What is the natural interest rate?

Transcription

1 Wha is he naural ineres rae? Henrik Lundvall and Andreas Wesermark The auhors work a he Moneary Policy Deparmen, Sveriges Riksbank. Wha real ineres rae should a cenral bank aim for if i wishes o aain a normal level of resource uilisaion? In modern moneary policy heory, he real ineres rae ha is consisen wih a normal level of resource uilisaion is usually called he naural ineres rae. One way of deermining wheher moneary policy is expansionary or conracionary is o compare he acual real ineres rae wih he naural ineres rae. One imporan characerisic of he naural ineres rae is ha is level varies over ime. This aricle analyses how differen ypes of macroeconomic disurbances of he ype ha were seen in he financial crisis can impac he naural ineres rae in a heoreical model of he economy. The nominal ineres rae is he compensaion ha a borrower pays o a lender in addiion o he borrowed amoun. I is measured as a proporion of he borrowed amoun and is expressed as a percenage. For example, banks ofen offer loans and savings a nominal ineres raes. The real ineres rae can be calculaed as he nominal ineres rae over he loan s mauriy minus expeced inflaion over he same period. The real ineres rae shows he purchasing power a borrower mus relinquish o gain access o he loan, and is he mos relevan facor for households and firms when hey decide o borrow money. The policy rae or repo rae is he nominal ineres rae a which banks can borrow from or inves in he Riksbank over he shor erm. The policy rae can also be calculaed in real erms by adjusing for expeced inflaion, which is more relevan when analysing he developmen of he real economy. The naural ineres rae is he real ineres rae ha would prevail if resource uilisaion in he economy was normal oday and was expeced o remain normal in he fuure. Wha do we mean when we say ha a cerain moneary policy is expansionary or conracionary? Mos of us would probably agree ha an expansionary moneary policy means ha he cenral bank holds he policy rae a a low level so as o increase resource uilisaion. Conversely, a conracionary policy means ha he policy rae is se a a relaively high level, which, in normal cases, leads o he dampening of resource uilisaion. Bu wha would be a more precise definiion of he conceps of expansionary and conracionary moneary policies? Is i possible o deermine an exac cu-off poin for he We have received assisance from many of our colleagues, and would paricularly like o hank Lars E.O. Svensson and Ulf Södersröm. 7

2 ineres rae, below which a cerain moneary policy can be characerised as expansionary and above which i can be said o be conracionary? In modern moneary policy heory, such a cu-off poin exiss for he real ineres rae, ha is, he nominal ineres rae minus expeced inflaion. This cu-off poin is usually called he naural real ineres rae or, more succincly, he naural ineres rae. One imporan characerisic of he naural ineres rae is ha is level varies over ime as a resul of macroeconomic disurbances affecing he economy. In heory, he level of he naural ineres rae mus firs be esablished, before i can be deermined wheher a cerain moneary policy is expansionary or conracionary. The aim of his aricle is o discuss wha is mean by he erm he naural ineres rae. Is saring poin is a descripion of he economy ha forms he mainsream of curren research on moneary policy, someimes known as New Keynesian heory. In he aricle, we describe some cenral relaionships in a simple version of a New Keynesian model, and, on he basis of hese relaionships, discuss he concep of he naural ineres rae. 2 The appendix includes a brief mahemaical descripion of he model. The aricle also includes a secion wih examples showing how he naural ineres rae is affeced by a number of differen macroeconomic disurbances. The naural ineres rae and moneary policy According o modern macroeconomic heory, a cenral bank normally wans o conrol boh he rae of inflaion and he level of resource uilisaion in he economy. A cenral bank ha conducs inflaion argeing and ries o hold inflaion sable around an inflaion arge usually has wo reasons for influencing resource uilisaion, he firs of which is direcly linked o he ask of mainaining price sabiliy. Resource uilisaion affecs firms coss, and he coss are decisive when firms price heir producs. For a cenral bank aiming o sabilise inflaion around an inflaion arge, i is hus very imporan o also sabilise resource uilisaion so ha he general cos level rises a a rae ha is compaible wih he inflaion arge. In addiion o he arge of sabilising inflaion, he cenral bank may also consider he sabilisaion of he real economy o be par of is objecive. This need no conflic wih he ask of mainaining price sabiliy: given ha households and firms rus ha he cenral bank reurns inflaion o arge in he long erm, here is normally scope for rying o find a balance in he shor and medium erm beween he arge of sabilising inflaion and he ambiion of sabilising he real economy. Such rade-offs are relevan when he economy is affeced by macroeconomic disurbances driving inflaion and resource uilisaion in 2 The concep of a naural ineres rae was inroduced by Knu Wicksell in a series of heoreical works published around 900. By he naural ineres rae, Wicksell mean a real equilibrium ineres rae ha was independen of he acual bank ineres raes and which was deermined by he real disurbances affecing he economy. A cenral bank wishing o hold prices sable should ake acion aimed a holding he acual bank ineres raes level wih he naural ineres rae. In recen decades, his concep has become an imporan componen of wha is known as New Keynesian heory, alhough he meaning of he concep has parly changed. Wicksell s influence on modern moneary policy heory is considered o be highly significan by a number of researchers, and, consequenly, he erm Neo-Wicksellian model is occasionally used insead of New Keynesian model. See Wicksell (898) and Woodford (2003), paricularly chapers and 4. 8

