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GUIDELINES TO ADVANCED MACROECONOMICS Notes, Legend and Model Descriptions Krisztián KOPPÁNY Széchenyi István University, Győr KEYNESI KIADÁSI-JÖVEDELMI MULTIPLIKÁTOR MODELLEK 1.1 ONE-REGION KEYNESIAN MULTIPLIER MODELS What you know about John Maynard Keynes? Google him using the slide with some keywords below! John Maynard Keynes (1883-1946) Microversus Macroeconomics Great Depression „But this long run is a misleading guide to current affairs In the long run we are all dead.” A Tract on Monetary Reform (1923), Ch 3, p 80 Active Government Policy Multiplier, Richard Kahn Source: https://noehernandezcortez.wordpress.com/2010/11/10/paul-samuelson-sobre-keynes/ 12 Krisztián KOPPÁNY John Maynard Keynes (1883-1946) is one of the greatest and most influential economists of the twentieth century His thoughts fundamentally changed the way the economy works, especially the macroeconomy In his work published in 1936, he formed an economic model significantly different from the mainstream at the time The global economic crisis that broke out in 1929 played a major role in this, to the solution of which the mainstream could not provide a meaningful answer Of course, there have been serious economic problems and market imbalances in the past, but these have not caused much of a break and created a crossroads in the development of economics This is obviously also due to the level of development of economics at that time By the 1930s, however, our discipline already had a mature micro-theory, the most important message of which was that economic automatisms Krisztián KOPPÁNY steer markets towards equilibrium, and this mechanism would sooner or later balance all markets The equilibrium is stable and general During the Great Depression, the above theorem seemed to be false, and even if it was true in the long run, it must have failed in the short run, at the level of national economic processes Keynes said that “… long run is a misleading guide to current affairs In the long run we are all dead.” He tried to provide a corresponding solution to the problems of the economy with insufficient demand He called for the active economic role of the state and the increase of government orders The multiplier is Keynes' theoretical tool With this he demonstrates and calculates the beneficial consequences of extra budget spending The idea, by the way, was not originally from Keynes, but from one of his students, his later colleague Richard Kahn To demonstrate the operation of the multiplier, first take a country with no foreign economic relations or any other territorial unit smaller or larger In the first step, therefore, we examine the closed economy of a single region 1.1.1 Closed economy Y C C(Y) I G C0 ˆ c c AS or YS AD or YD Yp P Ye ˆ 1− c Yield as Value Added Macroeconomic Value Added = Gross Domestic Product (GDP) Y = GDP GDP form approaches Production approach: Y = Gross Output – Intermediate Consumption (Intermediate Consumption: current use of raw materials, parts and components, and purchased services); Y = the value of final products Income approach: Value Added becomes the income of primary resources (Labour, Capital), Y = primary incomes Expenditure approach (ex post): the value of final products equals the use of them by households (consumption, C), business companies (investment, I), and government (government spending, G) Consumption consumption as the function of macroeconomic income Investment Government spending autonomous consumption (hypothetical consumption in the case of zero income) marginal propensity to consume, dC/dY average propensity to consume or consumption rate C/Y Aggregate Supply, final products supplied Aggregate Demand, demand for final products as planned expenditures, YD = C + I + G potential GDP Price level equilibrium income or equilibrium GDP simple Keynesian income-expenditure multiplier Krisztián