The third implication was that it people and lirms had rational expectations it was wrong to think of policy as the control of a complicated but passive system. Rather, the right way was to think of policy as a game between policy-makers and the economy. The right tool wasn't optimal control but game theory. .And game theory led to a different vision ol policy. A striking example was the issue of time inconsistency discussed hy Finn Kydland and Fdward Prescott alien both at Carnegie Mellon, now at the University of California and Arizona State University an issue that we discussed in Chapter 25. Good intentions on the part ot policy-makers could actually lead to disaster.
To summarise when rational expectations were introduced, Keynesian models couldn't be used to determine policy, Keynesian models couldnt explain long-lasting deviations ol output Irom its natural level, and the theory' of policy needed to be redesigned, using the tools ol game theory.
The integration of rational expectations
As you might guess Irom the tone ot Lucas and Sargent's quote, the intellectual atmosphere in macro¬economics was tense in the early 1970s. But within a few years a process ol integration (ol ideas, not people because tempers remained high had started and it was to dominate the 1970s and the 1980s.
Fairly quickly, the idea that the concept ot rational expectations was the right working assumption gained wide acceptance. This wasn't because macroeconomists believe that people, lirms and partici¬pants in financial markets always lorm expectations rationally. But the concept ol rational expectations appears to be a natural benchmark, at least until economists have made more progress in understanding whether and how actual expectations systematically differ from rational expectations. Work then started on the challenges raised by Lucas and Sargent.
The implications of rational expectations
First, there was a systematic exploration ot the role and the implications of rational expectations in goods markets, in financial markets and in labour markets. Much of what was discovered has been presented in this book already. For example:
• Robert Hall, then Irom MIT and now at Stanlord. showed lhat, if consumers are very loresighicd 1 in the sense defined in Chapter I6i. then changes in consumption should be unpredictable: the best forecast ol consumption next year would be consumption this year: Put another way, changes in consumption should be very hard to predict. I his result came as a surprise to most macroeconomists at the lime, but it is in lact based on a simple intuition: il consumers are very foresighted, they will change their consumption only when they learn something new about the future. But, by definition, such news cannot be predicted. This consumption behaviour, known as thc random walk of consumption lias served as a benchmark in consumption research ever since.
Edward C. Prescott
• Rudiger Dornbusch, who was Irom MIT, showed that the large swings in exchange rates under flexible exchange rates, which had previously been thought ol as the result ol speculation bv irrational investors, were fully consistent with rationality. His argument, which we saw in Chapter 21. was that changes in monetary policy can lead to long-lasting changes in nominal interest rates, and lhat changes in current and expected nominal interest rates lead in turn to large
LPILOGUF: THF STORY OF MACROECONOMICS chapter 28
changes in thc exchange rate. Dornhusch's model known as thc overshooting model of exchange rates, has become the benchmark in discussions ol exchange-rate movements.
Wage setting ancl price setting
Second, there was a systematic exploration of the determination ol wages and prices going lar beyond the Phillips curve relation. Two important contributions were made by Stanley Fischer, then at MIT and now Governor of the Hank ol Israel, and John Taylor, then from Columbia University and now at Stanford. Both showed that the adjustment ol prices and wages in response to changes in unemploy¬ment can be slow even under rational expectations.
They pointed to an important characteristic ol both wage setting and price setting thc staggering ol wage and price decisions. In contrast to thc simple story we told earlier, where all wages and prices increased simultaneously in anticipation ot an increase in money, actual wage and price decisions arc staggered over time. So, there isn't one sudden, synchronised adjustment ot all wages and prices to an increase in money. Rather thc adjustment is likely to be slow, with wages and prices adjusting to the new level of money through a process ol leapfrogging over time. Fischer and Taylor thus showed that the second issue raised bv the rational expectations critique could be resolved, that a slow return of output to its natural level can be consistent with rational expectations in the labour market.
Thc theory of policy
Third, thinking about policy in terms of game theory led to an explosion of research on the nature ol the games being played, not only between policy-makers and the economy but also between policy¬makers- between political parties, or between the central bank and the government, or between governments ot different countries. One ol the main achievements of this research has been the development of a way ol thinking more rigorously about such tuzzy notions as credibility', reputation' John B.Taylor and 'commitment . At the same time, there has been a distinct shilt in focus from 'what governments should do to what governments actually do', and so an increasing awareness ot the political constraints that economists should take into account when advising policy-makers.
To summarise: By the end ol the 1980s the challenges raised by the rational expectations critique had led to a complete overhaul ol macroeconomics. Thc basic structure had been extended to take into account the implications ot rational expectations, or more generally ot forward-looking behaviour by people and firms. Indeed, what wc have presented in this book is what we see as the synthesis that has emerged and that now constitutes the core ol macroeconomics.
Belore we summarise what we sec* as thc core of macroeconomics—something we will do in thc last section, let us turn briefly to current research. Much of it is still too speculative to have made il inio the core, but no doubt some of it will do so soon.
28.4 RECENT DEVELOPMENTS
Since the late 1980s three groups have dominated thc research headlines: the new classicals the new Keynesians and the new growth theorists. (Note ihe generous use of thc word new. Unlike producers of laundry detergents economists stop short of using new and improved . But the subliminal message is the same.)
New classical economics and real business cycle theory
The rational expectations critique was more than just a critique ol Keynesian economics. It also offered its own interpretation ol fluctuations. Instead of relying on imperfections in labour markets, on the slow adjustment ot wages and prices and so on. to explain fluctuations, Lucas argued, macroeconomists should see how tar ihey could go in explaining fluctuations as the effects ol shocks in competitive markets with fully flexible priccs and wages.
Stanley Fischer
This is thc research agenda lhat has been pursued by the new classicals. Thc intellectual leader is Fdward Prcscott, and the models he and his lollowers have developed are known as real business cycle
< RBC) models. These models assume that output is always at its natural level That means lhat a.l fluctuations in output are movements of the natural level of output, as opposed to movements of output away from its natural level.
Where do these movements come from? The answer proposed by Prescott is technological progress. As new discoveries are made, productivity increases, leading to an increase in output. The increase in productivity leads to an increase in the wage, which makes it more attractive to work, leading workers to work more. Productivity increases therefore lead to increases in both output and employment, just as wc observe in the real world.
The RBC approach has been criticised on many fronts. As we discussed in Chapter 12. technological progress is the result ot very many innovations, each taking a long time to dilluse throughout the economy. It is hard to see how this process could generate anything like the large short-run fluctuations in output lhat we observe in practice. It is also hard to think ol recessions as times ol technological regress, times in which productivity and output both go down. Finally, as we have seen, there is very strong evidence lhat changes in money, which have no effect on output in RBC models, in fact have strong effects on output in the real world.
At this point, most economists don't believe that the RBC approach provides a convincing explanation of major fluctuations in output. But the approach has proved useful. It has reinforced the important point that not all fluctuations in output are deviations ol output Irom its natural level. At a more technical level, the RBC approach has provided several new techniques lor solving complex models, which are widely used in research today. It is likely to evolve rather than disappear. Some RBC models have started introducing nominal rigidities along the lines ol Fischer and Taylor. These models imply that output fluctuations come not only Irom productivity shocks but also Irom changes in nominal money.