3 opposie direcions, for example supply shocks. Anoher reason for he cenral bank o influence resource uilisaion may hus be ha he sabiliy of he real economy is seen as a moneary policy arge in iself. Under an inflaion-argeing regime, moneary policy is normally a maer of finding a pah for he policy rae ha gives good forecass for inflaion and resource uilisaion. Good forecass mean a forecas for inflaion ha deviaes as lile as possible from he inflaion arge, and a forecas for producion and employmen ha deviaes as lile as possible from a normal level of resource uilisaion. Normal resource uilisaion and he naural ineres rae Resource uilisaion is hus one of he mos imporan macroeconomic variables for a cenral bank. Bu how can he level of resource uilisaion be measured, and wha is mean by he expression a normal level of resource uilisaion? One frequenly used measure of resource uilisaion is he oupu gap, which measures he difference beween he acual oupu level (acual GDP) and he poenial oupu level (poenial GDP). When acual GDP is equal o poenial GDP, he oupu gap is zero and resource uilisaion is said o be normal. If he oupu gap is posiive, so ha acual GDP is higher han poenial GDP, resource uilisaion is said o be higher han normal, while, conversely, a negaive oupu gap means ha resource uilisaion is lower han normal. 3 So wha is mean by he poenial oupu level, and how can i be ha he acual oupu level can differ from he poenial level? In New Keynesian heory, poenial GDP is usually defined as he level of oupu ha would arise if all prices and wages were fully flexible. Full flexibiliy means ha all prices and wages are adjused immediaely o changes in economic condiions. However, here is a lo of evidence ha suggess ha prices and wages change relaively infrequenly hey are sluggish. So, why is i reasonable o define poenial GDP as he level ha would prevail if all prices and wages were flexible? According o he heory, he sluggishness is he reason ha acual GDP generally differs from is poenial level. In a marke economy, prices and wages play a cenral role, in ha hey convey informaion from one firm o anoher, and beween firms and households. Prices convey informaion o households regarding firms marginal cos levels: differen firms relaive prices signal differences beween heir relaive producion coss. If prices are sluggish, here is a risk ha households will ge he wrong signals concerning relaive coss and will hus demand oo much of hose goods ha are comparaively expensive o produce. This could lead o he misallocaion of resources wihin individual firms and indusries, and in he economy as a whole. This laer siuaion will be he case if he economy s average price or wage level is no adjused fas enough when he economy is affeced by aggregae disurbances. 3 However, here are several oher measures of resource uilisaion in addiion o he oupu gap. Examples of oher measures are he hours gap, which measures he deviaion beween he acual number of hours worked and he poenial number of hours worked, and he unemploymen gap, which specifies he difference beween he acual level of unemploymen and unemploymen when prices and wages are flexible. 9

4 If, on he oher hand, prices and wages are fully flexible, no such mismanagemen of he economy s oal resources will arise. For his reason, we le poenial GDP be equal o he level of oupu ha would arise if price and wage levels were flexible. This level of oupu is also occasionally called he naural oupu level. 4 However, if an economy reaches is poenial oupu level and has a normal level of resource uilisaion, his does no mean ha his economy will always grow in accordance wih he economy s long-erm growh rae. For example, produciviy and demand shocks will affec an economy wih flexible wages and prices, hus divering he economy from is long-erm growh rae. One price ha is of paricular ineres for moneary policy is he reurn on savings he ineres rae. When firms and households decide o borrow or save money, he real cos or reurn is deermined by he real ineres rae. The real ineres rae corresponds approximaely o he nominal ineres rae minus he inflaion ha is expeced o occur during he period which he money was len. As prices of goods and services in general change fairly infrequenly, inflaion is relaively sluggish. Of course, he sluggishness of price and wage formaion means ha he rae a which prices increase inflaion changes more slowly han would have been he case had all prices and wages been flexible. Jus as sluggishness in price and wage formaion creaes a gap beween acual GDP and poenial GDP, he same sluggishness creaes a gap beween he acual real ineres rae and he ineres rae ha would apply if all prices and wages were flexible. Consequenly, o he naural or poenial oupu level here is a corresponding concep of a naural ineres rae, ha is, he real ineres rae ha would arise if prices and wages were fully flexible and resource uilisaion was normal. The naural ineres rae can be regarded as he ineres rae ha would prevail if here was no need for moneary policy o sabilise he real economy. Before we discuss he quesion of which facors deermine he naural ineres rae, here may be reason o commen on he definiion of he erm we are using here. In he heoreical lieraure on moneary policy, he poenial oupu level and he naural ineres rae are deermined by he equilibrium of flexible prices and wages. In he empirical lieraure, oher definiions of he erm poenial oupu level are ofen used. Naurally, by analogy wih such alernaive definiions of he oupu gap, alernaive definiions of he level of he real ineres rae ha is compaible wih a normal level of resource uilisaion can be made. Wha deermines he naural ineres rae? The ineres rae is deermined by demand and supply in he credi marke. To undersand which facors influence his marke, i is helpful o sar by examining a sylized model, in which a represenaive household decides how much money o save (or borrow), and how much o use for consumpion. In modern macroeconomic heory, i is assumed ha he 4 Misallocaion of resources can arise for many oher reasons han jus nominal consrains. However, when discussing moneary policy, i is naural o focus on hese nominal consrains, since hese are he causes of misallocaion ha he cenral bank can affec. 0

