Inflation and relative-price changes in the Swedish economy

Transcription

1 Inflaion and relaive-price changes in he Swedish economy BY BENGT ASSARSSON Beng Assarsson works in he Moneary Policy Deparmen, Sveriges Riksbank, and in he Deparmen of Economics, Uppsala Universiy. Shocks o diverse markes generae changes in relaive prices some nominal prices rise, ohers fall. If all prices were perfecly flexible, such price movemens would largely cancel ou and leave inflaion unaffeced. In pracice, however, cerain prices end o be sicky because price adjusmens are cosly. In such cases, prices are adjused quickly only in he even of large shocks, no when he shocks are small. The posiively skewed disribuion of relaive-price changes hen resuls in a emporary increase in inflaion. This has been he case in Sweden and explains a large par of he shor-run flucuaions in CPI inflaion over he pas quarer-cenury. The variance and skewness of relaive-price changes also explain shorcomings in exising models of inflaion. I am graeful for commens on an earlier version from Per Jansson, Magnus Jonsson and Saffan Vioi, as well as for daa provided by Micke Andersson, Måren Löf and Josef Svensson. Rigidiies in connecion wih major and minor shocks A familiar phenomenon in he analysis of price-seing and inflaion is he sizeable rigidiies ha occur in price adjusmens and he marked differences in his respec beween firms. Due o hese rigidiies, various marke condiions may change wihou leading o he price adjusmen ha should normally occur. A basic explanaion for hese rigidiies is ha he coss associaed wih alering prices may make i more profiable o absain from or pospone an adjusmen. The cos of price adjusmen makes a price change more probable if he marke shock is large han if i is small. If a few large shocks ha moivae relaive-price increases are counered by numerous small shocks ha call for relaive-price reducions, i may be mainly he increases ha acually occur as nominal-price adjusmens. Such a posiively skewed disribuion of relaive-price changes implies increased inflaion, while a disribuion ha is negaively skewed lowers inflaion. When his heory was pu forward and esed in he mid ECONOMIC REVIEW 3/

2 I es wheher he variance and skewness in he disribuion of relaive-price changes can improve radiional models of inflaion. 1990s, i provided a beer explanaion of inflaion s hisorical pah in he Unied Saes 1. In his aricle I describe he heory and apply i o daa for he Swedish economy for he period The aim is o sudy wheher he variance and skewness in he disribuion of relaive-price changes can improve radiional models of inflaion. For his purpose I exend radiional price equaions or Phillips curves o include hese new measures and examine he effecs. I also use he daa on variance and skewness in an aemp o explain residuals or forecasing errors, ha is, unexplained inflaion, in oher models of inflaion. The empirical resuls show ha variance and skewness in relaiveprice changes make an imporan conribuion o he explanaion of he developmen of inflaion in Sweden during he period analysed here. The new measures improve convenional price equaions and indicae ha several models which have been used in he pas are probably misspecified. Relaive-price changes and inflaion The larger he shock, he greaer he probabiliy of a nominal-price change. If a shock (for example, a supply shock) occurs in a marke and generaes an increase in supply relaive o demand, he relaive price will end o fall and an equilibrium wih a lower price will be esablished. If no shocks occur in oher markes and here are no price rigidiies, he nominal price will hen fall as well. Bu if he price is nominally rigid because an adjusmen enails a cos for he firm, he shock will no necessarily lead o a nominal price fall; ha will depend on wheher or no he benefi of a lower price of moving owards he opimal price exceeds he cos of adjusing he price. The larger he shock, he greaer he probabiliy of a price adjusmen. The full range of relaive shocks includes a number of large posiive and large negaive shocks ha resul in a lower and a higher price, respecively, as well as numerous small shocks ha do no generae price adjusmens because in hese cases he benefi of a price adjusmen does no ouweigh is cos. Figure 1 presens a symmeric disribuion of relaive shocks ha is mached by he disribuion of firms desired relaive-price changes. The shaded segmens of he disribuion represen he shocks which are so large ha hey lead o price adjusmens. These segmens can be called acion ranges. The unshaded segmen conains he shocks in he disribuion ha do no generae any price changes; his can be called he range 1 See Ball & Mankiw (1994, 1995). 44 ECONOMIC REVIEW 3/2004

