Silviase/jgov_v1.4_full_ann huggingface dataset:
# 日 本 輸 出 入 銀 行

## 総括貸借対照表

借方	贷方
科目	昭和45年度末决算額(円)	昭和46年度末予定額(円)	昭和47年度末予定額(円)	科目	昭和45年度末决算額(円)	昭和46年度末予定額(円)	昭和47年度末予定額(円)
貸付金	1,596,715,938,414	1,856,124,668,320	2,267,124,668,320	借入金	1,141,836,000,000	1,336,597,000,000	1,681,969,000,000
支払承諾見返	40,386,422,045	39,434,566,045	45,328,589,045	資金運用部借入金	1,141,836,000,000	1,332,472,000,000	1,674,344,000,000
有価証券	11,822,253,350	16,017,000,000	16,076,000,000	一般会计借入金	0	4,125,000,000	7,625,000,000
現金預付金	356,965,397	444,260,734	207,616,734	支払承諾	40,386,422,045	39,434,566,045	45,328,589,045
2動產不動產	1,488,722,851	2,010,296,851	2,098,663,851	雑勘定	17,443,825,797	21,010,614,797	24,445,059,797
雑勘定	8,630,304,551	11,630,852,551	15,405,453,551	仮受金	36,831,531	22,811,531	22,811,531
仮払金	269,590,250	6,328,250	6,328,250	未払利息その他	16,057,888,648	19,638,697,648	23,073,142,648
未収貸付金利息	8,236,502,321	10,633,220,321	13,574,130,321	未經過割引料その他	1,349,105,618	1,349,105,618	1,349,105,618
その他雑勘定	124,211,980	991,303,980	1,824,994,980	貸倒準備金	9,572,579,129	13,432,754,022	16,266,092,022
資本金	448,300,000,000	513,300,000,000	576,300,000,000
準備金	1,861,779,637	1,861,779,637	1,861,779,637
積立金	0	0	24,930,000
利益金	0	24,930,000	45,541,000
一般勘定利益金	0	0	0
特別勘定利益金	0	24,930,000	45,541,000
合計	1,659,400,606,608	1,925,661,644,501	2,346,240,991,501	合計	1,659,400,606,608	1,925,661,644,501	2,346,240,991,501
# 日 本 輸 出 入 銀 行

一般勘定

損益計算書

損失	利
科目	昭和45年度決算額(円)	昭和46年度予定額(円)	昭和47年度予定額(円)	科目	昭和45年度決算額(円)	昭和46年度予定額(円)	昭和47年度予定額(円)
借入金利息	76,911,052,051	93,042,287,671	113,902,366,671	贷付金利息	73,627,377,655	91,722,530,845	110,833,906,939
庁貸付金利息	282,190,291	0	0	保証料	129,940,653	126,349,000	130,577,000
業務委託費	26,987,995	37,328,977	34,120,977	有価証券利息	275,848	165,000	170,000
事務費	1,539,781,187	1,688,590,000	1,895,087,000	受入雑利益	2,345,823	0	0
予備費	0	290,000,000	300,000,000	受入手數料	6,449,355	0	0
2動産不動産価額償却	51,251,471	63,453,000	80,240,000	有価証券利益	577,018,800	619,732,000	416,250,000
雑損	1,004,021	660,013	0	雑益	3,949,870	41,437,000	7,877,000
未經過割引料その他れい入	1,349,105,618	1,349,105,618	1,349,105,618	未払利息その他れい入	13,060,851,068	16,057,888,648	19,638,697,648
未収貸付金利息れい入	6,061,089,732	8,236,502,321	10,633,220,321
貸倒準備金繰入	1,185,746,706	3,860,174,893	2,833,338,000
利益金	0	0	0
合計	87,408,209,072	108,568,102,493	131,027,478,587	合計	87,408,209,072	108,568,102,493	131,027,478,587
# 日 本 輸 出 入 銀 行

