Higher education in Iran: An investigation of its expansion during 2005–2015 period using a control function approach

Abstract

This article aims at investigating the significant higher education expansion in the Islamic Republic of Iran during 2005–2015 period through employing the production function of higher education. Avoiding simultaneity and selection problems in the presence of shocks, we have used a novel method from industrial organization discipline introduced by Rovigatti and Mollisi [1] – which is officially offered embeded in a Stata ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ module – by providing different production function estimators (Olley-Pakes, Levinsohn-Petrin, and Wooldridge) using provincial data on Iran. Our empirical results reveal that physical capital is the most critical determinant of higher education graduates. The results also uncover some important facts about the contribution of academic staff to the process of graduation. Compared to other conventional estimation methods, we also provide evidence on the superiority of this innovative method, which is far beyond its original context.

Keywords

Higher education production function productivity shocks control function

1. Introduction

According to endogenous models for economic growth, human capital is one of the crucial sources of cross-country differences in the context [2]. As a developing economy, one of the main concerns of the Islamic Republic of Iran is sustainable growth, in which human capital plays an important role. The great effort in authorities and policymakers to expand higher education in Iran would seem to reflect this circumstance.

From three decades ago, the higher education of Iran has experienced substantial expansions in quantity: the number of students graduated has increased by an average annual rate of about 10%, and the number of higher education institutions (HEIs) has approximately tripled [3]. During the 2000s, the pace of the expansion dramatically increased, exceeding the 18–29 years old population growth rate and significantly accelerated from 2005 to 2015, as shown in Fig. 1.

Figure 1.

Number of students to the population aged 18 to 29 years (%). Source: the authors’ calculation and illustration based on the data retrieved from the Statistical Centre of Iran website [70] and the Institute for Research and Planning in Higher Education (IRPHE) [68] in EViews ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 10 on Microsoft Windows 10 Enterprise platform.

The expansion has been implemented mostly by funding new HEIs. To familiarize the readers with the context, Section 1.1 of this paper provides more information on higher education in Iran as much as it is related to the domain of this study; however, the concentration is not on the policies, but on their effects on university behavior as a result of the changes followed by the implementation of policies named.

Similar to other policies implemented on a country-wide scale, the policy of higher education expansion in Iran might have been followed by some changes in the behavior of stakeholders affected by the polices who – in our case – consist of HEIs and academic staff as well as students and graduates.

On the other hand, some studies suggest that econometric methods can study university behavior. Ehrenberg’s [4] systemic review summarises areas of research in econometrics of higher education, establishing the following five categories:

(1)

Estimating rates of return to higher education.

(2)

Determinants of college enrolment, college graduation and choice of major.

(3)

The academic labor market.

(4)

Models of university behavior.

(5)

Higher education as an industry and higher education governance.

in which higher education production functions fall into the 4 ${}^{\rm th}$ category as functions that model behavior of university [4]. So, production functions can be utilized to analyze the complex behavior of higher education.1 Thus, the following hypotheses are formed to be investigated in the production function context:2

(H.1) The major role in fulfilling the ultimate goal of Iranian HEIs, i.e., the graduation of students, is mainly done by the physical capital of the HEIs, not the staff, (H.2) Some ranges of faculty members may contribute negatively to the process of graduation

Still, it should be noted that the estimation of production function often faces two issues of “simultaneity” and “selection problem”. Simultaneity refers to the issue that observed inputs may be correlated with unobserved shock, and therefore ordinary least square (OLS) estimator will yield biased and inconsistent estimates [6, 7]. Historically, the selection problem refers to when firms observed in the market are not necessarily a random drawn from the population of interest. The issue is problematic in panel data, providing observations on firms over time. The sample of firms that survive over time might not be random, and this will introduce bias [8].

To deal with the issues, Olley and Pakes, Levinsohn and Petrin, Wooldridge, Ackerberg, et al., and Rovigatti and Mollisi have evolved literature. They have proposed solutions by introducing new methods to estimate production functions [7, 8, 9, 10]. Although the literature is evolved in the context of the Industrial Organization in economics, this paper assumes features of the model are applicable to the context of higher education. As it would be explained in the following sections, here we assume each province as a firm that is not randomly selected over time, so the so-called selection problem maintains in the new context. Also, as the behavior is investigated in an era of gradual – but major – expansion in higher education in general,3 simultaneity is also a potential issue to avoid. Thus, at least, attempting to apply this new method in higher education studies may create a new vibe in the literature (in case of success) or would be evidence of inappropriate application (if it fails).

This paper aims to investigate the stated hypotheses about university behavior using an approach following the modern literature on this subject. To do this, first, the current Iranian higher education system is briefly explained using the available data, then, a survey of literature on the subject will be presented. Next, the estimation approaches will be introduced, and then, the process of estimation in the production function framework is applied. Finally, the estimation results will be described and discussed in the context of the production function framework, followed by a comparison to common panel data methods.

1.1 Higher education in Iran

1.1.1 The system and behaviour

According to article 3 of the Constitution of the Islamic Republic of Iran, “free education and physical training for everyone at all levels, and the facilitation and expansion of higher education” is guaranteed [11]; As a result, considering the vastness (17 ${}^{\rm th}$ largest in the world) and the population (approximately 80 million) of the country [12], Iranian higher education consists of a large network of public, state-run and private HEIs. In general, non-medical state-run universities are under the direct supervision of Iran’s Ministry of Science, Research and Technology (MSRT), Ministry of Education4 (especially branches of Technical and Vocational University and Farhangian University5), or other executive organs. Medical state-run universities of Iran are under the supervision of the Ministry of Health and Medical Education (MHME). There are, also, a relatively large number of public HEIs (or semi-public6), which are mostly a branch of one of two comprehensive universities: University of Applied Science and Technology (UAST) and Payame Noor University (PNU). Furthermore, a relatively large number of private universities are currently active in the country, most of which are branches of Islamic Azad University (IAU). Figure 2, illustrates the diversity explained above and its changes over time in more detail.

Figure 2.

The number of higher education institutions in Iran. Note: the data for Ministry of Education is partly approximated and imputed ( $\pm$ 50 precision) for 2011 and next years due to lack of a proper report and structural changes, including the dependence of former Teaching Schools and their integration in the form of a new comprehensive university: Farhangian University. Source: The data received from the Institute for Research and Planning in Higher Education (IRPHE) [68] on authors’ request, which are restructured, subjected to summation, and illustrated by authors in Excel ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 2016 from Microsoft Office Professional Plus software package in Microsoft Windows 10 Enterprise platform.

To provide information on how the system functions, it is important to know that, funded by the government, state-run universities provide free education and many facilities for students, and their quality is relatively higher, so they are very competitive. These universities accept students based on a comprehensive centralized exam called konkûr, which is administered once every year by MSRT for each post-secondary stage7 [13, 15]. Students’ scores in the exam and their preferences determine the university they are accepted in. Other public and private HEIs also refer to konkûr scores to accept students, especially in more competitive positions, but they also accept students based on their backgrounds and secondary school scores; however, it is often not hard to get accepted in these universities if the student would be able to afford admission and tuition fees.

Another important feature of Iranian higher education is the centralized governance over the system by the Supreme Council of the Cultural Revolution (SCCR), MSRT, and MHME. In summary, after the Cultural Revolution preceded by the Islamic Revolution in Iran, Islamicisation was one of the central policies exerted by the highest policymaking position for education in Iran: SCCR [16]. As a result, general frameworks and policies by SCCR, and MSRT/MHME as executive organs, are mandatory in almost all categories of HEIs, so the system is highly centralized, especially in internal structure and curriculum respect. This condition has made it possible to assume similarities of the system and analyze it in a homogenous framework.

Most Iranian HEIs are educational rather than research universities, so their ultimate goal is to graduate students and award them with degrees. One possible implication, in the absence of proper regulation, would hypostatically be that private HEIs, pursuing financial purposes, increase their rate of graduation. This explains the rationale behind H.1.

As another consequence, faculty members serve educational purposes most often and are assumed to play a key role in the system. In such circumstances, the promotions8 in the hierarchy of departments9 for faculty members are awarded according to centrally announced circulars and instructions based on either educational and research backgrounds.10 The hierarchy mentioned is as it comes below in Iran:

•

Educational Staff (Kadr-e-Amûzeshî): The university employees in departments. They may be easily substituted or moved to non-educational offices of institutions.

•

Assistant Lecturers (Morbbî Amûzeshyar): The faculty members who usually hold a Bachelor’s degree and instruct technical, vocational, or experimental courses. They are not promoted until they gain a higher degree. They may have a less stable position in the faculty.

•

Lecturers (Morbbî): The faculty members who hold a Master degree or Doctor of Medicine, usually instructing Associate degree (Kârdânî) courses. They are not promoted until they gain a Ph.D.

•

Assistant Professor (Ostadyâr): The faculty members holding a Ph.D. who usually instruct undergraduate courses. They can get promoted generally based on their years of service, courses instructed, articles published, books authored, and supervision of Master theses.

•

Associate Professor (Daneshyâr): More experienced faculty members who are the former Assistant Professors who are promoted. They usually instruct graduate courses and can supervise more Theses or Ph.D. dissertations. Their promotion conditions are similar to Assistant professors with more strict measures.11

•

Professor (Ostâd): The highest rank in the department with years of experience who are promoted, Associate professors. They usually supervise Ph.D. students and often instruct graduate courses.

It should be noted that the tradition of academic freedom, Assistant Professors, Associate Professors, and Professors usually have a stable position once they are employed.

As was mentioned, the main purpose of most universities is education, so research officially takes place only in graduate levels in the form of theses (to achieve a Master degree or Doctor of Medicine) and dissertations (to achieve Ph.D.)12. Moreover, as promotion measures are quantitative rather than qualitative, these conditions lead to a conflict of interests, in several forms:

(1) (1)

Faculty members would try to instruct as many classes as possible to facilitate their promotion procedure.

(2)

Assistant – (and less likely Associate) Professors may focus on research to achieve higher ranks so that they have less time to devote to education, which is their main mission.

(3)

Faculty members may take advantage of students’ efforts forcing them to research to get better scores and publish the results in his/her name.

(4)

Scholars may focus on less practical, but easy to publish, topics out of their department mission (or even far from their area of expertise).

(5)

Graduate students are discouraged from pursuing their topics of interests, from focusing on more favorable subjects for journals and easy-to-publish topics.

The presence of such behavior would harm the education process and decrease the graduation rate, but unfortunately, not enough precautions were initiated to prevent these conditions.13 The premise explains the rationale behind H.2.

1.1.2 The expansion (2005–2015)

As was mentioned earlier, Iran’s higher education has expanded on a large scale from 2005 to 2015. This is not the only expansion in Iranian higher education. The system has experienced similar expansions after IAU and PNU were founded [21]. However, the expansion started in 2005 and lasted until 2015 has had a profound effect on the system and has changed it substantially [22]. The following paragraphs first explain why authorities decided to expand higher education, then, present the process of expansion in data descriptively.

