Was the Barrier to Labor Mobility an Important Factor for the Prewar Japanese Stagnation?

Transcription

1 MPRA Munch Personal RePEc Archve Was the Barrer to Laor Molty an Important Factor for the Prewar Japanese Stagnaton? Shuhe Aok Graduate School of Economcs, Unversty of Tokyo 9. Aprl 2008 Onlne at MPRA Paper No. 878, posted 9. Aprl :47 UTC

2 Was the Barrer to Laor Molty an Important Factor for the Prewar Japanese Stagnaton? Shuhe Aok Graduate School of Economcs, Unversty of Tokyo Aprl 9, 2008 Astract Usng a smple framework, I reexamne the Hayash and Prescott hypothess (2006) that a arrer to laor molty that mantaned hgh agrcultural employment was a cause of the stagnaton n the prewar Japanese economy. I fnd that the laor msallocaton etween the agrcultural and non-agrcultural sectors had larger negatve effects on the prewar Japanese aggregate productvty than on the postwar aggregate productvty. However, ths s not ecause the wage dfferental etween the sectors was larger ut ecause the agrcultural nomnal share was larger n prewar Japan. Fnally, I show that a model that does not assume a arrer to laor molty can explan the change n the prewar and postwar agrcultural employment rate and nomnal share. These results suggest that factors other than laor msallocaton are responsle for the stagnaton n the prewar Japanese economy. Keywords: agrculture; arrer to laor molty; prewar Japan; resource msallocaton; two-sector model JEL classfcatons: E, N3, N5, O, O4 Graduate School of Economcs, Unversty of Tokyo, 7-3-, Hongo, Bunkyo-ku, Tokyo , Japan. Emal: shuhe aok@mal.goo.ne.p.

3 Introducton In contrast wth the post-world War II prosperty, the prewar Japanese economy was relatvely stagnant n terms of per capta GNP and aggregate productvty. Hayash and Prescott (2006) (hereafter HP) propose a hypothess that ths stagnaton was caused y a arrer to laor molty etween the agrcultural and non-agrcultural sectors; further, they argue that t dsappeared after Japan lost the war and was occuped y the Alled Powers. They consder the hgh agrcultural employment n prewar Japan as evdence of the arrer, and develop a model to evaluate the effect of the arrer on the prewar Japanese GNP and aggregate productvty. Ths paper reexamnes whether hgh laor mmolty was a cause of the stagnaton n the prewar Japanese economy. For ths purpose, I frst develop a smple accountng framework that measures the effect of laor msallocaton on aggregate productvty. I fnd that the magntude of the measured msallocaton effect on aggregate productvty s larger n prewar perod than n the postwar perod, whch confrms wth HP s hypothess. Next, usng ths framework, I decompose the change n the prewar and postwar msallocaton effects nto the effect y the change n the wage dfferental etween sectors and the effect of the change n the sectoral nomnal share. I fnd that all the changes n the measured msallocaton effect arse from the effect y the change n the sectoral nomnal share and that the degree of wage dfferental s smlar efore and after the war. Ths result s n sharp contrast to the lterature on msallocaton, where dfferences n prces (output and factor prces) are the causes of msallocaton. 2 However, even f the wage dfferental etween sectors has remaned unchanged, t does not necessarly mply that the arrer to laor molty dd not exst. In addton, the motvaton of HP s to explan the relatvely hgh agrcultural employment rate n prewar. Therefore, I examne whether a model that does not assume a arrer to laor molty can explan the change n the prewar and postwar sectoral nomnal share and the change n the agrcultural employment rate. I fnd that a model of structural transformaton, developed y Latner (2000), Golln, Parente and Rogerson (2002), Golln, Parente and Rogerson (2007), and Duarte and Restucca (2007), among others, can help answer these questons. The results of my nvestgaton suggest that a arrer to laor molty mght not have een an mportant factor for the stagnaton of the prewar Japanese economy, and that other factors are By focusng on the effect of laor msallocaton on aggregate productvty, I can examne the msallocaton effect n an analytcally smple way. 2 See e.g., Restucca and Rogerson (2007), Restucca, Yang and Zhu (2008), Hseh and Klenow (2007), and Alfaro, Charlton and Kanczuk (2007) among others. 2