3 of inacion. Noe ha he mean value of he relaive shocks is (by definiion) zero. 2 Figure 1. A symmeric disribuion of relaive shocks Range of inacion If he disribuion is symmeric, as in Figure 1, here are equal numbers of large posiive and large negaive shocks. Tha is no he case in Figure 2, where he disribuion is posiively skewed. This means ha he unusually large posiive shocks ounumber he unusually large negaive shocks in he acion ranges. The posiive skewness herefore leads o an increased rae of inflaion. A negaive skewness, as in Figure 3, has he opposie effec. A posiively skewed disribuion means ha he unusually large posiive shocks ounumber he unusually large negaive shocks, which can lead o an increased rae of inflaion. Figure 2. A posiively skewed disribuion of relaive shocks Range of inacion Figure 3. A negaively skewed disribuion of relaive shocks Range of inacion 2 See he appendix, where inflaion as well as he variance and skewness in relaive-price changes are defined. ECONOMIC REVIEW 3/

4 The posiive relaionship beween he skewness of relaive-price changes and inflaion is due o price rigidiies. Over a longer period, skewness has been found o be posiive in a number of counries. If he disribuion is skewed o he righ, an increased variance will magnify he posiive skewness and lead o a furher increase in inflaion. The disribuion of relaive shocks also represens firms desired relaive-price changes, which are no observable. Due o he cos of adjusing prices, he corresponding nominal-price changes will no all occur immediaely. Using daa simulaions, Ball & Mankiw found a clear correlaion beween desired and acual relaive-price changes, which means ha he skewness of observed, acual relaive-price changes can be used in he empirical analysis. 3 The posiive relaionship beween he skewness of relaive-price changes and inflaion is due o price rigidiies whereby price adjusmen o shocks is no complee in he shor run. In ime, however, he price adjusmens will be made even if he shocks are small, making i reasonable o suppose ha in he nex period he skewness will affec inflaion negaively insead of posiively. So in a dynamic economeric model here should be a negaive correlaion beween inflaion and he lagged skewness. Over a longer period, skewness has been found o be posiive in a number of counries. Trend inflaion can accoun for his, ha is, inflaion being posiive in he long run. Relaive-price reducions can hen be achieved by keeping he nominal-price consan. This can be seen as a range of acion o he lef in he disribuion (he negaive ail) ha is smaller han he range of acion o he righ (he posiive ail). I can be menioned ha he observed relaionship beween skewness and inflaion also has some alernaive explanaions ha are no necessarily based on price rigidiies. 4 Variance is a measure of he dispersion in a disribuion. Variance and skewness can co-vary and affec inflaion. 5 Figure 4 illusraes his: wih he symmeric disribuion in he upper figure, an increased variance exends he wo ails equally; if he disribuion is skewed o he righ as in he lower figure on he oher hand, an increased variance magnifies he posiive skewness and hereby leads o a furher increase in inflaion. 3 See Ball & Mankiw (1995), where he disribuion of price-adjusmen coss was assumed o follow he exponenial disribuion and he disribuion of relaive shocks/desired price changes follows a normal disribuion wih skewness/symmery. The assumpions were chosen so ha he maximum deviaion beween desired and acual prices was 15 per cen. An inacion range of 15 per cen is consisen wih empirical sudies on he frequency of price adjusmens: Apel, Friberg & Hallsen (2001), Assarsson (1989) and Blinder (1991). Ball & Mankiw s simulaions demonsraed a monoonic posiive relaionship beween he desired and he acual price changes. 4 Produciviy shocks can generae a posiive relaionship beween skewness and inflaion in some models: Aukrus (1970) and Balke & Wynne (1996). The business cycle can influence inflaion and skewness in he same direcion, see Assarsson (2003). The relaionship may also have a purely saisical explanaion, see Ball & Mankiw (1999), Bryan & Cecchei (1999a) and Bryan & Cecchei (1999b). 5 See Ball & Mankiw (1995). 46 ECONOMIC REVIEW 3/2004