New Keynesian economics
The term new Keynesians denotes a loosely connected group ol researchers who share a common belief that the synthesis that has emerged in response to thc rational expectations critique is basically correct. But they also share thc belief that much remains to be learned about the nature ot imperfections in diflerent markets and about the implications ol those imperfections lor macroeconomics.
One line of research has focused on the determination ol wages in the labour market. We discussed in Chaptcr 6 the notion ol efficiency wages—the idea lhat wages, il perceived by workers as being loo low. may lead to shirking by workers on the job, to problems ol morale within lhe firm to difficulties in recruiting or keeping good workers, and so on. One influential researcher in this area has been George Akerlot from the University of California at Berkeley, who has explored the role of norms the rules that develop in any organisation—in this case, thc firm—to assess what is lair or unfair. This research has led him and others to explore issues previously lelt to research in sociology and psychology, and to examine their macroeconomic implications.
Another line of new Keynesian research has explored the role ot imperfections in credit markets. Except lor a discussion ol the role ol banks in the Great Depression and ihe current Japanese recession, we have typically assumed in this book lhat the effects ol monetary policy worked through interest rates, and that firms and people could borrow as much as they wanted at the market interest rate. In practice, most people and many lirms can borrow only from banks. And banks oltcn turn down potential borrowers, despite thc willingness ol these borrowers to pay the interest rale charged by the bank. Why this happens, and how it affects our view of how monetary policy works, has been the subject ol much research, in particular by Ben Bernanke ol Princeton, the current governor ol the Federal Reserve Board.
Yet another direction ol research is nominal rigidities. As we saw earlier in the chapter. Fischer and Taylor have shown that, with staggering of wage or price decisions, output can deviate from its natural level lor a long time. This conclusion raises a number of questions. If staggering of decisions is responsible, at least in part, lor fluctuations, why don't wage sellers and price setters synchronise their decisions? Why aren't prices and wages adjusted more often? Why aren't all prices and all wages
fcPILOGUE: HE SIORY OF MACROECONOMICS chaptc-' 28
changed, say. on the lirst day ol each week? In tackling these issues. Akerlof and N. Gregory Mankiw (from Harvard University) have derived a surprising and important result, often referred to as thc menu cost explanation ol output fluctuations.
Wage setters or price setters are largely indifferent about when and how often they change their own wages or prices. (For a retailer, changing the prices on the shelf every day or every week doesn't make much dilference to profits.) Even small costs ol changing prices such as those involved in printing a new menu, for example—may lead to inlrequent and staggered price adjustment. This staggering leads to slow adjustment of the price level, and to large aggregate output fluctuations in response to movements in aggregate demand In short, decisions that dont matter much at the individual level how often to change priccs or wages' lead to large aggregate ellects slow adjustment ol the price level, and large eflects ol shilts in aggregate demand on output ).
New growth theory
After being one ol the most active topics of research in thc 1960s, growth theory' went into an intellectual slump. Since thc late 1980s, however, growth theory has made a strong comeback. The set of new contributions goes under the name ot new growth theory.
Two economists, Robert Lucas the same l.ucas who spearheaded the rational expectations critiquei and Paul Romer, then from the University of Calilornia at Berkeley, now at Stanford, have played an important role in delining the issues. When growth theory laded in the late 1960s, two issues were left largely unresolved. One issue was thc determinants ol technological progress. The other was the role ol increasing returns to scale—whether, say, doubling capital and labour may actually lead to more than a doubling ol output. These are the two main issues on which new growth theory has concentrated.
The discussions ot technological progress in Chapter 12 and ol thc interaction between technological progress and unemployment in Chapter I T reflect some ot the advances that economists have made on this front. One example is the work of Philippe Aghion 1 Irom Harvard University , and Peter Howitt from Brown University) who have developed a theme lirst explored by Joseph Schumpeter in the 1930s, thc notion lhat growth is a process ol creative destruction, in which new products arc constantly introduced making old ones obsolete. Another example is the work at Alwyn Young (from the University ot Chicago on growth in last-growing Asian countries, which wc discussed in Chapter 12.
Research has also tried to identify the precise role ol specific institutions in determining growth Andrei Shleifer (from Harvard University has explored lhe role ot different legal systems in affecting the organisation ot the economy, from linanciai markets to labour markets, and, through these channels, the effects ot legal systems on growth. Daron Acemoglu (from MIT) has explored how to go from correlations between institutions and growth —democratic countries are on average richer—lo causality from institutions to growth—does the correlation tell us that democracy leads to higher output per person, or does it tell us lhat higher output per person leads lo democracy, or lhat some other lactor leads to both more democracy and higher output per person? Examining the history of former colonies, he argues that their growth performance has been very much shaped by thc type ot institutions put in place by their colonisers, thus showing a strong causal role of institutions on economic performance.
Towards an integration
In the 1980s and 1990s, discussions between these three groups, and in particular between new classicals and new Kevncsians, were often heated. New Keyncsians would accuse new classicals ol relying on an implausible explanation ol fluctuations and ignoring obvious imperfections,- new classicals would in turn point to the ad hoc nature ot some of the new Keynesian models. From the outside—and indeed sometimes Irom the inside—macroeconomics looked like a battlefield rather than a research field.
I hings have very much changed and a synthesis is emerging. Methodologically, il builds on the RBC approach and its careful description ol the optimisation problems ol people and lirms. Conceptu¬ally, it recognises the potential importance, emphasised by the RBC approach and the new growth theory, ol changes in the pace ol technological progress. But it also allows lor many ol the imperfections
emphasised hy thc new Keynesians. from the role ol bargaining in the determination ot wages, to the role of imperfect information in credit and financial markets, to the role ol nominal rigidities in creating a role lor aggregate demand to alfect output. There is no convergence on a single model or on a single list ol important imperfections, but there is broad agreement on the framework and on thc way to proceed.
A particularly good example ol this convergence is thc work of Michael Woodford from Columbia) and of .lordi C.ali Irom Ponipcu labra in Catalonia). Woodlord. Gali and a number of co-authors have developed a model, known as the new-Keynesian model, lhal embodies utility and profit maximisation, rational expectations and nominal rigidities. You can think of it as a high-tech version of thc model lhal was presented in Chaptcr 17. This model has proven extremely uselul and influential in thc redesign ol monetary policy—from the locus on inflation targeting to the reliance on interest rate rules—which we have discussed throughout this book. It has also led to the development ol a class of larger models that build 011 its simple structure but allow for a longer menu ol imperfections and thus must be solved numerically. These models, which arc now used in most central banks, arc known as dynamic stochastic general equilibrium (DSCE) models. How to specify, to estimate and to simulate these models is one ol the major topics of research in macroeconomics today. Estimating the parameters and forecasting these modern macroeconomic models has meant lhat researchers have to have excellent skills in both macroeconomics and econometrics. One ol the world's leading practitioners is Adrian I'agan from the University of New South Wales.