5 household s choice will be forward-looking he household will choose consumpion and savings o maximize he payoff from consumpion oday and in he fuure. To undersand households behaviour, wo basic assumpions are made regarding how consumpion is valued over ime. The firs basic assumpion concerns how he household values variaions in consumpion. Le us assume ha he household has a given amoun of consumer goods a is disposal, and ha he household mus deermine how his consumpion is o be allocaed over ime. Will he household allocae is consumpion evenly over ime, or will i consume large amouns in cerain periods and less in ohers? I is reasonable o assume ha an increase of consumpion is valued relaively highly if he iniial level of consumpion is low, while an equally large increase is worh less if he level of consumpion is high. An opimising household will hus plan is consumpion so ha he value of consumpion increases oday and omorrow are equal. This means ha households prefer consumpion ha is fairly equal across ime o consumpion ha varies across ime. In oher words, he household has a basic desire o consume approximaely he same amoun in all ime periods. An example of his is pension savings. Afer reiremen, income drops significanly for mos households, and, o avoid an old age spen in relaive povery, i is very common for households o save a porion of heir income during heir working years. Anoher example is ha households ofen build up a cerain savings buffer ha can be used in imes when expenses are unexpecedly high. The assumpion of consumpion smoohing has been an imporan par of macroeconomic heory since he 950s, when Modigliani and Brumber (954) and Friedman (957) launched heir hypoheses on life cycle savings and permanen income. The second basic assumpion is ha households ges a higher payoff from consumpion early on, raher han consumpion aking place a some poin far in he fuure. Quie simply, households value consumpion aking place oday or omorrow slighly higher han equivalen consumpion aking place in one year s ime. 5 I could be said ha he value of consumpion declines he furher ahead in ime i akes place. 6 The wo assumpions of he household s preferences ha we have described deermine he choice beween consumpion and saving. The household s preference for smooh consumpion means ha he household has reason o save during periods in which is income is unusually high and o cu back on saving (or borrow money) during periods 5 In heoreical models, his is capured by he size of he household s subjecive discoun facor. A higher value for he discoun facor means ha households value consumpion oday and in he fuure more equally. 6 I is possible o describe hese wo assumpions in a more echnical manner. If households choose curren and fuure consumpion o maximise β u( c ), =0 in which β is a subjecive discoun facor and u( c ) is he households benefi from consuming c, hen β capures he households ime preference, and he degree of concaviy in u capures he households aversion for variaion of consumpion over ime. If β is less han one, households are impaien, which is o say ha hey value consumpion oday higher han consumpion in he fuure.

6 in which income is unusually low. By using he credi marke, he household can hus sever he consumpion level from he income level a any poin in ime. However, he household s impaience is a force pushing in he opposie direcion, as his impaience means ha he household does no necessarily have reason o fully equalize consumpion across ime. Insead, consumpion is allowed o decline somewha over ime. As we have seen, consumpion aking place oday is valued slighly higher han ha aking place in he fuure. If he household s preferences sugges ha consumpion will decline over ime, he reurn on saving (posiive ineres) creaes a couneracing incenive. If he household chooses o pospone a lile of oday s consumpion o a laer poin in ime, he household will be compensaed via ineres and will laer be able o consume a lile more han i has refrained from consuming oday. All oher facors being equal, he higher he ineres rae is, he greaer he reason for he household o pospone some of is consumpion. Thus, here is a relaionship beween consumpion and ineres raes. In an economy where GDP and consumpion grow over ime, he rae of growh will have a significan impac on he real ineres rae. As consumpion grows, households have incenives o borrow o smooh consumpion over ime. If growh increases, households have incenives o borrow more, in urn driving up he real ineres rae. In normal New Keynesian models, he conclusion of his analysis is ha he real ineres rae is primarily deermined by he growh in consumpion expeced by he represenaive household and by he srengh of he household s ineres in consuming oday raher han a a laer dae. The household s expeced growh in consumpion is, in urn, closely linked o he expeced growh rae of GDP. Because a single household is small relaive o he size of he credi marke, changes in ha household s saving decisions have no impac on he equilibrium ineres rae. However, he ineres rae is affeced if changes occur ha cause many households o simulaneously change heir balance beween consumpion and saving. Assume, for example, ha news of macroeconomic developmens leads he average household o expec higher fuure rises in income han have previously been he case. As households prefer o spread consumpion evenly over ime, he average household hus has reason o decrease is curren saving level. Households cu back on heir saving and immediaely sar o adjus heir consumpion o he higher expeced income. The resul is ha ne demand for loans increases, which, in urn, leads o a rise in he ineres rae. If he average household becomes more opimisic regarding fuure growh raes, his will lead o an increase in he naural ineres rae. If uncerainy over is fuure income increases, i is reasonable for a household o increase is buffer of saved funds, so ha hese savings can be used in case fuure income should be paricularly low. Inuiively, we can regard his scenario as an example of he average household s impaience. In his case, many households simulaneously become less impaien. The resul is ha savings increases and he naural ineres rae falls. This example is a reasonable inerpreaion of he changes in households saving paerns ha 2

