Working Less and Bargain Hunting More: Macro Implications of Sales during Japan s Lost Decade

Transcription

1 Working Less and Bargain Hunting More: Macro Implications of Sales during Japan s Lost Decade Nao Sudo, Kozo Ueda y, Kota Watanabe z, and Tsutomu Watanabe x November 4, 2 Abstract We examine macroeconomic implications of sales. By focusing on te fact tat bargain unting is time consuming, we construct a DSGE model wit sales and ouseolds endogenous bargain unting. Te model reveals tat trend declines in ours worked during Japan s lost decade account for actual rises in a sales frequency, rises in te fraction of bargain unters, and a part of actual declines in in ation rates. Te real e ects of monetary policy weaken, because sales prices are frequently revised and endogenous bargain unting enances te strategic substitutability of sales. Keywords: sales; monetary policy; lost decades; time use JEL classi cation: E3, E5 Deputy Director, Researc and Statistics Department, Bank of Japan ( nao.sudou@boj.or.jp). y Director and Senior Economist, Researc and Statistics Department, Bank of Japan ( kouzou.ueda@boj.or.jp). z Institute for Monetary and Economic Studies, Bank of Japan ( kouta.watanabe@boj.or.jp). x Hitotsubasi University and te University of Tokyo ( watanabe284@gmail.com). Te autors tank Kosuke Aoki and te sta of te Researc and Statistics Department and te Institute for Monetary and Economic Studies (IMES), te Bank of Japan, for teir useful comments. Te autors also tank Kevin Seedy for saring teir code. Views expressed in tis paper are tose of te autors and do not necessarily re ect te o cial views of te Bank of Japan.

2 Introduction Two remarkable observations during te Japan s lost decades since 99s are a cange in rms price setting strategy togeter wit a cange in ouseolds working beaviors. Japanese rms increase te number of sales, temporary cuts of goods prices from regular prices, gradually but monotonically. Consequently, ouseolds purcase greater number of goods at te sale price rater tan at te regular price. During te same period, ours worked per worker displays a secular decline partly re ecting te statutory reduction in ours worked, jitan, and possibly a demograpic cange, dampening output (Hayasi and rescott (22)). In te current paper, we ask if sales conducted by rms play an important in te variations of output and in ation in te Japanse economy, in relation wit te ouseolds time allocation decision between labor input, leisure, and searcing for ceaper goods. To tis end, we investigate te source and macroeconomic implications of sales by extending te work of Guimaraes and Seedy (2, ereafter GS). GS (2) develop a DSGE model in wic te economy consists of two classes of consumers, price-insensitive customers called loyal customers and price-sensitive customers called bargain unters. Wile a proportion of te two classes of consumers is xed, since rms cannot tell tem apart, te rms best pricing strategy is ten to old periodic sales. In contrast to GS (2), te ouseold in our model makes endogenous decision about te intensity by wic it responds to a relative price di erentials among items. Eac ouseold consists of an in nite number of soppers, and it cooses a portion of soppers acting as loyal customers and tose acting as bargain unters. Wit a sizable number of bargain unters, te ouseold can substitute away from a relatively expensive brand item. Because te searcing activity for a lower price reduces te time available for labor input and leisure, owever, te increases in bargain unter comes at a cost to te ouseold. We reveal tat macroeconomic implications are greatly modi ed wen considering sales and endogenous bargain unting. We report mainly two ndings. First, Japan s trend declines in ours worked account for actual trend rises in sales frequency during Japan s lost decade, if te canges in ours worked are driven by tecnology or demand socks. In addition, our model suggests a downward (upward) trend in te fraction of loyal customers (bargain unters). Trend declines in ours worked contribute, in part, 2

3 to actual declines in te in ation rate. Second, te e ect of an accommodative monetary policy sock on real economic activity is mitigated, wen bargain unting is endogenous. Te sock increases ours worked, wic, in turn, increases (decreases) te fraction of loyal customers (bargain unters). Firms lower teir sales frequency. Since sales-priced goods are sold more tan normal-priced goods in terms of quantity, tose canges in ouseolds and rms actions yield a downward pressure on aggregate demand for goods. Te real e ects of monetary policy diminis. Tis result is also explained by intensi ed strategic substitutability of sales. Suppose tat all rms but rm A raise teir sales frequency. As in GS (2), it loses an incentive for rm A to raise its sales frequency, because its decreases te marginal revenue from sales. In our model, additional cannel emerges. Wen all rms but rm A raise teir sales frequency, an aggregate price falls. Tat increases aggregate demand for goods, and in turn, aggregate demand for labor. Houseolds supply more labor and lose time in bargain unting. Te fraction of loyal customers (bargain unters) increases (decreases). By observing tis, rm A lowers its sales frequency. Suc intensi ed strategic substitutability of sales mitigates te real e ect of monetary policy. Te following two papers suggest tat ours worked and bargain unting closely interact. First, Aguiar and Hurst (27) use scanner data and time diaries to examine ouseolds substitution between sopping and ome production. Tey nd tat older ouseolds sop te most frequently and pay te lowest price. Second, Lac (27) analyzes store-level price data following te unexpected arrival of a large number of immigrants from te former Soviet union to Israel. He nds tat te immigrants ave a iger price elasticity and a lower searc cost for goods tan te native population. Regarding sales models, Varian (98) sows rms randomizing pricing strategy in te presence of informed and uninformed consumers. Keoe and Midrigan (2) develop a DSGE model tat incorporates not just menu cost associated wit regular prices but also cost associated wit deviations of sale prices from regular prices. 2 Te structure of tis paper is as follows. Section 2 provides evidence for endogenous bargain unting by looking at Japan s micro price data. Section 3 develops a model. Section 4 presents te model s impulse responses. Section 5 discusses Japan s lost decade. See also asigian and Bowen (99), Sorensen (2), Brown and Goolsbee (22), McKenzie and Scargrodsky (24), asigian, eltzman, and Sun (23). 2 Altoug tey are not te model of sales, Benabou (988) and Watanabe (28) construct a model incorporating consumer searc and price setting. 3

