(PDF) Institutional Quality, Financial Development, Interaction, and Macroeconomic Volatility: Ardl Co Integration Approach

PSCR23_proof ■ 6 February 2015 ■ 1/6 + MODEL H O S T E D BY Available online at www.sciencedirect.com ScienceDirect 59 60 1 61 2 62 Pacific Science Review xx (2015) 1e6 3 www.elsevier.com/locate/pscr 63 4 64 5 65 6 66 7 8 Institutional quality, financial development and OFDI* 67 68 9 69 10 Yu Wang a,*, Liwei Cheng a, Hao Wang b, Liangyu Li a 70 11 71 12 a School of Economics, DUT, China 72 13 b School of Economics, DBUFE, China 73 14 74 Available online ▪ ▪ ▪ 15 75 16 76 17 77 18 78 Abstract 19 79 20 80 21 Using a panel of 73 countries from 2000 to 2008, this study uses Investment Development Path theory as a framework that utilises institutional quality (IQ) as a threshold for the effect of economic development on OFDI. Using the dynamic threshold 81 22 82 23 model, we find new evidence that the strong promoting effect is initiated when IQ is within a certain interval, which is supple- 83 24 mentary to IDP theory. Finally, we propose the corresponding advice. 84 25 Copyright © 2014, Far Eastern Federal University, Kangnam University, Dalian University of Technology, Kokushikan University. 85 26 Production and Hosting by Elsevier B.V. All rights reserved. 86 27 87 28 88 29 Keywords: Institutional quality; Financial development; OFDI; Dynamic threshold 89 30 90 31 91 32 92 33 Introduction economic development and summarises the character- 93 34 istic five stages of FDI/OFDI; only if the GDP per 94 35 The OLI theory [6] determines that MNEs should capita reaches 3000e4000 US dollars (approximately 95 36 have an ownership advantage, location advantage and 7000e8000 in US dollars today) will the OFDI begin 96 37 internalisation advantage before OFDI and should to scale. However, the Investment Development Path 97 38 become the theory that explains OFDI in emerging theory is contrary to the fact that a large quantity of 98 39 99 countries early in their development. The Investment OFDI throughout the world comes from emerging 40 100 41 Development Path theory (Dunning, 1981) indicates markets, such as China and India, where the income 101 42 that a country's FDI/OFDI depends on its level of level is low. The phenomenon may result from the 102 43 promoting function of government and the financial 103 44 * Institutional quality was introduced as a dummy for policy lib- advantage from excessive foreign exchange reserves 104 45 eralisation [5] and then extended into other detailed indicators, such under the condition of a domestic institutional void and 105 46 as trade and foreign exchange liberalisation, privatisation reform, the relative lag of economic development (large in 106 47 enterprise restructuring reforms, overall institutional reforms, and 107 gross but low on average), realising a leapfrog devel- 48 Q1 competition reforms [15]. 108 49 * Corresponding author. opment path for its OFDI. In addition, some other 109 50 E-mail addresses:

(Y. Wang), cliwei60@ emerging countries that have reached the required per 110 51 126.com (L. Cheng),

(H. Wang), capita income still strongly promote the OFDI, such as 111 52

(L. Li). Brazil and Russia. 112 53 Peer review under responsibility of Far Eastern Federal Univer- Most emerging markets experience a long term 113 54 sity, Kangnam University, Dalian University of Technology, central economy and a short time market economy, so 114 55 Kokushikan University. 115 56 116 57 http://dx.doi.org/10.1016/j.pscr.2014.08.023 117 58 1229-5450/Copyright © 2014, Far Eastern Federal University, Kangnam University, Dalian University of Technology, Kokushikan University. Production and Hosting by Elsevier B.V. All rights reserved. Please cite this article in press as: Y. Wang et al., Institutional quality, financial development and OFDI, Pacific Science Review (2015), http:// dx.doi.org/10.1016/j.pscr.2014.08.023 PSCR23_proof ■ 6 February 2015 ■ 2/6 + MODEL 2 Y. Wang et al. / Pacific Science Review xx (2015) 1e6 1 a large proportion of state-owned enterprise exists and purpose and leapfrog development, the former theories 60 2 the market mechanism is not