Initially, the Iranian government intended to keep higher education state-run, but, gradually the approach to higher education governance was adjusted due to the growing demand for higher education and the increase in the young population [23]. On October 15, 1985, SCCR announced the procedure and regulations to start private HEIs [24], and private HEI began to start their activity from the 1990s to a limited extent. In the 2000s, fewer restrictions were enforced upon private HEIs, so they expanded their activity, and many new institutions entered the market [23]. Since the number of state-run HEIs did not decrease, the activity of private HEIs leads to the expansion of higher education.14 Also, public and semi-public HEIs was founded in the era nurturing the changes and expansion, and also altogether probably affecting the functions of the university that we call “university behavior” in this paper.

Additionally, the Forth Program for Economic, Social, and Cultural Development of Islamic Republic of Iran (2005–2010), Part one (Knowledge-Based Economic Growth in Interaction with Global Economy), Chapter four (Development Based on Knowledge), Article 49 and Article 50, emphasize on diversification of admission in universities, implying more intake, and also the public provision of higher education, especially for low-lying and deprived areas [27]. This law was one of the main steps to amplify the expansion, especially concerning public and state-run HEIs.

Other scholars have also discussed the reasons why higher education in Iran expanded to a large extent. Arjomandi and Samiei state that the creation of a mid-class social class hoping for higher social status and the insufficiency of the labor market to respond to the demand for employment are the main reasons encouraging participation in higher education [22]. Memarzadeh and Mardani have found that technological purposes of gaining a greater power and the necessity of achieving higher equity among geographical regions have been the main drivers of higher education expansion [28]. Others may also refer to business objectives that HEIs, especially private ones, are following [29].

To give more details, as it is depicted in Fig. 2, for the interval between 2005 and 2015, the number of HEIs has grown annually 9.37% on average from about 1148 to about 2859 institutions, so the number of HEIs has approximated doubled during these years. Furthermore, the proportionate number of UAST branches has risen from 17% to 33%. The same number for private universities has also grown from 3% to 11%. On the contrary, the proportionate number of universities linked to the Ministry of Education has dropped from 25% to 10%, and IAU had 18% of HEIs in 2018 while its share had been 24% in 2005. The proportionate number of other universities has not changed substantially.

As the data for the number of students for each category of the universities mentioned in Fig. 2 is not available, so the total number of students is for the same period, and the average number of students per institution is provided in Figs 3 and 4.

Figure 3.

Number of higher education students in Iran. Note: the number of students for Payame Noor University in 2011 and 2018 was rounded upward in data sources, so it is not precise. In addition, annual data for all categories of HEIs were not found, so the data for one or a few years is provided these HEIs. Source: The data provided by IRPHE [68] for the total number of students and HEIs, except for Ministry of Education, which is approximated based on the IRPHE data, the data retrieved from Farhangian University website [92] and the data retrieved from Technical and Vocational University website [93], Payame Noor University, which was retrieved from the university’s website [94], PNU News Agency and YJC [95, 96], and University of Applied Science and Technology, which was retrieved from the university’s website [97]. The illustration of data is done by authors in Excel ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 2016 from Microsoft Office Professional Plus software package in Microsoft Windows 10 Enterprise platform.

Figure 4.

The average number of students in HEIs. Note: the data illustrated in this figure is calculated by dividing the total number of students in each category of HEI to the number of the institution for the relevant year. Source: the data is calculated by the authors based on the data presented in Figs 2 and 3. Calculations and the illustration are done in Excel ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 2016 from the Microsoft Office Professional Plus software package in Microsoft Windows 10 Enterprise platform.

Based on the data presented, the total number of tertiary education students in Iran has grown 127% from 2117471 in 2005 to 4811581 in 2015. Moreover, the number of students in MSRT increased by 82% in the same period, and many other HEIs has experienced similar expansions (e.g., for 2008 to 2015: MHME 75%, AIU 29%, other private universities 196%, and for 2007 to 2011: PNU about 61%). According to the available data (Fig. 4 specifically), the “massification” of higher education in this era is mostly the outcome of founding new HEIs rather than increasing each university’s intake, because the average number of students in one HEI has decreased in the period of expansion (by $-$ 8.76% in average). Except for MHME (with 80% increase in the average number of students per HEI from 2006 to 2014), other private universities (with 49% increase in the average number of students per HEI from 2008 to 2015), and PNU (which seems to have experienced growth in the average number of students per HEI), other HEIs have not increased the size of each unit student-wise in average. These facts support our first hypothesis (H.1).

The expansion has increased the participation rate in higher education and has positively affected the educational attainment. Still, some studies also point out negative side-effects and failures of the expansion including unbalanced growth [30], negative cultural consequences [31], its negative effects on marriage market for the woman [32], and increasing unemployment [33, 34, 35]; however, this paper aims to investigate the university behavior with an emphasize on graduation in terms of the number of graduates in a new framework.

The higher education system of Iran has evolved in other aspects too during recent years, most of which are not explained above; but, explaining these details are out of this paper’s domain and irrelevant to the subject of study, so, it is recommended to refer to the relevant studies such as Hamdhaidari et al. [16] for the detailed explanation.

1.2 Review of the literature

The efficiency and productivity of HEIs have been the subject of many kinds of research. There is a vast body of literature on production function estimation in higher education [36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48], where there are several inputs, and one output considered and productivity of each unit and return to scale are the main concerns, althogh a variety of estimation methods (e.g. Ordinary Least Squares [OLS], Spatial methods [e.g. SLX], Two-Stage Least Squares [2SLS] or Generalized Method of Moments [GMM]) and different data sets (panel data or time series) have been applied. The efficiency of HEIs is also measured and compared by utilizing benchmarking methods such as Data Envelopment Analysis (DEA) or Stochastic Frontier Analysis (SFA) (where there are some units, considering multiple inputs and outputs, and the relative efficiency is to be calculated) [49, 51, 52, 53]. Here our focus is on the productivity of inputs and returns to scale to investigate university behavior, so this section discusses the literature on higher education production functions rather than others.15

As was mentioned earlier, several studies have proposed and discussed the application of production functions in higher education (e.g., see Hopkins’ critical review of 32 studies on higher education production functions during the 1970s [40, 55]). Also, Ehrenberg’s review of the econometrics of higher education (both methodology and literature) have covered 40 years of study with a special focus on empirical research [4]. He discusses rates of return to higher education estimation, academic labor market studies, the literature related to institutional behavior, the studies considering higher education as an industry. He proposes some future areas of research [3].

Naderi thoroughly reviews the literature and considers 11 applications of the production function in higher education research analysis and its priorities, along with the identification of problems and challenges faced in application [56]. In what follows, a selection of relevant empirical studies focusing on estimation of higher education production functions is briefly reviewed about their estimation.

Da Silva Freire and da Silva apply production functions to the Portuguese higher education system and focus on the economies of scale existence and substitutability of production factors: professors and assistant professors. In this way, data on two Portuguese higher education institutions16 for the 1958–1970 period were used to estimate Cobb-Douglas production functions. The authors found that if the number of graduates is considered a product, it would be necessary to introduce time as a representative of technological progress. Additionally, they outline merits and the limitations of utilizing production functions for policymaking purposes [3, 38].

Chizmar and Zak have investigated some theoretical and empirical implications of introducing multiple outputs into economic education production functions. They proposed a simultaneous equations system that also embodies three empirical approaches, using data collected in a large section of economic principles in the fall of 1978 at Illinois State University; the sample consisted of 175 students. Their findings show that all three approaches prove the existence of trade-offs within the learning process, and substitution appears less difficult when outputs are modeled as joint products [3, 57].

Dolan and Schmidt examine the relative contributions of human and physical resources in the production of private undergraduate education, and the significance of simultaneity among students, faculty and institutional output evaluated by quality, using a three-stage least-squares technique within a theoretical framework emphasizing the interdependence of inputs and outputs in higher education. Microdata of 360 private individuals, mainly undergraduate, colleges, and universities of the United States, was used for the year 1981. Their results indicate the importance of quality faculty in human capital production [3, 58].

Sameti et al. used a simultaneous equation system to study the performance of 21 Iranian public universities in 1994–1998 period, considering endogenous variables of education quality (i.e., “the ratio of admitted undergraduates to total master degree candidates”), admission policies (i.e., “the proportion of the admitted undergraduate students through general entrance exams”), and staff quality (i.e., “the proportion of academic staff holding assistant professorship or higher ranks”). They show that staff quality and educational budget affect education quality positively, and admission policies and administrative budgets have negative effects on improvement [3, 59].

Bratti et al. have specified a growth model using a qualitative measure of human capital development to test the dependency of economic growth on human capital development in an area were among the universities located in Italy, the most efficient are evaluated. In their model, university efficiencies (in conjunction with a customary quantitative measure of human capital development: number of graduates) are represented by a stochastic frontier Cobb-Douglas production function based on 72 Italian universities’ data over the 2003–2011 period. Being estimated on a panel data framework, their evidence suggests that both indicators of human capital development have a positive and significant impact on GDP per capita, and knowledge spillovers occur between areas through the geographical proximity to the efficient universities, suggesting that the geography of production is affected [60].

Mihaljevic applies education production functions to test the significance of a complex set of factors on student attainment measured by GPA in the Croatian higher education system. His data consist of 3,856 students who had completed their first-year courses derived from a large dataset of the entire student population on 4-year programs of a large Croatian higher education institution (HEI) for the period 1994–2003. Implementing OLS estimation, he finds that paying tuition fees, being a full-time student and effort measured by the number of exam attempts, negatively influence GPA; in contrast, the relevance of educational background (secondary school education related to student’s present field of study) and mothers’ education (as a proxy for family socioeconomic status) positively affect student attainment in Croatia [61].

Soo estimates the production function for university students in English universities – using data from the NSS and HEPI surveys of 2006 and 2007 – to find the determinants of university students’ performance. The paper’s key finding is that “prior education and the quality of teaching are the most significant determinants of university degree performance.” He controls for unobserved student ability using a 2SLS/GMM approach, which indicates that it is student ability that drives the significance of prior education; taking student ability as the control variable, prior education no longer has a significant effect on degree performance [3, 62].

Naderi examines the application of production functions to evaluate developments of the Iranian higher education system over three decades from 188 to 2014. He uses a variety of production function forms to evaluate the main determinants of Iran’s higher education performance and takes advantage of cointegration analyses to avoid spurious regressions problem and also derive long-run and short-run relationships between the variables of the study. The paper’s findings show that Iranian higher education production functions conform to both polynomial cubic and Cobb-Douglas forms in estimation. Academic staff and the number of institutions are the main determinants of higher education outputs in both the long-run and short-run. Furthermore, Naderi finds that the Iranian higher education system performs under increasing return to scale with some degrees of inefficiency [3].