5 Figure 4. Relaionship beween variance and skewness in he disribuion of relaive shocks Range of inacion Range of inacion The posiive relaionship beween inflaion and he variance in relaiveprice changes has been horoughly explored in he lieraure. The causal relaionship goes from variance o inflaion according o some heories and in he opposie direcion or hrough a hird variable according o oher heories. 6 Phillips-curves wih measures of variance and skewness Le us now see how he insighs acquired so far can be incorporaed in wha is oherwise a radiional economeric analysis of price-seing and inflaion. In a marke wih perfec compeiion, a firm is no in a posiion o se he price, which canno deviae from he esablished marke price. In a marke wih limied compeiion, a firm can chose a cerain price and observe how i influences demand and hereby he firm s profi. The less compeiion here is, he higher will be he price ha is se in he marke. In his way, a price ha is opimal for he firm in relaion o demand and he compeiion is esablished and applies for he long run provided marke condiions do no change. A price ha is opimal for he firm in relaion o demand and he compeiion is esablished for he long run. 6 Inflaion affecs he variance in relaive-price changes in Assarsson (1986), Cukierman (1979), Cukierman (1982), Cukierman (1983), Cukierman & Wachel (1982), Lucas (1973), Parks (1978) and Sheshinski & Weiss (1977). The variance in relaive-price changes affecs inflaion due o asymmeric price adjusmen in Tobin (1972). ECONOMIC REVIEW 3/

6 The cos of changing he price may cause he firm o refrain from an adjusmen despie a change in he marginal cos. The opimal price depends on he firm s marginal cos. Coss are deermined by inpu prices on for insance raw maerials, energy, wages and capial coss or rens. Coss are also relaed, of course, o he volume of oupu. The marginal cos (he cos of producing an addiional uni) normally depends on he same facors. 7 The cos of changing he price may cause he firm o refrain from a price adjusmen despie a change in he marginal cos. Bu how can his be aken ino accoun when explaining he pah of inflaion in price equaions or Phillips curves? Doing so has proved difficul in pracice. When a price adjusmen is being considered on accoun of increased coss, he firm looks ahead and ries o assess wha he marginal cos is likely o be in he fuure. If he cos increase is expeced o persis, he price evenually will be raised more or less immediaely. However, such forward-looking price equaions (Keynesian Phillips curves) have proved difficul o handle empirically, 8 parly because he expeced fuure marginal coss are no observable. Insead I shall es Ball & Mankiw s heory abou he effec of variance and skewness in relaive-price changes o explain he pah of inflaion in Sweden. To his end, a number of alernaive Phillips curves ha include measures of variance and skewness are specified. In order o avoid unduly narrow specificaions, I have chosen o presen he resuls wih a model ha is so general ha several alernaive specificaions can be derived as special cases. The calculaions show ha he effecs of he measures of variance and skewness are robus for alernaive specificaions. The general model is: π = β 0 + β 1 w + β 2 ρ + β 3 π 1 + β 4 (U U ) + β 5 p oil + β 6 p meals + β 7 p food(a) + β 8 pfood(b) + β 9 g where inflaion is dependen on wage changes w, capial coss ρ, lagged inflaion 9 π 1, he oupu or unemploymen gap U U (where U is equilibrium unemploymen) and supply or price shocks, which are price changes for oil (π oil ), meals (π meals ), food producs from indusrialised counries, (π food(a) ) and food producs from developing counries (π food(b) ). g is a produciviy shock measured as a Solow residual. 10 β i are parameers o be esimaed. 7 A mahemaical descripion is given in he appendix o his aricle. 8 See Bårdsen, Jansen & Nymoen (2002). 9 Price inflaion is dependen on wage inflaion, which depends in urn on expeced inflaion. I follows ha inflaion in period -1 can mirror wage inflaion in period. 10 Inflaion and he skewness in relaive-price changes can boh be driven by produciviy shocks; Balke & Wynne (2000). By including produciviy changes, one can obain some indicaion of how hey affec he equaion compared wih he skewness measure. 48 ECONOMIC REVIEW 3/2004

