t = 1 (‘Keynesian sticky prices’ — see (20.1.1), p. 219 above), the deviations from control in real and nominal GNE at t = 1 are identical.
The smoothed current value γ of the natural growth rate does appear on the right of (11.4.2), but does not deviate from control under a fiscal shock. 5 Recall that, in MM’s wage equation/Phillips curve (5.5.12) [p. 1071, all right-hand variables are lagged.
YL is not an explicit variable in MM — see (7.2.2), p.117 for its definition.
Actually, nominal labour income YL rises by a slightly lower percentage than employment. In equation (7.2.2), transfer payments ø fall by 0.70 per cent due to the fall in unemployment and associated benefits. Employment E, we have seen, rises by 1.13 per cent; the wage rate W and the policy parameters R do not change, while nominal GDP (GDP$ in the notation of Part 2) rises by 0.93 per cent.
The other variables on the right of equation (7.2.5) with potential to affect the jump in CR are nominal wealth Ω (defined at the top of p. 120) and the consumption price index pc. The latter experiences a tiny jump due to a 0.08 per cent jump at t=1 in the rental price of housing services, while the former is subject to offsetting influences: (a) bond holdings B fall by 0.34 per cent, while (b) the local-currency value of private debt denominated in foreign dollars falls by 2.79 per cent due to the instantaneous appreciation at t=1 of 2.79 percent in the local dollar (jump in log ψ = 0.0279). The ratios of bonds and such debt respectively to total private wealth on the control path are 0.0967 and 0.0886. Hence the jump in nominal wealth at t=1 is -0.0967x0.34 + 0.0886x2.79 = 0.21 per cent. The elasticity of equilibrium private consumption C* with respect to wealth in (7.2.5) is . Hence wealth contributes about 0.07 percentage points of the total jump of 0.79 per cent in C.
With no change in the payroll tax in this simulation, the two wage variables W and WB exhibit identical deviations from control. See (10.2.1), p.150.
The consumption price increases because of a rise in the rental price of housing.
Hicks (1939, Ch. II) pointed out that if an aggregate consists of two or more parts whose relative prices do not change, then for practical purposes the aggregate behaves as a single good, or composite commodity.
It is usual to set the numeraire to unity. Below we have inadvertently left the value of E at about 1.04, an artefact of the model’s calibration. This has no effect on the interpretation of the results.
Exercise 27.2 (Homogeneity of S3MM): (a) real homogeneity of 1st degree. Represent the variables of S3MM as a vector (Q’, P V’)’ , where Q’, P’, and V’ are sub-vectors of real magnitudes, nominal prices, and nominal values, and prime (‘) denotes transposition. Show that if (Q’, P’, V’)’ is a solution of S3MM, then so is (λQ’, P W’)’, where λ is any positive scalar. (b) nominal or price homogeneity of degree zero. Show that if (Q’, P’, V’)’ is a solution of S3MM, then so is (Q’, λP’, W’)’, where is any positive scalar. (If you need help with this exercise, try Dixon, Parmenter, Powell and Wilcoxen (1992), pp. 73–96.)
The computations on S3MM were carried out using version 5.4 of J. M. Horridge’s excellent equation-solving package ESP. We are grateful to Mark Horridge for making the software available and generously giving assistance with its use.
Exports are disaggregated in MM into ‘commodities’ and other; the inverses of the corresponding export demand elasticities in MM’s parameter file were -0.1803 and -0.0917 respectively. The value for the export-demand price flexibility used in S3MM is -0.1215, which lies between these values.
This can best be seen in (27.5.31). Recall that pY acts as the real exchange rate, a crucial variable in the movement between steady states in the case of the neo-Keynesian closure of S3MM (see row 22 of Table 27.5.4).
There has been no change in the quantity of labour available to the sector, and the real wage has increased; capital availability has increased, and the real marginal product of capital rB/pY has not changed; hence real value added in the private sector has increased (which is consistent with being per cent above control in colunm [41, row 9 of Table 27.5.4).
Yaari (1964) demonstrates that real consumption will be increasing along an optimal consumption path only if the pure time preference discount rate is less than the market interest rate. The ratio of the former to the latter rate is closely connected with savings behaviour; for instance, in Lluch’s (1973) extended linear expenditure system (ELES), this ratio is the marginal propensity to consume; it follows that consumption grows with time only if the marginal propensity to save is positive.
At this point we have a conflict with the initial notion that YD is fixed; as we have seen, the consumption function cannot be operating and produce the neutral impact on output shown in column [2] of Table 27.5.4.
Given that the elasticity of real consumption with respect to real private disposable income in (27.5.13) is, it is not difficult to construct numerical examples in which this result is apparent.
If necessary, review Figure 10.4.2, p. 162 above. for an excellent exposition of how these transformation and expansion (contraction) effects work in an AGE model, see Higgs (1986), especially pp. 8–14
For reasons not investigated here, it is clear that in the case of exports X, the favourable transformation effect and the unfavourable contraction effect almost exactly balance, so that the recorded change in exports is effectively zero.
In the context of S3MM this result raises the conundrum: if the economy as a whole is on its inter-temporal budget constraint with (27.5.22) enforced, but consumers are not on theirs (with (27.5.23) not being enforced in the Neo-Keynesian closure), how is the apparent shortfall made up? There is no explicit answer in S3MM, but we note that an appropriate inflow of unrequited transfers from overseas to consumers would allow a reworking of the model in the direction of solving the conundrum. In particular, with an appropriate matching of the ratio of unrequited transfers to GDP with the consumption function parameters and with growth and interest rates, it may be possible to rewrite the intertemporal budget constraints in a way which removes the conflict between the consumers’ intertemporal constraint and the consumption function. This requires further research. In the meantime we note that the presence of unrequited transfers in MM is an important element in that model’s intertemporal budget picture, and that computationally MM does follow a balanced growth path. It is possible that all the growth rates of variables in MM conform to the strict neo-classical analysis, but that the level of private real consumption does not, the difference in MM’s long-run level from neo-classical sustainability (as portrayed in S3MM) being financed by unrequited transfers. Again, more research is needed.
See footnote 8, p. 356 above.
In HSM, the budget is balanced and the government carries no debt. In MM, the tax reaction function (22.5.1) [p.236] ensures that there is no change in the public debt to GDP ratio (which is 1:1 on the control path and in the new steady-state solution).
The public consumption and the public employment components of the fiscal shock work in opposite directions in MM’s steady state (see columns f5] and [8] of Table 27.5.5). In the case of debt, the public consumption component wins, and long run debt is slightly above control.
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© 1995 Springer-Verlag Berlin Heidelberg
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Powell, A.A., Murphy, C.W. (1995). A Fiscal Shock. In: Inside a Modern Macroeconometric Model. Lecture Notes in Economics and Mathematical Systems, vol 428. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-00771-6_27
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