4 responsle for the prewar Japanese stagnaton. The remander of the paper s organzed as follows. Secton 2 presents a two-sector model. Usng ths model, Sectons 3 and 4 explan how to measure the effect of laor msallocaton on aggregate productvty and how to decompose the msallocaton effect nto several factors. Usng the framework developed n the aove sectons, Secton 5 measures the msallocaton effect and conducts the decomposton. Fnally, Secton 6 develops a model that does not assume a arrer to laor molty, and shows that ths model can explan the change n the prewar and postwar agrcultural employment rates and nomnal share. 2 Two-Sector Model There are two sectors n the economy agrcultural and non-agrcultural. The producton functon for each sector s Y = A K θ Lη, {a, n}, () where Y, A K, and L are sectoral output, productvty, captal, and laor, respectvely, and the suscrpts a and n denote agrcultural and nonagrcultural sectors, respectvely. The producton functons are the same as those n HP. Captal and laor nputs are homogeneous etween sectors. As n HP, the wage rate n each sector can e dfferent due to the arrer to laor molty, ut otherwse, frms are compettve. Then, the frst-order condtons (FOCs) are r = θ p Y K, (2) w = η p Y L, (3) where p s the output prce and r and w are the factor prces of captal and laor, respectvely. Fnally, the resource constrants are gven as follows: K = K a + K n, L = L a + L n, where K and L are the aggregate captal and laor supply, respectvely. 3

5 Under ths settng, the allocaton of captal and laor n each sector can e wrtten as follows (for the dervaton, see Appendx A): K = σ θ K, (4) θ L = σ η η λ L L, (5) where σ s sectoral nomnal share p Y /( p Y ), θ σ θ, η σ η, and λ L w σ η η = w From the last equaton, we fnd that λ L s a functon of the sectoral nomnal shares and wage ratos. Suppose that there s no arrer to laor molty. Then, w a = w n. In ths case, λ L ecomes equal to unty. On the other hand, f there s a arrer, λ L s not equal to unty, and thus, the laor allocaton devates from the no arrer case. Emprcally, λ L s derved from (5). σ η η w. w 3 Msallocaton Effect on Aggregate Productvty Ths secton analyzes how a arrer to laor molty affects the prewar Japanese aggregate productvty. For ths purpose, I frst compare the output of the actual economy wth a arrer, Y, wth that of a fcttous economy wthout a arrer, Y n. (The superscrpts and n denote arrer and no arrer economes, respectvely.) In the no arrer economy, wa n = wn n n (thus, λ L = ) and that the productvty of each sector s the same n the two economes. 3 The Tornqvst ndex of the output dfference etween the economes s defned as follows: ( ) Y σ ln, Y n where σ (σ +σ n )/2. The reason I use the Tornqvst ndex s ts tractalty. 4 Dewert (978) shows that the Tornqvst ndex s numercally very close 3 Ths assumpton s slghtly dfferent from HP s. They assume that n the no arrer economy, wa n h a = wn n h n, where h s the numer of hours worked and s exogenously gven. For smplcty, I assume wa n = wn n. If my assumpton s the same as that of HP, the effect of laor msallocaton on aggregate productvty generally decreases. 4 Ths ndex also has a mcrofoundaton. See Appendx B. 4

6 to the Fsher ndex (whch s used n HP). By susttutng (), (4), and (5) n ths defnton, I otan ( ) Y σ ln ( ) ( ) σ Y n η ln λ L + θ K L ln + η ln, (6) K n L n where θ σ θ, and η σ η. 5 I defne the dfference n aggregate productvty as follows: ( ) A ln ( ) ( ) ( Y σ A n ln Y θ K L ln η ln n K n Ths s the standard defnton of the dfference n aggregate productvty. By rewrtng (6), usng the defnton of aggregate productvty, I otan ( ) A ln σ A n η ln λ L. (7) The RHS captures the effect of laor msallocaton on aggregate productvty. Note that f w a = w n, then the RHS ecomes zero. I refer to the RHS as the (aselne) msallocaton effect. 4 Decomposton of the Msallocaton Effect Even f the wage dfferental etween the agrcultural and non-agrcultural sectors n prewar Japan s as large as that n postwar Japan, the prewar msallocaton effect can e large ecause the sectoral nomnal share, σ, also affects the msallocaton effect. In order to dentfy the sectoral nomnal share effect, I also calculate the msallocaton effect of prewar Japan, where the wage dfferental etween sectors changes to the average wage dfferental of the postwar perods ut sectoral nomnal shares are calculated from the prewar data. I refer to ths as the counterfactual msallocaton effect. The counterfactual msallocaton effect can e calculated as follows: where λ (wpost pre L w post σ pre pre η ln λ ) (wpost L w post σ pre η w post η pre w post 5 Other terms are approxmately zero. For detals, see Appendx C. L n ). ), (8). 5

