The Effect of a Discount Rate on Price Change Behavior: An Empirical Analysis. Robert Stretcher 1. and. Hiranya K Nath 2. February 2004 (Preliminary)

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1 The Effec of a Discoun Rae on Price Change Behavior: An Empirical Analysis Rober Srecher and Hiranya K Nah February 4 (Preliminary) Absrac: This paper examines if here is any empirical evidence o suppor he resuls of a muli-period general equilibrium exension of Mankiw s menu cos model (Nah and Srecher, 3) ha indicae ha wih high discoun raes firms will be less likely o change prices in response o a moneary shock. Using he level of medium erm real ineres raes as a proxy for he discoun rae and producer price indices for fifeen major commodiy groups we examine how ineres raes affec firms decisions o change prices. Impulse responses calculaed from a simple mulivariae VAR model of producer prices and real ineres rae sugges ha excep for a few commodiy groups, namely farm producs, processed foods and feeds, fuels, relaed producs and power and lumber and wood producs, a higher ineres rae seems o persuade mos firms in he oher commodiy groups no o change prices. Keywords: Discoun rae; Menu cos; Mulivariae VAR; Impulse response JEL Classificaion: E3; E3 Deparmen of General Business and Finance, Sam Houson Sae Universiy, Hunsville, TX ; Phone: ; rsrecher@shsu.edu Deparmen of Economics and Inernaional Business, Sam Houson Sae Universiy, Hunsville, TX ; Phone: ; eco_hkn@shsu.edu

2 . Inroducion I is by now a commonly acceped view among economiss ha nominal rigidiies are he mos ap characerizaion of he shor run behavior of he economy. However, he heories ha have been proposed o explain sluggish adjusmens of prices and wages are varied and numerous. One of he heories ha gained populariy among a secion of economiss in recen years suggess ha firms are required o incur some coss o change prices. These coss are ofen associaed wih prining menus, and herefore referred o as menu coss. According o his menu coss heory, since changing prices is cosly, many firms do no respond immediaely o a shock by changing prices, and as a resul, real variables such as oupu have o bear he brun. Some economiss, however, cas doubs on his explanaion because hese menu coss are evidenly small. Mankiw (99) uses parial as well as general equilibrium models o show ha hese small menu coss are in fac capable of producing large business cycles. Considering monopolisically compeiive firms ha se prices, he argues ha hough menu coss may be small, he incremenal profis ha resul from price changes may be even smaller and, herefore, firms are beer off by no changing prices in response o a demand shock. In Mankiw s model, he decision of he firm depends on a comparison beween one-ime menu coss and he change in single-period profi. Nah and Srecher (3) argue ha if he firms consider changes in heir fuure sream of profis (ha would resul from he decision o change price) hen small menu coss may no be able o dissuade hem from changing prices. This exends he resuls of Srecher (), which presens a parial equilibrium analysis of non-marke clearing firm behavior o

3 show ha inroducion of he opporuniy cos of capial o discoun fuure incremenal profis will reduce he abiliy of small menu coss o generae large business cycles. One of he implicaions of Nah-Srecher exension of Mankiw Model is ha wih a high real ineres rae (a proxy for discoun rae), firms are less likely o change prices and wih a low real ineres rae hey are more likely o change prices for given menu coss. In oher words, small changes in he aggregae price level are associaed wih high ineres rae and large changes are associaed wih low ineres rae. This paper examines if here is any empirical evidence o suppor hese resuls indicaed by a muli-period general equilibrium exension of Mankiw s menu cos model (Nah and Srecher, 3). Using he level of medium erm real ineres raes as a proxy for he discoun rae and producer price indices for fifeen major commodiy groups, we examine how ineres raes affec firms decisions o change prices. Simple correlaion beween he inflaion-adjused medium erm ineres rae and changes in he producer prices indicaes significan negaive or weak relaionship only for a few commodiy groups, and is no very informaive. However, impulse responses calculaed from a simple VAR model of producer prices and real ineres rae sugges ha excep for a few commodiy groups, namely Farm producs, Processed foods and feeds, Fuels, relaed producs and power and Lumber and wood producs, a higher ineres rae seems o persuade mos firms in oher commodiy groups no o change prices. The following consideraions should be aken ino accoun while evaluaing he conribuions of his paper. Firs, here are no reliable daa on menu coss for mos indusries in he economy. There have been only a handful of sudies ha collec and 3