7 This equaion is hen augmened wih measures of variance and skewness (VS in he following): β 10 σ 3 + β 11 σ β 12 σ 2 + β 13 σ 3 σ 2 which are hus inended o cach he effecs of skewness, lagged skewness, variance and he ineracion of variance and skewness. In accordance wih he heory above, he coefficiens are expeced o have he following signs: β 10 > 0, β 11 < 0, σ 2 > 0,β 13 > 0. Various special cases of Phillips curves can be derived as resricions on he parameers and he effecs of he VS measures can be sudied on each of he curves. For example, he resricions (β 0, β 1, β 2, β 9, β 10, β 11, β 12, β 13 )= 0and β 3 = 1 lead o he Phillips curve π = π 1 + β 4 (U U ) + price shocks which can be given a microeconomic foundaion in erms of unsynchronised labour marke conracs. 11 One way of assessing he VS measures abiliy o explain inflaion s hisorical pah is o analyse wheher hese measures can explain forecasing errors (residuals) generaed by inflaion models ha are used in pracice. I have herefore generaed or obained residuals from some models: an unresriced vecor auoregression (VAR) for shor-run inflaion wih he variables CPI, wage coss, capial coss, produciviy, impor prices, GDP and he ineres rae A Bayesian VAR model ha is one of he models used in he Riksbank 12 and is a Bayesian varian of he so-called FOA-VAR model 13 acual residuals from predicions by he Naional Insiue of Economic Research 14 One way of assessing he VS measures abiliy o explain inflaion s hisorical pah is o analyse wheher hese measures can explain forecasing errors generaed by inflaion models. If he models are specified correcly, here should be no paerns in he residuals obained wih hem. Thus, in a regression wih he residuals as dependen variable, no independen variables should be significan and R 2 should be low. I aemp o explain he residuals wih he VS variables. Significance and high R 2 sugges ha i is jus hese variables which are lacking in he models from which he residuals come. 11 See Taylor (1980). 12 See Andersson (2004); hese residuals were provided by Michael K. Andersson. 13 See Jacobson e al. (1999, 2001). 14 Forecasing errors provided by Måren Löf. ECONOMIC REVIEW 3/

8 Inflaion Skewness conribued o he high rae of inflaion ; afer ha he conribuion from skewness decreased and lowered he rae of inflaion in he lae 1990s. Ball & Mankiw (1995) sudied he effecs on price equaions for American producer prices in he period on an annual basis, ha is, for a oal of 41 observaions. As he analysis concerns price sickiness in he shor run, i is perhaps more appropriae o use more frequen daa. I herefore chose quarerly daa based on a decomposiion of he CPI ino 71 iems for he period Figure 5 illusraes he skewness in he relaive-price changes. Price changes are measured as he logarihmic difference beween quarers. 16 A smoohed measure (using an HP filer) is also shown in he figure. 17 An upward endency can be noed in he second half of he 1980s. In he period , when Sweden had adoped he policy of inflaion argeing, skewness decreased. So according o he heory, skewness conribued o he high rae of inflaion ; afer ha he conribuion from skewness decreased and lowered he rae of inflaion in he lae 1990s Figure 5. Skewness in relaive-price changes Per cen , Skewness in relaive-price changes Skewness smoohed wih an HP filer Noe. Skewness is defined in he Appendix o his aricle. Source: Saisics Sweden, consumer price index. 15 Analyses a Uppsala Universiy show ha a furher decomposiion ino up o abou 350 represenaive goods gives similar resuls; Peersson & Wiksröm (2004). 16 The logarihmic difference muliplied by 100 approximaes he percenage change. 17 The HP filer is a mehod for calculaing he rend in a ime series, see Hodrick & Presco (1997). The smoohing was done simply o give a beer illusraion of developmens in he period sudied here. The smoohed series was no used in he regressions. 50 ECONOMIC REVIEW 3/2004