## 一 般勘定

貸 借 対 照 表

借方	贷方
科目	昭和45年度末决算額(円)	昭和46年度末予定額(円)	昭和47年度末予定額(円)	科目	昭和45年度末决算額(円)	昭和46年度末予定額(円)	昭和47年度末予定額(円)
贷付金	1,596,715,938,414	1,831,883,297,628	2,242,213,297,628	借入金
支払承諾見返	40,386,422,045	39,434,566,045	45,328,589,045	資金運用部借入金	1,141,836,000,000	1,332,472,000,000	1,674,344,000,000
特別勘定貸	0	20,946,350,692	18,950,907,692	支払承諾	40,386,422,045	39,434,566,045	45,328,589,045
有価証劵	11,822,253,350	16,000,000,000	16,000,000,000	雑勘定	17,443,825,797	21,010,614,797	25,445,059,797
現金預付金	365,965,397	443,952,734	207,451,734	仮受金	36,831,531	22,811,531	22,811,531
2動產不動產	1,488,722,851	2,010,296,851	2,098,663,851	未払利息その他	16,057,888,648	19,638,697,648	23,073,142,648
雑勘定	8,630,304,551	10,793,250,551	13,746,610,551	未經過割引料その他	1,349,105,618	1,349,105,618	1,349,105,618
仮払金	269,590,250	6,328,250	6,328,250	貸倒準備金	9,572,579,129	13,432,754,022	16,266,092,022
未収貸付金利息	8,236,502,321	10,633,220,321	13,574,130,321	資本金	448,300,000,000	513,300,000,000	576,300,000,000
その他雑勘定	124,211,980	153,701,980	166,151,980	準備金	1,861,779,637	1,861,779,637	1,861,779,637
利益金	0	0	0
合計	1,659,400,606,608	1,921,511,714,501	2,338,545,520,501	合計	1,659,400,606,608	1,921,511,714,501	2,338,545,520,501
特別勘定
損益計算書
損益
科目	昭和46年度予定額(円)	昭和47年度予定額(円)	科目	昭和46年度予定額(円)	昭和47年度予定額(円)
利益金	24,930,000	45,541,000	贷付金利息	8,093,000	41,915,000
有価証券益	16,837,000	3,626,000
合計	24,930,000	45,541,000	合計	24,930,000	45,541,000
特別勘定
贷借对照表
借方	贷方
科目	昭和46年度末决算額(円)	昭和47年度末予定額(円)	科目	昭和46年度末予定額(円)	昭和47年度末予定額(円)
贷付金	24,241,370,692	24,911,370,692	借入金
有価証券	17,000,000	76,000,000	一般会计借入金	4,125,000,000	7,625,000,000
現金預付金	308,000	165,000	一般勘定借	20,946,350,692	18,950,907,692
雑勘定	積立金	0	24,930,000
未決資付金利息	837,602,000	1,658,843,000	利益金	24,930,000	45,541,000
合計	25,096,280,692	26,646,378,692	合計	25,096,280,692	26,646,378,692
昭 和 45 年 度 日本 輸 出 入 銀 行

財産目録（昭和46年3月31日現在）

摘 要	金 额(円)	摘 要	金 额(円)
贷 付 金	1,596,715,938,414	日本興業銀行	2,422,797
贷 付 金	3,611口	日本興業銀行別口	121,124,733
割 引 手 形	106口	動 座 不 動 座	1,488,722,851
支 払 承 諾 見 返 債務保証見返	459件	土 地 17箇所	801,072,984
有 価 証 券	11,822,253,350	建 物 22棟	661,007,887
銘柄額面	延22,978m²の35%、延2,244m²の5%及び延9,401m²外	26,641,980
国 債 食糧証券	11,900,000,000円	什 器	8,630,304,551
そ の 他 債 券 電信電話債券	4,580,000円	雑 勘 定	269,590,250
現 金 預 付 金	356,965,397	仮 拟 金	8,236,502,321
現 金	874,057	未 収 貨 付 金 利 息	124,211,980
当 座 預 付 金	356,091,340	そ の 他 雑 勘 定	1,659,400,606,608
日本銀行	232,543,810	合 計	1,659,400,606,608
## コード番号について

1 コード番号設定の目的

コード番号設定の目的は、予算の内容について、その分析を多角的に行なうため、経費の性質、分類等を明らかにすることにある。

## 2 コード番号の読み方

（１）各政府関係機関に付した４桁の数字は、左から１桁は公社、公庫及び銀行別区分のコード番号、次の３桁は公社、公庫、銀行ごとに付したコード番号である。なお、この３桁のうち、末尾の１桁の１から始まる数字は公社ごとに付した勘定のコード番号である。

（２）三公社(勘定区分のあるものは勘定。以下同じ。)の項別区分の表、収入支出予定額科目別表及び事業計画表中の収入支出予定額内訳の表の収入及び支出の各項に付した２桁の数字は、三公社ごとに付した収入及び支出の項のコード番号である。