4 Section 6 concludes tis paper. 2 Evidence for Endogenous Bargain Hunting In tis section, we document various evidence to motivate and justify our modelling strategy regarding endogenous bargain unting. First, from a goods-demand side, we look at Japan s ouseold survey on time use. We sow te existence of time use eterogeneity in working and sopping across di ering coorts as well as its canges in te last two decades. Second, from a goods-supply side, we look at Japan s oint-of-sales (OS) data and present time-series pats of some economic variables associated wit sales. We examine canges in te sales frequency. Te fraction of loyal customers (bargain unters) is ardly observable. So we infer its movement by calibration based on te GS (2) model or te calculation of a price elasticity. 2. Survey on time use We begin by looking at Survey on Time Use and Leisure Activities. Te survey is conducted by te Statistical Bureau every ve years. It asks around 2, people in 8, ouseolds about teir daily patterns of time allocation. Questionnaire includes time use in working and sopping. In tat respect, tis survey elps us examine teir relationsip, wic is te key to our model. Tables and 2 sow summary results of ouseolds time use in sopping and working (including commuting time for work and scool), respectively. Te sample is tat of over 5 year old. Numbers in te tables indicate minutes per week. Two results are wort igligting. First, sopping time is longer for tose wo are not working tan tose wo are working. We also nd tat female spends longer sopping time tan male. Second, sopping time continued to increase from 986 to 26, in particular for male. At te same time, ours worked continued to decline, altoug tey picked up sligtly in 26. Tose results appear to provide a support for our assumption tat bargain unting depends negatively on ours worked. 4

5 Table : Time Use in Sopping (minutes) Bot Male Female Working Not working Working Not working Working Not working Source: Statistical Bureau, Survey on Time Use and Leisure Activities Table 2: Time Use in Working (including commuting time, minutes) Bot Male Female Working Not working Working Not working Working Not working Source: Statistical Bureau, Survey on Time Use and Leisure Activities Figure demonstrates te life cycle patterns of time use as of 26. We see a negative correlation between time in sopping and time in working, in particular, for male and people up to about 75 year old. For male, ours worked peak at around 45 year old, and at te age, time in sopping its a bottom. After tat age, ours worked decline and time in sopping rise. Over 8 year old, time in sopping begins to drop. Tis result is in line wit Aguiar and Hurst (27). Wen we point out tat Japan s rapid aging population as in uenced bargain unting as well as working, readers may wonder if bargain unting is totally exogenous caused by te demograpic reason. We do not deny tis possibility, but using a model, we consider an endogenous relationsip between bargain unting and working. 5

6 25 (minutes) Male (minutes) Time in sopping (left) Time in working (rigt) (minutes) Female (minutes) Time in sopping (left) Time in working (rigt) Figure : Time Use in Sopping and Working for Eac Age and Sex (minutes) Source: Statistical Bureau, Survey on Time Use and Leisure Activities 2.2 OS Data Next, from a goods-supply side, we examine indicators of sales using OS data. Te OS data are compiled by Nikkei Digital Media. 3 Wile existing literature often uses weekly or montly data (e.g., Bils and Klenow [24]), tis OS data are daily. Te sample period ranges from Marc, 988 to December, 27. Te data are reported from various retail sops, including GMS and supermarkets trougout Japan. Te products covered in te data are restricted to ones wit a product code, known as te JAN code. Te OS contains processed foods and domestic articles, but not perisables, services, or expensive durable goods. For eac item and eac sop, amount sold and proceeds are reported daily. Eac price is calculated as a unit price wit proceeds being divided by amount sold. roceeds 3 See Abe and Tonogi (2) for te pevious study using te OS data. 6

7 exclude consumption tax. Te unit price may be decimal due to te consumption tax, time sale during a day, and several oter reasons Sales frequency Figure 2 demonstrate te aggregate, montly time-series movements of tree variables wic are associated wit sales and serve as key variables to te GS model. 5 Tey are te ratio of a sales price markup to a normal price markup ; te ratio of quantities sold at sales price to tose at regular price ; and te frequency of sales s. Among tem, tis paper s focus is on te sales frequency s: Clearly, te sales frequency continues to rise during Japan s lost decade. Markup ratio mu // 992// 996/9/ 2/7/ 24/5/ 28/3/ Quantity ratio ci // 992// 996/7/ 2/4/ 24// 27//.45 Sales freq s // 992// 996/9/ 2/7/ 24/5/ 28/3/ Figure 2: Key Sales Variables Implied from OS Data Fraction of loyal customers We calibrate key deep parameters based on te GS model. In GS (2), aforementioned tree variables in Figure 3 serve as targets to calibrate tree key deep parameters. Calibrated deep parameters are te elasticity of substitution between product types ; te 4 Te revised tax law was put into e ect on April, 24, requiring sops to display teir retail prices including consumption tax. Tis revision causes discontinuity in te OS data on tat period, altoug te tax rate was uncanged and te OS data continued to compile proceeds excluding tax. 5 For details, see Appendix A. 7