Liu empirically analyzes the heterogeneous and spatial effect of higher education on the regional TFP growth using a dynamic spatial (SLX) econometric model with provincial panel data from 2003 to 2016. They assume that Higher education in China can affect total factor productivity (TFP) growth and, therefore, sustainability. Their results indicate that “different levels of higher education have significant effects on TFP growth and are mainly reflected in the spatial spillover effect.” In conclusion, they suggest that “the Chinese government can promote TFP growth and economic sustainability by expanding the scale of bachelor and doctoral education and improving the quality of technical and master education” [63].

The above survey of literature has focused on the applications of higher education production functions and the methods implemented. As indicated, these studies cover developed, and developing countries, including Iran, showing the application of production functions in higher education has been of interest to researchers and policymakers during the past several decades. Besides, different methods of estimation were applied to, most often, Cobb-Douglas form of the production function. However, the literature has not taken into account the potential biases occurring as a result of simultaneity and selection issues. The following sections of this article provide a detailed analysis of the common estimation biases named and introduce recent developments of econometric literature to deal with the issues. Then, the edge-breaking control function approach, introduced by 1 [1], is applied to the data of the Iranian higher education system following different frameworks, and the results are discussed.

2. Materials and methods

2.1 Empirical methodology

The correct estimation of total factor productivity has been the main topic of many seminal econometric articles [1, 5, 64]. In the context of firms’ production response to positive productivity shocks, they expand their output level and demand more input; in contrast, in case of negative shocks, they do the opposite [1]. One of the recent comprehensive contributions to the literature is the Rovigatti and Mollisi study, which summarises the literature and also contributes to the literature by the application of a control function approach in estimation. They explain that:

“The positive correlation between the observable input levels and the unobservable productivity shocks is a source of bias in ordinary least squares (OLS) when estimating total-factor productivity. Various methods have been proposed to tackle this simultaneity issue, and according to their approaches, it is possible to group them into three families: fixed-effects (FE), instrumental-variables (IV), and control function approach. In the latter group, Olley and Pakes are the first to propose a two-step procedure aimed at overcoming the endogeneity: they use the investment level to proxy for productivity. Their approach has been refined by Levinsohn and Petrin and Ackerberg et al. Wooldridge proposes a novel estimation setting, showing how to obtain the Levinsohn-Petrin (LP) estimator within a system generalized method of moments (GMM) econometric framework, which can be estimated in a single step, and showing the appropriate moment conditions.” [1]

All these models assume that the firm’s dynamic profit-maximization problem at each period $t$ : the idiosyncratic productivity shock ( ${\xi}_{t}$ ) does not affect the choice of state variables’ level, which is taken at $t-b$ but only affects the level of free variables. So, ${\xi}_{t}$ is not correlated to “the contemporaneous value of the state and to all the lagged values of the free and state variables, and all of these are valid instruments for parameter identification” [1]. The estimation methodology of the present article is essentially based upon the work of Rovigatti and Mollisi.

2.1.1 Control function approach

To introduce the control function approach and for the rest of the analysis, the production function form is considered to take the form of Cobb-Douglas [65] for firm $i$ at time $t$ :

$\displaystyle y_{it}=\alpha+{\bm{w}}_{it}\bm{\beta}+{\bm{x}}_{it}\bm{\gamma}+{% \omega}_{it}+{\varepsilon}_{it}$ (1)

in which $y_{it}$ is value-added or logarithm of gross output, ${\bm{w}}_{it}$ is a $1\times J$ vector of the logarithm of free variables, and ${\bm{x}}_{it}$ is a $1\times K$ vector of the logarithm of state variables. The random component ${\omega}_{it}$ is “the unobservable productivity or technical efficiency,” and ${\varepsilon}_{it}$ is “an idiosyncratic output shock distributed as white noise.” Following the Olley-Pakes (OP) and Levinsohn-Petrin (LP) methods [7, 8] it is assumed that productivity develops according to a first-order Markov process:

$\displaystyle{\omega}_{it}=E({\omega}_{it}|{\Omega}_{it-1})+{\xi}_{it}=E({% \omega}_{it}|{\omega}_{it-1})+{\xi}_{it}=g({\omega}_{it-1})+{\xi}_{it}$ (2)

in which ${\Omega}_{it-1}$ is the information set at $t-1$ and ${\xi}_{it}$ is the productivity shock, that is “assumed to be uncorrelated with productivity ${\omega}_{t}$ and with state variables $x_{it}$ ” [1].

2.1.2 Olley-Pakes method

The first study that proposes a consistent two-step estimation procedure for Eq. (1) is (OP) [8]. Their main point is to derive a proxy from the firm’s investment levels as a variable for ${\omega}_{it}$ and prove their estimates of productivity are consistent under several assumptions, including:

(1) (1)
The investment policy function is $i_{it}=f({\bm{x}}_{it},{\omega}_{it})$ , which is invertible in ${\omega}_{it}$ ; and, $i_{it}$ is increasing in ${\omega}_{it}$ monotonically.
(2)
The state variables are decided at time $t-1$ and develop according to $i_{it}$ investment policy function.
(3)
The free variables ${\bm{w}}_{it}$ are nondynamic (i.e., their choice at t does not impact future profits), and are chosen at time $t$ after firm realizes productivity shocks.

Therefore, considering Eqs (1) and (2), the investment policy function, $i_{it}$ , is orthogonal to the state variable in t, the way that $E(i_{it}|{\bm{x}}_{it})=0$ and is invertible, yielding the following productivity proxy:

$\displaystyle{\omega}_{it}=f^{-1}(i_{it},{\bm{x}}_{it})=h(i_{it},{\bm{x}}_{it})$ (3)

as an unknown function representing observable variables. Also, substituting Eq. (3) into Eq. (1), Equation (4) is obtained:

$\displaystyle y_{it}=\alpha+{\bm{w}}_{it}\bm{\beta}+{\bm{x}}_{it}\bm{\gamma}+h% (i_{it},{\bm{x}}_{it})+{\varepsilon}_{it}=\alpha+{\bm{w}}_{it}\bm{\beta}+h(i_{% it},{\Theta}_{it}(i_{it},{\bm{x}}_{it}))+{\varepsilon}_{it}$ (4)

where ${\Phi}_{it}(i_{it},{\bm{x}}_{it})={\bm{x}}_{it}\bm{\gamma}+h(i_{it},{\bm{x}}_{% it})={\bm{x}}_{it}\bm{\gamma}+{\omega}_{it}$ is defined. Eq. (4) is a

“partially linear model identified only in the free-variable vector ${\bm{w}}_{it}$ , and can be nonparametrically estimated approximating ${\Phi}_{it}(i_{it},{\bm{x}}_{it})$ by an $n$ th-degree polynomial $\hat{\Phi}$ or by a local linear regression (first stage). This yields a consistent estimate of the free variables’ parameters $\hat{\bm{\beta}}$ . Then, using Eq. (2), it becomes possible to estimate $\bm{\gamma}$ by rewriting the model for $y_{it}-{\bm{w}}_{it}\hat{\bm{\beta}}$ conditional on ${\bm{x}}_{it}$ :

$\displaystyle y_{it}-{\bm{w}}_{it}\hat{\bm{\beta}}={\alpha}_{0}+{\bm{x}}_{it}% \bm{\gamma}+g({\omega}_{it-1})+e_{it}$ (5)

where $e_{it}={\xi}_{it}+{\varepsilon}_{it}$ . Given ${\hat{\omega}}_{it}={\hat{\Phi}}_{it}-{\bm{x}}_{it}\bm{\gamma}$ , Eq. (5) becomes

$\displaystyle y_{it}-{\bm{w}}_{it}\hat{\beta}={\alpha}_{0}+{\bm{x}}_{it}\gamma% +g({\hat{\Theta}}_{it-1}-{\bm{x}}_{it-1}\gamma)+e_{it}$ (6)

where the function $g(\cdot)$ can be left unspecified and estimated nonparametrically.”

If it is assumed that $g(\cdot)$ follows a random walk, Eq. (6) can be restated as

$\displaystyle y_{it}-{\bm{w}}_{it}\hat{\beta}={\alpha}_{0}+({\bm{x}}_{it}-{\bm% {x}}_{it-1})\gamma+{\hat{\Theta}}_{it-1}+e_{it}$ (7)

where incorporates the true values of ${\gamma}^{}$ :

$\displaystyle e_{it}=y_{it}-{\bm{w}}_{it}\hat{\beta}-{\alpha}_{0}-{\bm{x}}_{it% }{\gamma}^{}-g({\hat{\Theta}}_{it-1}-{\bm{x}}_{it-1}\gamma)$ (8)

Considering Eq. (7),

“residuals $e_{it}$ can be used to build a GMM estimator exploiting the moment conditions $E[e_{it}x^{k}_{it}]=0$ , $\forall k$ (second stage), where $x^{k}$ are the single elements of vector $\bm{x}$ . The ${\gamma}^{}$ vector is the vector of parameters that minimizes the criterion function:

$\displaystyle{\gamma}^{}=\operatorname{argmax}\left\{\sum_{k}{{\left(\sum_{i}% {\sum_{t}{e_{it}x^{k}_{it}}}\right)}^{2}}\right\}.$ (9)

2.1.3 Levinsohn-Petrin method

A major drawback of the OP approach, according to common industry practices, is the violation of monotonicity assumption (1); that is, “investments are not decided at each point in time but are postponed for a few years before being made all at once.” Levinsohn and Petrin [7] try to solve this problem by “exploiting intermediate input levels as a proxy variable for ${\omega}_{it}$ ” [1]. The LP methodology is based on the following assumptions:

(1) (4)
After observation of a productivity shock, firms adjust their “optimal level of intermediate inputs according to the demand function $m({\omega}_{it},{\bm{x}}_{it})$ ”.
(5)
The intermediate input function is $m_{it}=f({\bm{x}}_{it},{\omega}_{it})$ , invertible in ${\omega}_{it}$ . Also, $m_{it}$ is increasing in ${\omega}_{it}$ monotonically.
(6)
The state variables develop according to the investment policy function $i(\cdot)$ , being decided at $t-1$ .
(7)
The free variables ( ${\bm{w}}_{it}$ ) are nondynamic, and “their choice at $t$ does not impact future profits, and are chosen at time $t$ after the firm realizes productivity shock” [1].

