Silviase/jgov_v1.4_full_ann huggingface dataset:
所 管 別 及 び 会 計 別	事 項	計	画	支 出 及 び 支 出 予 定 の 状 況 等
総 額 (千円)	実 施 年 度	事 業 内 容	昭和47年度までの支出額及び支出額見込 (千円)	昭和48年度以降支出予定額 (千円)	昭和49年度以降支出予定額 (千円)	摘 要
(特定多目的ダム建設工事勘定)	直轄流況調整河川事業昭 和 48 年 度河川総合開発事業費補助昭 和 47 年 度治水ダム建設事業費補助昭 和 47 年 度河川 改 修 受 託 工 事昭 和 48 年 度	300,000	昭和48年度及び昭和49年度	利根川広域導水事業の建設工事及びこれに附帯する工事	-	200,000	100,000	昭和49年度完成予定
1,242,000	昭和47年度以降4 箇年度	八戸川八戸ダムの建設工事及びこれに附帯する工事の事業費の一部補助	12,000	348,000	882,000	昭和50年度完了予定
500,000	昭和47年度以降4 箇年度	野呂川野呂川ダムの建設工事及びこれに附帯する工事の事業費の一部補助	15,000	200,000	285,000	昭和50年度完了予定
735,000	昭和48年度以降3 箇年度	阿武隈川堰ほか1堰の管理者からの委託に係る阿武隈川堰及び菊池川山鹿大堰の建設工事	-	70,000	665,000	昭和50年度完成予定
多目的ダム建設事業	4,631,000	169,000	1,033,000	3,429,000
紀の川大滝ダム建設工事昭 和 47 年 度昭 和 48 年 度九頭竜川真名川ダム建設工事昭 和 47 年 度昭 和 48 年 度仁淀川大渡ダム建設工事	592,000	昭和47年度以降3 箇年度昭和48年度以降5 箇年度	ダムの建設工事及びこれに附帯する工事同	169,000	383,000	40,000	昭和49年度完成予定昭和52年度完成予定昭和50年度完成予定昭和50年度完成予定
4,039,000	-	650,000	3,389,000
3,163,000	92,000	571,000	2,500,000
1,015,000	昭和47年度以降4 箇年度	同	92,000	471,000	452,000
2,148,000	昭和48年度以降3 箇年度	同	-	100,000	2,048,000
6,748,000	535,000	1,282,000	4,875,500
所 管 別 及 び 会 計 別	事 項	計	画	支 出 及 び 支 出 予 定 の 状 況 等
総 額 (千円)	実 施 年 度	事 業 内 容	昭和47年度までの支出額及び支出額見込 (千円)	昭和48年度以降支出予定額 (千円)	昭和49年度以降支出予定額 (千円)	摘 要
昭 和 46 年 度	5,250,000	昭和46年度以降5 箇年度	ダムの建設工事及びこれに附帯する工事	535,000	1,090,000	3,569,500	昭和50年度完成予定国庫債務負担行為を実行しなかつた額 55,500 千円昭和51年度完成予定
昭 和 48 年 度	1,498,000	昭和48年度以降4 箇年度	同	-	192,000	1,306,000
北上川御所ダム建設工事	6,242,000	昭和46年度以降5 箇年度	ダムの建設工事及びこれに附帯する工事並びにダムの建設に必要な用地の取得	4,179,991	484,500	680,000	昭和50年度完成予定国庫債務負担行為を実行しなかつた額 897,509 千円