7 (The superscrpts pre and post denote prewar and postwar Japan, respectvely.) Emprcally, the postwar average of the rato of wage rate, w post /w post, s measured usng a frm s FOC (3). Usng the counterfactual msallocaton effect, the dfference n prewar and postwar aselne msallocaton effect s decomposed as follows: σ pre pre η ln λ L σ post post η ln λ L = + σ pre pre η ln λ L σ pre pre η ln λ (wpost L w post } {{ } Wage dfferental term σ pre pre η ln λ (wpost L w post ) σ post post η ln λ L ) }{{} Sectoral nomnal share term (9) If the dfference n the aselne msallocaton effects etween the prewar and postwar Japan s due to the change n wage dfferental, the wage dfferental term accounts for most of the dfference. On the other hand, f the dfference n the sectoral nomnal share s the cause of the dfference n aselne msallocaton effects, the sectoral nomnal share term accounts for most of the dfference. 5 Measurement Ths secton measures the prewar ( ) and postwar ( ) averages of the aselne and counterfactual msallocaton effects, usng (7) and (8), and conducts decomposton, usng (9). I use the dataset provded y HP. As n HP, for laor nput L, I use hours worked tmes employment n ther data. For the sectoral nomnal share, I use the value added share n ther data. In order to calculate the msallocaton effects, I have to assume the sectoral nomnal share under no arrer condton. I assume that the sectoral nomnal share under the no arrer condton s the same as that under the arrer condton (referred to as case ). As a roustness check, I also calculate the aselne and counterfactual msallocaton effects, usng the smulaton result of the sectoral nomnal share under the no arrer condton n HP (referred to as case 2). Case 2 s provded only for the prewar averages snce ther smulaton result s avalale only n prewar perod. Fnally, followng HP, I specfy the laor share parameter of the agrcultural sector, η a, as 0.638, and that of the non-agrcultural sector, η n, as 2/ These values are the laor shares of value added n ther paper.. 6

8 Tale reports the results. The magntude of the prewar aselne msallocaton effect s larger than that of the postwar aselne msallocaton effect, whch s consstent wth HP. On the other hand, the magntude of the counterfactual msallocaton effect s also large. Tale 2 reports the decomposton. Ovously, the sectoral nomnal share term occupes the entre dfference n the prewar and postwar msallocaton effects. The reason for ths s that the wage dfferental etween sectors s rather road n the postwar perod: the prewar average of the wage rato etween sectors w a /w n s 0.33, whle the postwar average s Predcton of Sectoral Shares Usng a No Barrer Model Even f the wage dfferental etween sectors s the same efore and after the war, t does not necessarly mply that a arrer to laor molty does not exst. In addton, the motvaton of HP s to explan the relatvely hgh agrcultural employment rate n prewar Japan. Therefore, ths secton demonstrates that a model of structural transformaton can explan the change n prewar and postwar sectoral employment rate and the nomnal share wthout assumng a arrer to laor molty. 7 In the model, households only care to consume the susstence amount of agrcultural goods ā. Then, the followng equaton holds: ā = Y a N = Y a N a N a N, where N a and N denote the agrcultural and total employment. 8 As n Duarte and Restucca (2007), I assume that the agrcultural laor productvty Y a /N a s exogenously gven. 9 Then, gven ā, from the aove equaton, I can otan the model predcton of agrcultural employment share N a /N. Fgure plots the data and model predcton of the agrcultural employment rate (I assume 0.08 for ā). The model fts the postwar data and the prewar data after 90 farly well. In addton, I can also derve the model predcton of the sectoral nomnal share. 0 The model predcton of the sectoral nomnal share also fts the data after 90 well, when the wage 7 Ths secton draws on Nakamura (2008), who compares the postwar Japanese data on sectoral employment rate wth the predcton of Duarte and Restucca s (2007) model. 8 Here, I smply assume that the total employment s equal to the total populaton. 9 Ths assumpton mght e prolematc. Endogenzng the captal accumulaton has een left for future research. 0 Usng (3), I can otan the model predcton of the agrcultural nomnal share as 7