7 arose during he deep recession of , when households saving, as a proporion of disposable income, rose sharply. The naural ineres rae hus primarily depends upon he growh in consumpion expeced by he average household, and on households impaience. Households expeced growh in consumpion is, in urn, closely linked o he expeced growh rae of GDP. According o heory, here is hus a close connecion beween macroeconomic developmens (growh in GDP) and flucuaions in he level of he naural ineres rae. Sluggish prices give he cenral bank power: he moneary policy ransmission The naural ineres rae is hus he price of saved funds ha would have arisen had all prices and wages been flexible. However, as acual economies are characerised by sluggishness in price and wage formaion, here is no reason o expec ha he acual real ineres rae should coincide wih he naural real ineres rae. Insead, in acual economies, he shor-erm real ineres rae is deermined by he cenral bank. In his secion, we firs summarise how he cenral bank deermines he real ineres rae. Following his, we discuss wha happens if and when he cenral bank chooses o se he real ineres rae a a level differing from he naural ineres rae. The framework for he implemenaion of moneary policy akes differen forms in differen counries. In Sweden, he Riksbank conrols he ineres rae by deermining he erms and condiions for he banks overnigh deposis in and loans from he Riksbank. These erms and condiions, in urn, se he limis for he ineres rae charged by he banks o each oher when hey lend money o each oher overnigh. By way of repo ransacions and wha are known as fine-uning operaions, he Riksbank ensures ha his ineres rae lies close o he repo rae deermined by he Riksbank s Execuive Board. By conrolling he ineres rae charged by he banks o each oher when hey need o borrow money or inves a surplus, he Riksbank indirecly influences he ineres raes offered by he banks o heir cusomers, namely households and firms. In he previous secion, we menioned ha inflaion is a sluggish variable. One consequence of his is ha he cenral bank s conrol of he nominal ineres rae also means ha i conrols he real ineres rae, as he sluggishness of price and wage formaion means ha inflaion changes relaively slowly. When he cenral bank adjuss he real ineres rae, by adjusing he policy rae, he oal demand in he economy is affeced. In an acual economy, his akes place hrough several channels, for example hrough firms invesmen decisions and by influencing he exchange rae. In his aricle, we focus on he channel ha depends on households choices beween consumpion and saving. To briefly describe how changes in he real ineres rae influence resource uilisaion and inflaion, we can consider an example in which inflaion risks being above arge and he cenral bank hus decides o raise he ineres rae. Assume ha resource uilisaion is normal o sar wih, bu ha he privae secor has inflaion expecaions ha are clearly above he inflaion arge. This could, for example, be due o expecaions of high fuure 3

8 wage increases, which, in urn, are influencing he cos siuaion in he business secor. When inflaion expecaions are high, acual inflaion also risks being above arge. Normal resource uilisaion means ha he acual real ineres rae iniially coincides wih he naural ineres rae. To preven inflaion from rising above arge, he cenral bank raises is ineres rae. This higher real ineres rae changes he condiions for households choice beween consumpion and saving: saving becomes more profiable, a he same ime as i becomes more expensive o borrow money. When households cu down on consumpion, demand in he economy decreases. This makes firms decrease producion, which means ha heir demand for labor and equipmen also declines. In urn, his leads o a gradual decrease in he rae of wage increases. The rae of price increase for exising capial also declines. When firms realize ha cos pressure is easing off, hey adjus heir prices accordingly: inflaion becomes lower han i would have been if he cenral bank had lef is ineres rae unchanged. By raising he real ineres rae above he naural ineres rae, he cenral bank has caused a drop in economic aciviy. The lower level of demand has led o a lower level of resource uilisaion: firms have reduced boh heir labour force and heir demand for equipmen. A low level of resource uilisaion has, in urn, led firms coss o increase a a lower rae han would oherwise have been he case, and he rae of price increase has hereby been dampened. However, he cenral bank s abiliy o influence he real ineres rae is only shorerm. The average real ineres rae over longer periods is deermined by oher facors han moneary policy, for example by he economy s long-erm growh rae, household impaience and any axes on capial. The conclusion is hus ha he cenral bank can allow he acual real ineres rae o deviae from he naural ineres rae for shorer periods, bu, in he long run, he cenral bank finds iself forced o ac so ha he acual real ineres rae, on average, is fairly close o he naural ineres rae. The naural ineres rae and he objecive of moneary policy The aiude moneary policy should ake owards changes in he naural ineres rae obviously depends on he aims of he cenral bank. In general, i can be said ha he greaer he emphasis placed by he cenral bank on sabilising resource uilisaion, he greaer reason i has o adjus he acual real ineres rae o changes in he naural ineres rae. This is a consequence of he definiion of he erm: we have defined he naural ineres rae as he real ineres rae ha corresponds o a normal level of resource uilisaion. In many cases, an inflaion arge also jusifies adjusing he acual real ineres rae o flucuaions in he naural ineres raes. An acual real ineres rae above he naural ineres rae implies a downward pressure on firms cos levels, as resource uilisaion would hen end o fall below a normal level. This kind of conracionary policy hus leads o a lower inflaion rae. Similarly, an expansionary moneary policy, in which he acual real ineres rae is held below he naural ineres rae, leads o rising cos levels. Inflaion will hen end o rise. 4