perfect. Once OFDI is appear to be lacking full explanatory power. The 61 3 62 treated as a native economic strategy, the strong power research in OFDI of Russia finds that we must augment 4 63 5 and administrative methods from the government will the traditional OLI and IDP theory and must introduce 64 6 still promote the international firms under the condition the country specific institutional factors to the theories 65 7 of a low level of economic development. However, in (Kalotay, 2007). In addition, the theory should embed 66 8 developed economies, because of the sound institu- three types of explanatory variables into the MNE 67 9 tional quality (IQ), high economic development and theories: imperfect capital markets, special ownership 68 10 core technology controlled in firms, the support from advantages, and institutional factors [5,17]. The 69 11 70 government declines into a secondary position. The research of Buckley [5] found that the liberalisation of 12 71 13 dynamic process reminds us that a nonlinear influence government policy has a significant effect on Chinese 72 14 of economic development on OFDI comes into being, OFDI, emphasising the importance of institutional 73 15 which depends on a certain level of institutional quality factors. However, in this paper, only dummy variables 74 16 in the economy, causing a first increased then are used to capture the change in institutions, so in later 75 17 decreased development path. The dynamic process is research, continuous, endogenous institutional vari- 76 18 also a valid supplement to Dunning's IDP theory. ables are used to explain OFDI in emerging countries. 77 19 78 Based on this background, the paper integrates the All of the studies found important evidence that spe- 20 79 21 institutional quality (including the strength of legal cific institutional reforms, such as the liberalisation of 80 22 rights index, the overall institutional reform, the pri- trade and foreign exchange, privatisation, competitive 81 23 vatisation process and trade openness) into the eco- reform and overall institutional reform, will affect 82 24 nomic development stage, extends the IDP theory OFDI in emerging markets significantly. Further, the 83 25 effectively, and utilises a regression model based on range of the study extends from emerging countries, 84 26 the concept of dynamic panel threshold model (DPTM) such as China, India, and Russia, to Malaysia, 85 27 86 and dynamic panel to test the nonlinear influence and Thailand, Latin America, Central Europe, East Europe 28 87 29 leapfrog development characteristic of OFDI using and all emerging countries. The extant framework of 88 30 country specific institutional quality as a threshold. theories also extend from traditional ideas (OLI, IDP, 89 31 Our fitted model allows the relationship between eco- Natural-based view, and internationalisation theory) to 90 32 nomic development and OFDI to be piecewise linear, LLL theory, the strategy tripod (resource, industry, and 91 33 with the IQ as a regime-switching trigger. Using cross- institution), imperfect capital markets, special owner- 92 34 country data from 73 economies from 2000 to 2008, ship advantage and institutional factors embedded in 93 35 94 we find strong evidence of threshold effects in the traditional MNEs theories. 36 95 37 economic-development-OFDI link. Specifically, we 96 38 find that the strong promoting effect of economic The influence of financial factors on OFDI 97 39 development on OFDI begins only when the IQ is 98 40 within a certain interval. At this time, the strong ben- Froot [8] first proposed the question of low effi- 99 41 efits of economic development exist. ciency in financial markets and explored the effect of 100 42 The paper is structured as follows. Section 2 re- exchange rate on FDI. Later, many reports in the 101 43 102 views the literature, and further development of our literature started to focus on effect of exchange rate on 44 103 45 hypothesis is presented in Section 3. Section 4 dis- transnational M&A in the condition of financial in- 104 46 cusses the results and performs a series of robustness efficiency and then extended to