9 dfferental etween sectors s assumed to e constant over tme and equal to the postwar average (see Fgure 2). References Alfaro, Laura, Andrew Charlton, and Fao Kanczuk (2007) Frm-Sze Dstruton and Cross-Country Income Dfferences, Aprl. Mmeo. Dewert, W Erwn (978) Superlatve Index Numers and Consstency n Aggregaton, Econometrca, Vol. 46, No. 4, pp , July. Duarte, Margarda and Dego Restucca (2007) The Role of the Structural Transformaton n Aggregate Productvty, Workng Papers tecpa-300, Unversty of Toronto, Department of Economcs. Golln, Douglas, Stephen Parente, and Rchard Rogerson (2002) The Role of Agrculture n Development, Amercan Economc Revew, Vol. 92, No. 2, pp , May. Golln, Douglas, Stephen L. Parente, and Rchard Rogerson (2007) The food prolem and the evoluton of nternatonal ncome levels, Journal of Monetary Economcs, Vol. 54, No. 4, pp , May. Hayash, Fumo and Edward C. Prescott (2006) The Depressng Effect of Agrcultural Insttutons on the Prewar Japanese Economy, March NBER Workng Paper No. 208, March Hseh, Chang-Ta and Peter J. Klenow (2007) Msallocaton and Manufacturng TFP n Chna and Inda, NBER Workng Papers 3290, Natonal Bureau of Economc Research, Inc. Latner, John (2000) Structural Change and Economc Growth, Revew of Economc Studes, Vol. 67, No. 3, pp , July. follows: σ a = w a L a /η a w a L a /η a + w n L n /η n = ( N w ah a + ηa η n w nh n ), N a where h denotes the numer of hours worked. Precsely speakng, unlke the prevous sectons, the wage dfferental here s not the wage dfferental per hour ut the dfferental per worker. 8

10 Nakamura, Naotaka (2008) Effect of Demographc Transton on Structural Transformaton (n Japanese), Master s thess, Graduate School of Economcs, Unversty of Tokyo. Restucca, Dego and Rchard Rogerson (2007) Polcy Dstortons and Aggregate Productvty wth Heterogeneous Plants, Workng Papers tecpa- 283, Unversty of Toronto, Department of Economcs. Restucca, Dego, Denns Tao Yang, and Xaodong Zhu (2008) Agrculture and Aggregate Productvty: A Quanttatve Cross-Country Analyss, Forthcomng n Journal of Monetary Economcs. Appendx A Dervaton of (4) and (5) (5) can e derved as follows: L = (4) can e derved n the same way. w L w w L w L = p Y η w p Y η w L = σ η w σ η w L = σ η η λ L L. B A Mcrofoundaton of the Tornqvst Index Suppose the aggregator functon Y = Y (Y a, Y n ) (t can e nterpreted as the utlty functon or the aggregate producton functon). I assume that the aggregator functon s constant returns to scale and that Y Y = p (then, 9

11 Y = p a Y a + p n Y n ). By applyng the mean value theorem, I otan ( ) Y (Y ln a, Yn ) = ( ) ln Y Y ln Y (Ya n, Yn n ) ln Y Y n = ( ) Y σ ln. Y n The last equaton s approxmately equal to the Tornqvst ndex. C Dervaton of (6) In order to derve (6), we need to show that terms θ σ θ θ ln ( ) σ θ θ and η ( ) σ η ln σ η are approxmately zero ( denotes the dfference). These η η terms are approxmately zero, ecause when γ =, the followng relaton holds: γ ln γ γ γ γ = = 0. 0

12 Baselne Counterfactual Prewar Postwar Dfference Prewar Case 9.43% 3.84% 5.58% 9.69% Case % 6.97% Tale : Baselne and counterfactual msallocaton effects. Notes: The values under the prewar correspond to the average and the values under the postwar correspond to the average. The dfference mples the dfference n the prewar and postwar msallocaton effects. Case denotes the case where the sectoral nomnal share under the no arrer condton s the same as that under arrer. Case 2 denotes the case where the sectoral nomnal share s orrowed from the smulaton result of Hayash and Prescott (2006). Wage dfferental term Sectoral nomnal share term 0.27% 5.85% Tale 2: Decomposton of the dfference n the prewar and postwar aselne msallocaton effects. Note: The sum s equal to the dfference n the prewar and postwar msallocaton effects.

13 Fgure : The data and model predcton of the Japanese agrcultural employment rate. Fgure 2: The data and model predcton of the Japanese agrcultural nomnal share. 2