According to assumptions (5)–(7), “intermediate input demand is orthogonal to the set of state variables in $t$ such that $E(m_{it}|x_{it})=0$ and $m_{it}$ can be inverted”, and the following technical efficiency proxy is derived:

$\displaystyle{\omega}_{it}=h(m_{it},{\bm{x}}_{it})$ (10)

As an unknown function representing observable variables Substituting Eq. (10) into Eq. (1), the following equation is obtained:

$\displaystyle y_{it}=\alpha+{\bm{w}}_{it}\beta+{\bm{x}}_{it}\gamma+{\delta m}_% {it}+h(m_{it},{\bm{x}}_{it})+e_{it}={\bm{w}}_{it}\beta+{\Theta}_{it}(m_{it},{% \bm{x}}_{it})+e_{it}$ (11)

in which ${e}_{it}={\xi}_{it}+{\varepsilon}_{it}$ [1].

Equation (11) “is a partially linear model identified only in the free variable vector but not in the proxy variable, $m_{it}$ . Similar to OP, Eq. (11) can be nonparametrically estimated, approximating ${\Theta}_{it}(m_{it},{\bm{x}}_{it})$ ” (equivalent to $\alpha+{\bm{x}}_{it}\gamma+h({\bm{x}}_{it},m_{it})$ ), “by an $n$ th-degree polynomial or by local linear regression (first stage)” [1]. At $[{\gamma}^{},{\delta}^{}]$ , the residual function $e_{it}$ can be defined as:

$\displaystyle e_{it}=y_{it}-{\bm{w}}_{it}\hat{\beta}-{\bm{x}}_{it}{\gamma}^{}% -g({\hat{\Theta}}_{it-1}({\delta}^{})-{\bm{x}}_{it-1}\gamma)$ (12)

“However, $e_{it}$ is no longer a combination of pure errors. The intermediate input variable is correlated with the error term given the firms’ response to the technology efficiency shock ${\xi}_{it}$ . Thus, nonlinear least squares would provide inconsistent estimates, and relying on a GMM estimator is mandatory. The GMM estimator might be constructed by exploiting the residuals $e_{it}$ and the set of moment conditions $E[e_{it}x^{k}_{it}]=0,\forall k$ , where $k$ is the index of the instrument vector $\bm{z}=[{\bm{x}}_{it},m_{it-1}]$ .

$\displaystyle\begin{bmatrix}{\gamma}^{}\\ {\delta}^{}\end{bmatrix}=\operatorname{argmax}\left\{\sum_{k}{{\left(\sum_{i}% {\sum_{t}{e_{it}x^{k}_{it}}}\right)}^{2}}\right\}$ (13)

consistently estimates the set of parameters ${[\gamma,\delta]}^{\rm T}$ .” [1]

2.1.4 Ackerberg-Caves-Frazer correction

An unrealistic assumption in OP and LP is that firms can adjust some inputs instantly and at no cost when they are subject to productivity shocks. However, Aackerberg, Caves, and Frazer (ACF) and Bond and Söderbom remark that $\bm{\gamma}$ “can be consistently estimated in the first stage only if the free variables show variability independently of the proxy variable” [1, 10, 66]. Otherwise, their coefficients would not be not-identifiable as a result of perfect collinearity in the first-stage estimation. Particularly, in LP, it is assumed that intermediate inputs are allocated simultaneously at time $t$ . This implies that ${\bm{x}}_{it}$ is chosen as a function of productivity and state variables ${\bm{x}}_{it}$ : $m_{it}=m({\omega}_{it},{\bm{x}}_{it})$ and $l_{it}=l({\omega}_{it},{\bm{x}}_{it})$ [1].

Applying monotonicity condition Eq. (5), ACF yields $l_{it}=l[h(m_{it},{\bm{x}}_{it}),{\bm{x}}_{it}]$ and so collinearity arises in the nonparametric polynomial approximation ${\hat{\Theta}}_{it}$ . In the same way, the OP estimator is also affected by collinearity. Ackerberg et al. propose an alternative approach based on the following assumptions:

(11) (8)
$p_{it}=f({\bm{x}}_{it},l_{it},{\omega}_{it})$ is the proxy variable policy function, which can be inverted in ${\omega}_{it}$ . Also, $p_{it}$ is increasing in ${\omega}_{it}$ monotonically.
(9)
The decision time for state variables is $t-b$ .
(10)
$l_{it}$ is chosen at $t-\zeta$ ; $0<\zeta<b$ . The free variables ( ${\bm{w}}_{it}$ ) are chosen at $t$ , after realization of the firm productivity shock.
(11)
“The production function is value-added in the sense that the intermediate input $m_{it}$ does not enter the production function to be estimated” [1].

As Rovigatti and Mollisipropose, assumption (11) is necessary because bond and Söderbo have shown that, under the ACF assumptions, “a gross output production function is not identified without imposing further restrictions of the model” [1, 66]; so, ACF corrections do not apply to this article’s data and to summarise, the further information on ACF is skipped (for more information see Ackerberg et al.).
2.1.5 Wooldridge method

Addressing the OP and LP problems, Wooldridge (2009) proposes to replace the two-step estimation procedure with a GMM setup similar to that in Wooldridge (1996) [1, 9, 67]. Particularly, “he shows how to write the relevant moment restrictions in terms of two equations that have the same dependent variable ( $y_{it}$ ) but are characterized by a different set of instruments” [1]. This approach “overcomes the potential identification issue highlighted by ACF in the first stage” and obtains robust standard errors (instead of bootstrapped standard errors in OP and LP), “accounting for both serial correlation and heteroscedasticity” [1].

In the first stage estimation of both OP and LP, it is assumed that

$\displaystyle E({\varepsilon}_{it}|{\omega}_{it-1},w_{it},x_{it},m_{it},w_{it-% 1},x_{it-1},m_{it-1},\ldots,w_{i1},x_{i1},m_{i1})=0$ (14)

This is

“without imposing any functional form on the control function ${\omega}_{it}=h(\cdot,\cdot)$ . The second stage assumption exploits the Markovian nature of productivity and the assumed orthogonality between productivity shocks and current values of the state variables, as well as between productivity shocks and past realizations of the free variables and the intermediate inputs.”

Based on LP and Eq. (2), the implication is

$\displaystyle E({\omega}_{it}|x_{it},w_{it-1},x_{it-1},m_{it-1},\ldots,w_{i1},% x_{i1},m_{i1})=f[h(x_{it-1},m_{it-1})]$ (15)

in which no functional form is imposed on $f(\cdot)$ as for $h(\cdot,\cdot)$ . Assumptions (14) and (15) lead to the results [1]:

$\displaystyle y_{it}=\alpha+{\bm{w}}_{it}\beta+{\bm{x}}_{it}\gamma+h({\bm{x}}_% {it},{\bm{m}}_{it})+{\upsilon}_{it}$ (16) $\displaystyle y_{it}=\alpha+{\bm{w}}_{it}\beta+{\bm{x}}_{it}\gamma+f[h(x_{it-1% },{\bm{m}}_{it-1})]+{\eta}_{it};\quad{\eta}_{it}={\xi}_{it}+{\upsilon}_{it}$ (17)

The estimation approach of Roviggati and Mollisi propose is to deal with the unknown functional forms using $n$ th-degree polynomials in $x_{it}$ and $m_{it}$ , where the limiting case ( $n=1$ ) is “with $x_{it}$ and $m_{it}$ entering linearly should always be allowed”. Particularly, if it is assumed that

$\displaystyle h({\bm{x}}_{it},{\bm{m}}_{it})={\lambda}_{0}+k({\bm{x}}_{it},{% \bm{m}}_{it}){\lambda}_{1}$ (18)

where $k(\cdot,\cdot)$ is a $1\times Q$ collection of functions, $f(h)={\delta}_{0}+{\delta}_{1}h+{\delta}_{2}h^{2}+\ldots+{\delta}_{G}h^{G}$ ; If for simplicity it is assumed that $G=1$ and ${\delta}_{1}=1$ , and making the substitution in Eqs (16) and (17), the result is

$\displaystyle y_{it}=\zeta+{\bm{w}}_{it}\beta+{\bm{x}}_{it}\gamma+k({\bm{x}}_{% it},{\bm{m}}_{it}){\lambda}_{1}+{\upsilon}_{it}$ (19) $\displaystyle y_{it}=\theta+{\bm{w}}_{it}\beta+{\bm{x}}_{it}\gamma+k({\bm{x}}_% {it-1},{\bm{m}}_{it-1}){\lambda}_{1}+{\eta}_{it}$ (20)

“where $\zeta$ and $\theta$ are the new constant parameters obtained through the aggregation of all the constant terms” [1].

Considering $G=1$ and ${\delta}_{1}=1$ , the system GMM would have linear moments. The act of choosing instruments for Eqs (19) and (20) is “straightforward and reflects the orthogonality conditions listed above: Particularly, the results’ equations are

$\displaystyle{\bm{z}}_{it1}=(1,{\bm{x}}_{it},{\bm{w}}_{it},k({\bm{x}}_{it},{% \bm{m}}_{it}))$ $\displaystyle{\bm{z}}_{it2}=(1,{\bm{x}}_{it},{\bm{w}}_{it-1},k({\bm{x}}_{it-1}% ,{\bm{m}}_{it-1}))$ (21) $\displaystyle{\bm{Z}}_{it}=\binom{{\bm{z}}_{it1}}{{\bm{z}}_{it2}}$ (22)

“For each $t>1$ , the usual GMM with IV setup applies, and the moment conditions are derived from the residual functions

$\displaystyle{\bm{r}}_{it}(\theta)=\binom{r_{it1}(\theta)}{r_{it1}(\theta)}=% \binom{y_{it}-\zeta-{\bm{w}}_{it}\beta-{\bm{x}}_{it}\gamma-k({\bm{x}}_{it},{% \bm{m}}_{it}){\lambda}_{1}}{y_{it}-\theta-{\bm{w}}_{it}\beta-{\bm{x}}_{it}% \gamma-k({\bm{x}}_{it-1},{\bm{m}}_{it-1}){\lambda}_{1}}$ (23)

and $E[{\bm{Z}}^{\prime}_{it}{\bm{r}}_{it}(\theta)]=0$ .

In this leading case, the estimation is particularly straightforward because the whole system boils down to a linear estimation problem. Following Wooldridge [9], we can rewrite the system as ${\bm{y}}_{it}={\bm{X}}_{it}\bm{\theta}+{\bm{r}}_{it}$ , where ${\bm{y}}_{it}$ is a vector containing $y_{it}$ twice $\ldots$ , $\bm{\theta}$ is the vector of parameters of interest, ${\bm{r}}_{it}$ is defined as above, and

$\displaystyle{\bm{X}}_{it}=\begin{bmatrix}1&0&{\bm{w}}_{it}&{\bm{x}}_{it}&k({% \bm{x}}_{it},m_{it})\\ 0&1&{\bm{w}}_{it}&{\bm{x}}_{it}&k({\bm{x}}_{it-1},m_{it-1})\end{bmatrix}$ (24)

Using ${\bm{Z}}_{it}$ as above yields consistent estimates” [1].