4 analyze menu coss daa for seleced U.S. indusries. Second, i would be more appropriae o use acual price daa raher han price indices. Moreover, he fac ha we use aggregae PPIs (which roughly correspond o -digi SIC indusries) camouflages he underlying price movemens, hus revealing lile abou individual firm s pricing behavior. Las bu no leas, if discoun rae influences firm s pricing behavior via is use in calculaion of presen value of fuure profis, i is difficul o know which discoun raes he firms acually use or if here are wide differences in discoun raes used by differen firms. In spie of hese caveas, his paper is, o our knowledge, a firs aemp in examining he effecs of discoun raes on he pricing behavior of he firms. The fac ha here is some evidence of high ineres raes persuading firms no o change prices also provides furher encouragemen for fuure research. The res of he paper is organized as follows. Secion discusses he heoreical background of he curren empirical invesigaion. In secion 3, we discuss daa and empirical mehodology. Secion 4 presens he resuls, and provides an analysis of he resuls. In secion 5, we include our concluding remarks.. Theoreical Background Nah and Srecher build a general equilibrium model which differs from he one in Mankiw (99) in wo ways: firs, he represenaive consumer maximizes life-ime uiliy ha involves iner-emporal ransfer of resources. Second and more imporanly, he monopolisically compeiive firm bases is decision o change price on a comparison of he menu coss eiher wih he change in single-period profi, or wih he discouned 4

5 presen value of he changes in all fuure profis, depending upon wheher i perceives he aggregae demand shock o be emporary or permanen. In heir model, he represenaive consumer maximizes her lifeime uiliy given by he following funcion: d φ M U = β ( φ) y + θ i, di log L () = P where <β< is he discoun facor, y i, is he quaniy of good i she consumes in period, φ is he reciprocal of he elasiciy of subsiuion beween differen goods produced by he firms and <φ<, d M is her money demand in period, P is he general price level, L is he labor supply, and θ is he money demand parameer (θ>). The general price level P is he geomeric average of all P i, s, where P i, is he nominal price of he good produced by firm i in period, and is given as follows: P = exp log Pi, di () The consumer faces he following budge consrain d Pi, yi,di + B + M = WL + R B + M + Π (3) where W is he nominal wage 3 in period, B is he amoun len in period, R is he ineres rae in period, M is he money supply and Π is he oal profis of he firms. Each firm produces is oupu using labor only, and he echnology is given by he producion funcion: y i, = L i, (4) 3 Since labor is mobile across firms, nominal wage rae is he same in all firms. 5

6 where L i, is he labor inpu used by firm i in period. The firm faces a demand funcion implied by he uiliy maximizaion and he firm chooses y i, and P i, in each period such ha is profi is maximized. The firm is also required o incur a cos o change price, he menu cos as represened by he following funcion: z i, =g (i) W = g (i) M θ (5) The firm s decision o change price depends on a comparison of hese coss wih poenial gains from such a change. Following a moneary shock ha is perceived o be ransiory, φ φ if z i > ( y y ) ( y y )) W, hen firm i does no change is price. Here y and y are profi maximizing levels of oupu of firm i associaed wih wo differen levels of money supply before and afer he moneary shock, and he expression on he righ hand side of he inequaliy represens incremenal profis ha resul from price change. However, if he moneary shock is perceived o be permanen, he decision o change price will depend on a comparison beween z i and discouned presen value of φ φ incremenal profis, [ ( y y ) ( y y )] W ( ) β Nah and Srecher recognize ha he single-period Mankiw model is consisen wih an infinie discoun rae (herefore fuure changes in profi are essenially zero in he presen). Adjusmen of he Mankiw model o include a reasonable (finie) discoun rae resuls in he following conclusion: if he firms perceive he aggregae demand shock o be permanen hey may require no 'small' bu 'relaively large' menu coss o dissuade hem from changing prices. In ha case, heir decision o change prices will depend on a comparison beween one-ime menu coss and discouned presen value of all fuure incremenal profis ha would resul from such price changes. Thus in his empirical. 6