8 elasticity of substitution between brands for bargain unters ; and te fraction of loyal customers : We calibrate parameters montly to investigate teir canges. In doing so, we assume tat te economy is at steady state at every period. Admittedly, tis approac lacks justi cation. Te following result is presented for te sake of illustration. Figure 3 demonstrate te istorical movements of te tree calibrated parameters. We nd tat te fraction of loyal customers is not constant, altoug GS (2) assume its constancy. Te fraction of loyal customers tends to decrease over te sample period, partly owing to te steady increase in te sales frequency. As for oter parameters, we nd tat te two elasticity parameters increase. Tat re ects a relative increase in sales prices to normal prices, wile a relative quantity sold at sales prices to normal prices remains almost constant. 6 Elast bw product types epsilon 4 Elast for bargain unters eta Loyal customer fraction lambda Figure 3: Key Sales arameters Calibrated by te GS Model Looking at te fraction of loyal customers more closely, it is noticeable tat it moves closely wit labor market variables. In Figure 4, we plot te istorical movements of labor market indicators on a left axis and te fraction of loyal customers on a rigt axis. Two labor market indicators are () ours worked denoted by and (2) ours 8

9 worked times employment divided by te population over 5 denoted by e. 6 Te grap sows srinking labor markets in te 99s. Tree forces are considered to be present. First, Japan was faced wit te so-called lost decade after te burst of te asset price bubble in te early 99s. Tat led to te prolonged recession. Second, te statutory jitan contributed to te fall in ours worked. Jitan was gradually introduced by te government toroug revisions of te Labor Standards Law: 988:Q to 993:4Q and 997:2Q to 998:4Q, wile te extent of jitan varied across industries and establisment sizes. 7 Tird, demograpic canges may ave contributed to te declines in ours worked and employment, because Japan is one of te most rapidly growing aging countries. Casual observations suggest a positive correlation between labor supply and te fraction of loyal customers. Te trend declines in ours worked and employment are accompanied by te trend decrease in te fraction of loyal customers in te 99s. In te early 2s, te labor market recovered sligtly. Coerently, te fraction of loyal customers picked up e (left scale) (left scale) λ (rigt scale) Hours worked and employment are taken from Montly Labour Survey in businesses wit 3 or more employees. Hours worked represent tose per capita. Te data are seasonally adjusted and expressed as a logaritm deviation from teir mean. 7 Before te revision, legal work ours were 48 per week. Legal work ours were gradually reduced to 4. Hours worked exceeding tis legal limit sould be compensated by at least a 25-percent premium. See Kawaguci, Naito, and Yokoyama (28) for te analyses on jitan and Kuroda (2) for te counter-argument asserting tat ours worked ardly declined wit demograpic canges controlled. 9

10 Figure 4: Fraction of Loyal Customers and Labor Market Indicators Source: Ministry of Healt, Labour and Welfare Montly Labour Survey rice elasticity Te above discussion is logically inconsistent, owever, because we used te GS model in wic te fraction of loyal customers is assumed to be constant wit te aim of examining te properties of te time-varying fraction of loyal customers. Witout relying on a speci c model like te GS model, we tus consider evidence for canges in bargain unting. To tis end, we look at ow a price elasticity canges over time. Bargain unters are considered to be more price sensitive tan loyal customers. Terefore, if te fraction of loyal customers (bargain unters) decreases (increases), te price elasticity sould rise. Figure 5 plots te time-series movement of te price elasticity. Tat exibits an upward trend in its absolute term, suggesting tat ouseolds become more price sensitive. Te price elasticity does not necessarily comove wit te two labor market indicators, but teir trends move in te same direction e (left scale) (left scale) Elasticity (rigt scale) Figure 5: rice Elasticity and Labor Market Indicators Source: Ministry of Healt, Labour and Welfare Montly Labour Survey

11 To sum up, tose observations support te idea tat ouseolds bargain unting is endogenous, depending on teir time spent in labor supply. As ouseolds are busy in work, tey save time for bargain unting, contributing to an increase (decrease) in te fraction of loyal customers (bargain unters). 3 Model Bearing te endogenous fraction of loyal customers in mind, we construct a sales model. Our model owes its great deal to GS (2). 3. Setup Houseold function: were C t We assume a coort of ouseolds wo as te following lifetime utility U(t) j E t v(c t+j ) Zt+j ( L t+j ) L H t+j + L ( ) L j ; (3.) is aggregate composite of di erentiated consumption goods tat is de ned below, H t is ours worked, and L t is te sare of soppers tat are cosen to be loyal customers in te coort ( < L t < ). Z t represents a stocastic sock to utility weigt of te labor supply, wit its logaritm deviation denoted by " t. Te sare of loyal customers L t is endogenous, wit its mean : arameter is te subjective discount factor ( < < ), and L, L > represent te elasticity of utility from being loyal customers. Te function v(c t ) is strictly increasing and strictly concave in C t ; and v(x t ) is strictly increasing and convex in X t. Te overall aggregator of consumption is given by C " Z Z B ( ) # c(; b) ( ) db d ; (3.2) were c(; b) is te ouseold s consumption of brand b 2 B of product type 2. GS (2) give te example suc tat product types include beer and dessert and brand includes Corona beer and Ben & Jerry s ice cream. As in assumed in GS (2), we set >, so tat bargain unters are more willing to substitute between di erent brands of a speci c product type tan ouseolds are to substitute between di erent product types.