2.2 Data and descriptive statistics

To estimate the production functions, the data referring to the Iranian higher education system were obtained from the Institute for Research and Planning in Higher Education (IRPHE) [68]. These data include series of the number of Graduates (as dependent variable), number of Students, Professors, Associate Professors, Assistant Professors, Lecturers, Assistant Lecturers, Educational Staff for each province of Iran from 2005 to 201717. Also, the overall Government Budget devoted to HEIs of each province from 2005 to 2017 was provided from the Plan and Budget Organization [69] on the authors’ request. The number of HEIs in each province was estimated based on the data for assigned students, Government Budget, and the overall number of professors and educational staff. As for control variables, Regional Gross Domestic Product (RGDP) and Provincial Population of each province were extracted from data provided by the Statistical Center of Iran [70] for the interval being studied.18

The data is structured as a standard balanced panel data set following the methodology. Table 1 represents the abbreviation of variables studied and their sources. It should be noticed that the names in Table 1.19

Table 1
Variables, abbreviations, and sources

Variable	Abbreviation	Source
Number of Graduates	grad	[l]Institute for research andplanning in higher education
Number of current students	st
Number of professors	prof
Number of associate professors	acprof
Number of assistant professors	asprof
Number of lecturers	lctu
Number of assistant lecturers	aslctu
Number of educational staff	edust
Number of HEIs	hei	Author’s estimation
Government budget devoted to HEIs	bud	Plan and budget organization
Regional gross domestic product (RGDP)	rgdp	Statistical center of Iran
Provincial population	rpop	Statistical center of Iran

Note: Government Budget devoted to HEIs is in billion Iranian Rials (IRR), Regional Gross Domestic Product is based on value added and in Iranian Rial (constant 2016 prices), and Provincial Population is in thousands.

Furthermore, Table 2 provides brief descriptive statistics of the variables being studied.20

Table 2

Descriptive statistics

	grad	st	hei	prof	acprof	asprof
Mean	18675.62	116901.2	72.08587	128.0634	255.8559	1105.222
Maximum	212577	1054015	723	2746	4511	14180
Minimum	549	2823	6	0	0	5
Standard deviation	25034.28	144289.2	92.72544	357.8667	614.0028	1907.938
No. of observations	360	360	361	347	354	360
	lctu	aslctu	edust	bud	rgdp	rpop
Mean	1795.389	113.4403	3.42E+03	5.88E+10	2.50E+03	2.50E+08
Maximum	11809	779	2.99E+04	3.70E+12	1.62E+04	4.01E+09
Minimum	22	0	85	43994.08	539.459	8994286
Standard deviation	1949.214	134.8387	4.17E+03	3.39E+11	2.67E+03	4.72E+08
No. of observations	360	352	360	390	390	390

Source: Authors’ Estimation in EViews ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 10 in Microsoft Windows 10 Enterprise platform.

As Renfro discusses, it is necessary to consider the way data is structured and how calculations are done in econometrics [71, 72]; while most of the calculations are done using econometric software packages in different platforms, it is important to note their characteristics consequently [73]. As a result, the following paragraphs explain the relative background of this paper.

In this paper, three software packages were used to work with the data and do calculations and derive econometric results: Excel ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 2016 from Microsoft Office Professional Plus software package, Stata ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 15, and EViews ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 10. All the software packages are installed and run in the Microsoft Windows 10 Enterprise platform.

Microsoft Office Excel ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ has been widely used as one of the best software packages to manipulate data, especially in econometrics (see, for example, Barreto and Howland [74], Halkos [75], Hill et al. [76], and Briand and Hill [77]). Excel ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 2016 from Microsoft Office Professional Plus software package is one of the newest versions of the software which is user-friendly and reliable to do calculations in. The data reposition, restructuration to panel data (longitudinal) format, basic calculations, and illustration of figures in this paper are mostly done in the mentioned version of the software.

Stata ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ is a well-known and reliable software for scientific research, especially following quantitative methodologies [78] (see, for example, Baum [79], Acock [80], Rabe-Hesketh and Skrondal [81], Cameron [82], Roßmann et al. [83]). Being the newest version, Stata ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 15 has many official modules to run a range of basic to advanced econometric models introduced officially in the software package or the Stata Journal published by SAGE. One of these newest modules is prodest, introduced in Rovigatti and Mollisi [1], which is the base of main econometric models in this study.

EViews ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ is a professional software offering “academic researchers, corporations, government agencies, and students access to powerful statistical, forecasting, and modeling tools through an innovative, easy-to-use object-oriented interface.” [84] (see examples of these applications in: Vogelvang [85], Agung (2013, 2011a, 2011b) [86, 87, 88]). EViews ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 10 has the options needed to do run panel data models [86], so it was used to run the models as ordinary equivalents of the main novel method of this study to reveal the contrast.

2.3 Estimation

Three different methods of production function estimation apply to Iranian higher education data, following the control function approaches proposed by Rovigatti and Mollisi [1]. In this section, these methods are precisely applied to data, and the estimation results are reported and compared.

Following the instructions, the natural logarithmic form of the variables being studied must be categorized as state variables, free variables, proxy variables, or optionally control and endogenous variables. No literature or study is present to reference here as a guide for this categorization, so the variables fall into each category based on the authors’ perception of the Iranian higher education system.

As for state variables, the number of university staff with more stable positions in each province, and also according to Naderi [3], the number of HEIs in each province, are considered to be state variable. Although most studies have considered academic staff as labor [3], which is expected to be interpreted as free or proxy variable here, in the case of Iran, this variable should be assigned as a state variable due to the stability of faculty position in the country. In other words, the justification here is that in response to productivity shocks, the variables cannot be adjusted easily according to academic integrity and – more basically- the labor force law of Iran. So, the list of state variables is: log(prof)21, log(acprof), log(asprof), log(lctu), and log(hei).

As for free and proxy variables, the number of university staff with less stable positions in each province, and also the government budget devoted to HEIs of each province, are considered to be free and proxy variables. The instability of assistant lecturers and educational staff, as it is observed, makes these individuals easiest to adjust in case of policy shocks, the decline in the number of assignments, or when the HEI faces a budget shortage. Also, the government budget devoted to HEIs functions very similar to an investment in the literature; therefore, bud is also considered as a free variable. Hence, the list of free variables is: log(aslctu), log(edusta), and log(bud).

As for free and control and endogenous variables, the provincial GDP and population are considered to represent the economic and demographic status of each province, which indirectly affect HEIs and the level of university supply. Moreover, the number of current university students in each province is also considered as endogenous because, the majority of educational staff time, and also budget goes for all students, not only the ones who graduate. As a result, log(rgdp) and log(rpop) are control variables and log( $\bm{st}$ ) is the endogenous variable.

In conclusion, the production function of higher education for Iranian provinces is assumed to have a Cobb-Douglas form and is specified in a baseline form as

$\displaystyle\log({grad)}_{it}={\bm{w}}_{it}\bm{\beta}+{\bm{x}}_{it}\bm{\gamma% }+{\omega}_{it}+{\varepsilon}_{it}$ (25)

where $\log({\rm grad})_{it}$ is the logarithm of the number of university graduates in each province $i$ and year $t$ , ${\bm{w}}_{it}$ is a $1\times 3$ vector of the logarithm of free variables: aslctu, edusta, and bud. Also, ${\bm{x}}_{it}$ is a $1\times 5$ vector of the logarithm of state variables: prof, acprof, asprof, lctu, and hei. The random component ${\omega}_{it}$ is the unobservable productivity or technical efficiency, and ${\varepsilon}_{it}$ is an idiosyncratic graduation shock distributed as white noise.

Olley-Pakes Estimation. Table 3, indicates the results of production function estimation for the higher education of Iran provinces in the Olley-Pakes (OP) framework and according to the control function approach. Here, once log(bud) functions as a proxy variable, so its corresponding coefficient drops as in OP, and the other times, log(aslctu) and log(edusta) are treated as proxies so that their coefficients does not appear in the results.

Table 3

Olley-Pakes Estimation Results

VariablesProxy	Budget (bud)	Asi. Lecturer (aslctu)	Edu. Staff (edust)
Professors (prof)	$-$ 0.100 (0.083)	$-$ 0.138* (0.079)	$-$ 0.128 (0.097)
Associate professors (acprof)	0.125 (0.106)	0.190* (0.100)	0.196 (0.121)
Assistant professors (asprof)	$-$ 0.266** (0.120)	$-$ 0.262** (0.112)	$-$ 0.461*** (0.103)
Lecturer (lctu)	0.572*** (0.150)	0.423** (0.169)	0.443*** (0.138)
Higher education institutions (hei)	0.709*** (0.104)	0.730*** (0.146)	0.810*** (0.166)
Budget (bud)	–	0.002 (0.031)	0.000 (0.020)
Assistant lecturer (aslctu)	$-$ 0.039 (0.040)	–	$-$ 0.038 (0.033)
Educational staff (edust)	$-$ 0.037 (0.042)	0.004 (0.049)	–
Provincial GDP (rgdp)	$-$ 0.098 (0.070)	$-$ 0.130 (0.092)	$-$ 0.094 (0.088)
Provincial population (rpop)	$-$ 0.101 (0.085)	$-$ 0.008 (0.107)	0.081 (0.111)
Wald CRS test	3.88	1.64	1.56
( $p$ -value)	(0.05)	(0.20)	(0.21)
Number of observations	311	311	311

*( $p<0.10$ ) significant at 90%, **( $p<0.05$ ) significant at 95%, ***( $p<0.01$ ) significant at 99%, Source: Authors’ Estimation in Stata ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 15 in Microsoft Windows 10 Enterprise platform.

Levinsohn-Petrin Estimation. Table 4, indicates the results of production function estimation for the higher education of Iran provinces in the Levinsohn-Petrin (LP) framework and according to the control function approach. Here, once log(bud) functions as a proxy variable, and the other times’ log(aslctu) and log(edusta) are treated as proxies.

Table 4

Levinsohn-Petrin estimation results

VariablesProxy	Budget (bud)	Asi. Lecturer (aslctu)	Edu. Staff (edust)
Professors (prof)	$-$ 0.156*** (0.054)	$-$ 0.013 (0.066)	0.009 (0.062)
Associate professors (acprof)	0.250*** (0.071)	$-$ 0.002 (0.075)	0.101 (0.065)
Assistant professors (asprof)	$-$ 0.449*** (0.103)	$-$ 0.222* (0.120)	$-$ 0.288*** (0.090)
Lecturer (lctu)	0.530*** (0.108)	0.473*** (0.099)	0.509*** (0.158)
Higher education institutions (hei)	0.689*** (0.119)	0.715*** (0.162)	0.257* (0.140)
Budget (bud)	$-$ 0.005 (0.032)	0.002 (0.027)	0.000 (0.021)
Assistant lecturer (aslctu)	$-$ 0.039 (0.035)	$-$ 0.059 (0.049)	$-$ 0.038 (0.041)
Educational staff (edust)	$-$ 0.037 (0.049)	0.004 (0.058)	0.090 (0.072)
Provincial GDP (rgdp)	0.018 (0.071)	$-$ 0.069 (0.053)	$-$ 0.143** (0.056)
Provincial population (rpop)	$-$ 0.001 (0.087)	$-$ 0.011 (0.071)	$-$ 0.065 (0.081)
Wald CRS test	2.88	2.52	21.65
( $p$ -value)	(0.09)	(0.11)	(0.00)
Number of observations	311	311	311

Wooldridge Estimation. Table 5, indicates the results of production function estimation for the higher education of Iran provinces in Wooldridge framework and control function approach. Here, once log(bud) functions as a proxy variable, so the relevant coefficient drops, and in the other models log(aslctu) and log(edusta) are treated as proxies, so their proxies are not reported as the methodology implies. Also, as the number of observations doesn’t match when log(bud) and log(edusta) are proxies, the control variable is omitted in estimation.