other aspects for 105 47 tests, in which we explore alternative measures of IQ, finance and FDI [1,12] or the financial development in 106 48 while Section 5 provides some conclusions. country level [2]; subsequently, reports studied the 107 49 influence of firm specific capital cost on FDI [7], 108 50 Review of the literature constructed the relationship between financing and 109 51 110 domestic OFDI on a theoretical basis [10,14], and 52 111 53 The influence of institutional factors on OFDI combined country specific financial advantage and firm 112 54 specific financial advantage to explore enterprises’ 113 55 The OLI theory usually supposes that the MNEs foreign investment in the condition of financial 114 56 should have ownership advantages before OFDI, while constraints. 115 57 the IDP theory emphasises in which stage the MNEs When financial markets are (partially) segmented, 116 58 from emerging economies may begin to invest abroad. one can distinguish between two main groups of 117 59 118 However, for the characteristics of asset-seeking mechanisms, whereby a firm's financing may have an Please cite this article in press as: Y. Wang et al., Institutional quality, financial development and OFDI, Pacific Science Review (2015), http:// dx.doi.org/10.1016/j.pscr.2014.08.023 PSCR23_proof ■ 6 February 2015 ■ 3/6 + MODEL Y. Wang et al. / Pacific Science Review xx (2015) 1e6 3 1 effect on its propensity for undertaking FDI: reactive Methodology in the empirical research 60 2 and proactive firm behaviour [13]. The first group re- 61 3 62 fers to opportunistic firm behaviour in response to There are two items that must be addressed when 4 63 5 financial market imperfections. The second group constructing a dynamic PTM. First, one of the re- 64 6 contains measures that were undertaken to improve the gressors is the lagged dependent variable, which makes 65 7 availability of capital and/or to lower the cost of cap- our model a dynamic panel model (DPM). If we use 66 8 ital. Oxelheim [13] took imperfect international the regular fixed-effect model of panel model analysis, 67 9 financial integration as their point of departure. They then there would be bias caused by the correlation 68 10 assumed a two-tier world capital market with partial between the lagged dependent variable and the resid- 69 11 70 segmentation, where a local firm can choose to stay in ual. To address this bias, we use the system generalised 12 71 13 its home market and face the local cost of capital or method of moment (GMM) proposed by Blundell and 72 14 invest in ‘proactive financial strategies’ to interna- Bond [4] to conduct the estimation [15]. Second, if the 73 15 tionalise its cost of capital and reap the benefits of the panel data are nonlinear, then one must use PTM to 74 16 economies of scale and scope attributable to a multi- reveal the properties. Overall, the two questions can be 75 17 national firm. Such financial strategies may include solved individually, and if they were to be solved 76 18 cross-listing its stock in a more liquid stock market, simultaneously, then the residual may have an auto- 77 19 78 foreign issuing of equity and/or debt, and ‘bonding’ correlation problem. Overall, we estimate the model 20 79 21 strategies to reduce information asymmetries. These using two steps: (1) the static PTM (see Ref. [9] and 80 22 types of strategy, they suggest, may foment a financial (2) the DPTM. Once g is identified, estimates of the 81 ∧ 23 advantage vis-a-vis competitors e or eliminate a slope parameters follow as bðgÞ: Finally, we test the 82 24 financial disadvantage e which can be exploited by significance of threshold g via a model-based boot- 83 25 undertaking FDI. Tolmunen and Torstila [16] study one strap, the validity and properties of which have been 84 26 such proactive strategy. They found that European established in Ref. [9]. 