7 invesigaion we will focus on he case in which moneary shocks are perceived o be permanen. 3. Daa and Empirical Approach 3. Daa We use monhly daa on producer price index 4 (PPI hereafer) for 5 major commodiy groups, for a period from January 969 o Ocober. These are -digi commodiy groups covering agriculure, foresry, mining and manufacuring - as defined by he Bureau of Labor Saisics (BLS). The daa have been exraced from he fp sie for Producer Price Index mainained by he BLS. We also use monhly daa on - year ineres rae ineres rae on one-year reasury noes for he same sample period, obained from he Board of Governors, Federal Reserve Sysem. Because we are ineresed in examining he effecs of real and no nominal ineres rae on he price change behavior, we calculae real ineres rae by using he Fisher equaion r = π (6) i e where r is he real ineres rae in period, i is he nominal ineres rae and e π is he expeced inflaion in period. Expeced inflaion rae, π e, is defined as log firs difference in PPI (for all iems) beween period + and. Table presens he summary saisics of price changes and real ineres rae. As we can see from he able, fuels and relaed producs has he larges mean price change 4 Because we are invesigaing he price seing behavior of he firms PPI is more appropriae han CPI or oher price daa. Ideally, we would like o use daa on acual prices and no price indices, as se by he firms. Since i is difficul o find a comprehensive daa se on acual prices we would be conen wih price index. Since price indexes are averages of all underlying prices which may vary in erms of heir sluggish behavior, he following analysis ha uses aggregae price indices will be indicaive raher definiive. 7

8 over he sample period. I is also he mos volaile commodiy group. pulp, paper and allied producs and misc. producs are wo oher caegories ha experience relaively higher average price changes. In erms of volailiy, farm producs are almos as volaile as fuels and relaed producs. Among oher caegories, lumber and wood producs and processed foods and feeds are relaively more volaile han ohers. 3. Empirical Approach As explained above, if he firms make decisions abou changing prices based on a comparison beween menu coss and he discouned presen value of fuure profis hen one would expec a negaive correlaion beween real ineres rae and changes in prices: high real ineres raes will be associaed wih low price changes and low real ineres rae wih high price changes 5. In order o have a very general idea of he naure of he relaionship beween real ineres rae and price changes, we shall firs calculae he correlaion beween π i,, he change in price of commodiy i beween period and -, and r -, he real ineres rae in period -. Moreover, since he objecive is o examine if he levels of real ineres rae affec firm s decision o change price we are no ineresed in he direcion of price changes. Raher we would be more ineresed in he magniudes of price changes. Therefore, we shall also calculae he correlaion beween he absolue value of price changes and one period lagged real ineres rae. However, he correlaion coefficien does no say much abou he dynamics of a relaionship beween wo variables and hus, may conceal imporan informaion abou he effec of ineres raes on he price change behavior. Therefore, we shall resor o a 5 Ideally, high ineres raes will be associaed wih no price change (price change = ) and low ineres raes will be associaed wih some nonzero price change (price change ) if he predicions of he model are o be correc. Since we use price indices which are essenially weighed averages of various prices, i makes more sense o expec relaively low and high price changes in absolue erms. 8

9 more advanced ime series echnique o invesigae he relaionship beween real ineres rae and changes in prices. We shall examine he impulse response funcions derived from a mulivariae vecor auoregression (VAR) model of differen commodiy prices and real ineres rae. Inuiively, as we allow differen prices and he real ineres rae o inerac among hemselves in a mulivariae VAR seing, we can find ou from he impulse responses how sluggish differen commodiy prices are in response o a posiive change in he real ineres rae. We use he following vecor auoregression (VAR) model of commodiy prices and real ineres rae: Y P = Φ iy i i= + ε (7) where: Y is a 6 vecor of 5 PPIs and real ineres rae 6 in period ; Φ i a 6 6 marix of coefficiens of Y a lag i; ε is a 6 vecor of whie noise error erms. Noe ha i indexes he lag lengh and p is he maximum number of lags included in he VAR model. We shall use various informaion crieria (Akaike Informaion Crierion, Schwarze-Bayes Crierion, Hannan-Quinn Informaion Crierion) o selec he appropriae lag lengh. Once we esimae he appropriae model, we use he parameer esimaes o derive he impulse response funcions. In paricular, we are ineresed in he responses of PPIs o a one percenage poin increase in real ineres rae. 6 Because we are no ineresed in he ime series properies of he series a hand and are narrowly focused on how real ineres rae affecs pricing behavior, we are no worried abou he order of inegraion for he daa series we use in he VAR model. As Sims (98), Doan (99) and ohers argue, he goal of VAR analysis is o deermine he inerrelaionships among he variables, no he parameer esimaes. However, Augmened Dickey Fuller ess indicae ha all prices are uni roo processes and herefore, hey need o be differenced for saionariy. 9