Table 5

Wooldridge estimation results

VariablesProxy	Budget (bud)	Asi. Lecturer (aslctu)	Edu. Staff (edust)
Professors (prof)	$-$ 0.044 (0.045)	$-$ 0.028 (0.054)	$-$ 0.058 (0.646)
Associate professors (acprof)	0.440*** (0.100)	0.180* (0.109)	0.215 (1.615)
Assistant professors (asprof)	$-$ 0.864*** (0.182)	$-$ 0.502** (0.207)	$-$ 0.247 (2.580)
Lecturer (lctu)	0.814*** (0.095)	0.786*** (0.108)	0.971 (1.454)
Higher education institutions (hei)	1.038*** (0.125)	0.905*** (0.147)	0.599 (2.119)
Budget (bud)	–	$-$ 0.021 (0.024)	0.074 (0.289)
Assistant lecturer (aslctu)	$-$ 0.216*** (0.044)	–	$-$ 0.058 (1.214)
Educational staff (edust)	0.100 (0.065)	0.100 (0.074)	–
Provincial GDP (rgdp)	0.282*** (0.041)	$-$ 0.018 (0.033)	$-$ 0.178 (1.078)
Provincial population (rpop)	–	$-$ 0.682 (1.241)	–
Wald CRS test	12.81	0.05	0.02
( $p$ -value)	(0.00)	(0.82)	(0.89)
Number of observations	271	271	271

Pooled, Fixed Effects, and Random Effects Estimation. To distinguish the methodology with the common methods of panel data estimation, Pooled, Fixed Effects, and Random Effects Estimation (with and without time fixed dummy variables if available) were done on the dataset. Table 6 depicts the results.

Here, the model is specified differently as

$\displaystyle\log({grad)}_{it}=\alpha+{\bm{X}}_{it}\bm{\delta}+{\mu}_{i}+{% \gamma}_{t}+{\varepsilon}_{it}$ (26)

where $\log({grad)}_{it}$ is the logarithm of the number of university graduates in each province $i$ and year $t$ , $\bm{X}$ is the vector of explanatory variables, ${\mu}_{i}$ and ${\gamma}_{t}$ are variables for province and time effects variables, respectively. ${\varepsilon}_{it}$ is the error term, which is distributed normally with zero means.

Table 6

Pooled, fixed effects and random effects estimation results

MethodVariables	Pooled (1)	Pooled ${}^{i}$ (2)	[c]FixedEffects (3)	[c]FixedEffects ${}^{i}$ (4)	[c]RandomEffects (5)
Constant	[c]3.528***(0.597)	[c]4.221***(0.426)	[c] $-$ 9.136(5.822)	[c]0.766(4.387)	[c]3.528***(0.537)
Professors (prof)	[c] $-$ 0.071**(0.034)	[c] $-$ 0.034*(0.021)	[c] $-$ 0.062(0.041)	[c] $-$ 0.060**(0.026)	[c] $-$ 0.071**(0.030)
Associate professors (acprof)	[c]0.146***(0.047)	[c]0.048*(0.029)	[c]0.168***(0.053)	[c]0.070*(0.036)	[c]0.146***(0.042)
Assistant professors (acprof)	[c] $-$ 0.292***(0.076)	[c] $-$ 0.018(0.048)	[c] $-$ 0.174*(0.098)	[c]0.002(0.064)	[c] $-$ 0.292***(0.068)
Lecturer (lctu)	[c]0.608***(0.064)	[c]0.240***(0.044)	[c]0.684***(0.071)	[c]0.214***(0.055)	[c]0.608***(0.058)
Higher education institutions (hei)	[c]0.701***(0.105)	[c]0.666***(0.075)	[c]0.600***(0.124)	[c]0.502***(0.092)	[c]0.701***(0.094)
Budget (bud)	[c]0.030**(0.014)	[c]0.007(0.008)	[c]0.070***(0.020)	[c]0.013(0.013)	[c]0.030**(0.013)
Assistant lecturer (aslctu)	[c] $-$ 0.033(0.025)	[c] $-$ 0.008(0.017)	[c] $-$ 0.027(0.029)	[c] $-$ 0.012(0.021)	[c] $-$ 0.033(0.023)
Educational staff (edust)	[c] $-$ 0.013(0.040)	[c]0.054(0.044)	[c] $-$ 0.201***(0.048)	[c]0.006(0.055)	[c] $-$ 0.013(0.036)
Provincial GDP (rgdp)	[c]0.060*(0.035)	[c] $-$ 0.013(0.025)	[c]0.074(0.079)	[c] $-$ 0.040(0.085)	[c]0.060*(0.031)
Provincial population (rpop)	[c] $-$ 0.152***(0.053)	[c]0.088**(0.039)	[c]1.431*(0.870)	[c]0.738(0.584)	[c] $-$ 0.152***(0.047)
Wald CRS test	0.12	0.92	3.69	0.58	0.15
( $p$ -value)	(0.73)	(0.34)	(0.05)	(0.45)	(0.70)
Number of observations	311	311	311	311	311

${}^{i}$ Models (2) and (4) are estimated with time fixed dummies. *( $p<0.10$ ) significant at 90%, **( $p<0.05$ ) significant at 95%, ***( $p<0.01$ ) significant at 99%, Source: Authors’ Estimation in EViews ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 10 in Microsoft Windows 10 Enterprise platform.

The reliability of fixed and random effects models and time-dummy variables are checked via the Redundant Fixed Effects test [89] and Correlated Random Effects test, also known as the Hausman test [90]. Table 7 shows the results of the mentioned tests for the panel data models represented in Table 6.

Table 7

Reliability tests for pooled, fixed effects and random effects models

Test category	Model	Statistic name	Statistic value	Degree of freedom	Probability
[l]Redundantfixedeffectstests	(2)	Period F	55.714207	(10, 290)	0.0000
		Period Chi-square	333.388111	10	0.0000
	(3)	Cross-section F	3.430897	(29, 271)	0.0000
		Cross-section Chi-square	97.257125	29	0.0000
	(4)	Cross-section F	2.087123	(29, 261)	0.0014
		Cross-section Chi-square	64.862086	29	0.0001
		Period F	42.600652	(10, 261)	0.0000
		Period Chi-square	300.993071	10	0.0000
		Cross-Section/Period F	17.390688	(39, 261)	0.0000
		Cross-Section/Period Chi-square	398.39	(39, 261)	0.0000
Hausman test	(5)	Cross-section F	83.57	10	0.0000

Source: Authors’ Estimation in EViews ${}^{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\textregistered}$ 10 in Microsoft Windows 10 Enterprise platform.

As the results in Table 7 imply, in models (2) and (3) the null hypothesis of redundancy of fixed effects is rejected, so these models should consider both period and cross-section fixed effects as it is in the model (4); So, (2), (3) and consequently (1) are not reliable without the time and cross-sectional fixed effects. Also, according to the Hausman test, the null hypothesis of random effects existence is rejected in (5), and the model is unreliable. Hence, model (4) is the only ordinary panel data model that is here subject to interpretation and comparison.

3. Results

In this section, the results of different production function estimations are explained in detail. Generally, models are reliable, and their results are occasionally significant and comparable with the literature. Also, the differences between the usage of various proxies need to be considered. According to Levinsohn and Petrin [7], the results of ordinary panel data models are biased in free and state variables, so they also need to be checked. The estimation results are represented in Table 3 to Table 5, and – as all variables are in logarithmic form – the coefficients show elasticity of the factor in production. Panel data results are not discussed here, but they are reviewed in the next section.

Generally, the proxy in the OP model should be an investment that is similar to the budget variable, bud, here. Hence, the other variables (i.e., aslctu and edust) do not perform well in OP framework [8]. On the other hand, LP accepts other variables as proxies so the models in which aslctu and edust perform as proxies of productivity shocks are reliable [7]. But as Wooldridge applies the GMM approach and studies parameters in a two-equation system, it clarifies identification issues better and provides simpler and more efficient estimators [9]. As a result, OP results when bud is proxy are far stronger than other cases in OP, LP results are preferred to OP, and Wooldridge results are stronger than LP. Also, Wooldridge results and the low level of robustness when edustis proxy, cast doubt on its properness as a proxy in this framework.

As for state variables, the coefficient for profis estimated to be negative, however most of the time, insignificant and varies between $-$ 0.156 and $-$ 0.138 in case of being significant (i.e., in OP[aslctu]22 and LP[bud]). As it was discussed and the lower significance level shows, LP[bud] result is accepted better. This means a 100% increase in the number of professors in a province leads to about a 14% decrease in the number of graduates in that province. Particularly, when productivity shock is from the bud, professors incur negative effects in the graduation process by the amount mentioned.

The elasticity coefficient of acprofis positive and indicates to be significant in 4 estimations (i.e., OP[aslctu], LP[bud] and Wooldridge[bud& aslctu]) with values around 0.180 to 0.440, meaning that a 100% increase in acprof is predicted to cause an 18 to 44% increase in grad. In particular, acprof is about 7 to 26% more affected when the productivity shock is from bud, in comparison with the situation in which aslctu is considered as the productivity shock.

Same as prof, the elasticity of asprofis negative, but significant for mosf of the cases (except for Wooldridge[edust]), varying from $-$ 0.864 to $-$ 0.222, which is interpreted to decline the antilog value of grad22 to 86% if the referring value in level is doubled. According to LP and Wooldridge, asprof response to bud shock is 23 to 36% stronger in magnitude than in response to aslctu. Also, it can be inferred that the response to edust shocks is weaker than the response of asprof to bud shocks. However there is not enough evidence to compare asprof’s response to edust shocks with the same results from aslctushocks.

lctueffects are also significant (except for in Wooldridge[edust]) but positive, valuing from 0.423 to 0.814; It predicts that if the number of lecturers grows 100%, the number of graduates will grow by around 42 to 81%. Particularly, there is not much difference between the lctu response to different shocks, but, approximately response to bud shocks are slightly stronger here.