85 27 86 firms that have cross-listed their stock in a US stock In step 1, we utilise the static PTM proposed by 28 87 29 market are significantly more likely to make acquisi- Hansen [9] to explore the nonlinear characteristic of 88 30 tions in the US. They interpret the results in terms of the panel data. If we were to assume that there is only 89 31 the European firms' need for a viable ‘M&A currency’ one threshold in the model, then the model can be 90 32 and their need to reduce information asymmetries, and expressed as 91 33 overcoming home bias. The above study presented 92 34 yi;t ¼ mi þ b'1 xi;t I qi;t g þ b'2 xi;t I qi;t > g þ ei;t ð1Þ 93 another way of stating the need to reduce a financial 35 94 ownership disadvantage. where mi is the country fixed effect; xi;t is the exogenous 36 95 37 variables; qi;t is the threshold variable, i ¼ 1…N denotes 96 38 Data and methodology the country; t ¼ 1…T denotes the time; and g is the 97 39 threshold value. Ið,Þ in Eq. (1) is the indicator function. 98 40 Data If the condition in the parentheses holds, then I ¼ 1; 99 41 100 otherwise, I ¼ 0. 42 101 43 The data set consists of cross-country observations Assume b ¼ ðb'1 ; b'2 Þ' and define the xi;t ðgÞ as 102 for 73 economies (46 emerging countries and 27 44 developed countries, presented in Table 3) from 2000 103 45 xi;t I qi;t g 104 to 2008. All data were extracted from the World Bank xi;t ðgÞ ¼ ð2Þ 46 xi;t I qi;t > g 105 47 Database (WBD) or Economic Freedom of the World: 106 48 2010 Annual Report and expressed as the percentage Then we can simplify Eq. (1) as 107 49 of GDP, except IQ, GDP per capita, and hr. As for the 108 50 financial factors, we focus only on the credit market yi;t ¼ mi þ b' xi: ðgÞ þ ei;t ð3Þ 109 51 110 and equity market because they are the most feasible 52 For each i, take the average of Eq. (3); then we 111 53 sources of financing for the majority of emerging and 112 derive 54 developed countries in our sample. Similar to Stoian 113 55 [15]; we utilise the strength of legal rights index (slr), yi: ¼ mi þ b' xi: ðgÞ þ ei: ð4Þ 114 56 which measures the degree to which collateral and 115 57 bankruptcy laws protect the rights of borrowers and we can write Eq. (5) as 116 58 lenders and thus facilitate lending; slr has a range from 117 59 1 to 10 (1 ¼ weak to 10 ¼ strong) (see Table 1). Y * ¼ X * ðgÞb þ e* ð5Þ 118 Please cite this article in press as: Y. Wang et al., Institutional quality, financial development and OFDI, Pacific Science Review (2015), http:// dx.doi.org/10.1016/j.pscr.2014.08.023 PSCR23_proof ■ 6 February 2015 ■ 4/6 + MODEL 4 Y. Wang et al. / Pacific Science Review xx (2015) 1e6 ' 1 The residual is eb* ðgÞ ¼ Y * X * ðgÞ b b; and the sum Let the GMM estimator matrix be b qðb r'; b b Þ and 60 2 of the squared error S*1 ðgÞ is 1 61 3 b q ¼ X R* 'W * AN W * 'X R* X R* 'W * AN W * 'Y ð12Þ 62 4 S*1 ðgÞ ¼ e* ðgÞ' e* ðgÞ ð6Þ P 63 5 In Eq. (12), AN ¼ ½ð1=NÞ Ni¼1 Wi* 'HWi* 1 ; where 64 6 To obtain the optimal threshold value, one can H is a (T-2) (T-2) matrix. 65 7 repeat the estimation process described above, using 66 8 the g within the possible value range to achieve S1 ðgÞ: 67 Model specification and empirical results 9 68 The g value that corresponds to the minimum S*1 ðgÞ is 10 69 11 the optimal threshold value g b: Model specification 70 12 The estimator matrix of the threshold regression is 71 13 b qðbg Þ; the residual is eb* ðb g Þ; and the residual variance According to the depiction in Section 3, we define 72 14 is our basic model to capture the influence of economic 73 15 * development on OFDI, utilising IQ as a threshold: 74 1 1 b s eb*1 g b eb g b ¼ S*1 g b 2¼ 16 ð7Þ 75 17 NðT 1Þ NðT 1Þ ofdiit ¼a þ fofdiit1 þ b'1 investit þ b'2 financeit 76 18 77 After we obtain g b ; we must test for the existence of þ b'3 controlit þ b4 gdp,Iðr1 : iq <g1 Þ 19 ð13Þ 78 20 the threshold effect. The null hypothesis is H0 : b1¼ b2 : þ b5 gdp,Iðr2 : g1 iq g2 Þ 79 21 In step 2, we use the GMM method proposed by þ b6 gdp,Iðr3 : iq > g2 Þ þ εit 80 22 Blundell and Bond [4] to conduct the estimation. We 81 23 82 transform the PTM in the first step into a linear panel where ofdi is outward foreign direct investment over 24 83 25 data model. By using the dummy variable, we can still GDP from 2000 to 2008; invest is an investing indicator 84 26 reveal the nonlinear characteristic identified in step 1. vector that includes the annual fixed assets investment 85 27 In addition, we add