10 4. Resuls In Table, we presen he correlaion coefficiens beween price changes and one period lagged real ineres raes for each commodiy group over he sample period. In column, we repor he correlaion coefficiens of one period lagged real ineres rae wih he absolue value of price changes. A comparison beween column and column reveals ha only for processed foods and feeds he correlaion changes from highly saisically significan o highly saisically insignifican. Among ohers, for hides, skins, leaher, and relaed producs and meals and meal producs, he correlaion coefficiens changes from being negaive o being posiive hough in boh cases hey coninue o remain insignifican. Only for farm producs and lumber and wood producs, he correlaion coefficien is significanly negaive. Moreover, for commodiy groups namely, processed foods and feeds, hides, skins, leaher, and relaed producs, fuels and relaed producs and power and meal and meal producs he correlaion coefficiens beween absolue values of price changes and real ineres raes are small and saisically insignifican, indicaing week relaionship. I seems o sugges ha hese prices do no respond o real ineres raes in a sysemaic way. However, i may include cases in which no/small changes in prices are associaed wih large real ineres raes which, in urn, will be evidence in suppor of he predicions of he model. We also presen he scaer plos of he absolue price changes and one period lagged real ineres raes in Figure. Alhough for a few commodiy groups here are some discernible paerns as refleced by he correlaion coefficiens, for mos here are relaively fewer observaions on high real ineres raes being associaed wih low price

11 changes. In mos cases he observaions are concenraed around 5 percen for real ineres rae, and price changes below percen. As discussed in he previous secion, we would like o invesigae he relaionship beween real ineres rae and he price change behavior of he firms from a dynamic poin of view. Therefore, we esimae a VAR of 5 PPIs and real ineres rae. The firs consideraion in a VAR esimaion is o selec he appropriae lag lengh of he endogenous variables. The sandard pracice is o sar wih a reasonably long lag lengh and pare i down o he appropriae lag by looking a various informaion crieria (see Enders (995) for a discussion). Since we use monhly daa, we sar wih lags and calculae Akaike Informaion Crierion (AIC), Schwarze-Bayes Informaion Crierion (SBIC) and Hannan-Quinn Informaion Crierion (HQIC). The values are repored in Table 3. The lag lengh wih he lowes value of he relevan informaion crierion is considered o be he mos appropriae. As we can see from he able, hese crieria selec hree differen lag lenghs: SBIC selecs a lag lengh of ; HQIC selecs and AIC selecs. We esimae wo specificaions of he VAR model: wih lag and wih lag. We hen use he parameer esimaes o derive impulse response funcions for each of he 5 PPIs in response o a change in real ineres raes. We examine he responses of hese prices o a one percen poin increase in real ineres rae, in he period following he change. Inuiively, as he real ineres rae increases he discouned value of all fuure profis will be lower and as a resul i is more likely ha fewer firms will change prices for given menu coss. The absolue values of changes in PPIs in response o a change in real ineres rae derived from he esimaes of boh specificaions of he VAR models are

12 repored in Table 4. As we can see from he able, excep for Farm producs, Processed foods and feeds, Fuels and relaed producs and power and Lumber and wood producs, mos changes are negligible. Tha seems o sugges ha wih higher real ineres raes mos firms in hese commodiy groups (oher han he four menioned above), are less willing o change prices. We also presen he graphs of he impulse response funcions in Figure and Figure 3 derived from he esimaions of he wo specificaions of he VAR model respecively. As we can see from hese figures, excep for he four commodiy groups menioned above, none of he ohers experiences large changes in PPIs over monh ime horizon. For fuels and relaed producs and power and lumber and wood producs, he changes coninue o ge bigger over he monh ime horizon. For farm producs and processed foods and feeds, on he oher hand, he changes sar geing smaller afer a few monhs. One should be exremely careful in inerpreing he resuls. Firs, we have no explicily alked abou aggregae moneary shocks. Nor do we explicily incorporae changes in money supply in our VAR model. Because all firms in he economy are subjec o same moneary shock, excep for is implicaions for relaive price changes in he shor run (which, by he way, may resul from differen degrees of price rigidiies across firms/indusries ha we invesigae here) we do no include he moneary variable in our model. Second, one underlying assumpion of he menu cos model is ha he firms are monopolisically compeiive so ha hey can se prices. However, some firms may have lile or no power o se prices. Accordingly, here may be wide differences in he degree of compeiiveness among he indusry groups. For compeiive indusries he