The number of higher education institutions in each province is the last state variable, indicating high robustness in all models (except for in Wooldridge[edust]). Putting LP(edust) aside23, the elasticity of the number of graduates to the number of higher institutions in each province is estimated from 0.689 to 1.038, predicting approximately a 70 to 104% increase in graduation in response to a 100% increase shock in number of HEIs. In particular, as heiperforms as capital here, and if the productivity shock is from bud it responds about 3 to 13% stronger than in response to aslctu.

Free variables in this study – which are used interchangeably as proxies – are not significant and also does not show stable positive or negative values, except for aslctu. The variable representing the number of assistant lecturers is estimated to affect grad in negative ways in all models, with the significant value of $-$ 0.216 in Wooldridge(bud). The model’s prediction suggests that if the number of assistant lecturers is doubled, the HEIs in a province will face a 21.6% fall in a number of their graduates. To sum up, it is concluded that free variables show insignificant elasticities near to zero, sometimes negative and sometimes positive, except in the model mentioned.

Mainly, the performance of proxies should be evaluated by their support of literature, which will be discussed later. But, as LP provides their coefficient while they perform as a proxy, it may be potentially informative to consider proxy coefficients in LP. However, no strong conclusion can be derived this way here. This evidence provides a suggestion that maybe the set of proxies can be chosen better; however, the lack of data for this case being studied stops the research from going further.

Control variables (i.e., rgdp and rpop) have not been significant in most of the models, except LP(edust) and Wooldridge(bud) which show negative and positive results, valued $-$ 0.143 and 0.282, respectively. As bud has performed stronger and Wooldridge is preferred to LP, a 0.282 coefficient is taken and interpreted that a 100% increase in regional GDP leads to a 28.2% increase in graduations. This result can be justified better than a negative result.

Wald test joint hypothesis was the constant return to scale (CRS) condition (sum of coefficients equals 1). The results approve CRS conditions when bud is the proxy and in LP(edust) but is rejected in other models, including the panel data model (4).

Besides, Levinsohn and Petrin [7] suggests that the ordinary least squares estimator leads to biased coefficients. To compare the results, maximum and minimum coefficients (preferably the significant ones) of OP, LP, and Wooldridge estimation are compared with the panel data model (4). Table 8 provides a comparison using the Z statistic introduced by Paternoster et al. [91].

Table 8
Comparing OP, LP and wooldridge results with panel data model (4) results

		state variables					free variables
VariableModel		prof	acprof	asprof	lctu	hei	bud	aslctu	edust
[c]OP, LP andWooldridge	Maximum coefficient	$-$ 0.138	0.440	$-$ 0.222	0.814	1.038	0.074 ${}^{i}$	$-$ 0.038 ${}^{i}$	0.100 ${}^{i}$
[c]OP, LP andWooldridge	Minimum coefficient	$-$ 0.156	0.180	$-$ 0.864	0.423	0.257	$-$ 0.021 ${}^{i}$	$-$ 0.216	$-$ 0.037 ${}^{i}$
Panel Data Model (4)		$-$ 0.060	0.070	0.002 ${}^{i}$	0.214	0.502	0.013 ${}^{i}$	$-$ 0.012 ${}^{i}$	0.006 ${}^{i}$
Z statistic	Maximum coefficient	$-$ 5.555	$-$ 3.481	1.647	$-$ 5.466	$-$ 3.454	$-$ 0.211	0.665	$-$ 1.104
( $p$ -value)		(0.000)	(0.000)	(0.050)	(0.000)	(0.000)	(0.416)	(0.253)	(0.135)
Z statistic	Minimum coefficient	$-$ 7.408	$-$ 0.958	4.489	$-$ 1.176	1.462	1.246	4.184	0.584
( $p$ -value)		(0.000)	(0.169)	(0.000)	(0.120)	(0.126)	(0.106)	(0.000)	(0.280)

${}^{i}$ not significant. Source: the paper’s findings.

The comparison reveals that the absolute values of state variables are mostly underestimated in the model (4).

In conclusion, implementing the most recent contributions of econometrics in estimating production functions provides better results in comparison with ordinary methods. Additionally, all the models show that the most important factor in “producing” graduates is the number of higher education institutes (HEIs), which stands for items like educational space, the facilities, etc.; in a word, the capital. Then, assistant professors and lecturers are the most important determinants discovered to affect the number of graduations. However, assistant professors affect the process negatively. In lower ranks, stand associate professors and professors in order, both with negative effects. Also, the government budget allocated to HEIs proxies the productivity shocks better than other free variables with stronger magnitudes.

4. Discussion

This article tries to investigate the properties affecting the number of HEI graduates in Iran, considering a provincial data from 2005 to 2017 from, following production function framework and newest estimation methods. In this way, first, a review of the literature was surveyed. Next, the control function approach developed by Rovigatti and Mollisi [1] was introduced, and then the data described, and estimation was done.

The estimation is done considering the number of HEIs, full, associate, and assistant professors as a state variable, and three productivity shocks as a proxy (and interchangeably free variables): government budget, number of assistant lecturers, and number of educational staff.

The estimation results show that state variables are mostly robust, despite free variables that are not significant often. Also, the number of HEI is found to be the most effective factor in the number of higher education graduation rates with up to 1.036 elasticity. After that, lecturers and associate professors are estimated as the most important positive determinants of higher education in Iran, with up to 0.814 and 0.440 elasticities, respectively. Assistant professors and professors affect the number of graduations negatively: assistant professors with a higher magnitude than associates, up to $-$ 0.864 and professors less than lecturers, i.e., up to $-$ 0.156. Besides, budget and assistant lecturers perform better than educational staff as a proxy for productivity shocks. Entire significant factors of production response to productivity shock stronger when they are proxied in the budget than in case assistant lecturers are proxy, but their signs do not change in response to different productivity shocks.

As the data structure for this study and also the case is similar to Naderi [3], the comparison with his results is easily available; however, the comparable estimation’s dependant variable are students, not graduates. Anyway, in that model, professors and associate professors have positive effects on the production process, but assistant professors show negative effects. The difference is that also, in this paper, the corresponding results are negative for both full and assistant professors. Naderi [3] justifies the result by considering the shortages in the supply of higher grades of academic staff, which is dominated by a hierarchical structure and time-consuming processes; in other words, when associate professors were not available, assistants had to be employed. This is also proposed that base on the academic promotion rules in Iranian higher education, which involve assistant professors informal procedures and distract their attention from education quality by creating incentives counteracting truly beneficial educational activities (e.g., demanding the high number of indexed journal articles instead of article quality or industry fund attraction), may affect the contribution of assistant professors in a negative way. On the other hand, most of the time, the process of promotion to full professorship takes as much a long time that the holders of the position are often old and not motivated to put enough time and effort into the graduation of students whom in the majority are in undergraduate level.

In conclusion, this paper tries to estimate the higher education production function of Iran in order to investigate university behavior, following the literature and available data of Iranian provinces from 2005 to 2017. In this way, a cutting-the-edge method introduced by Rovigatti and Mollisi [1] is applied to different estimators of production function (i.e., Olley-Pakes, Levinsohn-Petrin, and Wooldridge). The method considers productivity shocks and avoids simultaneity and selection problems that occur in OLS or Fixed-Effects Estimation. The results approve the importance of physical capital, which is proxied by the number of HEIs and then human capital, especially associate professors and lecturers. It is also understood that full and assistant professors negatively affect the process of graduation. In addition, the budget is found to proxy for productivity effects better than assistant lecturers, and educational staff fails to successfully proxy for those shocks. The constant return to scale hypothesis is approved in stronger models but fails in the others.

Footnotes

It should be noted that production function has other major applications, e.g. total factor productivity (TFP) estimation [], which are out of this study’s purpose.

The rationale behind the hypotheses is explained in Section 1.1.

The data presented in following sections prove this claim that all 31 provinces of Iran have been engaged in the expansion.

The Ministry of Education in Iran focuses on primary and secondary education; so, the purpose of the universities linked to the ministry is primarily to train teachers and expand vocational training.

These two universities gradually gained their independence and are managed independently, but they serve the proposes of Ministry of Education and have a key role in educating future teachers.

As these universities are financed by private funds (especially, from the tuition fees that students pay) and make some decisions independently, it is more appropriate to call them semi-public, rather than public universities.

Post-secondary stages in Iran (and their equivalent in United States) consist of: Kârdânî (or Fogh-e-diplom; equivalent to Associate Degree), Kâreshenâsî (or Lîsâns; equivalent to Bachelor Degree), Kâreshenâsî-e-Arshad (or Fogh-e-Lîsâns; equivalent to Master Degree), Doctorâ-ye-Herfe’ei (for medical, dentistry and pharmacy students; equivalent to Doctor of Medicine) and Doctorâ-ye-Takhassosî (equivalent to Ph.D.) See Nuffic and WENR [13, ] for more details.

Here, promotion means ascending to higher academic ranks, i.e. earning a higher salary and being exposed to better opportunities and positions.

Generally, each HEI consists of one or more faculty (dâneshkadeh), and the faculties consist of departments (Gorooh-e-Amûzeshî) to which faculty members are assigned.

To familiarize with the faculty members’ condition in Iran, see: Asghari, Salehi Emran and Ghanavati, Jafari and Shafiei, and Abili [17, 18, 19, ].

For example, they should publish articles in internationally-indexed peer-reviewed journals.

however, there are a number of internationally-ranked research universities (such as Sharif University of Technology or University of Tehran), in which research activities are often considered as one of the main purposes of the university and takes place in other forms such as industry or government contracts and research projects.

Recently, some regulations have been considered by HEIs to avoid conflict of interests.

see also Arani et al. and Araste and Jamshidi [25, ].

For more information on other straits of the literature, see Naderi [].

the Arts and Law Faculties of Coimbra and Lisbon Universities and the Higher Institute of Engineering of Lisbon.

It should be noted that Persian calendar (also named Jalali calendar), which is the official calendar of Iran, is different from AD calendar (and starts from 621 AD). Academic calendar in Iran starts from about the first day of Autumn in Persian calendar (or a few days sooner) that is around September 15th. The data in this study is gathered beginning of 1383–1384 academic year which has started from September 18 ${}^{\rm th}$ , 2004. But for simplicity, we would refer to that year by “2005”. So is for other years referred in this paper (e.g. 2014 means 1392–1393 academic year). The years 2016 and 2017 (after the expansion era) were also included to enrich the data set.

Details on the provincial data are provided in Appendix.

Further explanation on what the abbreviations and the academic positions mean is provided in Section 1.1.

For more details on the data check for the data supplemented online or contact the authors.

The function of natural logarithm in this article is presented by log( $\cdot$ ); so, for example, log( $x$ ) means the natural logarithm of variable (or value) $x$ .