昭 和 46 年 度	5,000,000	昭和46年度以降5 箇年度	ダムの建設工事及びこれに附帯する工事	1,370,775	511,000	2,094,000	昭和50年度完成予定国庫債務負担行為を実行しなかつた額 1,024,225 千円
利根川川治ダム建設工事	13,647,000	260,000	2,338,000	11,049,000
昭 和 47 年 度	6,500,000	昭和47年度以降4 箇年度	同	260,000	1,704,000	4,536,000	昭和50年度完成予定
昭 和 48 年 度	7,147,000	昭和48年度以降4 箇年度	同	-	634,000	6,513,000	昭和51年度完成予定
芦田川河口堰建設工事	2,600,000	531,000	1,759,000	310,000
昭 和 47 年 度	1,720,000	昭和47年度以降3 箇年度	芦田川河口堰の建設工事及びこれに附帯する工事	531,000	1,039,000	150,000	昭和49年度完成予定
昭 和 48 年 度	880,000	昭和48年度及び昭和49年度	同	-	720,000	160,000	昭和49年度完成予定
太田川高濑堰建設工事	1,468,000	310,000	788,000	370,000
昭 和 47 年 度	928,000	昭和47年度以降3 箇年度	太田川高濑堰の建設工事及びこれに附帯する工事	310,000	488,000	130,000	昭和49年度完成予定
昭 和 48 年 度	540,000	昭和48年度及び昭和49年度	同	-	300,000	240,000	昭和49年度完成予定
荒川大石ダム建設工事
所 管 別 及 び 会 計 別	事 項	計画	支 出 及 び 支 出 予 定 の 状 況 等
総 額 (千円)	実 施 年 度	事 業 内 容	昭和47年度までの支出額及び支出額見込 (千円)	昭和48年度以降支出予定額 (千円)	昭和49年度以降支出予定額 (千円)	摘 要
昭 和 47 年 度 遠賀川河口堰建設工事 昭 和 48 年 度 荒川滝沢ダム建設工事 昭 和 48 年 度 阿賀野川大川ダム建設工事 昭 和 48 年 度 北海道多目的ダム建設工事 石狩川大雪ダム建設工事 昭 和 47 年 度 昭 和 48 年 度 沖縄多目的ダム建設事業 沖縄北部河川安波・普久川・新川ダム建設工事 昭 和 48 年 度	2,620,000	昭和47年度以降4 箇年度	ダムの建設工事及びこれに附帯する工事	30,000	1,170,000	1,420,000	昭和50年度完成予定
800,000	昭和48年度及び昭和49年度	遠賀川河口堰の建設工事及びこれに附帯する工事	-	613,000	187,000	昭和49年度完成予定
250,000	昭和48年度及び昭和49年度	ダムの建設工事及びこれに附帯する工事	-	90,000	160,000	昭和49年度完成予定
731,000	昭和48年度及び昭和49年度	同	-	110,000	621,000	昭和49年度完成予定
2,272,680	180,000	1,099,500	993,180
727,680	昭和47年度以降3 箇年度	同	180,000	349,500	198,180	昭和49年度完成予定
1,545,000	昭和48年度及び昭和49年度	同	-	750,000	795,000	昭和49年度完成予定
3,510,000	昭和48年度及び昭和49年度	ダムの建設工事及びこれに附帯する工事	-	1,156,000	2,354,000	昭和49年度完成予定
合 計 上 記 の ほ か	543,031,477 年額 1,332,220	59,766,453 -	200,825,379 472,949	280,004,436 年額 490,733 以内