13 resuls may no be analyzed in he ligh of he predicions of Nah-Srecher model. Moreover, as poined ou by Nah (), in he shor-run, secor-specific facors play a dominan role for changes in prices of mos commodiy groups. Alhough such facors may include price seing behavior of firms wih marke power, hey may also include oher facors. Finally, he relaionship beween price changes and real ineres raes may be characerized by imporan nonlineariy. For example, if ineres rae is already relaively high an increase may be immaerial for price change behavior of he firms. On he oher hand, a a relaively low level of real ineres rae, his may no be he case. The esimaed model in his paper does no make a disincion beween hese wo cases. To capure such nonlineariy, we need a much richer framework. Neverheless, he curren sudy provides a very general idea abou he effec of real ineres rae on he price change behavior - which is indicaive of empirical suppor for he predicions of Nah-Srecher exension of Mankiw model. 5. Conclusion This paper examines if here is any empirical suppor for he resuls of a muliperiod general equilibrium exension of Mankiw s menu cos model (Nah and Srecher, 3) ha indicaes ha wih high discoun raes firms will be less likely o change prices in response o a moneary shock. Using he level of medium erm real ineres raes as a proxy for he discoun rae and producer price indices for fifeen major commodiy groups we examine how ineres raes affec firms decisions o change prices in response o aggregae moneary shocks. However, impulse responses calculaed from a simple VAR model of producer prices and real ineres rae sugges ha excep for a few 3

14 commodiy groups, namely farm producs, processed foods and feeds, fuels, relaed producs and power and lumber and wood producs, a higher ineres rae seems o persuade mos firms in oher commodiy groups no o change prices. Possible exensions of his sudy will include similar analyses using more disaggregaed price daa, possibly acual price daa. Furher knowledge of various discoun raes moniored by differen firms or/indusries will also be useful. 4

15 Table : Summary Saisics of Monhly Price Changes and Real Ineres Rae : January 969 Ocober (Variables are in percenages) Commodiy Groups Mean Farm Producs. (.3) Processed foods.3 and feeds (.7) Texile producs. and apparel (.) Hides, skins,.35 leaher, and relaed producs (.5) Fuels and relaed.54 producs and power (.3) Chemicals and.39 allied producs (.4) Rubber and plasic.8 producs (.3) Lumber and wood.36 producs (.8) Pulp, paper, and.43 allied producs (.3) Meals and meal.35 producs (.4) Machinery and.3 equipmen (.) Furniure and.6 household durables (.) Nonmeallic.38 mineral producs (.3) Transporaion.3 equipmen (.3) Miscellaneous.4 producs (.5) Real ineres rae 6.97 (.4) Noe: Sandard errors are in parenheses. Sandard Deviaion Minimum Maximum

16 Table : Correlaion of monhly price changes wih one period lagged real ineres rae: January 969 Ocober Commodiy Groups Farm Producs Processed foods and feeds Texile producs and apparel Hides, skins, leaher, and relaed producs Fuels and relaed producs and power Chemicals and allied producs Rubber and plasic producs Lumber and wood producs Pulp, paper, and allied producs Meals and meal producs Machinery and equipmen Furniure and household durables Nonmeallic mineral producs Transporaion equipmen Miscellaneous producs Monhly price changes and real ineres rae Absolue value of monhly price changes and real ineres rae () () -.*** (-4.4) -.8*** (-3.6).4*** (.8) -.6 (-.) -.6 (-.8).9* (.74).5*** (.9) -.4*** (-4.7).6*** (3.4) -. (-.7).3*** (6.4).*** (4.6).** (.44).6*** (3.).7 (.35) -.** (-.) -.4 (-.79).7*** (3.4).4 (.68) -. (-.8).** (.5).6*** (3.4) -.9* (-.76).** (.). (.44).9*** (5.86).*** (4.3).3*** (.59).*** (3.93).** (.3) Noes: -saisics for he es of significance of he correlaion coefficiens are in parenheses. The sample size is 38. *** Significan a he percen level ** Significan a he 5 percen level * Significan a he percen level 6

17 Table 3: Lag order selecion crieria for appropriae VAR model of 5 PPIs and real ineres rae in he U.S.: January 969 Ocober Lag AIC SBIC HQIC