9 Can he VS variables explain inflaion? The economeric calculaions were done o analyse he exen o which he skewness and variance in relaive-price changes can explain he pah of inflaion. They can also be used o sudy wheher he effecs are hose he heory predics. Sweden abandoned he fixed exchange rae in November 1992 and hen moved successively o an inflaion-argeing moneary policy. Nominal prices are probably sickier when inflaion is low han when i is high, since wih low inflaion, price adjusmens are less beneficial (shocks bring he prices closer o he opimal levels). I herefore esed wheher he equaions changed beween hese wo periods. Column (i) in Table 1 presens resuls of esimaions based on he general equaion, which includes inpu prices, unemploymen, some dummy variables for exreme values and he VS variables in accordance wih he heory. 18 The oher columns conain he resuls wih differen specificaions, ha is, excluding in urn inpu prices (ii), unemploymen (iii), price shocks and produciviy changes (iv) and he VS measures (v). The firs hing o noe is he posiive correlaion beween inflaion and skewness and he negaive sign of he lagged effec, which agrees wih he heoreical predicions. 19 The posiive effec of variance on inflaion is also in line wih he heory, whereas he negaive effec of he ineracion of variance and skewness is no. However, his effec is only saisically significan in specificaion (ii) in Table 1. In specificaions (ii) (v) he exclusion of differen variables reduces he general model and one can see how his affecs he correlaion coefficien R 2 or he sandard error 20 in he equaion. Tha provides an indicaion of each variable s imporance in explaining he variaion in he rae of inflaion. The resuls show ha he disribuional measures are mos imporan. The difference beween he observed rae of inflaion and he rae prediced by he model averages ±0.50 per cen (he sandard error in he regression) bu grows o ±0.76 per cen when he VS variables are excluded. When inpu prices, unemploymen and price shocks ogeher wih produciviy shocks, respecively, are excluded, he sandard error grows considerably less, o around 0.56 per cen in each case. Thus, he VS variables are he mos imporan facors for explaining he variaion in he rae of inflaion. The VS variables are he mos imporan facors for explaining he variaion in he rae of inflaion. 18 Since variables are in difference form, he long-erm price level may no be deermined in a reasonable manner in he equaion. However, he resuls are qualiaively he same when he equaion is esimaed insead in error-correcion form. The level erm in such an equaion comes ou in accordance wih he heory bu is no saisically significan. 19 This coefficien was falsely negaive for American daa, see Ball & Mankiw (1995). 20 R 2 and he sandard error in he regression are explained in he appendix o his aricle. ECONOMIC REVIEW 3/