28.5 COMMON BELIEFS
SUMMARY
• The history of modern macroeconomics starts in 1936. with the publication ol Keynes's General Theory of Employment. Interest ami Money. Keynes's contribution was formalised in the IS-I.M model by John Hicks and Alvin I lansen in the 1930s and early 1940s.
• The period from the early 1940s to the early 1970s can be called the golden age of macroeconomics. Among the major developments were the development of the theories ol consumption, investment, money demand and portfolio choice,- the development ol growth theory- and the development ol large macroeconometric models.
• The main debate during the 1960s was between Keynesians and monetarists. Keynesians believed that developments in macroeconomic theory allowed lor better control ot the economy. Monetarists, led by Milton Friedman, were more sceptical of the ability of governments to help stabilise the economy.
• In the 1970s macroeconomics experienced a crisis, for two reasons. One was thc appearance ol stagflation, which came as a surprise to most economists. The other was a theoretical attack led by Robert I.ucas. Lucas and his followers showed that when rational expectations were introduced (I i Keynesian models couldn't be used to determine policy. 2 Keynesian models couldn't explain long-lasting deviations of output from its natural level, and 3 the theory ol policy needed to be redesigned, using the tools of game theory.
• Much of the 1970s and 1980s was spent integrating rational expectations into macroeconomics. As reflected in this book, macroeconomists are now much more aware of the role ol expectations in determining the effects ol shocks and policy, and of the complexity ol policy, than they were two decades ago.
• Recent research in macroeconomic theory is proceeding along three lines. New classical economists are exploring the extent lo which fluctuations can be explained as movements in lhe natural level of output, as opposed to movements away from the natural level ol output. New Keynesian economists are exploring more formally the role ol market imperfections in fluctuations. New growth theorists arc exploring ihe role of RucD and ol increasing returns to scale in growth. These lines are increasingly overlapping, and a new synthesis appears to be emerging.
FP1LOGUF: THE STORY OF MACROECONOMICS
chapte- 28
• Despite thc differences there exists a set ol propositions on which most macroeconomists agree. Two of these propositions are: ( I > in the short run, shilis in aggregate demand affect output and
21 in the medium run output returns to its natural level.
KEYTERMS
business cycle theory, 635
effective demand, 6.35
liquidity preference, 636
neoclassical synthesis, 6.36
Keynesians, 63"
monetarists, 637
Lucas critique, 639
random walk ol consumption, 640
staggering (ol wage and price decisions 64 I
• new classicals, 641
• real business cycle (RBC models, 64 I
• new Keynesians, 642
• nominal rigidities, 642
• menu costs, 64.3
• new growth theory, 643
• new-Keynesian model, 644
• dynamic stochastic general equilibrium (DSGD models. 644
FURTHER READINGS
• Two classics arc I. M. Keynes, The General Theory of Employment, Money, ami Interest (London: Macmillan Press, 1936), and Milton Friedman and Anna Schwartz, A Monetary History of the United States, 1867-1961) (Princeton, N1: Princeton University Press, 1963). Warning: The lirst makes for hard reading, and thc second is a heavy volume.
• For an account ol macroeconomics in textbooks since the 1940s, read Paul Samuclson's. Credo ol a lucky textbook author journal of Economic Perspectives, Spring 1997, pp. 153—60.
• In thc introduction to Studies in Business Cycle I'heory (Cambridge, MA: MIT Press. 1981), Robert Lucas develops his approach to macroeconomics and gives a guide to his contributions.
• The paper lhal launched real business cycle theory is F.dward Prcscott Theory ahead ol business cycle measurement', Federal Reserve Bank of Minneapolis Review, l all 1986, pp. 9-22. It is not easy reading.
• For more on New Keynesian economics, read David Romer. I he New Keynesian synthesis, lournal of Economic Perspectives, Winter 1993 pp. 5-22.
• For more on new growth theory, read Paul Romer, The origins of endogenous growth', lournal of Economic Perspectives, Winter 1991, pp. 3-22. A more complete treatment is given in Charles lones. An Introduction to Economic Growth, 2nd edn (New York W. W. Norton. 20021.
• For a detailed look al the history ol macroeconomic ideas, and in-depth interviews with most of the major researchers, read Brian Snowdon and Howard Vane, Modern Macroeconomics: Its Origins, Development and Current State (Cheltenham, UK: Edward Flgar, 2005).
• For two points ot view on thc state ot macroeconomics, read V. V. Chari and Patrick Kehoe, 'Macroeconomics in practice: How theory is shaping policy', and N. Greg Mankiw, The macro- economist as scientist and engineer , lournal of Economic Perspectives, Fall 2006.
• Most economics journals arc heavy on mathematics and are hard lo read. Bui a few make an effort lo be reader-1riendly. The lournal of Economic Perspectives in particular has non-technical articles on currcnt economic research and issues. The Brookings Papers on Economic Activity, published twice a year, analyse current macroeconomic problems, as does Economic Policy, published in Europe, which focuses more on European issues.
• Most regional LIS Federal Reserve Banks publish reviews with easy-to-read articles,- these reviews arc available tree of charge. Among them arc the Economic Review published by thc Cleveland Fed, the Economic Review published by the Kansas City Fed, the New England Economic Review published by the Boston Fed and ihe Review published by ihe Minneapolis l ed.
• In Australia, the Reserve Bank of Australia publishes readable articles in its monthly Bulletin. Its annual conference scries available at
• More advanced treatments ol currcnt macroeconomic theory—roughly at ihe level ot a lirst graduate course in macroeconomics are given by David Romer, Advanced Macroeconomics. 2nd edn (New York: McGraw-Hill, 2001) Olivier Blanchard and Stanley Fischer, Lectures on Macroeconomics Cambridge, MA: MIT Press, 1989), Maurice Obstfeld and Ken Rogotl, Foundations of International Macroeconomics (Cambridge, MA: MIT Press 19961, Michael Wickens, Macroeconomic Theory: A Dynamic General Equilibrium Approach (Princeton, N : Princeton University Press, 20081 and lordi C.ali, Monetary Policy. Inflation and the Business Cycle (Princeton, N1: Princeton Llniversity Press. 2008).
Appendices
APPENDIX 1 An Introduction to National Income and Product Accounts
This appendix introduces the basic structure and the terms used in thc national income and product accounts. The basic measure ol aggregate activity is gross domestic product or CDP. The national income and product accounts (NIPA or simply, national accounts) are organised around two disaggregations ol CDP. The lirst looks at income-. Who receives what: The other looks at product: What is produced, and who buys it?
The income side
Table Al l looks at the income side ol CDP— who receives what. The top part ol the table (lines I—71 goes Irom CDP to national income, the sum of the incomes received by the different factors of production. • The starting point, in line I is gross
domestic product or CDP It is defined as lhe market value of the goods and services produced hy labour and property located in Australia, in 2008, CDP was $i . 13 trillion.