12 We assume tat te bargain unters are agents tat can freely substitute from a relatively expensive brand b witin a type goods, and te loyal customers are agents tat cannot make suc substitutions. For te loyal customers, terefore, te relative price across matters but relative price across b does not matter in determining expenditure decision. Suppose tat all of soppers are bargain unters, ten te ouseolds demand toward a speci c brand b in type is given by c(; b) p(; b) p B () pb () C were p(; b) is te price of brand b of product type, p B () is an index of prices for all brands of product type, and is te aggregate price level. C is an aggregate consumption spending. By contrast, wen all of soppers are loyal customers, ten te ouseolds demand is given by pb () c(; b) C Since a ouseold consists of bargain unters as well as loyal customers, we assume tat te demand function for eac good is given as follows. 8 < c(; b) : p(;b) p B () pb () C for L population p(;b) C Te ouseold s budget constraint is given by for L population. (3.3) t C t + E t [Q t+jt A t+ ] W t H t + D t + A t ; (3.4) were W t is te wage, D t is dividends received from rms, Q t is te asset pricing kernel, and A t is te ouseold s portfolio of Arrow-Debereux securities. Te endogenous L t is te most important innovation made in tis paper. In coosing te optimal L t ; te ouseold confronts trade-o. On te one and, an increase in L t raises one s utility. As equation (3.) sows, it increases time for leisure by decreasing te time for bargain unting. On te oter and, te increase in L t decreases te bene t from bargain unting. Te ouseold decreases one s utility by selecting te suboptimal amount of demand as is speci ed by te bottom of te demand function 2

13 (3.3). Tis second e ect is more formally illustrated by te relationsip between utilityrelated consumption C t and spending-related consumption C t : Appendix sows tat C t depends on not only C t but also te following consumption wedge z t : 8 C t z t B;t t C t ; (3.5) and tat z t < and dz t dl t <. As te ouseold makes more bargain unting, L t decreases and F t increases. Houseolds enjoy iger utility from te same amount of consumption spending Ct. If te ouseold makes bargain unting for all goods, tat is, L t, ten we ave z t : Additionally, Calvo-type wage stickiness is introduced as in GS (2). Houseolds supply di erentiated labor inputs to rms. Wages can be adjusted at a probability of w : Firms A good ting in our model is tat rms beavior is depicted in te same way as GS (2). Firms in our model face te same demand function given by equation (3.3) as tose in GS (2). It is tus optimal for rms to randomize teir price across sopping moments from a distribution wit two prices. Firms set a normal ig price N;t wit te frequency of s and a low sale price S;t wit te frequency of s. Te only di erence from GS (2) is tat rms optimize teir pricing decisions by observing canges in te sare of loyal customers L t. As GS (2) argue, te strategic substitutability of sales plays a crucial role in rms pricing. Te more oters ave sales, te less an individual rm wants to ave a sale. Suppose tat oter rms always ave sales. If te individual rm stops a sale and sells its good at a normal price, its pro t increases, because price-insenstive loyal customers tend to buy te good even at te normal price. As an opposite case, suppose tat oter rms ave no sale. Because sales attract price-sensitive bargain unters, te individual rm can increase its pro t by aving sales. Suc strategic substitutability makes rms randomize teir price. Firms adjust teir normal prices wit Calvo-type price stickiness. In eac period, rms ave a probability of p to reset teir normal prices. Sales prices can be 8 Te utility-related consumption C also depends on te price ratio B, but tat does not in uence te ouseold s decision of L because te ouseold is a price taker. As in GS, te price index for bargain unters is te same for all product types tat is, B p B (). 3

14 adjusted freely. Wolesalers produce goods using a labor input wic consists of ours worked and te labor supply sock. roduction tecnology is subject to a AR() sock " a t : Monetary autority te monetary policy rule of A monetary autority sets a nominal interest rate i t following i t i t + ( ) N t + " i t; (3.6) were represents a policy inertia, represents te response to a normal price cange N t ; and " i t represents a sock to monetary policy. Resource constraint A resource constraint is given by Y t C t + Z g t ; (3.7) were Z g t " g t. is a government expenditure sock, wit its logaritm deviation denoted by Exogenous socks We consider four types of socks. Tey are socks to monetary policy, tecnology, government expenditure, and labor supply: " i t t i (3.8) " a t a " a t + t a (3.9) " g t g " g t + g t (3.) " t " t + t : (3.) As for te monetary policy sock, we do not assume an inertia, because te monetary policy rule is persistent by construction. 3.2 Key equations We provide key equations to te model in a log-linearized form. 4

15 Sales pricing It is optimal for a rm j to adjust its sale price p S;j;t by one-for-one wit a cange in its nominal marginal cost x t + p t ; p S;j;t x t + p t ; (3.2) were a real marginal cost is denoted by x t. Tis is te same as GS (2). As te sare of loyal customers l t increases, rms decrease te sales frequency s t : ss t B ' B x t ' B B A + l t : (3.3) ( )( )' B In te equation above, a term wit a underline represents a new term compared from GS (2). Like GS (2), an increase in te real marginal cost x t decreases te sales frequency. Because te sales price responds by one-for-one to te marginal cost, te sales price increases more tan te normal price. Tat decreases relative demand for sales, tereby decreasing te sales frequency. Fraction of loyal customers Te fraction of loyal customers l t is described by c + + y t "a t ( )" t (c + B + ( L ) + ( c ) f t x t + + )" g t w t + L ( )( ) l t ( )H l t + SN p SN;t + f t : (3.4) SN Two tings are wort noting. First, te fraction of loyal customers l t increases wit ours worked t, wic depends positively on aggregate demand y t. 9 lengten, te disutility from bargain unting increases. As ours worked Second, te fraction of loyal customers l t increases wit te consumption wedge f t. An increase in te consumption wedge means an increase in utility from a given amount 9 See also equation (C.2) 5