10 The errors in he regression wihou he VS variables for he period wih low inflaion are almos as large as for he highinflaion period wih he VS variables included. The changeover o argeing inflaion has alered inflaion s characerisics. The VS measures make a major conribuion o he explanaion of inflaion s hisorical pah and here is a considerable risk ha inflaion equaions which do no include hese variables are incorrecly specified. I have also esimaed he equaion wih he bes economeric fi he general equaion (i) including he VS variables separaely for wo periods: when inflaion was no argeed and wih inflaion-argeing. The resuls are presened in Table 2. A Chow es (which compares he sum of he residuals in he oal sample wih he sum in each sub-sample) shows ha he model is significanly differen in he wo periods; i will also be seen ha cerain parameers differ markedly beween he wo periods. The lower and less variable rae of inflaion in he more recen period is eviden in a sandard error in he equaion of only 0.34 per cen compared wih 0.54 per cen for he period when inflaion was no argeed. In he model wihou he VS variables he sandard error for he more recen period is 0.48 per cen. This warrans he conclusion ha on average, he error in he regression wihou he VS variables for he period wih low inflaion will be almos as large as for he high-inflaion period wih he VS variables included. A comparison of he equaions during he wo sub-periods in Table 2 reveals some ineresing differences. The effec of he VS variables is marked in boh periods bu relaively larger in he earlier one. The effecs of he cos variables also differ and seem o be larger in he laer period. All in all, he comparison suggess ha i is pruden no o calculae parameers based on he enire period and ha he characerisics of inflaion have been alered by he changeover o argeing inflaion. The higher coefficien for lagged inflaion in he laer period may be a sign ha inflaion expecaions and he focus on he inflaion arge have srenghened he role of price expecaions a he expense of oher variables. Table 3 shows wheher he VS measures can explain he residual series for inflaion ha were obained from calculaions wih alernaive inflaion models. In regression analyses a baery of ess is commonly used o deermine wheher or no he residual series are enirely random. In he analyses wih he VAR model I used ess for auocorrelaion and heeroscedasiciy. Boh ess indicaed ha he residual series for inflaion was random. Even so, in Table 3 all he VS measures are saisically significan and explain 37 per cen of he variaion in he residuals. Tha is a srong indicaion of errors in he specificaion of he VAR model. As Table 3 shows, an analysis of he residuals from he Bayesian VAR model gives much he same resul: he VS variables explain 35 per cen of he variaion in he residuals. The VAR models are esimaed wih quarerly daa and evaluaed wih quarerly changes. I have also sudied he characerisics of residuals from inflaion predicions by he Naional Insiue of Economic Research using monhly daa for he period ; he predicions, which are hose wih he mos recen informaion (ofen he monh before he forecas monh), are for annual changes and he VS 52 ECONOMIC REVIEW 3/2004

11 TABLE 1. RESULTS OF ECONOMETRIC ESTIMATIONS WITH VARIANTS OF PHILLIPS CURVES Dependen variable: CPI inflaion (π ) Period: Q Q No. of observaions: 94 No. of price indexes: 71 Columns: (i) general equaion, (ii) equaion wihou cos variables, (iii) equaion wihou unemploymen gap, (iv) equaion wihou price shocks and produciviy variable, (v) equaion wihou variance and skewness variables Variable Coefficien (p) (i) (ii) (iii) (iv) (v) Consan (0.0002) (0.0000) (0.0024) (0.7318) (0.0145) ULC (0.0022) (0.0000) (0.0012) (0.6363) ρ (0.0621) (0.0246) (0.0201) (0.0390) π (0.0032) (0.0000) (0.0002) (0.1649) U U (0.0001) (0.0000) (0.0017) (0.0000) π oil (0.0557) (0.2943) (0.0258) (0.5806) π meals (0.7849) (0.6033) (0.8462) (0.3291) π food(a) (0.4755) (0.4271) (0.4661) (0.5778) π food(b) (0.0156) (0.0160) (0.0866) (0.0196) σ (0.0002) (0.0000) (0.0058) (0.0001) σ (0.0230) (0.2989) (0.0011) (0.0150) σ (0.0000) (0.0000) (0.0000) (0.0000) σ 3 σ (0.2188) (0.0316) (0.7276) (0.1145) g (0.0001) (0.0000) (0.0036) (0.0060) DUMMY Q (0.0022) (0.0003) (0.0107) (0.0022) (0.0123) DUMMY Q (0.0000) (0.0019) (0.0000) (0.0003) (0.5611) DUMMY Q (0.0024) (0.0028) (0.0059) (0.0447) (0.3248) DUMMY Q (0.0018) (0.0102) (0.0064) (0.0034) (0.3676) R Sandard error in regression Mean: dependen variable Sandard deviaion: dependen variable R 2 is a muliple correlaion coefficien ha indicaes he proporion of he variance in inflaion ha is explained in he equaion. The sandard error in he regression is he square roo of he sum of he squared residuals divided by he number of observaions. The able also shows inflaion s mean value and sandard deviaion for he period covered by he daa. The dummy variables = 1 during he indicaed period, oherwise 0. ECONOMIC REVIEW 3/