(注) 单位未満を切り捨ててあるので、端数において符合しないものがあり、また、合計とは端数において合致しない。
## 8 継続費に関する調書

一 般 会 計

所 管 別及 び組 織 別	事 項	計画	支 出 額 及 び 支 出 予 定 額
総 額(千円)	実 施 年 度	内 容	昭和46年度未までの支出額(千円)	昭和47年度支出額及び支出額見込(千円)	昭和48年度(千円)	昭和49年度(千円)	昭和50年度(千円)	昭和51年度(千円)	昭和52年度(千円)
総 府 所 管(組織)
防 衛 本 庁	昭和45年度甲Ⅲ型警備艦建造費	10,981,532	昭和45年度から昭和49年度までの5歯年度	基準排水量4,700トン型1隻完成予定年度昭和49年度	2,026,814	4,541,999	1,534,455	2,878,264	-	-	-
昭和45年度乙型警備艦建造費	8,485,119	昭和45年度から昭和48年度までの4歯年度	基準排水量1,450トン型2隻完成予定年度昭和48年度	3,514,329	3,937,079	1,033,711	-	-	-	-
昭和45年度潜水艦建造費	7,188,735	昭和45年度から昭和48年度までの4歯年度	基準排水量1,800トン型1隻完成予定年度昭和48年度	2,329,744	2,777,361	2,081,630	-	-	-	-
昭和46年度甲Ⅳ型警備艦建造費	18,488,161	昭和46年度から昭和50年度までの5歯年度	基準排水量3,850トン型1隻完成予定年度昭和50年度	582,216	4,357,391	3,756,677	6,298,103	3,493,774	-	-
昭和46年度甲型警備艦建造費	6,229,048	昭和46年度から昭和49年度までの4歯年度	基準排水量2,100トン型1隻完成予定年度昭和49年度	556,537	639,850	3,404,700	1,627,961	-	-	-
昭和46年度乙型警備艦建造費	4,372,623	昭和46年度から昭和48年度までの3歯年度	基準排水量1,450トン型1隻完成予定年度昭和48年度	338,766	2,454,818	1,579,039	-	-	-	-
昭和46年度潜水艦建造費	7,565,595	昭和46年度から昭和49年度までの4歯年度	基準排水量1,800トン型1隻完成予定年度昭和49年度	797,643	2,367,046	2,187,619	2,213,287	-	-	-
昭和47年度乙型警備艦建造費	14,165,447	昭和47年度から昭和50年度までの4歯年度	基準排水量1,450トン型3隻完成予定年度昭和50年度	-	1,262,553	5,747,446	6,020,090	1,135,358	-	-
昭和47年度潜水艦建造費	8,554,981	昭和47年度から昭和50年度までの4歯年度	基準排水量1,800トン型1隻完成予定年度昭和50年度	-	971,734	2,920,053	2,185,889	2,477,305	-	-
昭和48年度甲Ⅳ型警備艦建造費	22,968,064	昭和48年度から昭和52年度までの5歯年度	基準排水量3,850トン型1隻完成予定年度昭和52年度	-	-	1,952,953	5,296,998	4,528,073	7,718,621	3,471,419
昭和48年度乙型警備艦建造費	5,101,807	昭和48年度から昭和51年度までの4歯年度	基準排水量1,500トン型1隻完成予定年度昭和51年度	-	-	466,991	717,058	2,656,869	1,260,889	-
所 管 別 及 び 组 織 別	事 項	計画	支 出 額 及 び 支 出 予 定 額
総 額 (千円)	実 施 年 度	内 容	昭和46年度 末までの支 出額 (千円)	昭和47年度支 出額及び支出 額見込 (千円)	昭和48年度 (千円)	昭和49年度 (千円)	昭和50年度 (千円)	昭和51年度 (千円)	昭和52年度 (千円)
昭和48年度潜水艦建 造費	9,808,169	昭和48年度から 昭和51年度まで の4箇年度	基準排水量 1,800トン型 1隻 完成予定年度 昭和51年度	-	-	964,898	2,912,074	3,074,729	2,856,468	-
合 計	123,909,281	10,146,049	23,309,831	27,630,172	30,149,724	17,366,108	11,835,978	3,471,419
行政事業レビューにおける平成27年度行動計画