（３）三公社の事業計画表中の収入支出予定額内訳の表の支出の各項別内訳に付した２桁の数字は、左から経済性質別（１桁）及び使途別（１桁）の各分類を明らかにするコード番号である。

（４）公庫及び銀行の収入の款項目別区分の表及び収入支出予定額科目別表の収入に付した６桁の数字は、左から款（２桁）、項（２桁）、目（２桁）をあらわすコード番号である。

(5) 公庫及び銀行の支出の事項別説明の表及び収入支出予定額科目別表の支出の各項に付した2桁の数字は、公庫及び銀行ごとに付した項のコード番号である。

(6) 公庫及び銀行の収入支出予定額科目別表の支出の各目に付した4桁の数字は、左から経済性質別(1桁)、使途別(1桁)の各分類を明らかにするコード番号及び従来の目の一連番号(2桁)である。

(7) 各種分類のコード番号は次のとおりである。

（イ）政府関係機関

1010	日本 専 壳 公 社	2030	農林漁業金融公庫
1020	日本 国有 鉄 道	2040	中小企業金融公庫
1021	損 益 勘 定	2050	北海道東北開発公庫
1022	資 本 勘 定	2060	公營企業金融公庫
1023	工 事 勘 定	2070	中小企業信用保険公庫
1030	日本 電 信 電 話 公 社	2080	医療金融公庫
1031	損 益 勘 定	2090	環境衛生金融公庫
1032	資 本 勘 定	2100	沖縄振興開発金融公庫
1033	建 設 勘 定	3010	日本開発銀行
2010	国 民 金 融 公 庫	3020	日本輸出入銀行
2020	住 宅 金 融 公 庫

(口) 経済性質別分類

1	財貨サービス購入、経常支出	6	控除項目、移転支出
2	"資本支出	7	"国債費
3	控除項目、会計間重複	8	"予備費
4	"経常補助金
5	"出資貸付金	9	"その他
(備考)
1. この分類は、国民経済計算上の政府の財貨サービス購入を算出する場合の便宜に供するためのものである。
2. 損益計算書の固定資産の減価償却費に資本支出を明らかにするコード番号2を付し、また、貸借対照表の資本支出に該当する項目については、その全額が資本支出となるのではなく、前年度額に対する当該年度の増(減)額が資本支出となるので、これを明らかにするためコード番号2の上に・を付して2と表示した。
(注) 政府関係機関については、国民経済計算上、支出予算によらないで、財務諸表(損益計算書及び貸借対照表)により資本支出のみを算出することとなっている。
(八) 使途別分類
1	人 件 費	5	補 助 費・委 託 費
2	旅 費	6	他 会 計 へ 繰 入
3	物 件 費
4	施 設 費	9	そ の 他
# Technology Adoption in Follower Countries: With or Without Local R&D Activities?

by

Yasuyuki Todo

May 2004

Economic and Social Research Institute

Cabinet Office

Tokyo, Japan
# Technology Adoption in Follower Countries: With or Without Local R&D Activities?

Yasuyuki Todo $ ^{*} $

May, 2004

## Abstract

This paper develops an endogenous growth model incorporating quality improvement, focusing on a follower country that lags behind the world technology frontier and adopts new technology with adaptation to local circumstances. We assume two forms of adaptation: inventive adaptation, which requires formal local R&D activities, and minor adaptation without R&D. Although current R&D activities expand local knowledge for future R&D, minor adaptation without R&D does not. The main result in the paper is that countries with sufficient local knowledge and skilled labor initially depend on technology adoption without R&D but then depend on local R&D, while other countries continue to depend on adoption without R&D. Switching regression using cross-country data supports the presence of multiple steady-state equilibria.

Keywords: technology adoption, inventive adaptation, multinational enterprises, local R&D activities, switching regression

JEL classifications: O33, O41
## 1 Introduction

Countries lagging behind the world technology frontier, or follower countries, $ ^{1} $ can benefit greatly from adopting new technology invented in countries at the frontier, or frontier countries. Evenson and Westpal (1995) argue that technology adoption is likely to require adaptation, since most technologies are sensitive to circumstantial differences between countries, such as those in climate, relative prices, and institutions. They also identify two distinct forms of adaptation: minor and inventive adaptation. Minor adaptation “involve(s) changes in the technique but leave(s) its core unaffected,” and is not associated with formal R&D activities. By contrast, inventive adaptation “make(s) use not of the (foreign) technique but of the knowledge that underlies it,” and hence requires formal local R&D activities. An example of minor adaptation is tightening bolts by hand rather than using robots. The modification of product designs to fit local circumstances should be defined as inventive adaptation.