yi;t1 as one of the regressors; as a over GDP (fix), annual R&D investment over GDP (rd), 86 28 result, our model is the DPDM with a nonlinear and foreign direct investment over GDP (fdi); finance is 87 29 characteristic. Following the specification of Eq. (5) a financial development indicator vector that includes 88 * 30 and by adding y1i;t ð¼ y*i;t1 Þ as one of the regressors, 89 private credit amount over GDP (credit) and stock 31 90 we specify the model as follows: market value over GDP (stock); control is a vector of 32 91 ' * ' * 33 y*i;t ¼ mi þ ry1* * i;t þ b1 xi;t DVðR1 Þ þ b2 xi;t DVðR2 Þ þ ei;t controlling variables hypothesised to affect OFDI, 92 34 which includes human capital (defined as average years 93 35 ð8Þ of secondary years, hr) and natural resource (defined as 94 36 total amount of natural resource stock over GDP, na- 95 37 Y * ¼ Y 1* r þ X R* b þ e* ð9Þ 96 ture). In our model, the IQ indicators act as sample 38 97 where DV(R1) and DV(R2) are the dummy variables splitting variables. The above specification allows the 39 98 40 that denote regimes 1 and 2, respectively, and the values effects of GDP per capita on OFDI to take on different 99 41 of the dummy variables come from the PTM estimation values, depending on whether the level of IQ is smaller 100 42 in step 1. or larger than the threshold g, and the corresponding 101 43 Before conducting the GMM estimation, we must coefficients are b4, b5, and b6. 102 44 ascertain whether the orthogonal condition holds. The 103 45 Empirical results 104 condition is: 46 h i 105 47 E y1* e * e * ¼ 0 s ¼ 2; :::; t 1; t ¼ 3; :::; T 106 48 1;ts i;t i;t1 According to the principle of the panel threshold 107 49 model, we estimate the model under the hypothesis of 108 h i no threshold, single threshold and double thresholds at 50 * * 109 E xR* 1;s ei;t e i;t1 ¼ 0 s ¼ 2; :::; t 1; t ¼ 3; :::; T: 51 the significance level of 1%, 5% and 10%, respectively. 110 52 ð10Þ The results are presented in Table 2, indicating that 111 53 double thresholds exist in the model. That is, there is a 112 54 It is obvious that as t becomes larger, the number of 113 nonlinear effect of economic development on OFDI 55 114 orthogonal conditions increases. Rewriting Eq. (10) using IQ as a threshold. The calculated thresholds are 4 56 115 57 into a matrix, we obtain Eq. (11): and 8. 116 h i Table 3 presents the results of estimating Eq. (16) 58 117 E Wi* ' e*i;t e*i;t1 ¼ 0 i ¼ 1; :::; N: ð11Þ 59 using slr as a threshold variable. Double thresholds (4 118 Please cite this article in press as: Y. Wang et al., Institutional quality, financial development and OFDI, Pacific Science Review (2015), http:// dx.doi.org/10.1016/j.pscr.2014.08.023 PSCR23_proof ■ 6 February 2015 ■ 5/6 + MODEL Y. Wang et al. / Pacific Science Review xx (2015) 1e6 5 1 Table 1 promotion from economic development and govern- 60 2 Descriptive statistics for the main variables. ment); the coefficients in the middle-IQ group are more 61 3 Variables Mean S.E Min Max 62 significant and larger than those in the high-IQ group, 4 63 5 Investment OFDI 3.1811 7.076 e 89.450 that is, promotion from most emerging country gov- 64 indicators FDI 5.1579 6.811 e 92.670 ernments is stronger than that in developed countries in 6 65 Fixed assets 21.711 5.047 10.37 42.540 the condition of an institutional void. As a result, the 7 66 R&D 1.0784 1.021 e 4.7700 8 promotion of economic development to OFDI is usu- 67 Financial Private 73.9902 53.88 e 319.56 9 development credit ally larger in the emerging countries, realising a leap- 68 10 Stock value 48.351 69.53 e 442.79 frog development path. This result is also beyond the 69 11 Controlling IQ 5.7656 2.390 1.000 10.000 70 prediction of IDP because it occurs regardless of the IQ 12 variables GDP/capita 14.237 15.36 0.370 87.340 71 13 factors and is also a valid supplement to IDP. The 72 Openness 94.106 63.10 20.49 456.65 14 Natural 9.5134 13.15 e 39.290 promotion function of the government in developed 73 15 resource countries decreases, that is, the country specific 74 16 Human 21.842 15.08 e 85.000 advantage is not significant, and the capital account 75 17 resource tends to converge, which is consistent with the pre- 76 18 diction of IDP theory. Regarding the effect of financial 77 19 78 Table 2 development on OFDI, both the credit market and the 20 79 21 LM-test for the threshold effect. stock market will promote OFDI. Although both co- 80 22 LM-test F-value P-value 1% 5% 10% efficients of the financial markets are significant, the 81 23 Null 14.947*** 0.0000 9.5628 4.3905 2.6224 credit market is more influential than the stock market. 