12 TABLE 2. GENERAL EQUATION ESTIMATED FOR PERIODS BEFORE AND WITH THE INFLATION TARGET. Dependen variable: CPI inflaion: π Period: Q o Q subdivided ino and No. of observaions: 94, of which 54 and 40, respecively, in he sub-periods No. of price indexes: 71 Variable Coefficien (p) 1980:3 1993:3 1994:1 2003:4 Consan (0.0550) (0.9638) ULC (0.0799) (0.0031) ρ (0.1201) (0.4997) π (0.0313) (0.0432) U U (0.0022) (0.7499) π oil (0.1726) (0.1875) π meals (0.6817) (0.0349) π food(a) (0.7085) (0.1214) π food(b) (0.0046) (0.8248) σ (0.0019) (0.0163) σ (0.1741) (0.0010) σ (0.0000) (0.0131) σ 3 σ (0.0572) (0.1873) g (0.0527) (0.9582) DUMMY Q (0.0025) DUMMY Q (0.521) DUMMY Q (0.0424) DUMMY Q (0.0028) R Sandard error in regression Mean: dependen variable Sandard deviaion: dependen variable ECONOMIC REVIEW 3/2004

13 measures have been calculaed correspondingly. The resuls are somewha weaker bu here, oo, he VS variables explain an appreciable par of he variance in he forecas errors. From his I conclude ha he VS measures make a major conribuion o explaining inflaion s hisorical pah and ha wihou hese variables here is probably a large risk of inflaion equaions being incorrecly specified. TABLE 3. REGRESSIONS WITH MODEL RESIDUALS Variable Model ε AS DEPENDENT VARIABLE VAR Bayesian VAR N. I. Economic Research Coefficien (p) Quarerly Quarerly Monhly Consan (0.000) (0.000) (0.001) ε (0.908) (0.292) (0.281) σ (0.000) (0.000) (0.062) σ (0.009) (0.017) (0.188) σ (0.000) (0.000) (0.002) σ 3 σ (0.003) (0.007) (0.474) R ,292 Noe: Quarerly changes have been used for he VAR models, 12-monh changes for he forecass from he Naional Insiue. Moneary policy is forward-looking Moneary policy in Sweden is based on a 2 per cen inflaion arge wih a olerance inerval of ±1 percenage poin. The moneary ransmission mechanism he ime lag before he policy is effecive calls for a forwardlooking perspecive in which policy reacs o predicions of inflaion abou wo years ahead. As nominal price rigidiies play a decisive par in he ransmission mechanism, i is imporan o capure hem in specificaions of price equaions and Phillips curves. Producer as well as consumer prices are evidenly sicky in a number of secors bu he par played by hese rigidiies in economic policy is less clear. Inerview sudies show ha here may be rigidiies in a number of secors whereby full price adjusmen o shocks can ake several years. Economeric sudies wih ime-series daa have yielded similar findings. In he absence of reliable mehods for incorporaing hese varying rigidiies in macroeconomic models, he inclusion of VS measures in price equaions seems o be a promising approach, parly because he hisorical pah is hen explained more saisfacorily. Nominal price rigidiies seem imporan and i is urgen o capure hem in specificaions of price equaions and Phillips curves. Full price adjusmen o shocks can ake several years. ECONOMIC REVIEW 3/