In practice, the main contribution to technology adoption with minor adaptation is made by the foreign direct investment (FDI) of the multinational enterprises (MNEs) of frontier countries, particularly those MNEs that are not engaged in R&D activities in the host country. Local R&D activities for inventive adaptation are often undertaken by local firms that have licensing agreements with firms in frontier countries or by MNEs with R&D units in the host country.

Whether a follower country depends on technology adoption with or without local R&D activities is likely to affect its long-run level of technology and output. Hence, this paper theoretically investigates how the levels of these two forms of technology adoption are determined in an endogenous-growth framework, of the type developed in Acemoglu et al. (2002) and Aghion and Howitt (forthcoming). Furthermore, we investigate whether R&D subsidies help follower countries to catch up with frontier countries.
Although there is much existing work on technology adoption in follower countries, to which we will refer later, a unique feature of our model is the following two assumptions on the differences between the two forms of adoption. First, adoption with minor adaptation does not require local knowledge in follower countries, whereas the extent of technology adopted by local R&D activities is positively correlated with the level of local knowledge. Second, current technology adoption through R&D expands local knowledge and hence the productivity of future R&D activities, whereas adoption without R&D does not affect the knowledge level.

To explain the second assumption, we compare licensing and FDI as examples of channels of technology adoption with and without R&D, respectively. Kim and Ma (1997) and Lall (2000) suggest that although production workers in MNEs can achieve operational capabilities, they cannot understand the principles of technologies. By contrast, R&D activities associated with licensing enable local workers to learn the knowledge of licensors. Furthermore, the knowledge spills over to other engineers through labor turnover, subcontracting, and formal and informal discussion. Hence, licensing expands knowledge in the economy. This assumption is also supported by Todo and Miyamoto (2002), who find, using Indonesian firm-level data, that the productivity of local firms is positively correlated with the magnitude of MNEs with local R&D but uncorrelated with the magnitude of MNEs without R&D.

Given these assumptions, the model obtains two major results. First, depending on initial conditions and parameter values, follower countries converge to a steady state in which there is either a positive level of local R&D activities or no R&D. If local knowledge is sufficiently unimportant in inventive adaptation, or if initial endowments of skilled labor and knowledge are sufficiently large, follower countries initially depend on technology adoption without local R&D but then increasingly depend on adoption with R&D as they catch up with frontier countries. By contrast, if the endowment of skilled labor is large but that of local knowledge is small, or if the endowment of skilled labor is small, follower countries converge to a steady state in which there are no local
R&D activities, or in practice, in which there are only MNEs without R&D.

The reason for this result is that there is a dynamic externality in technology adoption with local R&D activities but not in adoption without R&D. Since current R&D activities expand local knowledge and the productivity of future R&D, the development of local R&D may generate a virtuous cycle. However, countries with limited knowledge or little skilled labor cannot benefit from the virtuous cycle, because dynamic gains from current R&D are limited.

This externality leads to the second major result that the decentralized equilibrium is inefficient. Because private firms are unaware of the externality, they underinvest in R&D activities. Therefore, subsidies for R&D could increase output per capita in the long run. This implies that promoting local R&D activities by MNEs and licensing agreements with foreign firms are socially beneficial for follower countries, whereas promoting FDI without encouraging local R&D is less useful. Note that some East Asian countries that have achieved rapid growth have adopted such policies. For example, the governments of Japan and Korea encouraged licensing in the early stages of their development (Kim and Ma, 1997), and the Chinese government currently requires MNEs in some sectors, such as automobiles, to set up R&D units in China (Yusuf, 2003).

We test the model’s major assumptions and main results by using cross-country data. Of particular importance is testing whether there are two dynamic patterns in the level of local R&D, for which we use a switching regression model with unobservable regime change developed by Quandt (1972) and introduced to the growth literature by Bloom et al. (2003). We find weak evidence that supports the presence of multiple steady-state equilibria. Countries with large endowments of skilled labor and knowledge have a large probability of converging to a steady state in which R&D expenditures are positive, whereas countries with small endowments tend to converge to a steady state in which there are no R&D expenditures.

Since large R&D expenditures correspond to large income per capita, this result is consistent with Bloom et al. (2003), who found two types of steady state in terms of income per capita in cross-section of countries. In addition,
it is consistent with Bloom et al. (2002) who find evidence of variation in the steady-state levels of countries' total factor productivity (TFP), although they focus on geography and institutions as the major determinants of TFP levels, rather than, as in this paper, endowments of skilled workers and local knowledge. Multiple income-growth processes are also found in Quah (1993) and Fiaschi and Lavezzi (2003) who use Markov chain transition models.