Table A1.1 Australian GDP:The income side, year to June 2008 (A$ billion)
From gross domestic product to national income
1 Gross domestic product 1 130
2 Plus: net receipts of factor incomes from the rest of the world
3 Equals: Gross national income 1080 -51
4 Minus: consumption of fixed capital
5 Equals: Net national product 907
The decomposition of national income
6 Compensation of employees (wages and salaries) 538
7 Gross operating surplus (profits) 376
8 Gross mixed income (self-employed income, rents, interest, etc) 95
9 Indirect taxes less output and import subsidies 122
10 Net receipts of factor incomes from the rest of the world -50
1 1 Less consumption of fixed capital -173
907
SOURCE: ABS. cat. no. 5206
The next two lines take us Irom CDP to GNI the gross national income line 31. CNI is an alternative measure of aggregate output. It is defined as the market value of the goods and services produced by labour
and property supplied by Australian residents.
Until recently, most countries used GNI rather than CDP as the main measure ol aggregate activity. CDP has become more prominent because it represents the measure ol output used in macroeconomic theory. The difference between the two comes from the distinction between located in Australia' i used to define CDP) and supplied by Australian residents used to deline CNb. For example, prolit from an Australian-owned plant in Japan isn't included in Australian GDP, but it is included in Australian GNI.
Thus, to go Irom GDP to GNI we must lirst add receipts ol lactor income from the rest ol the world, which is income Irom Australian capital or Australian residents abroad, and then subtract payments of factor income to the rest of the world, which is income received by loreign capital and foreign residents in Australia. This is net primary incomes from non-residents. In 2008, payments to the rest ol the world exceeded receipts from the rest ol the world by $51 billion (line 2' so GNI was smaller than GDP by $51 billion.
• The next step lakes us from GNI to NNI the net national income i line 5). The difference between C.NI and NNI is the depreciation ol capital which is called consumption of fixed
capital in the national accounts (line -4). NN'I is defined as the income that originates in the production of goods and services supplied hy residents of Australia.
The bottom part of the table 1 lines 6-11
disaggregates national income into dillerent
types of income.
• Compensation of employees line 6), or labour income, is by tar the largest component, accounting for 59 per ccnt of national income. It is the sum of wages and salaries plus any supplements which range from employer contributions lor superannuation to exotic items such as employer contributions to marriage Ices to justices of thc peace.
• Gross operating surplus, or GOS iline 7). This includes all sources ol corporate profits, which are revenues minus costs including interest payments). II we subtract depreciation ol the capital stock, or thc part ol the consumption of fixed capital i in line I 3 i attributable to lirms, we would get net operating surplus.
• Gross mixed income (line 8 includes the income received by persons who arc self- employed that is, in unincorporated enterprises It is defined as the income of sole proprietorships, partnerships and tax-exempt cooperatives.
This measure includes rental income. II the national accounts counted only actual rents, rental income would depend on the proportion of apartments and houses that were rented versus owner-occupied. For example, if everybody becamc the owner of the apartment or the house in which they lived rental income would go to zero, and thus measured GDP would drop. To avoid this problem, national accounts treat houses and apartments as il they were all rented out. Thus, rental income is constructed as actual rents plus imputed rents on those houses and apartments that are owner-occupied.
• Indirect taxes less subsidies (line 9). Some of thc national income goes directly to thc government in thc form of sales taxes (e.g. C.ST), These laxes arc called indirect taxes. The rest goes to employees in lirms. Firms also get subsidies Irom thc government and so these have to be added in.
• Since we arc accounting lor net national income, we have to add net primary incomes from non-residents (line 10).
• Since we subtracted the total consumption of fixed capital by firms and households Irom GDP in line 4, wc need not allocate it in our decomposition ol income. So we subtract in line II.
Before we move to the product side, Table A 1.2 (overleaf) shows how we can go Irom national income to household disposable income—ihe income available to consumers after they have received transfers and paid taxes. Not all net national income ( line I > is distributed to persons in households.
• Some income doesn't go to households because it goes to the government as indirect taxes. So wc subtract this in line 2. (I.inc 2 in Table A 1.2 is equal lo line I I in Table A 1.1.)
• Some of the corporate profits arc retained by firms. So, thc first step is to subtract all corporate profits net ot firms' consumption ot capital (line 3) and add back thai part of profits that is distributed to persons, personal dividend income 'line 4). Similarly, not all interest payments paid by firms go to persons. The net effect of these calculations is included as other receipts in line 4.
• Finally, people receive income not only trom production but also from social benefits and transfers (line 5). These accounted tor $126 billion in 2008, or 14 per cent of net national income.
• Thc net result ol these adjustments is household income, the income actually received by persons (line 6 . Household disposable income (line 8) is then equal to household income minus personal income tax, which was 15 per ccnt of net national income in 2008 (line 7). In 2008 household disposable income was equal lo $696 billion, or about 62 per ccnt ol GDP.
Households use their disposable income lor consumption ot goods and services (line 9), and also for consuming their lixed capital (that is, depreciation ot their houses). This last amount in line 10 is estimated by the ABS. The rest ot income goes to household savings (line I I) and is a mere $4 billion in 2008. suggesting a household saving rate of just 0.006! (We need to be cautious about this because the ABSs estimate
ol depreciation lor households ignores the lact that consumption expenditures include DIY spending on houses.)
The product side
Table Al.3 looks at the product side of the national accounts, at who buys what. Let us start with the three components ol domestic demand: consumption, investment and government spending.
• Consumption, called household
consumption expenditures line 2 is by lar the largest component ol demand, accounting tor 55 per cent ot CDP. It is defined as the sum of goods ami services purchased hp persons resident in Australia.
Table A 1.2 From Australian national income to personal disposable income, year to June 2008 (A$ billion)
1 Net national income 907
2 Minus: indirect taxes -122
3 Minus: net profits -138
4 Plus: dividends and other receipts* 62
5 Plus: social benefits and transfers 126
6 Equals: Household income 835
7 Minus: income tax -139
8 Equals: Household disposable income 696
Use of household disposable income
9 Personal consumption expenditures 10 Consumption of fixed capital by households 627 65
1 1 Net savings 4
Derived as a balancing item.
SOURCE: ABS. cat no. 5206.
In the same way that ihev include imputed rental income on the income side, national accounts include imputed housing services as part ol consumption. Owners ol a house are assumed to consume housing services, for a price equal to the imputed rental income ol that house. Consumption is disaggregated into three components.- pure lases ol durable goods equal to almost 10 perccnt of consumption), non-durable goods (34 per cent and services (56 per cent i. Durable goods arc commodities lhat can be stored and have an average lile ol at least three years, motor vehicle purchases are the largest item here. Non-durable goods are commodities thai can be stored but have a lile of less than three years. Services are commodities that cannot be stored, so must be consumed at thc place and time ot purchase.
• Private investment is called gross fixed capital formation ' line 3). Ii is the sum ol two very different components:
— Non-residential investment line 4 is thc purchase ot new capital goods by lirms. These may be either structures (line .51— mostly new plants—or machinery and equipment line 6 , such as machines, computers or office equipment, and other less tangible investments.
— Dwellings (line 7) is the residential investment purchase ol new houses or apartments by persons.