9 However, in earlier secions, we have menioned ha various ypes of macroeconomic disurbances end o drive resource uilisaion and inflaion in differen direcions. In general, under such circumsances, here is reason for he cenral bank no o adjus he acual real ineres rae fully o changes in he naural ineres rae. For example, if inflaion increases a he same ime as resource uilisaion decreases, a shor-erm conflic will arise beween he arge of sabilising inflaion and sabilising resource uilisaion. If he cenral bank only ook consideraion of he arge of sabilising he real economy, fully adjusing he acual real ineres rae o changes in he naural economy would be jusifiable. Bu when consideraion is also aken of he arge of sabilising inflaion, here is reason o allow he acual real ineres rae o be higher han he naural ineres rae for a ime. On one hand, such a policy would conribue o holding resource uilisaion below a normal level for a longer period han would oherwise be he case. On he oher hand, his conracionary moneary policy would also conribue owards prevening inflaion from rising oo far above arge. In pracice, i is difficul o esimae he level of he naural ineres rae, jus as i is difficul o esimae he poenial level of oupu. 7 When he level of economic aciviy changes, i can ake ime before he cenral bank (and oher analyss) can deermine which underlying circumsances have changed and wha he consequences will be for fuure economic developmen. Resource uilisaion can hen fall below or rise above normal levels before moneary policy can reac. In addiion, i can ake ime o reurn resource uilisaion o normal levels using moneary policy. I is hus difficul o preven resource uilisaion from occasionally lying above or below normal levels. 8 Changes in he naural ineres rae some examples An economy is coninually affeced by differen ypes of disurbances. This, in urn, affecs imporan macroeconomic aggregaes such as consumpion and GDP. The aim of his secion is o explain, wih he help of a relaively simple macroeconomic model, how some of hese disurbances affec he naural ineres rae. The purpose is o describe, in an inuiive manner, he relaionship beween he real economy and he naural ineres rae. To his aim, we use a varian of a model presened by Gali (2008). We have aemped o selec disurbances ha could have caused he deep recession of 2008 and The model is simple and canno explain every aspec of he crisis. Consequenly, we do no aemp o relae he analysis included in he following secion o any empirical evidence. 7 See, for example, Jusiniano & Primicieri (200) and Laubach & Williams (2003). 8 For hese reasons, here may be reason o differeniae beween he naural ineres rae ha applies if resource uilisaion is iniially a a normal level, and he naural ineres rae ha applies if resource uilisaion is iniially below or above a normal level. In he laer case, we are hus ineresed in he level of he real ineres rae ha, if implemened, would be expeced o reurn he economy o is poenial GDP and growh rae wihin one or wo quarers. This disincion is relaed o he difference made in he heoreical lieraure beween an uncondiional and a condiional oupu gap. See also Adolfson, Laséen, Lindé & Svensson (200). 5

10 Unexpeced changes in produciviy Produciviy varies over ime and can have major effecs on economic developmens. When making assessmens of he level of resource uilisaion and he naural real ineres rae, i is imporan o aemp o deermine he exen o which posiive or negaive produciviy disurbances have been emporary or permanen. In pracice, produciviy can be affeced by many facors for example, variaions in he size of he capial sock or in how well he capial sock and he labour force s capaciy is being uilised (labour hoarding). In he model used here, produciviy disurbances are changes in oal facor produciviy. 9 Disurbances in producion echnology can be divided up ino emporary and permanen disurbances. 0 We will now examine examples of how a negaive produciviy disurbance affecs he economy, and analyse he difference beween emporary and permanen negaive disurbances. Figure. The effec on he naural ineres rae of unexpeced changes in produciviy Naural ineres rae Real rae Quarer The red dashed line shows he effec on he naural ineres rae of a emporary and unexpeced negaive change, while he blue dashed line shows he effec of a permanen and unexpeced negaive change. The scale on he verical axis is he yearly ineres rae in percen. The black line in Figure shows he naural ineres rae when he economy in he model grows along a balanced growh pah wih an annual real growh rae of 2 per cen. Growh is driven by gradual and permanen improvemens in he produciviy of he labour force. The level of he ineres rae can be relaed o he households choice beween consumpion and saving. As he economy is growing by 2 per cen per year, household consumpion is also growing by 2 per cen per year, which, in urn, leads o an ineres rae level ha is consan over ime. The ineres rae level will hen depend on he long-erm 9 A change of he oal facor produciviy means ha he oupu level changes, even hough he use of labour, capial and oher inpus remain consan. 0 In his secion, we use a simple New Keynesian DSGE model, similar o he model described in chapers 2 and 5 in Gali (2008) (see appendix). The economic environmen is very simple: we analyse a small, open economy in which he labour force is he only facor of producion. 6

11 growh rae and on household impaience. A long-erm growh rae higher han 2 per cen will mean ha he ineres rae will rise. As households prefer a smooh consumpion level over ime, a higher expeced growh rae means ha household demand for loans will increase: by borrowing money oday, households can immediaely sar o ranslae heir expeced fuure increase in income ino higher consumpion. This increased demand for loans will, in urn, drive up he real ineres rae. The blue and red lines in Figure show he effec on he naural ineres rae of a negaive disurbance o produciviy impacing he economy. The red line shows he effec of a emporary disurbance ha lowers he economy s poenial growh rae for a limied period. The effec on he economy s poenial oupu level is shown in Figure 2. Iniially, GDP develops according o he solid black line. Before he emporary disurbance affecs produciviy, firms and households expec he poenial GDP level o coninue o grow according o he dashed black line. Insead, in period, labour produciviy falls quie seeply, and, consequenly, he poenial level of GDP also falls, as shown by he red line in Figure 2. However, his fall in GDP is emporary, and, afer he disurbance in period, he poenial growh rae becomes slighly higher han 2 per cen. In he long erm, he economy is expeced o recover from he enire fall in oupu level. Figure 2. Impac on poenial oupu level of an unexpeced change of produciviy Producion GDP level Quarer The black dashed line shows privae-secor expecaions, in period zero, of he poenial oupu level en quarers ahead. The blue and red dashed lines show expecaions in period one, following a emporary (red line) and permanen (blue line) disurbance o produciviy. The real ineres rae is a forward-looking variable, and consequenly, o undersand he resuls of he model, i is imporan o undersand how he households in he model form expecaions of fuure developmens. When households make heir consumpion and savings decision, hey base heir choice on he real reurn hey expec o receive oday and in he fuure. We also assume ha households undersand how he model economy works. Poenial oupu level here refers o he producion level in an economy wih flexible prices. 7