KOPPÁNY Figure 1.1 Income-expenditure multiplier in the Keynesian cross YD YD = YS YD’ E YD D B C ΔG A ΔYe 45 Ye Y Ye’ P AS ΔYe Ye Ye’ Yp Y Y = C + I + G (1.1) ˆ C(Y) = C0 + cY (1.2) Substituting (1.2) to (1.1) yields ˆ +I+G Y = C0 + cY (1− cˆ ) Y = C0 + I + G Y= ( C + I + G) ˆ 1− c ˆ to 0.75, the multiplier will be If we set c = 1− 0.75 In Figure 1.1 the economy is in an initial equilibrium in point A, where effective demand (YD) and the supply of final products (Y) (or income) are equal An injection of extra government spending (∆G) moves the demand curve to left up In point B, the economy is in the state of excess demand Having enough production capacity (as shown in the bottom diagram, where actual GDP (Ye) is far from the full-capacity level (Yp, potential GDP), where supply can adapt to demand easily without significant price changes), production will grow to meet extra demand (see arrow form point B to C) Increasing production generates extra incomes and extra consumption expenditures Krisztián KOPPÁNY (from C to D), and a situation with excess demand (although a little smaller than before) occurs again The iteration process goes on until we reach the new equilibrium, ˆ is where the GDP is Ye’ The change in GDP (Ye’ - Ye) is higher (four times higher if c 0.75) than the initial change in government spending (∆G) 1.1.2 Open economy With an open economy model one can easily show that the multiplier can be below one, as well This gives a better description of the Hungarian economy, which has become more and more integrated into the world economy and global value chains in the last two and a half decades X M M(Y) m ˆ+m 1− c Exports Imports imports as the function of macroeconomic income import rate (in proportion to GDP) Simple Keynesian income-expenditure multiplier for open economy M+ Y = C + I + G + X Y = C+ I + G+ X − M (1.3) Y =C+I+ X −M (1.4) C(Y) = cY (1.5) M(Y) = mY (1.6) Substituting (1.5) and (1.6) to (1.4) yields Y = cY + I + X − mY (1− c + m) Y = I + X Y= (I + X ) 1− c + m = 0.952 1− 0.75 + 0.8 For a Hungarian case study using official statistical data from Central Statistical Office of Hungary (see http://www.ksh.hu/stadat_annual_3_1 STADAT Table 3.1.7) see 3_1_7ie DEFAULT.xls The solution and the Excel formulas are shown in the screenshots below Increasing import rates decreased significantly the simple Keynesian income-expenditure multiplier in Hungary With setting c = 0.75 and m = 0.8 the multiplier will be Krisztián KOPPÁNY Krisztián KOPPÁNY A Hungarian Case Study 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 Consumption rate 15 See 3_1_7i_KIINDULÓ.xls, 3_1_7ie DEFAULT.xls Krisztián KOPPÁNY 2015 2013 2014 2012 2010 2011 2009 2007 Import rate 2008 2005 2006 2003 2004 2002 2000 2001 1999 1997 1998 1995 1996 0,0 GDP multiplier Krisztián KOPPÁNY 1.2 MULTIREGION KEYNESIAN MULTIPLIER MODELS 1.2.1 Two-region model (EU-Hungary model) subscipts superscripts row s the region that the variable (GDP, expenditure or share) belongs/refers to the destination or origin region of an expenditure flow rest of the world share variables express the regional distribution of an expenditure flow subscripts: the variable that the share refers to superscripts: the region that the share refers to The GDP expenditure identity for Hungary and EU Yhu = Chu + Ihu + Xhu − Mhu , and (1.7) Yeu = Ceu + Ieu + Xeu − Meu (1.8) Chu = chuYhu (1.9) Ceu = ceuYeu (1.10) eu row Xhu = Xhu + Xhu (1.11) hu row Xeu = Xeu + Xeu (1.12) eu row Mhu = Mhu + Mhu (1.13) hu row Meu = Meu + Meu (1.14) Mhu = mhuYhu (1.15) Meu = meuYeu (1.16) eu row sM + sM =1 hu hu hu row sM + sM =1 eu eu eu row Mhu = sM mhuYhu + sM mhuYhu hu hu (1.17) hu row Meu = sM meuYeu + sM meuYeu eu eu (1.18) hu eu Xeu = sM mhuYhu hu (1.19) eu hu Xhu = sM meuYeu eu (1.20) hu row Yhu = chuYhu + Ihu + sM meuYeu + Xhu − mhuYhu eu row hu Yhu = Ihu + Xhu + ( chu − mhu ) Yhu + sM meuYeu eu Krisztián KOPPÁNY (1.21) row hu Yhu − ( chu − mhu ) Yhu = Ihu + Xhu + sM meuYeu eu (1− chu + mhu ) Yhu = Ihu + Xhurow + sMhu meuYeu eu Yhu = row hu I + Xhu + sM meuYeu eu 1− chu + mhu hu ( ) (1.22) eu row Yeu = ceuYeu + Ieu + sM mhuYhu + Xeu − meuYeu hu row eu Yeu = Ieu + Xeu + sM mhuYhu + ( ceu − meu ) Yeu hu (1.23) … Yeu = row eu I + Xeu + sM mhuYhu hu 1− ceu + meu eu ( row chu − mhu Yhu Ihu + Xhu + eu = row Yeu Ieu + Xeu sMhu mhu ) hu sM meu Yhu eu ceu − meu Yeu (1.24) (1.25) Y = o + OY (1.26) (E − O) Y = o (1.27) Y = (E − O ) o = Ro (1.28) −1 r r R = 1,1 1,2 r2,1 r2,2 Y1(hu) = r1,1o1 + r1,2o2 , Y2(eu) = r2,1o1 + r2,2o2 , ri , j = dYi doj Each ri,,j is a multiplier which expresses the change in country i's GDP caused by unit change in country j’s exogenous variables (investments and exports to the row) EQUATION CHAPTER (NEXT) SECTION Krisztián KOPPÁNY INPUT-OUTPUT TABLES AND MODELS The following table shows the general structure of an input-output table and the notations for the main parts of it billion HUF (unless indicated otherwise) Agriculture I ndustry Serv ices I mports Gross Value Added of which labour incomes Total Input Number of employees (thousand people) Emission of greenhouse gas (thousand tons) Z f x im’ va’ hi’ x’ em’ gh’ Agriculture I ndustry Z Serv ices Final demand Total Output f x im' va' hi' x' em' gh' the square matrix of the intersectoral transactions (intermediate consumption of the domestic industries that comes from the home economy) column vector of the final demand (or final use) for (of) sectoral output column vector of total sectoral output row vector of the import purchases of the domestic production sectors (intermediate consumption of the domestic industries that comes from abroad) row vector of sectoral value added (GDP at basic prices produced in each industry) row vector of sectoral household income (labour incomes paid to employees in each industry) row vector of total sectoral input (the transpose of output vector x, the output and the input of a sector is always the same, two sides of the same coin) row vector of sectoral employment (number of employees in each industry) row vector of sectoral greenhouse gas emission Next diagram shows the direction of causation in the demand-driven (pull) Leontief input-output model Values of the final demand for sectoral products are the exogenous variables, which pull the whole economy’s performance In the basic setting there are no capacity constraints, so any demand can be satisfied To this, companies in each sector must purchase inputs from other companies from the same or different industries (domestic intermediate consumption), from abroad (imports), and they need primary inputs (labour and capital) as well, for which they must pay The labour and capital income are the value added The demand for intermediate products generates more and more production rounds in the economy This multiplicative process results in a higher value of production, imports, value added, employment and greenhouse gas emission than it follows directly from the final demand impulse The total magnitude of the direct and indirect effects is involved and measured by the so-called Type multipliers Type multipliers Krisztián KOPPÁNY pertain to the open input-output model, where all final demand is exogenous, see the table below For the illustration of the direction of causation see arrows billion HUF (unless indicated otherwise) Agriculture Agriculture I ndustry Serv ices I mports Gross Value Added of which labour incomes Total Input Number of employees (thousand people) Emission of greenhouse gas (thousand tons) I ndustry Serv ices 462 315 231 273 819 420 2,100 530 3,710 2,650 12,720 6,890 3,180 26,500 265 1,855 6,095 3,445 14,840 9,275 26,500 288 1,170 2,543 7,510 37,940 10,270 Final Total Output demand 843 2,100 20,620 26,500 17,524 26,500 The model can be formalized and solved as follows Input coefficients for intermediate purchases from other domestic