1. 目的

金融庁の事業の実態（支出先や使途）を十分に把握した上で、自己点検を実施するとともに、その結果を事業の執行や予算要求に反映させることを目的とする。

### 2. 实施体制

（１）以下の者を構成員とする「金融庁行政事業レビュー推進チーム」（以下「チーム」という。）を設置する。

チームの構成員

統括責任者 総括審議官

副統括責任者 総務企画局総務課長

// 政策課長

チームメンバー 各局総務課長等

（２）外部有識者を複数名指名し、外部の視点を活用した行政事業レビューの点検に取り組むものとする。

（３）チームは以下の取組みを行うものとする。

（ア）事業所管部局による行政事業レビューシート（以下「レビューシート」という。）の適切な記入及び厳格な自己点検の指導

（イ）外部有識者の点検を受ける事業の選定及び外部有識者からの点検結果の聴取

（ウ）外部有識者による公開の場での点検の対象となる事業の選定及び点検結果の聴取

（エ）ア、イ及びウを踏まえた事業の厳しい点検（サマーレビュー）及び点検結果（所見）のとりまとめ

（オ）チーム所見を踏まえた事業の改善状況の点検

（力）金融庁全体の概算要求への反映状況の確認及びとりまとめ

（４）各局総務課長等は、チームの方針に従って、所管に係る事業及び行政事業レビューの実施を監督する。

（５）チームの庶務は、総務企画局総務課管理室が処理する。
### 3. 对象事業

行政事業レビューは、平成26年度に実施した事業（同年度限りで終了した事業を含み、事務的経費、人件費等は除く。）を対象に、その実績に基づいて実施する。

### 4. 事業の実態把握

事業ごとに最終的に①予算がどこに渡り、②何に使われているかに関し、必要に応じて現場確認を行うなど、各局課室において十分な把握に努める。

把握した結果については、事業ごとに、行政改革推進本部事務局の定めるレビューシートに記載する。

### 5. 各局課室による事業の自己点検

上記の事業の実態把握を踏まえ、それが本来の事業目的と合致しているか、真に効率的・効果的な支出となっているかなど、各局課室において自己点検を実施する。

### 6. レビュー対象事業以外の事業の自己点検

各局課室は、事業の有効性、効率性及び透明性を確保するため、レビュー対象事業以外に平成27年度新規事業及び平成28年度予算の概算要求において新規に要求する事業についても自己点検を行う。

### 7. 結果の公表、概算要求への反映

上記の自己点検の結果を反映した上でレビューシートを公表するとともに、それに対して国民からの意見を募集する（中間公表）。

さらに選定したレビューシートについて、外部有識者による、外部の視点を活用した点検を行う。また、チームの所見及び所見を踏まえた事業の改善点、平成28年度予算の概算要求額等を記入したレビューシート及び概算要求への反映結果を公表する。

### 8. その他の取組み

職員の認識や意欲の喚起に努めるとともに、職員からの意見・提言募集、人事評価への反映など、行政事業レビューの実効性を高め、その向上に資する施策について、積極的に取り組む。
ESRI Discussion Paper Series No.57

Quality Adjusted Cost Function in Japan’s Child Care Market: Evidence from Micro-level Data

by

Haruko Noguchi and Satoshi Shimizutani

August 2003

Economic and Social Research Institute

Cabinet Office

Tokyo, Japan
# Quality Adjusted Cost Function in Japan’s Child Care Market: Evidence from Micro-level Data $ ^{1} $

By

Haruko Noguchi and Satoshi Shimizutani

August 2003

Please address correspondence to:

Haruko Noguchi, Toyo-Eiwa University, Yokohama, Japan

Email: hnoguchi@newage3.stanford.edu

Satoshi Shimizutani, Cabinet Office, Tokyo, Japan

Email: satoshi.shimizutani@mfs.cao.go.jp
## Abstract

This is the first study that uses facility-level data to evaluate the cost efficiency of the child care market in Japan after controlling for quality of services. Japanese households in urban areas suffer from a severe undersupply of child care, and inefficient operation in public centers is allegedly responsible for the bottleneck. We take advantage of our unique and unusually rich data set on Japan’s child care centers collected in summer 2002. We estimate quality-adjusted cost functions to compare the efficiency between public and private licensed facilities. Our findings demonstrate that public centers are more inefficient than private facilities by 10 to 20 percent. Moreover, government subsidies contribute to the inefficiency in public centers. These findings suggest that efficiency improvements in public-owned centers and reduction of subsidies are indispensable for the breakthrough of the bottleneck of the child care supply in Japan.
### 1. Introduction

Japanese households in urban areas suffer from a severe undersupply of child care; inefficient operation in public centers is allegedly responsible for the bottleneck. Surprisingly, however, there has been little quantitative research on cost efficiency in the Japan’s child care industry. Obviously, it is impossible to draw any prescription to remedy the inefficiency without investigating what, and to what extent, factors contribute to higher costs.