This paper is closely related to the literature on technology transfer to less developed countries, which is extensive. However, some studies focus on a particular type of adoption, such as imitation through local R&D as in Grossman and Helpman (1991) and Barro and Sala-i-Martin (1997), and FDI as in Findlay (1978), Walz (1997), and Fosfuri et al. (2001). Although other studies such as Ethier and Markusen (1996) and Glass and Saggi (2002) incorporate two channels of technology transfer, FDI and licensing, they do not focus on the difference between these two channels in terms of the promotion of local knowledge. The model of Glass and Saggi (1999) combines FDI and imitation, but FDI is exogenous. The model of Saggi (1999), which assumes knowledge spillovers from licensing but not from FDI, is most closely related to our model. However, Saggi's model is a two-period duopoly game, whereas ours is a growth model with an infinite horizon, and hence Saggi's model does not feature multiple equilibria.

Our findings have significant implications for development policies. Until recently, FDI had been considered as the major source of technology transfer (Ito and Krueger, 2000, for example). Many studies have empirically tested for the effect of FDI on growth, including Borensztein et al. (1998), Sjöholm (1999), Haskel et al. (2002), among many others. $ ^{2} $ However, this paper suggests that promoting FDI may not be as beneficial as the existing literature implies unless it is associated with local R&D activities. $ ^{3} $ This conclusion accords with the
argument of Yusuf (2003) that East Asian countries that have absorbed much knowledge through FDI need more local R&D for further growth.

The rest of the paper is organized as follows. Section 2 describes the theoretical model, and Section 3 shows the equilibrium analysis. The empirical evidence supporting the model is presented in Section 4. Section 5 concludes the paper.

## 2 The Model

The model developed in this paper is a simple extension of a growth model incorporating quality-improving innovations such as those in Acemoglu et al. (2002) and Aghion and Howitt (forthcoming). This is a discrete-time model with overlapping generations, focusing on a small follower country that has a relatively low level of initial knowledge and adopts new technology developed at the world knowledge frontier.

### 2.1 Production

There are two types of worker, skilled and unskilled, in the follower country. Each worker lives for two periods, and the numbers of skilled and unskilled workers in each generation are constant and are denoted by H and L, respectively. Each worker supplies inelastically one unit of labor in the first period of her life and retires in the second period.

The final good is produced competitively using a continuum in the 0–1 interval of intermediate goods according to the following production function:

$$ Y_{t}=\left[\int_{0}^{1}(A_{t}(i)x_{t}(i))^{\alpha}d i\right]^{1/\alpha}, $$

where $ A_{t}(i) $ and $ x_{t}(i) $ are the quality of intermediate good i and the flow of good i used in period t, respectively, and $ \alpha \in [0,1] $ . The final good is fully consumed by either the “young” or “old” generation in each period, and its price is unity. The profit maximization for the final-good sector yields

$$ p_{t}(i)=Y_{t}^{1-\alpha}A_{t}(i)^{\alpha}x_{t}(i)^{\alpha-1}, $$

where $ p_{t}(i) $ is the price of good i in period t.
The market for each intermediate good is monopolized by a firm that improves the product quality using skilled workers $ ^{4} $ and thus receives patents for the good of that quality. We assume that each patent lasts for only one period and that any firm can produce any good of a quality that was achieved in the previous period because of costless knowledge diffusion. Therefore, the monopoly of the incumbent firm would be eliminated in the next period without further quality improvement. Additionally, we assume that costs of quality improvement for the incumbent firm are always smaller than those for any other firm, because of the incumbent's knowledge from its previous experiences. Accordingly, the incumbent firm in the initial period in each intermediate sector will engage in further quality improvement and monopolize the entire market in any period, as long as the profit from quality improvement is positive, as will be true in equilibrium under certain conditions.

Each of these intermediate firms produces one unit of its product from one unit of unskilled labor. Since production requires only unskilled labor whereas quality improvement requires only skilled labor, the decision of each intermediate firm on production is separable from its decision on quality improvement, which will be discussed later. Given equation (2) and $ A_{t}(i) $ , the monopoly firm producing good i maximizes its profit from production at time t, $ \pi_{t}(i) = \left(p_{t}(i) - w_{t}^{L}\right)x_{t}(i) $ , where $ w_{t}^{L} $ is the wage rate of unskilled labor. The solution leads to mark-up pricing:

$$ p_{t}(i)=w_{t}^{L}/\alpha. $$

These intermediate firms are owned by share holders, who receive the total monopoly profit as dividends. The behaviors of share holders will be described in detail in the consumption section.