industries (matrix A of direct technical coefficients or direct domestic requirements), imports (m’), value added (v’), household incomes (h’), and employment (e’) and greenhouse gas (g’) intensities can be obtained by dividing the corresponding value of the IO table by the column sums (i.e the total input), or, using matrix operations, by multiplying the corresponding matrix or vector by x −1 , which is the inverse of the diagonal output matrix A= m' = v' = h' = e' = g' = Krisztián KOPPÁNY Agriculture 0.2200 0.1500 0.1100 0.1300 0.3900 0.2000 0.1371 3.5762 I ndustry 0.0200 0.1400 0.1000 0.4800 0.2600 0.1200 0.0442 1.4317 Serv ices 0.0100 0.0700 0.2300 0.1300 0.5600 0.3500 0.0960 0.3875 A=Z x −1 −1 m = im' x −1 v = va x −1 h = hi x −1 e = em x −1 g = gh x 10 The basic equations and the solution of Leontief’s demand-driven IO model for output (and the other variables) can be obtained are the following Z x −1 x+f=x im = m Lf Ax + f = x va = v Lf f = x - Ax = (I - A) x (I – A) f = (I – A) −1 −1 hi = h Lf (I - A) x em = e Lf (I – A) f = x −1 L = (I – A) −1 gh = g Lf x = Lf Lf = x The Type input-output model is closed to the households In this case household consumption vector of the final demand is an endogenous variable in the model, and the values of it depend on labour incomes Extra labour incomes will result in a higher consumption, and this will launch a secondary multiplication process in the model As a result, we will have higher multiplier values for a narrow exogenous final demand base Type final demand multipliers of the (still exogenous) other final use (or final demand) are generally higher than their Type equivalents Next table and diagram show the direction of causation in the Type IO model (closed to households) billion HUF (unless indicated otherwise) Agriculture I ndustry Serv ices I mports Gross Value Added of which labour incomes Total Input Number of employees (thousand people) Emission of greenhouse gas (thousand tons) Agriculture I ndustry Serv ices 462 315 231 273 819 420 2,100 530 3,710 2,650 12,720 6,890 3,180 26,500 265 1,855 6,095 3,445 14,840 9,275 26,500 288 1,170 2,543 7,510 37,940 10,270 Households' Other final use Total Output consumption 300 543 2,100 2,000 18,620 26,500 7,000 10,524 26,500 3,575 4,925 24,938 19,620 With Type and models we can calculate Type and final demand multipliers Type multipliers involve only the direct and indirect effects through the upstream value chains (primary multiplication circle) Type multipliers also incorporate the socalled induced effects of a secondary multiplication process by the extra household consumption paid from extra labour incomes Multipliers can be expressed for each endogenous variable of the model, for example for output, import, value added, labour income, employment and GHG emission The following table shows some examples for the Type multipliers Krisztián KOPPÁNY 11 Output multiplier I mport multiplier Value added multiplier Labour income multiplier Employment multiplier (thousand people/billion HUF) Air pollution (GHG) multiplier (thousand tons/billion HUF) Agriculture 1.7498 0.3124 0.6876 0.3629 I ndustry 1.3716 0.5918 0.4082 0.2035 Serv ices 1.4461 0.2267 0.7733 0.4778 0.2085 0.0718 0.1339 5.0483 1.8681 0.7387 Here come some explanations for some values of the table Final demand output multiplier for Industry 1-unit change in the exogenous components of the final demand for industrial products causes 1.3716-unit change in the gross output (value of production) of the whole economy Final demand import multiplier for Services.1-unit change in the exogenous components of the final demand for services causes 0.2267-unit change in the imports of the whole economy Final demand value added multiplier for Agriculture.1-unit change in the exogenous components of the final demand for agricultural products causes 0.6876-unit change in the value added of the whole economy … Krisztián KOPPÁNY 12