This is the first study that uses facility-level data to evaluate the cost efficiency of the child care market in Japan. We focus especially on the efficiency gap in public and non-profit centers, both of which are dominant, by estimating cost functions $ ^{2} $ . When estimating cost functions, we pay attention to the difference in quality of services. Higher costs do not directly correlate with higher inefficiency, since such higher costs might be associated with higher quality. Moreover, to obtain policy implications for a more competitive market, we will focus on what causes inefficiency; government transfers, for example. To address these issues, we take advantage of an unusually rich and unique data set on the Japanese child care industry.

Our main results are previewed as follows. We clearly observe that public centers are more inefficient than private facilities by 10 to 20 percent. Moreover, subsidies from government contribute to the inefficiency in public centers. Our findings thus demonstrate that efficiency improvements in public-owned centers and reduction of subsidies are indispensable for the breakthrough of the bottleneck of the child care supply in Japan.

This paper is organized as follows. Section 2 provides a literature review on the costs and efficiency of child care, mainly in the United States. Section 3 describes the data set used in this study. Section 4 briefly describes the cost structure in Japan’s child care centers. Section 5 performs regressions of quality-adjusted cost functions in several forms and discusses the obtained
results. The final section concludes and offers policy implications regarding further reform in Japan’s child care market.

### 2. Literature Survey

Despite the importance of improving efficiency in the child care industry there have been surprisingly few quantitative studies in Japan. Some previous research used city/town/village level data (Hayashi (1996) etc.) and other studies relied on case studies in some specific local governments (Yamashige (2001)). These studies were seriously hampered by a lack of micro-level data, since we need more detailed facility-level information on child care costs and characteristics of each facility. In addition, they are especially problematic since they are not able to adjust for quality of care.

Noguchi, Shimizutani, and Suzuki (2003a,b) demonstrate that wages costs are apparently higher for care workers in publicly-owned centers than in private nonprofit or for-profits. Since child care is labor intensive, higher wage costs result in higher operational costs. These higher wage rates might be justified if the quality of care provided by public facilities was superior, but Noguchi and Shimizutani (2003) demonstrate that this is not the case. Yet, the extent to which costs are unjustified and what causes inefficiency remain two unexplored areas.

On the other hand, in the United States, a large number of studies take advantage of micro-level data from each center (Mukerjee and Dryden (1992), Mukerjee and Dryden (1993), Powel and Cosgrove (1992), Mocan (1995), Mocan (1997), Blau and Mocan (2002)).

Among these studies, Mocan (1995, 1997) focuses on the cost differences in nonprofit and for-profit centers. Mocan (1995) estimates multi-product translog cost functions for 399 child care centers from four U.S. states. After controlling for quality of child care by a quality index, nonprofit centers that receive public money tied to higher standards have total variable costs that are about 20 percent higher than other centers, keeping quality of services constant. On the other
hand, there is no significant difference between general categories of for-profit and non-profit centers. It costs 13 cents per hour per child to increase this average quality to the level considered appropriate by education experts. Moreover, Mocan (1997) obtains similar results to show no difference in average quality of the services and relative inefficiency between nonprofit and for-profit centers except centers that receive public money, which have higher variable costs.

### 3. Data Description

An empirical analysis of this study is based on a unique and unusually rich survey of child care centers. The survey was conducted by the Price Policy division of the Cabinet Office, Japanese government, in the summer of 2002. As far as we know, this data set is the first and most comprehensive survey on child care workers; it has the largest sample size and thus the best available data in Japan. We were able to perform the survey with special cooperation and deep understanding by local governments.