16 of consumption spending. As te wedge increases, te bene t from bargain unting diminises, raising te fraction of loyal customers. Te consumption wedge increases wit p SN;t ; wic increases wit te ratio of sales prices to normal prices: S;t N;t and decreases wit te sales frequency s t. In oter words, as sales prices increase to converge to normal prices or sales become less frequent, prices become omogenous and te consumption wedge increases. illips curve wit sales Te illips curve wit sales is given by t E t t+ + n o x t + (x t E t x t+ )+Al t + A(l t E t l t+ ) : (3.5) Compared wit te standard New-Keynesian illips curve, te equation as two new terms. First, as in GS (2), canges in te real marginal cost, x t ; in uence te in ation rate t. Tis is because te overall price canges troug exible sales prices as well as persistent normal prices. Second, unlike GS (2), te sare of loyal customers l t in uences te in ation rate. As te sare of loyal customers increases, te overall price increases. Tat results from te sift of demand for normal goods on a ouseold side and a decrease in sales frequency on a rm side. Te real marginal cost x t is described by x t + w t + + y t Bl t : (3.6) As in te standard New-Kayensian model, te real marginal cost increases wit bot te real wage w t and aggregate demand y t : Furtermore, it decreases wit te fraction of loyal customers l t. Its mecanism runs as follows. Wen te sare of loyal customers increases, demand for goods sold at te normal price increases and demand for goods sold at te sales price decreases. Suc a sift of demand is ampli ed by a decrease in rms sales frequency in response to te increase in te sare of loyal customers. Since sales goods are generally sold more tan normal goods in terms of quantity, total demand for te goods falls. Tat diminises te supply of te goods, and in turn, te real marginal cost. Moreover, te increase in te fraction of loyal customers functions to decrease te real wage for bot labor demand and supply reasons, decreasing te real marginal cost 6

17 furter. Te wage illips curve is given by W;t W;t+ + ( w)( w ) w + & [ c + + y t + + "a t ( )" t c " g t + B + L L ( )H +(c ) f t x t + w t l t ( )( ) l t : (3.7) On te labor demand side, for te same reason above, total demand for te goods falls, wic decreases labor demand, and in turn, te real wage. On te labor supply side, te fraction of loyal customers increases (decreases) to o set an increase (decrease) in ours worked. Tus, for a given level of ours worked, te degree of real wage increases (decreases) declines. 4 Impulse Response Functions We simulate impulse response functions (IRFs) of economic variables to four types of sock. Te rst sock is an accommodative sock to te monetary policy rule. Te second sock is a positive sock to wolesalers production tecnology. Te tird sock is a government spending sock as a demand sock. Te fourt sock is a labor supply sock. 4. Calibration Most of te calibration of our model parameters is based on GS (2). For monetary policy rule, we introduce an interest rate monetary policy rule, setting :8 and :5; wile central bank in GS (2) adopts money growt rate rule. In addition, we use parameters associated wit sales so tat tey are consistent wit Japan s OS data. Te detailed settings are sown in Table 3 below. As for te parameters associated wit te fraction of loyal customers L and L, we target a steady state level of te 7

18 fraction of loyal customers to calibrate L given L : Table 3a: Model arameters arameters Discount factor.9975 c Elasticity of consumption.333 Elasticity of labor supply.7 Elasticity of output to ours.667 Elasticity of marginal cost.5 & Elasticity bw di labor 2 p Calvo price stickiness.889 w Calvo wage stickiness.889 Mon pol rule inertia.8 Mon pol rule on in ation.5 Table 3b: ersistency of Exogenous Socks arameters a Tecnology Sock.85 g Government Expenditure Sock.85 reference of Labor Supply sock.85 Table 3c: arameters related to Sales Target variables rice ratio of sales to normal.883 Quantity ratio of sales to normal s Sales frequency.276 arameters Elasticity bw product types Elasticity bw brands Fraction of loyal customers.833 8

19 Target variable Fraction of loyal customers.9 arameter L Utility weigt.6e-4 L on loyal customers 5.3e-3 L Comparison between te standard New-Keynesian model and te GS model To understand GS s results, we begin wit presenting IRFs in te GS model, in comparison wit tose in te standard New-Keynesian model. By te GS model, we mean te model discussed above witout endogenous developments in te fraction of loyal customers. Te standard New-Keynesian model corresponds to te GS model witout sales. Figure 6 presents te IRFs of tree economic variables: aggregate demand, in ation rates excluding sales (normal price canges), and nominal interest rates. Te orizontal axis indicates time up to eigt quarters after a sock. Top and bottom panels demonstrate IRFs to te accommodative monetary policy sock and te positive tecnology sock, respectively. Dased and solid lines indicate IRFs in te GS model and in te standard New-Keynesian model, respectively. Te top left panel sows tat, as GS (2) argue, te real e ect of monetary policy in te model wit sales remains large, wic is close to tat in te model witout sales. Similarly, te bottom left panel sows tat te real e ect of te tecnology sock ardly canges by te incorporation of sales. Weter a price index includes sales or not, in ation rates become more volatile in te model wit sales tan in te model witout sales. In te model wit sales, sales prices keep a constant markup on marginal cost by exible adjustments. Tat makes te aggregate price index move more exibly tan te model witout sales. Since normal prices are reset wit te consideration of te aggregate price index, tey become more volatile in te model wit sales tan in te model witout sales. Neverteless, as GS argue, real e ects are similar between te two models, owing to sales being strategic substitutes. 9