• Government purchases line 8) arc equal to the sum ol general government consumption—purchases ot goods by thc government plus compensation ol government employees (government employees are thought ol as selling their services to the government)—and public gross fixed capital formation—government investment in buildings, public enterprises, and so on.
Note that government purchases don't include transfers trom the government or interest payments on government debt. These don l correspond to purchases of cither goods or services, and so are not included here. This means that the number for government purchases you see in line 8 in Table A 1.3 is substantially smaller than thc number you typically hear tor government spending—which includes transfers and interest payments.
Table A1.3 GDP.The expenditure side year to June 2008 (A$ billion)
1 Gross domestic product JJJLO
2 Personal consumption expenditures 627
3 Gross fixed capital formation 265
4 Non-residential investment 177
5 Structures
6 Machinery and equipment, etc. 77 100
7 Residential 88
8 Government purchases 250
9 General government consumption 200
10 Public gross fixed capital formation 50
1 1 Net exports -18
12 Exports 235
13 Minus: imports -253
14 Change in business inventories 5
15 Statistical discrepancy 2
SOURCE: ABS. cat. no. 5206,ТлЫс 46.
• The sum of consumption, investment and government purchases gives the demand for goods by Australian firms. Australian persons and the Australian government. II Australia were a closed economy, this would be the same as the demand for Australian goods. But because the Australian cconomy is open, the two numbers arc different. To get to the demand for Australian goods, we must make two adjustments. First, we must add the foreign purchases of Australian goods, exports i line 12). Second, we must subtract Australian purchases of orcign goods, imports (line 13). In 2008. exports were less than imports by $18 billion. Thus net exports (or. equivalently, thc trade balance were equal to minus $18 billion (line 1 I i or about 1.6 per cent of GDP.
• Adding consumption, investment, government purchases and net exports gives the total purchases of Australian goods. Production may, however, be less than those purchases if firms satisfy thc difference by decreasing inventories. Or production may be greater than purchases, in which case firms accumulate inventories. Thc second last line of Table A 1.3 gives thc change in business inventories line 14 also sometimes callcd (rather misleadingly) inventory investment. It is defined as the change in the physical volume of inventories held by business. Thc change in business inventories can be positive or negative. In 2008 it was positive: Australian production was greater than total purchases of Australian goods by $5 billion.
• Finally line 15 shows a S2 billion statistical discrepancy, which, though small, deserves a short discussion. National output is actually constructed in two independent ways. One is from the product side and calculating how much value-added took placc during thc year. The other is trom the expenditure side, calculating who spent what. The two measures typically ditler. and the difference is callcd the statistical discrepancy. In 2008, GDP calculated from the product side exceeded that calculated from the expenditure side by $2 billion. The statistical discrepancy is a reminder of the statistical problems involved in constructing the national income accounts.
Warning
National accounts give an internally consistent description ot aggregate activity. But underlying these accounts are many choices about what to include and what not to include, where to put some types ol income or spending, and so on. Here arc three examples:
• Work within the home isn't counted in CDP II, lor example, two women decide to babysit each other's child rather than lake care of their own child and pay each other for thc babysitting services, measured CDP will go up, while true CDP clearly doesn't change. The solution would be to count work within ihe home in СЮР, the same way that we impute rents lor owner-occupied housing. But, so lar, ihis hasn't been done.
• Thc purchase ol a house is treated as an investment, and housing services are then treated as pari ol consumption. Contrast this with thc treatment of motor vehicles. Despite the lact that they provide services for a long time—although not as long a time as houses do—purchases ol motor vehicles aren't treated as investment. They arc treated as consumption and appear in the national accounts only in the year in which they are bought.
• I irms' purchases of machines are treated as investment. The purchase of education is treated as consumption of education services. But education is clearly in part an investment: people acquire il in part to increase their future income.
The list could go on. However, the purpose of these examples isn t to make you conclude that national accounts are wrong. Most of the accounting decisions we iust saw were made lor good reasons, often because ot data availability or tor simplicity of treatment. Rather, the point is that to use national accounts best, you should understand their logic, but also understand the choices that have been made and thus their limitations.
KEY TERMS
• national income and product accounts (NIPAi, national accounts, 648
• gross domestic product (GDP). 648
• gross national income GNI i, 648
• net primary income Irom non-residents, 648
• net national income (NNI), 648
• consumption of fixed capital. 648
• compensation ol employees, 649
• gross operating surplus • COS i, 649
• net operating surplus, 649
• gross mixed income, 649
• indirect taxes. 649
• household disposable income, 649
household consumption expenditures, 650 durable goods, non-durable goods, services, 650
gross lixed capital formation. 650
non-residential investment, structures machinery and equipment, 650
dwellings, residential investment 650
government purchases, 650
general government consumption, 650
public gross fixed capital formation, 650
exports, imports, 651
net exports, trade balance, 651
changes in business inventories, 651
FURTHER READINGS
APPENDIX 2 A Maths Refresher
This appendix presents the mathematical tools and the mathematical results that arc used in this book.
Geometric series
Definition. A geometric scries is a sum ol numbers of the form
1 + x + .v2 + ... + x"
where x is a number lhat may be greater or smaller than one, and .v'' denotes x to the power M—that is. x times itself n times.
Examples of such series arc:
• Thc sum of spending in each round ol ihe multiplier Chapter 3). If с is ihe marginal propensity to consume, then the sum of increases in spending alter >? rounds is given by
I + с + с2 + ... + с"-'
I
I
• The present discounted value of a sequence of payments of one dollar each year for n years 'Chapter 14), when thc interest rate is equal to /':
I
l+i (I + 02 "' (I + /)"-'
Wc usually have two questions we want to answer when encountering such a series: What is the sum? Does the sum explode as wc let n increase, or does it reach a rinitc limit, and, il so, what is lhal limit?
The following propositions tell you what you need to know to answer these questions.
„II I
Proposition I tells you how to calculate the
Proposition I
+ X
I + X + x2 +■ ...
(A2.1)
I -X
Here is the proot: Multiply the sum by (I x), and use ihe fact that x"xh x"'!' that is, one has to add exponents when multiplying):
(I + X + X2 + ... + X")( 1 - X) = 1 + X + X2 +
... + x" — X
-X2- ... -X"
- x"-1 = 1 -Xя-
All the terms on thc right except lor the first and the last cancel Dividing both sides by (I -x) gives equation (A2.I).
This formula can he used lor any x and any п. If, for example, x is 0.9 and n is 10, the sum is equal to 6.86. If x is 1.2 and n is 10, thc sum is 32.15.
Proposition 2 tells you what happens as n gets large.
Proposition 2
If x is less than one. the sum goes to l/( I - x) as il gets large. Il x is equal to or greater than one, the sum explodes as n gets large.
Here is the proof: II x is less than one. then x" goes to zero as n gels large. Thus, Irom equation (A2.I the sum goes to I/(I — x). If x is greater than one then x" becomes larger and larger as n increases, I - x" becomes a larger and larger negative number, and the ratio ( I - x")/ (I - x) becomes a larger and larger positive number. Thus thc sum explodes as n gets large.
