The Keynesian multiplier, news and fiscal policy rules in a DSGE model Authors: George Perendia and Chris Tsoukis artilogica@btconnect.com c.tsoukis@londonmet.ac.uk London Metropolitan University
Abstract : • We extend the standard Smets-Wouters (2007) medium- sized DSGE model in two directions, namely to analyse the effects of news and the Keynesian multiplier, and secondly to incorporate a fiscal policy rule. • We show that both the news channel and the government spending fiscal policy rule significantly improve model fit to data. We then simulate the effects of monetary and of fiscal policy and particularly the role of the Keynesian vs. the neoclassical aspects of the model in driving the results.
Motivation Fiscal policy is again rising to prominence because: • Limited effectiveness of monetary policy (zero bound effects, etc); • In Europe, because of the loss of monetary sovereignty. But debate continues to surround the desirability and effectiveness of fiscal policy and the controversy surrounding the „Obama stimulus plan‟, the ARRA 2009*. • particularly government spending, • crystallised around the notion of the „Keynesian multiplier‟, the notion of a virtuous circle of government spending generating incomes-consumption-output-further incomes, etc.,... • both providing a rationale for fiscal policy via government spending. *) American Recovery and Reinvestment Act, 2009
Introduction – the multiplier (I): Two strands in the static multiplier literature: 1) a static variety of models seeks to re-discover the Keynesian multiplier in static monopolistic set-up. The balanced-budget multiplier emerges in the short run because of the virtuous circle: higher spending generating higher company profits then feed on to higher spending the multiplier vanishes in the long run because free entry eliminates all profits and breaks the virtuous circle. (Mankiw, 1988; Starz, 1989; Dixon, 1987; Dixon and Lawler, 1996; Heijdra, 1998, Heijdra, Ligthart and van der Ploeg, 1998; Sylvestre, 1993;)
Introduction – the multiplier (II): • 2) A second static strand of literature is purely neoclassical (Hall, 2009, Woodford, 2011, Mulligan, 2011): • Rational agents realise that government spending increases will be accompanied by tax increases; • Hence (rational consumer‟s) consumption declines („crowded out‟); • Output rises because a poorer consumer will work harder (will „buy less leisure‟); • But the output rises is less than the government spending increase. • Neoclassical conclusions are vigorously contested by the latest of Summers and DeLong (2012).
Introduction – the multiplier (III): A 3rd strand builds on (Neoclassical) intertemporal optimisation include response of consumption to changing interest rates, integrating fiscal policy with dynamic macroeconomics. But due to their diversity they fail to reach uniform conclusions; e.g. on, the magnitudes of short- relative to long-run multipliers, and whether or not private consumption is crowded out or in Mostly share with the static approaches the weakness that fiscal policy is entirely wasteful ! (Aschauer, 1985, 1988; Barro, 1989; Aiyagari et al ., 1990; Christiano and Eichenbaum, 1992; Baxter and King, 1993; Gali, Lopez-Salido and Valles, 2002)
Introduction: This paper seeks to enhance our understanding of of fiscal policy in the context of the business cycles and current crisis, and its potential for stabilisation. we utilise a standard medium-sized DSGE model as in Smets and Wouters (2007) (see also Drautzburg and Uhlig, 2010). Our innovation is twofold, to incorporate a Keynesian multiplier along the lines of the first strand of literature summarised above; and to account for fiscal policy that is not a random exogenous shock as usually modelled, but, instead: – may be endogenous, and, – may follow a fiscal policy rules akin to that of Taylor (1993) monetary policy rule.
Model of the Keynesian multiplier: To introduce the Keynesian multiplier, we employ a variant of the Euler equation for consumption that accounts for unexpected developments in output and the interest rate („news‟). Unexpected developments then adds up to output via national income accounting, and then further affects consumption due to our formulation of consumption with the news. a Keynesian multiplier structure arises around the backbone of intertemporal evolution of the Euler equation. Such a structure is absent in standard formulations, hampering a better understanding of the workings of fiscal policy.
Model of the Keynesian multiplier: The standard Euler equation shows the time profile of consumption and its response to incentives to save (the real interest rate) or consume now (rate of time preference); it is silent on how consumption responds to changes in lifetime resources. it takes into consideration the anticipated lifetime resources at the beginning of the planning period, but any subsequent revisions of those are not reflected in the path of consumption. Schematically, the Euler equation determines the slope of the consumption profile but not its position – see next slide.
Consumption profile over the lifetime Figure 1: Consumption and „news‟ logC t o t 1 t
Model of the Keynesian multiplier: In above figure the bold consumption profile is determined at t 0 . Euler eq. determines the slope – can change at any time. But, its position is determined only once, at t 0 (and implicitly), reflecting the lifetime resources anticipated then. However, if at t 1 , say, there is „news‟, a revision of lifetime fortunes (unanticipated at t 0 ) that might warrant a shift to a higher profile with the same slope (thinner line), this development will be lost in the Euler equation. This is a crucial omission, as at the core of the multiplier is the virtuous circle fiscal expansion – higher incomes over the lifetime – higher consumption – higher output and lifetime incomes, etc. (see Starz, Mankiw, and Dixon and others);
Model of the Keynesian multiplier: Naturally, all estimable Euler equations contain error terms, which may be interpreted as news about future resources (among other things), but these are entirely exogenous and random, hence unrelated to the logic of the multiplier above. One may say that the interest rate also reflect the „news‟, but this channel is much too indirect and uncertain to support a Keynesian multiplier.
Model of the Keynesian multiplier: To re-instate the multiplier via the effect of news on consumption, we adopt a variant of the „permanent income theory of consumption‟, following Obstfeld and Rogoff (1996, Ch. 2, equation 2.16). ~ (1) r s C A ( 1 ) E X / R ~ t t t t s t 1 r s 0 s Where ~ s R ( 1 r ) t t v v 1 , is the inverse of the discount factor, A t current wealth. X t is labour earnings plus monopoly profits, and linearisation gives eq. (2): ~ ~ X r ( 1 ) x 1 ( 1 )( 1 ) r /( 1 r ) y t s t s 1 t s 1 c a E E ~ ~ ~ ~ t t t t s s 1 ( 1 ) 1 ( 1 ) C r r r r s 0 s 0
Model of the Keynesian multiplier: Following Deaton (1990, Ch. 3), we use the period budget constraint in a beginning-of-period formulation in a linearised form (eq 3‟): X C ~ a ( 1 r ) a ( 1 ) x c ( 1 ) r t t 1 t 1 t 1 t A A and supplementing (3‟) into the consumption equation (2): X C ~ ( 1 r ) a ( 1 ) x c ( 1 ) r t 1 t 1 t 1 t A A ~ X r c ~ t C 1 r ~ ( 1 ) x 1 ( 1 )( 1 ) r /( 1 r ) y t s t s 1 t s 1 E E ~ ~ t t s s ( 1 ) 1 ( 1 ) r r r s 0 s 0
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