20 Monetary policy sock Demand Y GS model Standard model Inflation (excl sales) pi_n Nominal interest rate i Tecnology sock Demand Y GS model Standard model Inflation (excl sales) pi_n Nominal interest rate Figure 6: IRFs under te GS Model and standard model 4.3 E ects of endogenous bargain unting Now, we simulate IRFs in te model wit endogenous developments in te fraction of loyal customers, in comparison wit tose in te GS model. We plot te IRFs of nine economic variables. In te gures below, dotted lines indicate IRFs in te GS model. Tick and tin solid lines bot indicate IRFs in te model wit endogenous developments in te fraction of loyal customers, wit di ering elasticity parameter values L 3 and. A lower L implies a iger elasticity of te fraction of loyal customers Monetary policy sock Our simulation results reveal tat sales can alter macroeconomic implications greatly. Figure 7 presents IRFs to te accommodative monetary policy sock. Te e ect of monetary policy on demand diminises, in particular, wen L is as low as 3. Te mecanism runs as follows. In response to te monetary policy sock associated wit lowering te nominal interest rate, aggregate demand increases. Tat raises ours worked. Since ouseolds spend more time in works, teir disutility from bargain unting increases. Wit L as low as 3, te fraction of loyal customers (bargain unters) increases (de- 2

21 creases) in a relatively elastic manner. In viewing tis, rms lower teir sales frequency. Since sales-priced goods are sold more tan normal-priced goods in terms of quantity, te decrease in te sales frequency mitigates te increase in aggregate demand. Te attenuated real e ect of monetary policy is also explained by intensi ed strategic substitutability of sales. Suppose tat all rms but rm A raise teir sales frequency. As in GS (2), it loses an incentive for rm A to raise its sales frequency, because its decreases te marginal revenue from sales. In our model, additional cannel emerges. Wen all rms but rm A raise teir sales frequency, an aggregate price falls. Tat increases aggregate demand for goods, and in turn, aggregate demand for labor. Houseolds supply more labor and lose time in bargain unting. Te fraction of loyal customers (bargain unters) increases (decreases). By observing tis, rm A lowers its sales frequency. Suc intensi ed strategic substitutability of sales mitigates te real e ect of monetary policy. In ation rates excluding sales (normal price canges) also move very di erently in tis model, compared wit te GS model. In response to te accommodative monetary policy sock, in ation rates excluding sales increase far less in te model tan in te GS model. As we explained in te previous section, te increase in te fraction of loyal customers functions to decrease te real wage and te real marginal cost. Altoug te increase in ours worked yields an upward pressure on te real marginal cost, te e ect of te increase in te fraction of loyal customers functions dominates, wen L as low as 3. In contrast, te model yields greater increases in in ation rates including sales tan te GS model. Tis is because te aggregate price index increases wit bot te fraction of loyal customers and te sales frequency. Wen L is as ig as, IRFs resemble to tose in te GS model. Te fraction of loyal customers moves rigidly. Tat makes te model similar to te GS model in wic te fraction of loyal customers as in GS (2) is kept constant. 2

22 Demand Y GS model Our model (teta_l ) Our model (teta_l 3) Hours worked Nominal interest rate i Inflation (incl sales) pi Loyal customers' fraction l Real wage w Inflation (excl sales) pi_n Sales frequency s Real marginal cost x Figure 7: IRFs to an Accommodative Monetary olicy Sock Tecnology sock Wen te positive tecnology sock its te economy, our model yields greater e ects on aggregate demand and in ation tan te GS model. In tis type of sticky price model, te positive tecnology sock tends to decrease ours worked. Tat decreases (increases) te fraction of loyal customers (bargain unters). Firms react to te sock by increasing teir sales frequency. Because sales-priced goods are sold by a large amount, te increase in aggregate demand is magni ed. Te aggregate price falls, owing to te decrease in te fraction of loyal customers and te increase in te sales frequency. In contrast, te normal price increases. Tat results from increases in real wage and te real marginal cost, due to te decrease in te fraction of loyal customers. Altoug te grap plots only up to eigt quarters after te sock, in ation excluding sales stays negative in te medium term in all of te models. 22

23 Demand Y GS model Our model (teta_l ) Our model (teta_l 3) Hours worked Nominal interest rate i Inflation (incl sales) pi Loyal customers' fraction l Real wage w Inflation (excl sales) pi_n Sales frequency s Real marginal cost x Figure 8: IRFs to a ositive Tecnology Sock 23

24 4.3.3 Government expenditure sock Economic responses to te positive government expenditure sock resemble to tose to te accommodative monetary policy sock Demand Y GS model Our model (teta_l ) Our model (teta_l 3) Hours worked Nominal interest rate i Inflation (incl sales) pi Loyal customers' fraction l Real wage w Inflation (excl sales) pi_n Sales frequency s Real marginal cost x Figure 9: IRFs to a ositive Government Expenditure Sock Labor supply sock Finally, we simulate IRFs to a sock to labor supply. Tis sock is formulated, being motivated by Hayasi and rescott (22). In analyzing Japan s lost decade and incorporating te e ects of jitan, tey introduce te following utility function: log C t H t 4 E t; were H t and E t represent workweek lengt (ours) and te fraction of ouseold members wo work. Bot H t and E t contribute to production. For 99 to 992, tey take H t as exogenous. In our model, as we sowed in equation (3.), we replace te exogenous H t 4 for te labor supply sock Z t and te endogenous E t for labor supply H t 24