Application from Chapter I 4
I
I
Consider the present value ol a payment of $1 forever, starting next year, when the interest rate is /. Thc present value is given by
1
(A2.2)
(1+0 (I + 0 factoring out l/( 1 + i), rewrite ihis present
I
1 +
(1+0
(1 + i)
The term in brackets is a geometric series, with x 1/(1 + i). As thc interest rate i is positive, x is less than one. Applying proposition 2 when n gets large, thc term in brackets equals
I
I (l+i) (1+0
(I + i- I)
I
(I + 0
I
Replacing the term in brackets in the previous equation by (1 + i H gives
(i + о
(i + 0
Thc present value of a sequence ol payments of one dollar a year forever, starting next year, is equal lo $1 divided by the interest rate. Il i is
equal to 5 per cent per year, the present value equals $1/0.05 - $20.
Useful approximations
Throughout this hook we use several approximations that make calculations easier. These approximations are most reliable when the variables .v, у and ; below are small—say, between 0 per cent and 10 per cent. Thc numerical examples in propositions 3-8 below are based on the values .r - 0.05 and у = 0.03.
Proposition 3
(I + .r)( 1 + у) - (I + .r - у) (A2.3)
Here is the proof. Expanding (1 + .v)(l + y) gives (1 + .v)( I + y) ■= I + x + у + xy. II x and у are smal , then the product xy is very small and can he ignored as an approximation (for example, il .v - 0.05 and у - 0.03, then xy = 0.00151. So, I + ; 1 + y) is approximately equal to (1 + .r + y).
For thc values x and у above, for example, thc approximation gives 1.08 compared with an exact va'tie of 1.0815.
Application from Chapter 14
From the definition ol thc real interest rate the
nominal interest rate is given by
(I + if) - (1 + r,)(l + тт*;)
Using proposition 6 gives
(I +/,)-(! + r, + iri)
Simplifying:
i, ~ r, + if.
This gives us the approximation we use at many points in this book: the nominal interest rate is approximately equal to the real interest rate plus expected inllation.
Proposition 4
(I + x)2 ~ I + 2.T (A2.4)
Thc proof follows directly from proposition 3. with у - x. For the value of x = 0.05. thc approximation gives 1 .10, compared with an exact value of 1.1025.
Application from Chapter I 5 From arbitrage, thc relation between the two- year interest rate and the current and the expected one-year interest rates is given by
(1 + t3()3 = (1 + /„ )(1 + ifM)
Using proposition 4 lor the left side of the equation gives
(I + i»)2- I + 2ь,
Using proposition 3 tor thc right side of thc equation gives
(I + I,, )(1 + j'f,+1) - I + i„ + »f,+ l
Replacing in the original arbitrage relation gives
I + 2iv » 1 + !„ + if,., Or, reorganising:
'■'if + 'H-|) ——
The two-year interest rate is approximately equal to the average ol the current and the expected one-year interest rates.
Proposition 5
(I + x)"~ 1 + nx (A2.5)
Thc proof follows by repeated application of propositions 3 and 4. For example, (I + .r)3 = 11 + .r)-( I + .r) « (1 + 2.r)( I + л") by proposition 4, — (1 + 2.r + .y) = I + 3.v by proposition 3.
The approximation becomes worse as n increases, however. For example, for .r = 0.05 and II = 5, the approximation gives 1.25, compared with an exact value ol I 2763. For n = 10, the approximation gives 1.50, compared with an exact value of 1.63.
Proposition 6
(I + r)
(I + x-y) (A2.6)
(I + y)
Here is the proof: Consider the product of (I + x - у К I + у). Expanding this product gives (1 + * - y)( 1 + у) = 1 + x + xy — y7. If both x and у are small, then xy and y2 are very small, so (I + x - y)( I + у) «= (1 + .vj. Dividing both sides of this approximation by < 1 + y) gives thc proposition above.
For the values of .r 0.05 and у = 0.03, the approximation gives 1.02, while the correct value- is 1.019.
Application from Chaptcr I 8
Arbitrage between domestic bonds and foreign
bonds leads to the following relation:
U +Q
(I * 4) =—'
• i ~ E, E,
Using thc expressions for the left and right sides gives
Az
к
Or, equivalently,
1 +
(I = (1 +&)(> + gy)
From proposition 3, (I + g.) — ( I + gx + gv),
or. equivalcntly,
Using proposition 6 on thc right-hand side ol thc equation gives
+1, -
£L i - Cf
и +;,)-
Subtracting I irom both sides gives Fc - F
I — c,
E,
The domestic interest rate is approximately equal to the foreign interest rate minus thc expected rate of appreciation of the domestic currency.
These approximations are also very convenient when dealing with growth rates. Deline the rate ol growth of .t by gx&Ax/x, and similarly for z,g. and y,gy. Thc numerical examples below are based on the values gx = 0.05 and gy 0.03.
Proposition 7 If r = xy, then
& - Sx + Sy (A2.7)
Here is the proof: Let Az be the increase in z when x increases by Ax and у increases by Ду. Then, by definition.
z + Az = (x + Д.г )(y + Ду)
Divide both sides by z. Thc left side becomes z + Д: / Az *
Hz " gx - gy
For gx - 0.05 and gy = 0.03, thc approximation gives = 8 per cent, while thc correct value is 8.15 per cent.
Application from Chapter I 3
Lei thc production function be ol ihe form Y = NA. where Y is production, N is employment, and A is productivity. Denoting the growth rates of Y, N and A by gy, and gA respectively, proposition 7 implies
gr ~ gN + gA
(A2.8)
2 + Az =
The rale of output growth is approximately equal to thc rate ol employment growth plus the rate of productivity growth.
Proposition 8 If r - r/y, then
& - gx ~ gv
Here is thc proof: Let Д: be thc increase in z, when x increases by Дг and у increases by Ду. Then by definition,
■Г + Дг У + Ay
The right side becomes
(x + Ax)(y + Ду) (дг + Ax) (у + Ду)
Divide both sides by л. Thc left side becomes
(z + Az) I Az
Дг
X
Ay
У
where the lirst equality follows Irom thc fact lhat л xy, the second equality from simplifying each of thc two tractions.
The right side becomes
(.r + Дг) I (.v + Ax) у (у + Ду) z (у + Ду) .г
(х + Ах)/х 1 + (Ах/х)
■у + Ду)/у 1 + (Ду/у)
where the tirst equality comes from the tact that z - x/y, thc second equality comes trom rearranging terms, and the third equality comes trom simplifying.
Using the expressions for the lelt and right sides gives
I + (Дл'/.г)
I + Az/z
I + (Ay/у)
Or, substituting:
From proposition fi, I + = 1 + £,-£„), or, equivalently,
8z - Sx ~ Sy
for gx = 0.05 and gy = 0.03, the approximation gives y, = 2 per cent, while the correct value is 1.9 per cent.
