Output and Expenditure

Transcription

1 2 Output and Expenditure We begin with stati models of the real eonomy at the aggregate level, abstrating from money, pries, international linkages and eonomi growth. Our ausal perspetive depends on what we onsider to be held fixed, or exogenous. n the short-run the output of the eonomy is determined by the level of expenditure, whih is made up of three omponents: private onsumption, investment and government spending. These omponents of expenditure are in turn determined by variables like taxes and the real interest rate, whih are onsidered to be exogenous. This is the Keynesian perspetive. But in the long-run output is exogenous, being determined by the level of employment of the fators of prodution: apital and labour. This is the lassial perspetive, in whih the real interest rate adjusts to bring expenditure into line with the given level of output. An issue that arises under both the long- and the short-run is how to treat the publi setor balane, or the government finaning onstraint. Without a finanial setor in the model there is no mehanism to aumulate debt, so stritly speaking the government budget must be balaned. From a long-run perspetive this is as it should be, but should a balaned budget be imposed in the short-run too? t ould be argued that if the finanial onsequenes of a government surplus or defiit have little impat on the real eonomy in the short-run, they an be ignored. Below we present the simple short-run model in both versions, with an unbalaned budget and with a balaned budget. The different onsequenes show how important the assumption is.

2 22 hapter 2 2. S model with taxes in the short-run A linear version of a simple standard textbook model of the real maro eonomy omprises the following equations: E = + + () = E (2) = 0 + d (3) d = T (4) T = +t = 0 a (5) (6) where E is expenditure, is total output or DP, is onsumers expenditure, is investment, is urrent spending by the overnment, d is disposable inome, T is taxes and is the real interest rate. A bar over a variable indiates that the variable is exogenous, and variables labelled with zero subsripts interepts are shift parameters or exogenous shoks to the equations in whih they appear. A flowgraph of the S system is displayed in Figure 2.. t is onstruted by assuming that the left-hand side variable in eah equation is determined by that equation. Our ausal understanding is only ambiguous about the inome-expenditure identity (), but sine eah omponent of expenditure is determined by the other equations in the system, it is only the total that an be determined by that equation. Thus the topography of the flowgraph is uniquely determined by our ausal understanding of the model. How the graph is atually laid out is a matter of hoie: the prinipal riterion should be its intelligibility. n the ase of Figure 2.(b), the layout was seleted bearing in mind the intention to add on a graph of the LM system later.

3 Output and Expenditure 23 0 T - 0 T d t 0 -a simplifies to: (-t) -a (a) Strutural model (b) Semi-redued form Figure 2. The S subsystem The flowgraph in Figure 2.(a) displays the full detail of the model from the ausal transription of the equations. However, in pratial work it is desirable to keep only the essential detail needed for the purpose in hand, and by absorbing the intermediate variables T, d and aording to the rules set out in hapter, and ignoring the shift parameters 0 and 0, the flowgraph simplifies to that shown in Figure 2.(b), where the one loop L=( t) implies the system determinant = ( t), and Mason s rule immediately gives the familiar Keynesian multiplier formulae: d = d ( t), d = d ( t), d d = ( t), d d = ( t) ( t), d d = a ( t) d d = a( t) ( t) The standard diagrammati representation of the S system as found in maroeonomis textbooks (the Keynesian ross ) is reprodued as Figure 2.2.

4 24 hapter 2 E=++ E= ( t) a * Figure 2.2 The Keynesian ross diagram Note that the axes of the diagram on the right represent the two endogenous variables, and of the flowgraph of Figure 2.(b), and that the slopes of the two lines in the Keynesian ross diagram are given by the ar transmittanes and of that flowgraph. Now ondut the following thought experiment. Suppose that the real interest rate is redued by one unit (one perentage point, say), and examine the onsequenes for the equilibrium level of output *. The ++ line shifts upward by the indued hange in investment, a. t now rosses the E = line further to the right. But how muh further? t is not easy to see from the diagram, whih only gives us a qualitative answer ( * inreases). But the transmittane alulation from the flowgraph does give the result, as a /( ( t)), whih ould also be obtained from the equations by algebra. t turns out that this is a key transmittane in the larger S-LM system to be derived below: it is the absolute value of the slope of the S urve in - spae. To emphasize this, Figure 2.3 shows the redued form of the S flowgraph with only and exogenous variables as nodes, juxtaposed with the S urve. The redued form flowgraph of Figure 2.3 shows how DP is determined by the exogenous variables in the S system. n partiular we