12 Households have wha are known as raional expecaions. Afer a produciviy disurbance has aken place in he firs period, he households realise ha GDP and consumpion will grow faser han 2 per cen for a number of years, as he economy gradually reurns o he long-erm growh pah. This higher expeced growh rae means ha households have a srong incenive o borrow agains fuure income, which, in urn, iniially pushes up he ineres rae. When he economy laer approaches he long-erm growh rae, consumpion growh is more in line wih he long-erm growh rae, which, in urn, means ha he naural ineres rae approaches is long-erm level of 2 per cen. If, insead, he economy is impaced by a negaive, permanen produciviy disurbance, he effec on consumpion and ineres raes will be quie differen. The blue dashed line in Figure 2 illusraes ha he iniial fall in oupu is smaller 2 han when he disurbance is emporary. However, he growh rae coninues o be comparaively low for a couple of years, wih no expecaion of reaching he old growh pah. Afer a couple of years, he poenial growh rae again reaches abou 2 per cen, bu he poenial oupu level is permanenly lower han households and firms had expeced before he disurbance occurred. The effec on he naural ineres rae (he blue dashed line in Figure ) is a direc consequence of households expecaion ha he growh raes of GDP and consumpion will be lower han 2 per cen for he nex few years. The lower expeced growh rae means ha households incenive o borrow agains fuure income becomes weaker, which, in urn, pushes he ineres rae down. Evenually, he ineres rae gradually rises back owards is original equilibrium level, as he poenial growh rae reurns o 2 per cen. The conclusion of his analysis is hus ha he effec on he naural ineres rae of a disurbance o produciviy depends on wheher he disurbance is expeced o have emporary or permanen effecs. We have used a highly sylised model. In a more realisic model, for example one including capial, he effecs on he naural ineres rae will be slighly differen. 3 Fiscal policy: increased governmen spending When a governmen formulaes is fiscal policy, one of is objecives may be o sabilize resource uilisaion. So how is he naural ineres rae affeced by an increase in public expendiure? In he simple model we are sudying here, i has been assumed ha he public secor uses a porion of oupu for governmen spending. Household consumpion is equivalen o GDP minus governmen spending and ne expors. An increase in governmen spending is modelled as an unexpeced increase in he proporion of oal oupu uilised for governmen consumpion. The disurbance occurs in period, and enails an increase in he public secor s share of GDP, and also ha his share is expeced 2 This less severe iniial fall is due o he fac ha he permanen disurbance iniially is fairly small. The disurbance does no reach full effec unil several quarers laer. 3 See also Jonsson (2002). 8

13 o be higher han normal for a number of years. However, over ime, governmen spending as a share of GDP falls back o he level prevailing before he disurbance occurs. Figure 3. Effecs on poenial GDP, consumpion and he naural ineres rae of an unexpeced change in governmen spending Percenage change Real rae Producion Quarer Quarer Real rae Quarer Percenage change Consumpion The verical axis in he figure for GDP and consumpion shows he percenage deviaion from he long-run oupu and consumpion levels. The scale on he verical axis in he figure for he real ineres rae is in percen per year. The effecs on Swedish GDP, consumpion and he real ineres rae of an increase in governmen spending are shown as he red dashed line in Figure 3. The upper lef figure shows how he oupu level changes in relaion o he long-run oupu level of he economy (seady sae in he saionary model). The increase in governmen spending leads o an increase in aggregae demand, conribuing o an increase in GDP. The uilisaion by he public secor of a larger porion of oal oupu means ha privae consumpion becomes lower in relaion o he iniial posiion, as he increase in public expendiure via increased axes reduces he privae secor s scope for consumpion. However, as he disurbance dissipaes, boh public and privae consumpion reurn o he levels expeced before he disurbance occurred. One consequence of his is ha privae consumpion is iniially low in relaion o is long-erm level. Households willingness o smooh consumpion hus pushes up he demand for loans, in urn also pushing ineres raes up. Afer a while, he increase in governmen spending goes down, and consumpion and he naural ineres rae hus reurn o heir long-erm levels. Lower foreign GDP In his secion, we analyse he effecs on he domesic economy of an unexpeced fall in foreign GDP. The inernaional financial crisis and is effecs on Sweden s foreign rade have dramaically illusraed he Swedish economy s dependence on foreign counries. The effecs of a fall in foreign GDP on Swedish GDP, consumpion and he real ineres rae are shown as a red dashed line in Figure 4. 9

14 Figure 4. Effecs on poenial GDP, consumpion and he naural ineres rae of an unexpeced change in foreign GDP Percenage change Producion Percenage change Consumpion Real rae Quarer Quarer Real rae Quarer The verical axis in he figure for GDP and consumpion shows he percenage deviaion from he long-run oupu and consumpion levels. The scale on he verical axis in he figure for he real ineres rae is in percen per year. When oupu falls abroad, foreign demand for domesically-produced goods also falls. This leads, in urn, o a fall in domesic oupu and consumpion. 4 As in he case of a disurbance of governmen spending, his lower curren consumpion means ha households expec more rapid growh in heir consumpion in he fuure. Households willingness o mainain a smooh level of consumpion hus pushes demand for loans upwards for a period, and hus also pushes he naural ineres rae upwards. There is an indirec posiive relaionship beween he naural ineres rae abroad and he naural ineres rae in Sweden falling oupu abroad pushes down consumpion abroad, which, in urn, increases he naural ineres rae abroad. Conversely, a fall in he naural ineres rae abroad enails a fall in he naural ineres rae in Sweden. Increased precauionary saving In imes of economic uncerainy, here may be reason for households o increase heir savings. For example, consumpion fell sharply during he inernaional crisis of 2008, when he economic siuaion was more uncerain han normal. Recessions normally also enail lower demand for labour, which can impac individual households via unemploymen, emporary dismissals and oher risks affecing income from work. 5 Here, we carry ou 4 Among oher facors, he mechanism described here depends on households preferences: if he model s parameers assume oher values, he effec on domesic producion, consumpion and hus he real ineres rae can be he reverse. 5 The models we have used for our analysis in his secion do no allow any formal analysis of how uncerainy affecs decisions by households and firms. The mehod mos frequenly used o analyse moneary policy models enails linearising he model s equaions around he model s seady sae. One characerisic of his linear model is ha agens only ake accoun of he expeced fuure values of he sochasic variables affecing heir decisions; uncerainy concerning hese variables ha are capured by second-order erms or higher are no aken ino accoun. On he oher hand, he effec of households emporarily becoming more paien can be analysed. 20