Before performing the survey, we visited several local governments including Tokyo Prefecture, to ask their support in the survey. We explained the purpose of our research and consulted on several important issues with officials in charge of child care policies at local governments. Concretely, we discussed the detailed questionnaire, the feasibility of each question, and precision of responses.

A sample of the survey contains child care centers located in the entire 729 municipal areas of 10 prefectures in the Kanto Area; Tokyo, Kanagawa, Saitama, Chiba, Shizuoka, Yamanashi, Nagano, Gunma, Tochigi, and Ibaragi. Of 729 districts, we collected data from the 533 local governments. The response rate of 73.1 percent is remarkably high.

Local governments participating in the survey provided wealth information on child care facilities within the area, such as management type, size, service contents, and equipment. Moreover, they collected detailed information on all care workers in each facility, from 20 percent
of public centers and 40 percent of licensed private facilities by individual local government, which were randomly selected $ ^{3} $ . The sample size is 1,351 centers, including 639 public licensed centers and 712 licensed private centers $ ^{4} $ .

The basic statistics are reported in Table 1. Apparently, public centers are more costly than private ones. The average total operational costs in public centers are higher than those of private centers by approximately 6 percent. The differences are 2 percent for total wage benefits, 7 percent for total costs for human capital including non-wage benefits, and 6 percent for total costs other than labor costs, which includes rental costs. Since all observations have data on wage benefits but some centers do not have data on the non-wage benefits, we calculate them by estimating the non-wage costs function based on the samples that reported the data (see Appendix Table 1). Moreover, much smaller centers have data on the total costs other than labor costs. Since these costs, such as rents, are difficult to be estimated, the figures are calculated from limited samples that reported the figures $ ^{5} $ . Note that the sample size is 95 for public and 107 for private facilities only for total operational costs, total costs other than labor costs, and rents in Table 1.

Higher costs reflect higher factor prices. The wage costs are higher for public centers by 11 percent. Regarding the output indicators, the average age of children is clearly younger for private centers. This implies that costs would be higher for them than in public centers, since the number of care workers per child, which is determined by law, is much higher for younger children, as explained in the next section. If we check the characteristics of employees and facilities, we also note that public centers hire more non-regular workers. Nonetheless, total costs are higher for public facilities. Total hours of care are longer for private centers. There is not much difference in provision of special care.

Finally, we should pay attention to the differences in quality of care. This quality measurement
is taken from the results of the “total score” approach adopted in Noguchi and Shimizutani (2003). This approach classifies various indicators associated with user’s benefits into several categories. We adopt 40 detailed items classified into four categories indicating each facility’s characteristics: (1) structural index, (2) developmental psychological index, (3) parents’ convenience index, and (4) other indexes. The scoring methods are very straightforward and are the ones most commonly used (i.e. Mocan (1995)).

The bottom of Table 1 reports that the total score is higher for public centers, but this is not the case for some detailed categories. Public centers have higher scores in the structural index such as number of care workers per child. Both public and private facilities have similar scores in developmental psychological indexes and private centers score much higher in the parents' convenience index.

### 4. Cost Structure in the Japan’s Child Care Centers

Before estimating cost function, we should keep in mind a peculiar institution: the cost structure in the Japanese child care market. Figure 1 demonstrates what determines the operational costs in the child care industry. According to the national standard, half of the total amount of child care costs ((X) in the figure) consists of parents' payments ((d) and (e)), and the remaining half is subsidized by central and local governments ((c); a quarter from national and another quarter from local governments). Note that parents' payments are the same for public and private-licensed centers in each municipality.

We should note that the age structure and additional subsidies provided by each local government’s policy produce differences in cost across facilities.

First, cost per child varies greatly with age. Costs per child age zero to one are supposed to be four or five times as those of children age four or five. These age-dependent costs are attributed to the legal allocation of care worker per child. Each licensed child care center obeys the “minimum
requirements” to provide minimum a worker per three children age zero to one and a minimum of one worker per 30 children age four or older.