82 24 Single 7.1688** 0.0375 8.4970 3.2273 2.0309 This difference is because a bank dominated financial 83 25 Double 1.21 0.5349 7.3171 3.1569 1.9219 system exists in emerging markets, while a capital 84 26 dominated financial system exists in developed mar- 85 27 86 kets. In addition, in our sample, the number of 28 87 29 and 8) exist in the model, so the sample can be split emerging countries is greater than the number of 88 30 into three groups. Countries with a slr of less than 4 are developed countries. 89 31 classified into the low-IQ group (usually less devel- Two robustness checks are performed for the main 90 32 oped countries simultaneously accompanied by low regression. First, we assess the effect of outliers on the 91 33 economic development), those with slr of more than 8 estimation results. Following the idea proposed by 92 34 are classified into the high-IQ group (usually devel- Belsley [3]; the so-called DFITS statistic is used to flag 93 35 94 oped countries), and the others are classified into the countries with high combinations of residuals and 36 95 37 middle-IQ group (most emerging countries). The co- leverage statistics. Excluding the outliers does not 96 38 efficients on GDP per capita presented in Table 3 are change the basic format of Eq. (1). Second, we test 97 39 all insignificant in the low-IQ group; thus, they are whether the middle-IQ group can be split further into 98 40 consistent with the prediction of IDP (nearly no subgroups2. The result presents an insignificant p-value 99 41 100 42 101 43 Table 3 102 44 Regression results. 103 45 Variable Model 1 Model 2 Model 3 Model 4 104 46 Coefficient s.e. Coefficient s.e. Coefficient s.e. Coefficient s.e. 105 47 106 48 OFDI(-1) 0.9347*** 0.0456 0.9251*** 0.0424 0.9149*** 0.0415 0.8978*** 0.0408 107 49 Credit 0.0467*** 0.0039 0.0206* 0.0015 108 Stock 0.0267*** 0.0019 0.011** 0.0009 50 109 FDI 0.3083*** 0.0152 0.2765*** 0.0121 51 110 RD 0.1325 0.0221 0.1341 0.0246 0.1026 0.0115 0.1058 0.0132 52 111 Fix 0.0284 0.0021 0.1009 0.0112 0.1313* 0.0124 0.1754** 0.0129 53 112 Hr 0.0704 0.0051 0.0494 0.0022 0.0443 0.0036 0.0333 0.0031 54 Nature 0.0126 0.0013 0.0118 0.0011 0.0256 0.0026 0.0316 0.0031 113 55 Gdp(r1) 0.057 0.0051 0.0867 0.0069 0.0969 0.0072 0.1926 0.0191 114 56 Gdp(r2) 0.1662** 0.0184 0.181*** 0.0195 0.1827*** 0.0219 0.1803*** 0.0199 115 57 Gdp(r3) 0.0385 0.0027 0.0223 0.0021 0.0356 0.0024 0.114** 0.0119 116 58 117 ***, **, and * represent significance levels at 0.01, 0.05, and 0.1, respectively; r1, r2, and r3 represent the low IQ, middle IQ, and high IQ groups, 59 118 respectively. The s.e. denotes the robust standard error of each variable. Please cite this article in press as: Y. Wang et al., Institutional quality, financial development and OFDI, Pacific Science Review (2015), http:// dx.doi.org/10.1016/j.pscr.2014.08.023 PSCR23_proof ■ 6 February 2015 ■ 6/6 + MODEL 6 Y. Wang et al. / Pacific Science Review xx (2015) 1e6 1 of 0.651, which suggests that a three-regime specifi- economy and employment development in the home 59 2 cation is adequate. Therefore, the previous interpreta- country. 60 3 61 tion is unchanged and stable. 4 62 5 Uncited reference 63 6 Conclusion 64 7 [11]. 65 8 We presented new evidence on the role that institu- 66 9 tional quality plays in mediating the impact of economic References 67 10 development on OFDI based on data from 73 countries 68 11 [1] M. Aguiar, G. Gopniath, Fire-sale foreign direct investment and 69 from 2000 to 2008. One contribution of the paper is the 12 liquidity crisis, Rev. Econ. Stat. 87 (2005) 439e452. 70 13 adoption of the regression model based on the idea of a 71 [2] M. 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