5 Output and Expenditure 25 see that hanges in indue hanges in with transmittane a/( ( t)). varies inversely with, and the ovariation of and traes out the S urve on the right in Figure 2.3. hanges in government spending and taxes produe horizontal shifts in the S urve. ( t) ( t) a ( t) a ( t) S Figure 2.3 The S urve Exerise n the S model of setion 2., replae the linear tax funtion with a simple lump-sum tax: T = T. edraw the flowgraph and evaluate the transmittanes from exogenous variables to the endogenous variables. ondense the flowgraph to display just,,, T and. 2.2 Dynamis in the S model The model of Setion 2. is of an equilibrium system. However any explanation of what happens when an exogenous variable hanges is bound to involve dynamis. For example, an unplanned hange in stoks (inventories), persuades produers to redue output if stoks inrease or to inrease output if stoks fall. t is not diffiult to bring stoks or inventories expliitly into the model, but for simpliity we

6 26 hapter 2 merely replae the equilibrium ondition, equation (2), with the following simple dynami adjustment equation: = LE, whih says that output is equal to expenditure in the previous period. (-t) -a E L Figure 2.4 S model with simple dynamis The system determinant is = L( t). Using Mason s rule we derive the transmittanes implied by the model, for example the transmittane from autonomous taxes to DP: L = L( t) L=0 0 in the short-run, and L= ( t) in the long-run. The long-run orresponds to equilibrium, and we see that this agrees with the result of Setion 2.. Exerise 2 Find all the long- and short-run transmittanes from, and to, E and. 2.3 Short-run S model with a balaned budget n the absene of a monetary or finanial setor the government is unable to esape from the need to balane its budget. The obligation to math publi spending with tax reeipts is known as the government s

7 Output and Expenditure 27 budget onstraint. t has the effet of hanging the topography of the flowgraph of the model by introduing a onnetion between taxes and government spending. But how they are onneted depends on the manner in whih the budget is balaned. There are several ways in whih a balaned budget an be ahieved. The government ould balane its budget by adjusting the fixed element of taxes, or by hanging the marginal tax rate t, or by adjusting the level of government spending. The onnetions in the flowgraph and the behaviour of the model depend upon whih of these means is used to ahieve budgetary balane. Here we examine two senarios: (a) the government treats as fixed and adjusts to balane the budget, and (b) the government treats as fixed and adjusts to balane the budget. We keep the same equations as those of the model of setion 2. exept that the interest rate is omitted for simpliity and an equation for the balaned budget is introdued: = + + inome equals expenditure; = 0 + (-T) onsumption funtion; T = + t tax funtion; = T balaned budget. These equations give rise to different flowgraphs depending on whih variables are assumed to be exogenous. T t a. overnment sets T0 and adjusts to get a balaned budget 0 T b. overnment sets and adjusts T0 to get a balaned budget -t 0 Figure 2.5 Balaned budget models

8 28 hapter 2 Note that the flowgraph on the left has three loops, while that on the right has just one. This affets the system determinant i.e. the denominator in the formula of Mason s rule. Another important differene between these flowgraphs is the set of paths between variables. Note that on the left there is just one path from to, whereas on the right there are two. Exogenous Endogenous variables variables. d dt d d t ( )( t) ( )( t) ( ) t d 0 ( )( t) ( )( t) ( ) d ( t) ( t) 0 Table 2. Multipliers (transmittanes) in Model (a) Exogenous Endogenous variables variables. d dt d d 0 ( ) ( ) d 0 0 ( ) ( ) d 0 Table 2.2 Multipliers (transmittanes) in Model (b) Several interesting omparisons an be made. Firstly, note that the transmittanes ( multipliers ) are quite different from those of the model of Setion 2.. Seondly, by omparing Table 2. and 2.2, it an be seen that the DP multipliers from shoks to investment and onsumption are affeted by the manner in whih the government balanes its budget. Model (a) generally has the larger multipliers, however the onsumption multipliers are not affeted by the budget balaning sheme. Thirdly, the tables onfirm that Haavelmo s elebrated balaned budget result that