Application from Chapter 9
I et aggregate demand be given by
II - >1 .
where Vis output i is the nominal interest rate, and V, represents all those factors that are associated with output, income and aggregate demand growing at thc normal rate, It follows Irom propositions 7 and 8 that gy " gy ~ gi
where is the rate of growth ol aggregate- demand and 4*, is thc rate ot change of the interest rate. The rate of demand growth is approximately equal to the normal rate ot growth ot output minus the rate of change ot the interest rate.
Functions
We use Functions inlormally in this book, as a way of denoting how a variable depends 011 one or more other variables.
In some cases we look at how a variable V moves with a variable X. Wc write this relation as
V = /(X) (+)
A plus sign below X indicates a positive- relation: an increase in X leads to an increase
in Y. A minus sign below X indicates a negative- relation: an increase in X leads to a decrease in Y.
In some cases we allow thc variable Y to depend on more than one variable. For example we allow Y to depend on X and Z:
Y = f(X,Z) (+,-)
The signs indicate that an increase in X leads to an increase in Y. and that an increase in Z leads to a decrease in Y.
An example ol such a function is the investment function (5.1) in Chapter 5:
I = НУ, i) (+,-)
This equation says that investment, 1 increases with production. Y, and decreases with the interest rate, 1.
In some cases it is reasonable to assume that thc relation between two or more variables is linear. A given increase in X always leads to the same increase in Y. In that case, the function is given by
У = a + bX
This relation can be represented by a line giving Y tor any value of X.
The parameter 11 gives the value ol Y when X is equal to zero. It is called the intercept because il gives the value ol Y when the line representing lhe relation 'intercepts' - crosses) the vertical axis.
The parameter b tells us by how much Y increases when X increases by one. It is called the slope because it is equal lo the slope ol the line representing the relation.
A simple linear relation is the relation Y - X, which is represented by thc 45-degree line and has a slope of one. Another example of a linear relation is the consumption function ( 3.2) in Chapter 3:
С - c(l + c,Yn where С is consumption and Yp is disposable income. The parameter c0 tells us what consumption would be if disposable income were equal to zero. The parameter r, tells us by how much consumption increases when income increases by one unit; r, is called the marginal propensity to consume.
Logarithmic scales
A variable thai grows at a constant growth rate increases by larger and larger increments over time. Take a variable, X, that grows over time at a constant growth rate. say. at .3 per cent per year.
• Start in year 0 and assume that X - 2. So. a 3 per cent increase in X represents an increase ot 0.06 (0.03 X 2).
• Go to year 20. X is now equal to 2( 1.0.3)20 = 3.61. A 3 per cent increase now represents an increase of 0.1 I (0.03 x 3.61).
• Go to year 100. X is equal to 2( 1.03)100 = 38.4. A 3 per cent increase represents an increase ol 1.15 (0.03 x 38.4), so an increase about 20 times larger than in year 0.
II we plot X against time using a standard (linear! vertical scalc, the plot looks like Figure A2.1, panel (a). The increases in X are larger and larger over time (0.06 in year 0, 0.11 in year 20, 1.15 in year 100). The curve representing X against time becomes steeper and steeper.
Another way ot representing the evolution of X is to use a logarithmic scale to measure X on thc vertical axis. Thc properly ol a logarithmic scale is that the same proportional increase in this variable is represented by the same vertical distance on thc scale. So, the behaviour ol a variable such as X, which increases by thc same proporiional increase (3 per cent1 each year, is
now represented by a line. Figure A2.1, panel (b) represents thc behaviour of X, this time using a logarithmic scale on the vertical axis. The lact that the relation is represented by a line indicates that X is growing at a constant growth rate over time. The higher the rate of growth, the steeper the line.
In contrast to X. economic variables such as GDP don't grow at a constant growth rate every year. Their growth rate may be higher in some dccades, lower in others. A recession may lead lo a few years of negative growth. Yet, when looking at their evolution over time, it is often more intormative to use a logarithmic scale rather than a linear scale. Let's see why.
Figure A2.2, panel (a; plots real Australian GDP Irom 1000 to 2002 using a standard (linear) scale. Because real Australian GDP is about 24 times bigger in 2002 than in 1900, thc same proporiional increase in GDP is 24 times bigger in 2002 than in 1900. So, the curve representing the evolution ot GDP over time becomes steeper and steeper over time. It is very difficult to see trom ihe figure whether the Australian economy is growing taster or slower than it was fifty years or a hundred years ago.
Figure A2.2, panel (b) plots Australian GDP from 1900 to 2002, now using a logarithmic scalc. If the growth rate ol GDP was the same every year—so thc proportional increase in GDP
Figure A2.1 The evolution of X
(a) using a linear scale
X 30
0 20 40 60 80 100 (b) Time
0
0 20 40 60 80 100 (a) Time
(b) using a logarithmic scale
90 _ Linear scale
80 70 60 50 40 30 20 10 0
Figure A2.2
The evolution of Australian GDP from 1900 to 2002
(a) using a linear scale
(b) using a logarithmic scale
Logarithmic scale
1900 1910 1920 1930 I9« 1950 I960 1970 1980 1990 2000
was the same every year—the evolution of GDP would be represented by a line—the same way as the evolution of X was represented by a line in Figure A2.1. panel lb). Because the growth rate ol GDP isn t constant from year to year—so the proportional increase in GDP isn't the same every year—the evolution of GDP is no longer represented by a line. But it doesn't explode over time thc way it did in Figure A2.2, panel (at. And it is very informative. • In Figtire A2.2, panel (b), we have drawn a line to fit the curve Irom 1000 to 1929. and another line to fit thc curvc from 1950 to 1974. These two lines have roughly the same slope. What this tells us is that the average growth rate was roughly thc same during those two periods.
• Thc decline in output from 1929 to 1933 is very visible in Figure A2.2, panel lb). So is the strong recovery ol output lhat follows (with a relapse in World War II). By thc 1950s, output appears ю be back to its old trend line I his suggests lhat thc Great Depression wasn't associated with a permanently lower level ol output.
• A separate line is also drawn lor thc period 1975 to 2002. Comparing thai with the slope of the line from 1950 to 1974, you can see that thc later slope is a little smaller.
Note, in these three cases, how you couldn't have derived these conclusions by looking at Figure A2.2, panel (a), but you can derive them by looking at Figure A2.2, panel (h). T his shows the usefulness of using a logarithmic scale.
KEY TERMS
• linear relation, 656
• intercept, 656
• slope, 656
APPENDIX 3 An Introduction to Econometrics
How do we know thai consumption depends on disposable income? How do we know the value ol the propensity to consume?
To answer these questions, and, more generally, to estimate behavioural relations and find out the values of the relevant parameters, economists use econometrics—thc set ol statistical techniques designed for use in economics. Econometrics can get very mathematical but the hasic principles behind econometric techniques arc simple.
Our purpose in this appendix is to show you these basic principles. We will use as an example the consumption Iunction introduced in Chapter 3, and we will concentrate on estimating с,, the propensity to consume out ol disposable
Changes in consumption and changes in disposable income
The propensity to consume tells us by how much consumption changes lor a given change in disposable income. A natural first step is simply to plot changes in consumption versus changes in disposable income and sec how the
relation between the two looks. You can sec this in figure A3.1.