25 ( wit H t + L L t) L ( ) L : Bot Z t and H t contribute to production. Note tat, in our simulation, te elasticity of labor supply is.7, less tan one. In Hayasi and rescott (22), it equals one. Figure demonstrates tat, wen a sock increases labor supply, labor input and te fraction of loyal customers move in te opposite direction, unlike wen te above oter types of socks it te economy. Tis is because te positive sock " t decreases t, altoug total labor input ( t + " t ) increases. Te decrease in t functions to lower te fraction of loyal customers, wile te positive labor supply sock itself functions to raise te disutility of bargain unting and tereby te fraction of loyal customers. Wit te elasticity of labor supply below one, te former e ect dominates te latter; te fraction of loyal customers decreases. Altoug we do not sow ere, te fraction of loyal customers increases (uncanges), wen te elasticity of labor supply exceeds (equals) one Demand Y GS model Our model (teta_l ) Our model (teta_l 3) Labor input +e Nominal interest rate i Inflation (incl sales) pi Loyal customers' fraction l Real wage w Inflation (excl sales) pi_n Sales frequency s Real marginal cost x Figure : IRFs to a Labor Supply Sock 25

26 5 Wat Happened during Japan s Lost Decade As we see in Figure 2, te sales frequency s continues to rise during Japan s lost decade. In te current section, based on our model, we argue tat te working mecanism beind tis observation may be attributed to te decline in ours worked. We ten discuss te implications to te macroeconomy. 5. Explanation for metodology In doing simulation, we start wit boldly assuming tat only te tecnology sock drives te economy. We obtain te time-series pat of te tecnology sock tat accounts for actual ours worked in Japan. Altoug we do not fully claim te validity of tis assumption, we point out te following reasons. First, it is a natural step to regard te tecnology sock as a cief driving force of te economy, alongside te literature of RBC. In addition, Hayasi and rescott (22) argue tat te slowdown of te TF contributes to Japan s lost decade. Second, wen jitan sortened te workweek lengt, labor oarding may ave decreased. Resulting enanced labor e ciency is regarded as a positive tecnology sock. We x sales parameters calibrated for Japan s OS data and estimate te persistence of te tecnology sock only. Our sample ranges from 98Q to 28Q4. After obtaining te time-series pat of te tecnology sock, we calculate te time-series pats of te sales frequency, te fraction of loyal customers, te in ation rate, and te sales markup. We use two models: te GS model and our model wit endogenous developments in te fraction of loyal customers caracterized by L 3; wic is cosen to t data. For simplicity, we neglect te zero lower bound on te nominal interest rate, wic constrained te e ectiveness of monetary policy during Japan s lost decade. 5.2 Simulation results Figure illustrates tat our model explains te movement of te sales frequency very well. It plots te model-based and actual sales frequency. In terms of te direction of its trend and te size of its canges, te model-based sales frequency moves very closely to actual one. Bot series sow steady increases in te sales frequency in te 99s and 2s. In te 98s, wen te actual data are missing, our model suggests a stable sales 26

27 frequency. In comparison, te GS model predicts muc attenuated canges in te sales frequency, wic in te grap is almost at..34 Sales frequency s GS model data Our model (teta_l 3) Figure : Model and Actual Sales Frequency Our model demonstrates unobservable canges in te fraction of loyal customers. Figure 2 sows tis. Our model predicts tat te fraction of loyal customers stays almost constant in te 98s. In Japan s so-called lost decade, te 99s and 2s, it exibits a downward trend. ut di erently, te fraction of bargain unters increases during tat period. Obviously, in te GS model, it remains constant. To ceck weter te fraction of loyal customers actually decreased, we plot te time series of te price elasticity calculated from te OS data and te time use in sopping obtained from te survey data. Teir scales are adjusted to compare tree series in one grap. Te price elasticity increased in its absolute term. Tat indirectly supports a decrease in loyal customers, because te price elasticity of loyal customers is considered to be lower tan tat of bargain unters. 27

28 Fraction of loyal customers l GS model Time use in sopping (reversed) Our model (teta_l 3) Elasticity Figure 2: Model and roxy Fraction of Loyal Customers Next, we turn to in ation. Figure 3 sows simulation results wit actual price canged measured by CI and OS in an annual basis in percent. Using te tecnology sock obtained by te above metod, we simulate te time-series pat of in ation rate. Te model-based in ation rate excludes sales, so tat it corresponds to te o cial CI. Our model predicts muc attenuated uctuations in in ation rates, compared wit data. Our model as almost no advantage over te GS model. In terms of te trend, our model as well as te GS model generates te decline in te 99s and 2s, wic is consistent wit te data. 28

29 Inflation rate Our model (teta_l3) GS model Actual CI OS CI Figure 3: Model and Actual In ation Rate Te di erence between te aggregate price index and te normal price is demonstrated in Figure 4. Te aggregate price index includes sales prices. Te normal price index is te one wic corresponds to CI. Te aggregate price index was mostly negative during te lost decade, wic implies tat CI underestimates te de ation. Te GS model yields an attenuated di erence between te two price indexes. Tis is because te sales frequency ardly canges in te GS model. Tose model-generated series do not matc te actual series obtained from te OS, altoug tey are not directly comparable because weigts between sales and normal goods are di erent. 29