9 Output and Expenditure 29 DP and government spending hange by equal amounts holds irrespetive of how the budget balane is brought about (reall that dt =d in these models). To see this in model (a) where both T and are endogenous, note that d =dt ( =d ) when hanges. With the help of the flowgraph, let us onsider why onsumption is quite insensitive to hanges in taxes and government spending in these balaned budget models. n Model (a) there are two paths from to, with equal and offsetting transmittanes. An inrease in autonomous taxes raises total taxes, thereby depressing disposable inome, but the inrease in total taxes also raises government spending, and thereby DP by an equal amount, so there is no net effet on disposable inome. Hene onsumption annot hange. A similar story an be told for Model (b), beginning with a hange in government spending. Exerise 3 i. How does a balaned budget affet the slope of the S urve? ii. Add an equation for government spending, = 0 + g to the model of this setion and modify Figure 2.5b to reate a flow graph in whih, 0 and 0 are exogenous. onstrut a table of multipliers for this model and ompare them with those of the model of Fig. 2.5b. 2.4 Long-run S model What should be understood by the terms long-run and short-run depends upon the ontext. Often the term long-run refers to the steady-state equilibrium of a dynami system, while in a different ontext, usually miroeonomi, the term ould refer to a state in whih all fators of prodution are variable. n the present ontext the long-run is a state in whih output is at full apaity, onstrained by the given fator inputs, so it applies to the trend state of the lassial maroeonomy, abstrating from the business yle. Thus output and expenditure are pinned down, exogenous. But equilibrium in the S model still implies

10 30 hapter 2 that output equals intended expenditure (or intended savings equals intended investment), though this annot now be brought about by variations in aggregate demand; instead it is brought about by adjustment of the real interest rate. Figure 2.6(a) is essentially the same as Figure 2.5(b), but with a ouple of extra nodes to give a bit more detail. t represents the Keynesian short-run in whih total expenditure adjusts to bring about equilibrium in the system. By ontrast, although Figure 2.6(b) represents the same equations, it displays a flowgraph with ausality reversed between DP and the real interest rate. T -t 0 T -t 0 0 -a - 0 /a -/a - a. Short-run: exogenous and endogenous b. Long-run: exogenous and endogenous Figure 2.6 ausality reversal in the S model The long-run interpretation of the S model is in effet a version of the lassial loanable funds theory. With total output (and expenditure) given, an inrease in government onsumption or in private onsumption 0 must redue savings, and also investment. The interest rate has to rise in order to bring investment down to this lower level of savings. Also, with a given level of savings, a rise in autonomous investment 0 pushes up the real interest rate. Thus, with total output

11 Output and Expenditure 3 exogenous, a rise in any of the omponents of aggregate demand inreases the interest rate. But an inrease in output, although it must raise private onsumption and investment, will push the real interest rate down. Exerise 4 i. Asertain for yourself that the two flowgraphs of Figure 2.6 imply the same equations. Also, hek that the flowgraph proedure for ausality reversal enables 2.6(b) to be derived from 2.6(a). ii. ive an explanation of the long-run S model in terms of a traditional supply and demand type of diagram, with the interest rate on the vertial axis and savings and investment on the horizontal axis. iii. Suppose that the onsumption funtion depends on the rate of interest, = ( T) b. How does this affet the short-run sensitivity of to hanges in in the model of Figure 2.6(a)? How does it affet the long-run sensitivity of to hanges in in the model of Figure 2.6(b)?