Thc vertical axis in Figure A.3.1 measures the annual change in consumption minus the average annual change in consumption lor each year from 1984 to 2008 in Ausiralia. More precisely, let C, denote consumption in year t. Let AC, denote C, - C, |, the change in consumption from year I - I to year t. Let AC denote the average annual change in consumption since I960. The variable measured on the vertical axis is constructed as AC, - AC. A positive value ol the variable represents an increase in consumption larger than average, a negative value an increase in consumption smaller than average.
Similarly, thc horizontal axis measures the annual change in disposable income, minus the average annual change in disposable income sincc 1984, AY0l - AYb.
A particular square in the figure gives thc deviations of the change in consumption and disposable income Irom their respective means lor a particular year between 1984 and 2008. In 2008, for example, thc change in consumption was higher than average by about $100 million, thc change in disposable income was higher than average by about $150 million. ( For our purposes, it isn't important to know to which
Figure A3.1
Changes in consumption versus changes in disposable income. Australia. 1984-2008
125
2008
с
J 754
с О 'С A, £ Э «л С О
♦ ♦
25-
♦
-75-
-25-
(V 00 с п £ О
There is a clear positive relation between rates of change in consumption and rates of change in disposable income.
year each square refers, just what the set ol points in the diagram looks like. So except for 2008, the years aren't indicated in Figure A3.1 Figure A3.1 suggests two main conclusions:
1. There is a clear positive relation between changes in consumption and changes in disposable income. Most of the points lie
in thc upper-right and lower-left quadrants of thc ligure. When disposable income increases by more than average, consumption also typically increases by more than average.- when disposable income increases by less than average, so typically docs consumption.
2. The relation between thc two variables is good but not perfect. In particular, some points lie in the upper-lelt quadrant. These points correspond to years when smaller- than-average changes in disposable income were associated with higher-than-average changes in consumption. Econometrics allows us to state these two
conclusions more precisely and to get an estimate of thc propensity to consume. Using an econometrics software package, we can find the line that fits the cloud of points in Figure A3.1 best. This line-fitting process is callcd ordinary least squares (OLS Thc term least squares comes trom thc fact that thc line has the property of minimising the sum of the squared distances ol the points to the line—thus gives the least squares'. The word ordinary comes from the fact that this is thc simplest method used in econometrics fhe estimated equation corresponding to the line is called a regression, and thc line itself is called thc regression line
In our ease, the estimated equation is given by
(AC,-КС) - 0.55 (ДУ/)(-ЛУР) ■ Residual ((-statistic: 3.0)
R = 0.38 (A3.1)
1 he regression line corresponding to this estimated equation is drawn in Figure A.3.2. Equation (A.3.11 reports three important numbers. (Econometrics packages give more information than reported here,- a typical printout together with lunher explanations, is given in thc focus box 'A guide to understanding econometric results'.
• 1 he first important number is the estimated propensity to consume. Fhe equation tells us
that an increase in disposable income ol $1 billion above normal is typically associated with an increase in consumption ot $0.55 billion above normal. In other words the estimated propensity to consume is 0.55. It is positive, but smaller than I.
• Ehc second important number is the estimated /-statistic tor the estimated propensity to consume. A /-statistic greater than 2 tells us that we arc more than 05 per cent sure that the estimated parameter lor the propensity to consume differs from zero. In our regression the f-statislic is 6.5, and so we can be verv confident that our 0.55 estimate is significant.
• The second important number is R: - 0.63, which is a measure of how well the regression line lits.
Having estimated the effect ol disposable income on consumption, we can decompose the change in consumption for each year into that part that is due to the change in disposable income—the first term on the right in equation (A3.1 —and the rest, which is called the residual. For example, the residual for 2008 is indicated in Figure A3.2 by the vertical distance from the point representing 2008 to the regression line.
l! all the points in Figure A3.2 were exactly on the estimated line, all residuals would be zero.- all changes in consumption would be explained by changes in disposable income. As you can sec, however, this isn't the case. A*- is the statistic lhat tells us how well the line liis. R- is always between 0 and I. A value ot I would imply lhal the relation between the two variables is perfect, that all points are exactly on thc regression line. A value of zero would imply that thc computer can see no relation between ihe two variables. Thc value ot R of 0.63 in equation (A3.1 i is high, but not very high. It conlirms the message from Figure A.3.2: movements in disposable income clearly allcct consumption, but (here is still quite a bit of movement in consumption thai cannot be explained by movements in disposable income.
Correlation versus causality
What we have established so far is that
consumption and disposable income typically
move together. More formally, we have seen that there is a positive correlation the technical term lor co-relation—between annual changes in consumption and annual changes in disposable income. And we have interpreted this relation as showing causality—that an increase in disposable income causes an increase in consumption.
We need to think again about this interpretation. A positive relation between consumption and disposable income may reflect the effect ol disposable income on consumption. But il may also reflect the ellect of consumption on disposable income. Indeed the model developed in Chaptcr 3 tells us that if, lor any reason, consumers decide to spend more, then output and therefore income and, in turn, disposable income will increase. If part ol the relation between consumption and disposable income comes trom the ellcct of consumption on disposable income interpreting equation (A3.1) as telling us about the effect ot disposable income on consumption isn't right.
The regression line is thc line that fits the scatter of points best
An example will help here. Suppose consumption docs not depend on disposable income, so that the true value of f, is zero. (This isn't very realistic, but it will make the point most clearly. ) So draw the consumption function as a horizontal line a line with a zero slope in figure A.3.3. Next, suppose that disposable income equals Yp, so that the initial combination ol consumption and disposable income is given by point A.
Now suppose that, because ot improved confidence, consumers increase their consumption, so the consumption line shilts up. II demand affects output, then income and. in turn, disposable income increase, so that the new combination ot consumption and disposable income will be given bv, say. point В. It, instead, consumers become more pessimistic, the consumption line shifts down, and so does output, leading to a combination ol consumption and disposable income given by point D.
с
о
о. Е а
(А
С
о
■а -25
м с
-С
U
-75
-125
Figure A3.2 Changes in consumption and changes in disposable income: the regression line
Change in real disposable income (millions)
If we look at that economy, we observe points А, В and D. II, as we did above, we draw the best-lilting line through these points, we estimate an upward-sloping line, such as CC', and so estimate a positive value lor propensity to consume <.*,. Remember, however, that the true value ol Г) is zero. Why do we get the wrong answer—a positive value for c, when the true- value is zero? Because we interpret the positive relation between disposable income and consumption as showing the effect ol disposable- income on consumption, where, in fact, the relation reflects the effect ot consumption on disposable income: higher consumption leads lo
higher demand higher output, and so higher disposable income.
There is an important lesson here, the difference between correlation and causality. The fact that two variables move together doesn't
imply that movements in the first variable cause movements in the second variable. Perhaps the causality runs the other way: movements in the second variable cause movements in the first variable. Or perhaps, as is likely to be the case
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