The market clearing condition for unskilled workers yields $ \int_{0}^{1} x_{t}(i) di = L $ . Also, as we will find in the next subsection, the quality of any intermediate good is the same: $ A_{t}(i) = A_{t} \equiv \int_{0}^{1} A_{t}(i) di $ for any i, where $ A_{t} $ denotes the average
quality of intermediate goods. Thus, we obtain

$$ Y_{t}=A_{t}L, $$

and

$$ \pi_{t}(i)=(1-\alpha)A_{t}(i)L. $$

Equation (4) shows that given L, output per capita is proportional to the quality of intermediate goods. Hence, the growth rate of per capita output is equal to the rate of quality improvement.

### 2.2 Quality Improvement

Each intermediate firm can improve the quality of its product by technology adoption using skilled labor. Technology adoption can occur with either inventive adaptation through local R&D activities or minor adaptation without R&D. There are two differences between the two types of technology adoption. First, adoption without R&D does not require local knowledge in the follower country, while adoption with R&D does, and the extent to which R&D improves quality increases as local knowledge expands. Second, current local R&D activities raise the productivity of future R&D activities by expanding local knowledge, whereas technology adoption without R&D does not. These assumptions are justified by several empirical studies, as explained in the introduction.

Thus, we assume that quality in intermediate good sector i is given by

$$ A_{t}(i)=\eta M\big(H_{t}^{M}(i)\big)\bar{A}_{t-1}+\big(1+g\big)R\big(H_{t}^{R}(i)\big)\tilde{A}_{t-1}^{\phi}\bar{A}_{t-1}^{1-\phi}. $$

The first term on the right-hand side of this equation represents quality improvement without R&D. $ \bar{A}_{t-1} $ is the quality level at the world knowledge frontier at time t-1, which is assumed to be the same for all intermediate goods. Part of this frontier quality can be introduced through technology adoption with minor adaptation by, for example, MNEs without local R&D activities. $ ^{5} $ This type of adoption requires local skilled labor as managers, rather than engineers, who
learn production processes and new operational techniques from foreign manuals. $ H_{t}^{M}(i) $ denotes the number of these skilled workers in sector i at time t. Because the degree of quality improvement is an increasing function of the number of skilled workers employed, we specifically assume

$$ M(H_{t}^{M})=\left(\frac{H_{t}^{M}}{\bar{H}}\right)^{\mu}, $$

where $ \bar{H} $ is the total amount of skilled labor engaged in innovation at the world frontier, which is exogenously given, and $ \mu \in (0,1) $ . Since we further assume $ \eta \in (0,1) $ , $ M(\bar{H}) = 1 $ implies that even when the same amounts of skilled labor are engaged in quality improvement without R&D and innovation at the knowledge frontier, the follower country cannot achieve frontier quality. Note that the degree of quality achieved by this channel does not depend on the knowledge level of skilled workers, because their task, reading manuals, does not require a high level of knowledge.

The second term denotes quality improvement through local R&D activities. This type of technology adoption requires skilled labor and a combination of local and frontier knowledge for local R&D. $ H_{t}^{R}(i) $ is the number of skilled workers engaged in local R&D, and we assume

$$ R(H_{t}^{R})=\left(\frac{H_{t}^{R}}{\bar{H}}\right)^{\rho}, $$

where $ \rho\in(0,1) $ . $ \bar{A}_{t-1} $ , defined as the frontier quality at time t-1, also represents the knowledge level of the frontier countries at time t. $ \tilde{A}_{t-1} $ represents the knowledge level of local skilled workers at time t. We assume costless knowledge diffusion within the follower country, and thus each skilled worker shares the same local knowledge. Furthermore, since we assume that the local knowledge does not expand through technology adoption without local R&D, the local knowledge level is not equal to the total quality level achieved in the previous period, $ A_{t-1} $ . Rather, it should be represented by the quality level achieved by local R&D. Therefore, we assume

$$ \tilde{A}_{t-1}=(1+g)R\big(H_{t-1}^{R}(i)\big)\tilde{A}_{t-2}^{\phi}\bar{A}_{t-2}^{1-\phi}=A_{t-1}-\eta M(H_{t-1}^{M}(i))\bar{A}_{t-2}. $$