18 Table 4: Changes in PPIs in response o real ineres rae changes by percen poin Commodiy Groups Lag lengh = Lag lengh = Farm Producs.6. Processed foods and feeds.9.6 Texile producs and apparel.3. Hides, skins, leaher, and relaed producs.8.5 Fuels and relaed producs and power.6.6 Chemicals and allied producs.3.4 Rubber and plasic producs.. Lumber and wood producs Pulp, paper, and allied producs..5 Meals and meal producs.5.7 Machinery and equipmen.. Furniure and household durables..5 Nonmeallic mineral producs.. Transporaion equipmen.. Miscellaneous producs.4. 8

19 Figure : Scaer plos of Absolue Value of Price Changes and One Period Lagged Real Ineres Raes January 969 Ocober Farm Producs Processed foods and feeds Texile producs and apparel Real ineres raes (%) Real ineres raes (%) Real ineres raes (%) Hides,skins, leaher and producs Fuels and relaed producs and power Chemicals and allied producs Real ineres raes (%) Real ineres raes (%) Real ineres raes (%) Rubber and plasic producs Lumber and wood producs Pulp, paper and allied producs Real ineres raes (%) Real ineres raes (%) Real ineres raes (%) Meals and meal producs Machinery and equipmen Furniure and household durables Real ineres raes (%) Real ineres raes (%) Real ineres raes (%) Nonmeallic mineral producs Transporaion equipmen Miscellaneous producs Real ineres raes (%) Real ineres raes (%) Real ineres raes (%)

20 Figure : Impulse responses of 5 PPIs o a percen poin increase in real ineres rae derived from esimaed VAR wih lag lengh nahsrecher, realineres, chemicals nahsrecher, realineres, farmprod nahsrecher, realineres, fuels nahsrecher, realineres, furniure nahsrecher, realineres, hidesskins nahsrecher, realineres, lumber nahsrecher, realineres, machinery nahsrecher, realineres, meals nahsrecher, realineres, misc nahsrecher, realineres, nonmeallic nahsrecher, realineres, processed nahsrecher, realineres, pulp nahsrecher, realineres, realineres nahsrecher, realineres, rubber nahsrecher, realineres, exile nahsrecher, realineres, ransporaion sep 95% CI irf Graphs by irf name, impulse v ariable, and response v ariable

21 Figure 3: Impulse responses of 5 PPIs o a percen poin increase in real ineres rae derived from esimaed VAR wih lag lengh nahsrecher, realineres, chemicals nahsrecher, realineres, farmprod nahsrecher, realineres, fuels nahsrecher, realineres, furniure nahsrecher, realineres, hidesskins nahsrecher, realineres, lumber nahsrecher, realineres, machinery nahsrecher, realineres, meals nahsrecher, realineres, misc nahsrecher, realineres, nonmeallic nahsrecher, realineres, processed nahsrecher, realineres, pulp nahsrecher, realineres, realineres nahsrecher, realineres, rubber nahsrecher, realineres, exile nahsrecher, realineres, ransporaion sep 95% CI irf Graphs by irf name, impulse v ariable, and response v ariable

22 References Blinder, Alan S, Elie E.D. Canei, David E. Lebow and Jeremy B. Rudd, 998, Asking Abou Prices: A New Approach o Undersanding Price Sickiness. New York: Russell Sage Foundaion Doan, Thomas, 99, RATS User s Manual. Evanson, Ill:Esima. Enders, Waler, 995, Applied Economeric Time Series, New York: John Wiley & Sons, Inc. Mankiw, N. Gregory, 99, Small Menu Coss and Large Business Cycles: A Macroeconomic Model of Monopoly, in N. Gregory Mankiw and David Romer (eds): New Keynesian Economics, vol, Cambridge, MA: The MIT Press. Nah, Hiranya K,, Relaive Imporance of Secoral and Aggregae Sources of Price Changes, manuscrip. Nah, Hiranya K., and Rober Srecher, 3 Small Menu Coss and Large Business Cycles: An Exension of he Mankiw Model. Proceedings: Academy of Economics and Economic Educaion Research, 3. Sims, Chrisopher, 98, Macroeconomics and Realiy, Economerica 48, pp Srecher, Rober,, Discouning Price Rigidiies, Journal of Economics and Economic Educaion Research, vol. 3(): Taylor, John B. 998, Saggered Price and Wage Seing in Macroeconomics, NBER Working Paper # 6754, Cambridge, MA.