Second, the amounts of additional benefits provided by local governments are diverse. As stated above, the national standard assumes that half of total operational costs are supposed to be covered by parents' payments, and the remaining half by government subsidy (a quarter from local governments and a quarter from central government). However, each local government provides additional subsidies in the following three forms at their own burden. First, some governments exempt or decrease parents' payments from the national standards ((d)). Second, some governments allocate more child care workers per children than the standards dictate, which contributed to increase the operational costs ((b)). Third, some local governments offer higher wages than the national standard, which is based on a child care worker having five or six years of experience. If the government adopts the seniority system widely observed in Japan, it is obliged to pay more than what the national standard assumes ((a)). See Noguchi, Shimizutani and Suzuki (2003 a)).

Those peculiar cost structures in the Japanese child care industry imply that we should adjust these elements so that we could compare efficiency.

### 5. Estimation of Facility-level Cost Functions

In this section, we estimate quality-adjusted cost functions to assess efficiency, using two types of cost functions: the Cobb-Douglas cost function (1) and the translog cost function (2). As discussed in Mocan (1995, 1997), a cost function is more relevant to our study than a production function since we only need to assume a cost-minimizing behavior when nonprofits are operating in the market and input prices are assumed to be exogenously determined $ ^{6} $ . In addition, as Newhouse (1970) pointed out, a manager in nonprofits maximizes quality as well as quantity. Thus,
we estimate a “quality adjusted cost function” to include quality index as an explanatory variable to control for a manager’s preference and heterogeneity of outputs.

$$ \ln C=\alpha_{_{0}}+\sum_{_{i}}\alpha_{_{i}}\ln P_{_{i}}+\sum_{_{j}}\beta_{_{j}}\ln Y_{_{j}}+\sum_{_{k}}\gamma_{_{k}}X_{_{k}}+\delta Q+\lambda K+u $$

$$ \begin{aligned}\ln C=\alpha_{_{0}}&+\sum_{i}\alpha_{_{i}}\ln P_{_{i}}+\frac{1}{2}\sum_{i}\sum_{j}\beta_{_{ij}}\ln P_{_{i}}\ln P_{_{j}}+\sum_{k}\gamma_{_{k}}\ln Y_{_{k}}+\frac{1}{2}\sum_{k}\sum_{l}\delta_{_{kl}}\ln Y_{_{k}}\ln Y_{_{l}}\\&+\sum_{i}\sum_{k}\uprho_{_{ik}}\ln P_{_{i}}\ln Y_{_{k}}+\sum_{m}\upeta_{X}+\upmu_{Q}+\lambda_{K}+u\end{aligned} $$

$$ where\sum_{i}\alpha_{i}=1,\quad\sum_{j}\beta_{ij}=\sum_{j}\rho_{jk}=0\quad and\quad\beta_{ij}=\beta_{ji}. $$

First, the dependent variable is the log of total expenditure ( $ \ln C $ ) of individual child care centers. We have three different measures for the dependent variable: total wage costs, total costs for human capital, and total operational costs. Note that we have 1,351 samples for the former two variables but 202 for the total operational costs.

Second, we have sets of explanatory variables. $ \ln P $ is the log of factor prices that are represented by the hourly wage for all dependent variables and includes rents for the total operational costs regression. Rental costs include those paid for office space and equipment. $ \ln Y $ is the log of output embodied in number of children by age. In addition, X refers to other attributes of centers, including the log of total hours of care, special care (extra hours of care, holiday care, nighttime care, disability care, temporary care, post acute care, and special education program) and area dummies for nine prefectures (Tokyo Prefecture is the reference). Q stands for the quality of services measured as described in the data section.

The equation is estimated by the OLS (ordinary least squares) for equation (1). We use the Shepard's lemma to rewrite the equation (2) as the equation of shares of input ((3)). We perform the SUR (seeming uncorrelated regression) to estimate (2) and (3) jointly to improve the efficiency.