15 a simplified analysis of such risks by sudying he effecs of a reducion in household impaience. Figure 5. Effecs on poenial GDP, consumpion and he naural ineres rae of an unexpeced fall in households willingness o consume oday x 0-3 Producion Consumpion Percenage Percenage -0. change 5 change Quarer Quarer Real rae 2 Real rae Quarer The verical axis in he figure for GDP and consumpion shows he percenage deviaion from he long-run oupu and consumpion levels. The scale on he verical axis in he figure for he real ineres rae is in percen per year. A emporary fall in households willingness o consume oday emporarily pushes consumpion down. As consumpion propensiy is low in imes of crisis, households will wish o increase heir saving. In urn, he reduced ne demand for loans will push he real ineres rae down. Concluding remarks How moneary policy affecs he economy depend on he relaionship beween he level of he acual real ineres rae and ha of he naural ineres rae. The usual saring poin is ha moneary policy is characerised by is effec on resource uilisaion. We call a moneary policy conracionary if, in he medium erm, i is expeced o resul in resource uilisaion below he normal level, while a moneary policy ha leads o resource uilisaion above he normal level is called expansionary. In his perspecive, he definiion of wha consiues a normal level of resource uilisaion is cenral o he quesion of how moneary policy should be assessed. Here, we have used he New Keynesian definiion of normal resource uilisaion. The poenial or naural oupu level and growh rae are hose ha would prevail if all prices and wages were fully flexible. The sluggishness of price and wage formaion normally give rise o a difference beween acual GDP and he acual growh rae, on one side, and naural GDP and he naural growh rae on he oher. These differences imply deviaions in resource uilisaion from is normal level. Jus as nominal sluggishness gives rise o differences beween acual and naural GDP, a difference also arises beween he acual real ineres rae and he real ineres rae ha 2

16 would arise if prices and wages were flexible he naural ineres rae. In oher words, he naural ineres rae is he ineres rae ha is compaible wih a normal level of resource uilisaion. If he cenral bank equaes he acual real ineres rae wih he naural ineres rae, resource uilisaion can be expeced o be normal. An acual real ineres rae ha is lower han he naural ineres rae means ha acual GDP will be higher han naural GDP, so ha resource uilisaion will be higher han normal. When he cenral bank ses he acual real ineres rae below he naural ineres rae, moneary policy can hus be said o be expansionary. Conversely, an acual real ineres rae above he naural ineres rae leads o resource uilisaion being lower han normal. Moneary policy is hen conracionary. I could be asked in which way he definiion of he naural ineres rae conribues owards a consrucive discussion on moneary policy. Afer all, wheher a paricular announced moneary policy is expansionary or conracionary can be deermined hrough an examinaion of he forecas for resource uilisaion and inflaion included in he announced policy. The definiion of he naural ineres rae is reminiscen of an imporan insigh supplied by New Keynesian heory. The level of he real ineres rae ha is compaible wih a normal level of resource uilisaion varies over ime. The effors of a cenral bank o normalise resource uilisaion in a given siuaion is hus no he same hing as ha cenral bank s effors o bring he ineres rae o a cerain average, consan level. The level of he real ineres rae ha is compaible wih a normal level of resource uilisaion is, insead, highly dependen on he currenly prevailing macroeconomic circumsances. A problem is he significan difficulies associaed wih each esimaion of he naural ineres rae. I is ofen difficul o rapidly and correcly idenify he disurbances affecing he economy. As we have seen above, a change in produciviy (for example) can have compleely differen effecs on he naural ineres rae, depending on wheher his change is emporary or permanen. A closely-relaed difficuly is formed by wha is known as model uncerainy. Resuls from he scienific lieraure indicae ha differen economic models give differen predicions of how he naural ineres rae is affeced by differen disurbances. Empirical sudies of he naural ineres rae in oher counries also seem o produce quie varied views of he naural ineres rae. 6 Anoher imporan aspec deals wih he difference beween he real ineres rae a presen and he privae secor s expecaions of fuure real ineres raes. New Keynesian heory usually assumes ha all households and firms ake conscious and fully-informed decisions. One resul of his is ha expecaions of fuure developmens play an imporan par in mos economic decisions. Insead of only alking abou he naural ineres rae, i is hus ofen appropriae o consider he expeced pah for he naural ineres rae. 6 See, for example, Andres, Lópes-Salido & Nelson (2008), who esimae he naural ineres rae for he Unied Saes and compare wih oher sudies. 22