14 Agains he VS variables i migh be argued ha i is difficul or even impossible o predic variance and skewness bu such an argumen is fauly for several reasons. Moneary policy s perspecive is forward-looking, however, and calls for reliable predicions of inflaion abou wo years ahead. A model ha explains hisory successfully will no necessarily provide good forecass, jus as models ha are bad a explaining hisory may yield good forecass. Agains including he VS variables in price equaions i migh be argued ha i is difficul or even impossible o predic he fuure developmen of variance and skewness bu such an argumen is fauly for several reasons. For one hing, excluding he VS variables means acceping a fauly specificaion of he price equaions. Tha leads o erroneous esimaes of he effecs of oher variables in he price equaions, which can resul in urn in poorer inflaion forecass. 21 For anoher hing, he VS variables are presumably no very much more difficul o predic han many oher variables in macroeconomic models. Are he VS variables harder o predic han, for insance, asse prices, which are needed o forecas household consumpion expendiure or corporae invesmen? Moreover, he longerm equilibrium level of skewness is unusually simple o predic in ha in heory as well as empirically i is virually zero. 22 Inflaion in Sweden was overesimaed by mos forecasers in he period Migh he reason be ha he variance and skewness in he disribuion of relaive-price changes were no aken ino accoun, so ha he forecass failed o cach shor-run rigidiies in price-seing? Unusually high skewness in he period had an upward effec on he rae of inflaion (see Figure 5) bu in he period skewness decreased successively and may hus have helped o explain he fall in inflaion in hose years. 21 Compare he coefficiens in equaions (i) and (v) in Table 1. A wage change has a shor-run elasiciy of 0.2 in he model wih he higher momens as agains abou 0 in he incorrecly specified model wihou VS variables. 22 Experimens wih he basic macroeconomic model BASMOD (one of he models ha are used for forecasing a he Riksbank) have shown ha including he higher momens ends o improve forecass of inflaion and GDP growh. Those forecass were made wih a simple ARMA(1,1) ime-series model. When he above equaion is esimaed up o he end of 2001 in order o predic he pas hree years and he acual variance and skewness measures are used for hese hree years, he forecasing errors are only a hird of hose ha occur wihou variance and skewness measures. Work is in progress on improving and evaluaing inflaion forecass ha use he variance and skewness variables. 23 See Blix, Friberg & Åkerlind (2002). 56 ECONOMIC REVIEW 3/2004

15 Conclusions To sum up, i seems ha including he variance and skewness in he disribuion of relaive-price changes can appreciably improve he esimaion of Phillips curves for he Swedish economy. This can be seen as a way of caching price-seing differences beween firms in a few aggregaed index numbers. These indexes appear o mirror he fac ha for cerain firms, unusually large shocks are needed o induce a quick price adjusmen. I also looks as hough inflaion forecass can be improved wih he aid of hese variables, hough furher evaluaions are needed. Time series wih skewness are highly volaile (see Figure 1). Furher improvemens o analyses of his ype could presumably be achieved by using robus measures (excluding exreme observaions) of variance and skewness. 24 Improving inflaion forecass wih he aid of VS variables seems o be possible, hough furher evaluaions are needed. 24 Such measures have been used by Aucremanne e al. (2003). ECONOMIC REVIEW 3/

16 Appendix DEFINITIONS Measures used in he calculaions are defined below; hey apply o a decomposiion of he CPI ino 71 indexed iems. Inflaion: π = Σ 71 w logp i i i=1 w i = p i q i Σ j p j q j is he budge share for good i in period, p i is he price, q i is he volume and is he difference operaor. Variance in relaive-price changes: σ 2 = Σ71 i=1 w i ( logp i π )2 Skewness in relaive-price changes: σ 3 = Σ71 i=1 w i ( logp i π )3 σ 2 0 R 2 1 is he muliple correlaion coefficien, which measures how much of he variance in he dependen variable (in his case: inflaion) ha is explained in he model (by he independen variables). 1 The sandard error in he regression is measured as where n 1 Σn ε i=1 i 2 ε = π π^ is he residual (unexpeced inflaion) in he inflaion equaion. I is a measure of he average error, aking ino accoun ha residuals are boh posiive and negaive. THE FIRM S OPTIMAL PRICE The firm s equilibrium condiion is ha mr = mc, ha is, ha he marginal revenue equals he marginal cos. This condiion can be rewrien as: p = [ 1 H ε ] 1 mc where p is he firm s price, ε = δq p is he price elasiciy of demand and H δp q is an index for he degree of compeiion (0=perfec compeiion, 1=monopoly).The marginal cos is derived from a cos funcion wih inpu prices and he volume of producion as argumens. Noe ha i is only in a special case of he cos funcion ha he specificaion will include he oupu gap, ha is, he difference beween acual and poenial oupu. 25 The opimal price would always apply if price-seing did no enail a cos for he firm. 25 See Sbordone (2002). 58 ECONOMIC REVIEW 3/2004

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