30 Inflation rate (aggregate normal) Our model (teta_l3) GS model OS CI Figure 4: Model and Actual In ation Rate Di erence between Aggregated and Normal rice Indexes Figure 5 sows te time-series pat of te markup ratio of sales prices to normal prices. Te performance of our model is as poor as te GS model Markup ratio mu Bencmark (Tec sock, teta_l3) Gov sock, teta_l Labor sock, teta_l3 data Figure 5: Model and Actual Markup Ratio 3

31 In sum, tose simulation results suggest tat our model improves te GS model in explaining te extensive margin of sales (sales frequency) but not te intensive margin (sales markup). 5.3 Oter explanations Altoug we implemented simulation by assuming tat te temporary tecnology sock drives te economy, tis assumption is not necessarily guaranteed. Oter types of socks may be suitable to account for te actual decline in ours worked. Instead of transitory socks, structural canges may ave sifted ours worked in teir steady state. We ceck robustness of our results in tree ways. First, we investigate cases were oter socks tan te tecnology sock drive te decline in ours worked. Second, we investigate cases were ours worked canges in teir steady state. Tird, we investigate cases were an innovation in bargain unting tecnology in uences bargain unting in steady state Oter stocastic socks We consider two oter types of socks: a government expenditure sock and a labor supply sock. A government expenditure sock, in part, captures te idea tat te statutory decline in ours worked is subsidized by scal policy, in uencing governmental expenditure. Te government expenditure sock is also categorized as a demand sock, opposed to te tecnology sock analyzed above. If Japan s lost decade is understood as a situation were demand was insu cient, negative demand socks become a candidate for te driving force of te Japanese economy. For example, Sugo and Ueda (28) estimate a sticky-price DSGE model and nd tat an investment adjustment cost sock was a main driving force. Bayoumi (2) and Caballero, Hosi, and Kasyap (28) empasize a nancial reason including a zombie lending as a cause of Japan s lost decade. Altoug te nancial sock is not directly linked to te demand sock, te former is considered to in uence demand for investment on te rm side. A labor supply sock is motivated by Hayasi and rescott (22), as we explained in te previous section. Figure 6 sows tat, if we assume tat te government expenditure sock drives te actual canges in ours worked, our model performs as good as or even better tan te previous case wit te tecnology sock. First, as for te sales frequency, te model ts 3

32 te best wen L is. It tracks te trend rise in te sales frequency as te previous case. Moreover, it explains its fall around 25, as well. Second, te fraction of loyal customers is sown to decline over te 99s and 2s. Tird, as for te in ation rate and te di erence between te normal and aggregate price index, our model succeeds in yielding more volatile and closer movements to te actual one tan te previous case. On te oter and, if we assume te labor supply sock drives te actual canges in ours worked, our model predicts opposite movements. Te sales frequency continues to fall, and te fraction of loyal customers and te in ation rate continue to rise. Tey are contrary to data and our aforementioned simulation results. Its reason is understood from Figure 6. In te model, jitan is captured by a negative labor supply sock. To compensate te decrease in ours worked, labor supply t increases endogenously. Wit te labor supply elasticity below one, te increase in t is costly, preventing ouseolds bargain unting. Te fraction of loyal customers tus increases and te sales frequency decreases. As we noted in te previous section, if we assume te unit elasticity of labor supply, te sock as no e ect on total labor input, te sales frequency, and te fraction of loyal customers..4 Sales frequency s Bencmark (Tec sock, teta_l3) Gov sock, teta_l.5 Labor sock, teta_l3 data Figure 6: Model and Actual Sales Frequency 2 32

33 Fraction of loyal customers l Bencmark (Tec sock, teta_l3) Gov sock, teta_l Labor sock, teta_l Figure 7: Model and roxy Fraction of Loyal Customers 2 4 Inflation rate Actual CI Bencmark (Tec sock, teta_l3) Gov sock, teta_l Labor sock, teta_l Figure 8: Model and Actual In ation Rate 33

34 Inflation rate (aggregate normal) OS CI Bencmark (Tec sock, teta_l3) Gov sock, teta_l Labor sock, teta_l Figure 9: Model and Actual In ation Rate Di erence between Aggregated and Normal rice Indexes Markup ratio mu Bencmark (Tec sock, teta_l3) Gov sock, teta_l Labor sock, teta_l3 data Figure 2: Model and Actual Markup Ratio 2 As a bottom line, our exercise suggests tat bot demand and supply socks can 34

35 account for te rise in te sales frequency, te fall in te fraction of loyal customers, and, in part, te fall in te in ation rate, by matcing data for ours worked. Te labor supply sock, owever, yields completely opposite results Steady-state canges in ours worked An alternative approac to accounting for canges in sales beavior is to assume tat steady state as canged, instead of transitory socks. To examine tis possibility, we examine te e ects of canges in steady-state ours worked on te sales frequency and te fraction of loyal customers. We x parameters associated wit sales, suc as L ; L ; ; and, assuming tat steady-state ours worked cange for oter reasons. Oter reasons include canges in tecnology, monetary policy, and te ouseold preference outside te arguments in function () : Figure 2 sows tat decreases in steady-state ours worked raise te sales frequency and lowers te fraction of loyal customers. In te gure, te orizontal axis represents canges in steady-state ours worked in logaritm. Te scale of vertical axis is identical wit tat in te top panel of Figure 2. Tat suggests tat about ve to ten percent declines in ours worked account for te actual increase in Japan s sales frequency. Te bottom panel sows tat te declines in ours worked lead to declines in te fraction of loyal customers. 35