17 Appendix. Permanen oupu disurbances in Gali s model In his appendix, we describe how permanen produciviy disurbances or shocks can be added o a model ha closely follows Gali (2008). 7 In a model wih permanen produciviy disurbances and a growing echnology rend, such as he one we analysed in secion 2, cerain variables such as oupu and real wages, for example, will increase over ime. The growing variables are derended by dividing he variables ha grow over ime in he model by he (growing) level of echnology Z. This les us calculae, for example, oupu Y in erms of wha is known as oupu in efficiency unis Y / Z, which is consan over ime. 8 The difference beween he model in Gali and a model wih permanen disurbances in echnology is ha he consumers choice beween consumpion and saving wha is known as he Euler equaion is modified. Wihou permanen echnology shocks, his is: c = E ( c+ ) ( r ρ ), (A) σ where c is aggregae consumpion in period, E ( c + ) consumers expecaions in period of consumpion in he nex period, r he real ineres rae, σ (he inverse of) he ineremporal subsiuion elasiciy and ρ a parameer ha capures individuals subjecive ime preference. In a model wih permanen echnology shocks 9, he Euler equaion insead becomes: c + σ (A2) ( c + z ) ( r ρ ), = E + Z+ where z+ = log. Individuals also decide how o allocae ime beween leisure and Z work. Specifically, individuals choose leisure and work so ha he price of leisure real wages is equal o he marginal rae of subsiuion beween work (which provides more consumpion) and leisure: w p = c + n, (A3) where w is wages, p he price level, n hours worked and ϕ (he inverse of) he elasiciy of he number of hours worked wih regard o changes in real wages he Frisch elasiciy. 7 See Gali (2008), chapers 2 and 5. 8 In a model wihou capial, he (non-logarihmic) producion funcion is Y = A Z N, in which A is a echnological process wih a consan rend, Z is a echnological process wih a growing rend and N is hours worked. As GDP has a growing rend bu hours worked are consan in he long run, we rewrie he producion funcion in erms of efficiency unis as Y / Z = A N. 9 In a sandard model, he (non-logarihmic) Euler equaion (compare wih (7) in Gali) is given by σ σ ( C ) = βe [( C+ ) R ] where C is aggregae consumpion, β households subjecive discoun facor and R he σ σ real ineres rae. As consumpion grows over ime, we rewrie his as ( C / Z ) = βe [( C+ / Z+ * Z+ / Z ) R ]. We allow he discoun facor o be ime-varying and le ρ = log β. 23

18 Capial is ignored in he model, and oupu y is hen given by: y = a + n, (A4) where a is a emporary oupu shock. Firms maximise heir profis, and se prices and deermine employmen so ha labour coss he real wage are he same as workers marginal produc: w p = a n, (A5) In addiion, he economy is open and he model hus includes foreign rade. Aggregae consumpion hen consiss of goods produced boh in he counry and abroad. In he model, households also have he possibiliy of invesing in domesic and foreign bonds. In normal New Keynesian models, individuals choice of foreign and domesic asses gives an ineres rae pariy condiion in erms of nominal exchange raes and ineres raes. As we are analysing a model wih flexible prices and wages, we insead obain an ineres rae pariy condiion in erms of he relaionship beween changes in he real exchange rae q, he real ineres rae differenial beween Sweden and he res of he world, and a risk premium ha depends on he ne asse posiion b owards he res of he world: * * b ( r ρ ) ( r ρ ) + ε b, Eq q = (A6) + * where r is he real ineres rae abroad and ε b describes he sensiiviy of he real exchange rae o changes in he ne asse posiion. 20 The ne asses depend on yeserday s ne asse posiion and ne expors x : κb b + x, = where κ is a consan. In urn, ne expors depend on gross expors which closely follow * foreign GDP, y, and gross impors which are deermined by domesic consumpion and he real exchange rae: * x = y + ( ) q c, (A7) where α is he share of impors and η is he degree of subsiuabiliy beween domesically produced goods and impored goods. The resource consrain of he economy is given by * ( )( g) c + ( g) y + ( g) + q g g y = +, (A8) 20 In he model, we use he Euler equaions a home and abroad so ha (A6) becomes * * b E q q ( E c c ) ( E y y ) + b. + =

19 where g is governmen spending, γ is elasiciy beween impored goods and g is he average share of governmen spending ou of GDP. The model hen consiss of he equaions (A2)-(A8). The wo produciviy shocks follow he processes: z z = ρ z + η, z a = ρ a a a + η, z a where ρ z and ρ a are he degree of persisence in he shocks and η and η are innovaions. Foreign GDP, governmen spending and individual s subjecive ime preference follow he processes: y g * = = = y g y g * y g,,, y g ρ where ρ y, ρ g and ρ ρ are he degree of persisence in he shocks and, η, η and η are innovaions. When calculaing he effecs of he differen shocks, we se he ineremporal subsiuion elasiciy /σ o (in he case of produciviy shocks) or 0.3 (in oher cases), labour supply elasiciy /σ o and he impor share α o 0.4, elasiciy beween impored goods γ o and he proporion of governmen spending g o 0.2. In addiion, we se he risk premium parameer ε b o 0.0, he degree of subsiuabiliy beween domesically-produced goods and impored goods η o 4 and κ o (in he case of produciviy shocks) or (in he oher cases). We se he persisence parameers in boh produciviy shock processes o ρ = 0, 8 and ρ = 0, 7. We also deermine he long-erm growh rae and a z households ime preference so ha he real equilibrium ineres rae is wo per cen over he long erm. The persisence parameer in he shock processes o foreign GDP is 0.86, in governmen spending 0.9 and in individuals subjecive ime preference