The expression means: when the estimation method is Olley-Pakes and the proxy is aslctu. The other expressions in this format are interpreted the same.

The model’s result for the variable is an outlier, and considering its 90% confidence level and weakness of its proxy the coefficient can be ignored.

Acknowledgments

We greatly appreciate the valuable guidance of Dr. Abolghasem Naderi from the initial stages of this research until the revision stage, especially for suggesting the title and rewriting the asbstract. We also thank the instructive cooperation of Dr. Mohammad Javad Salehi and IRPHE staff, providing the majority of the data used in this study generously for the authors. Also, we would like to express our sincere gratitude to Dr. Charles Gilliland Renfro and two anonymous referees for their helpful comments, which enhanced the quality of this paper and tried their best to correct our mistakes. Indeed, all the responsibility for the content is refrenced to the author and none of the scholars named above.

Appendix

All 31 Iranian provinces are included in this study, but Tehran and Alborz are considered as one province, so the list of included provinces are as followed (with referenced table): Alborz and Tehran (Table 9), Ardebil (myblackTable 10), Bushehr (Table 11), Chahar Mahall and Bakhtiari (Table 12), East Azarbaijan (Table 13), Esfahan (Table 14), Fars (Table 15), Gilan (Table 16), Golestan (Table 17), Hamadan (Table 18), Hormozgan (Table 19), Ilam (Table 20), Kerman (Table 21), Kermanshah (Table 22), Khuzestan (Table 23), Kohgiluyeh and Buyer Ahmad (Table 24), Kordestan (Table 25), Lorestan (Table 26), Markazi (Table 27), Mazandaran (Table 28), North Khorasan (Table 29), Qazvin (Table 30), Qom (Table 31), Razavi Khorasan (Table 32), Semnan (Table 33), Sistan and Baluchestan (Table 34), South Khorasan (Table 35), West Azarbaijan (Table 36), Yazd (Table 37), and Zanjan (Table 38).

Table 9

The higher education data of Alborz and Tehran Provinces

	grad	st	hei	prof	acprof	asprof
2005	39442		29
2006	42195	241061	243	1032	1809	6295
2007	34715	240809	324	1263	2109	6732
2008	96945	348136	338	1067	1886	6923
2009	169358	636407	364	1595	2767	9529
2010	115657	753239	479	1616	2906	9809
2011	116032	793761	455	1768	3133	10238
2012	138695	844331	482	1834	3338	10675
2013	132551	819910	558	2281	4161	12889
2014	149807	972592	578	2247	3959	12811
2015	212577	1054015	723	2622	4511	13870
2016	189213	988055	700	2746	4445	14180
2017		1002031	691	2353	3956	11653
	lctu	aslctu	edust	bud	rgdp	rpop
2005				3.44E+11	4.80E+08	13107.3
2006	4185	209	8806	3.46E+11	6.00E+08	13422.9
2007	3901	212	7629	4.36E+11	7.70E+08	13649.7
2008	7961	158	3690	3.69E+11	9.90E+08	13880.4
2009	9817	253	17123	1.66E+12	1.10E+09	14115
2010	9850	351	14128	1.54E+12	1.30E+09	14353.7
2011	9468	316	19375	1.52E+12	1.60E+09	14596.5
2012	8838	442	16292	1.36E+12	2.00E+09	14864
2013	8871	365	23905	1.48E+12	2.60E+09	15136
2014	10654	209	25594	2.01E+12	3.10E+09	15413
2015	11476	447	29870	2.54E+12	3.30E+09	15694
2016	11809	233	22873	3.11E+12	3.80E+09	15980
2017	7278	155	28733	3.70E+12	4.00E+09	16180.2

Source: see Table 1 and Section 2.2.

Table 10

The higher education data of Ardebil Province

	grad	st	hei	prof	acprof	asprof
2005	2694
2006	2816	17177	16	3	5	157
2007	1368	7754	15	4	6	191
2008	8528	31763	22	3	6	298
2009	11756	56069	22	12	14	409
2010	10291	58974	31	17	19	460
2011	10126	63898	37	17	37	512
2012	11274	67282	36	14	26	348
2013	11716	67217	40	19	63	436
2014	11333	65070	36	17	73	468
2015	13051	73161	43	20	105	551
2016	11301	62979	41	34	164	610
2017		59495	41	48	151	588
	lctu	aslctu	edust	bud	rgdp	rpop
2005				8917652	1.80E+07	1220.88
2006	300	52	593	9293081	2.20E+07	1228.75
2007	254	9	462	14214638	2.80E+07	1232.39
2008	583		151	12874207	3.50E+07	1236.19
2009	1108	82	777	3.98E+08	4.00E+07	1240.14
2010	1096	99	1017	1.69E+08	4.70E+07	1244.23
2011	1638	92	1696	3.08E+08	6.00E+07	1248.49
2012	1162	111	954	2.84E+08	7.90E+07	1252
2013	1088	59	2255	4.27E+08	1.10E+08	1257
2014	1160	54	2873	8.40E+08	1.30E+08	1261
2015	1144	114	3008	1.05E+09	1.30E+08	1266
2016	1165	12	2697	1.54E+09	1.40E+08	1270.42
2017	546	4	3571	2.19E+09	1.50E+08	1274.28

Source: see Table 1 and Section 2.2.

Table 11

The higher education data of Bushehr Province

	grad	st	hei	prof	acprof	asprof
2005	1121
2006	854	9772	7	0	3	120
2007	1006	5312	9		3	138
2008	4773	21582	16		3	132
2009	7243	40016	16	8	4	213
2010	5478	50910	26	3	7	238
2011	6530	59742	31	4	8	275
2012	8997	66218	33	6	10	292
2013	10718	70840	45	7	19	314
2014	11346	78232	43	8	19	333
2015	16685	84442	47	9	32	454
2016	12479	66035	44	11	41	485
2017		58688	41	14	72	448
	lctu	aslctu	edust	bud	rgdp	rpop
2005				11440163	4.80E+07	871.191
2006	113	0	279	11897639	5.50E+07	886.267
2007	173	7	274	11897679	8.70E+07	913.696
2008	247	4	85	7574882	9.60E+07	942.045
2009	656	108	450	11019588	9.40E+07	971.347
2010	616	128	764	10709677	1.60E+08	1001.64
2011	706	55	1639	14070552	2.30E+08	1032.95
2012	884	81	894	22850964	2.80E+08	1058
2013	959	61	1792	36962922	4.40E+08	1083
2014	1152	52	2537	58450010	6.80E+08	1109
2015	1058	55	2753	86777567	5.30E+08	1136
2016	1043	46	2354	1.22E+08	6.10E+08	1163.4
2017	463	1	2992	1.68E+08	6.40E+08	1191.89

Source: see Table 1 and Section 2.2.

Table 12

The higher education data of Chahar Mahall and Bakhtiari Province

	grad	st	hei	prof	acprof	asprof
2005	3731
2006	2293	18618	17	0	12	203
2007	1384	9983	13	2	7	147
2008	4830	32692	20	4	22	199
2009	7650	39617	20	9	35	281
2010	6765	44108	27	8	44	316
2011	5913	45458	25	8	45	336
2012	10129	48838	27	12	58	356
2013	8105	48629	30	20	71	385
2014	8803	50818	27	18	78	446
2015	9863	50748	30	25	95	449
2016	9260	46229	30	27	122	517
2017		41182	28	36	170	447
	lctu	aslctu	edust	bud	rgdp	rpop
2005				83313438	1.20E+07	847.281
2006	165	10	445	85530078	1.50E+07	853.593
2007	89	5	437	1.32E+08	1.90E+07	861.064
2008	319		326	1.51E+08	2.30E+07	868.545
2009	505	84	663	5.62E+08	2.70E+07	876.036
2010	481	45	854	5.38E+08	3.30E+07	883.537
2011	520	210	1296	6.02E+08	4.40E+07	891.045
2012	895	180	1022	6.87E+08	5.60E+07	902
2013	879	146	1738	8.27E+08	6.90E+07	913
2014	970	127	1768	8.74E+08	7.50E+07	925
2015	1021	124	1991	8.39E+08	8.70E+07	936
2016	1261	121	1988	1.05E+09	9.90E+07	947.763
2017	487	17	2409	1.29E+09	1.00E+08	951.213

Source: see Table 1 and Section 2.2.

Table 13

The higher education data of East Azarbaijan Province

	grad	st	hei	prof	acprof	asprof
2005	8743
2006	12057	57939	57	101	173	888
2007	5529	44992	69	123	277	1018
2008	21242	102388	71	91	251	1038
2009	42534	175397	83	139	339	1460
2010	31844	196119	99	162	409	1536
2011	32906	211942	117	182	461	1866
2012	41396	233922	120	188	471	1793
2013	40298	218171	123	215	508	1894
2014	41494	219699	128	229	571	2058
2015	41735	221787	131	293	697	2348
2016	40709	207991	130	332	757	2505
2017		186491	127	338	721	2322
	lctu	aslctu	edust	bud	rgdp	rpop
2005				1.57E+09	6.80E+07	3572.42
2006	1076	68	1820	1.59E+09	8.30E+07	3602.86
2007	1044	72	2220	2.00E+09	1.10E+08	3626.73
2008	1574	39	358	3.39E+09	1.30E+08	3650.83
2009	3508	337	2550	1.11E+10	1.40E+08	3675.18
2010	3457	378	3009	1.48E+10	1.60E+08	3699.77
2011	5444	320	4065	2.14E+10	2.10E+08	3724.62
2012	4701	317	3351	1.39E+10	2.70E+08	3761
2013	4588	214	6004	2.48E+10	3.50E+08	3797
2014	5109	188	6229	3.43E+10	4.10E+08	3834
2015	5574	362	6414	3.90E+10	4.00E+08	3872
2016	5504	183	6384	4.95E+10	4.60E+08	3909.65
2017	2609	45	7165	5.53E+10	4.80E+08	3922.53

Source: see Table 1 and Section 2.2.

Table 14

The higher education data of Esfahan Province

	grad	st	hei	prof	acprof	asprof
2005	16057
2006	14871	101345	88	154	364	1352
2007	12071	57775	90	178	377	1393
2008	40101	184055	116	195	350	1324
2009	58623	243454	131	219	493	2163
2010	44036	264384	154	226	539	2015
2011	41474	294163	172	248	602	2214
2012	56880	318438	170	303	696	2608
2013	52538	306115	171	352	814	3013
2014	49937	325711	174	349	825	3009
2015	54029	318968	180	404	881	3056
2016	53007	298856	183	508	1070	3837
2017		281683	180	415	886	2608
	lctu	aslctu	edust	bud	rgdp	rpop
2005				1.03E+10	1.20E+08	4492.63
2006	1462	67	2873	1.04E+10	1.40E+08	4563.57
2007	1565	38	3438	2.34E+09	2.00E+08	4625.88
2008	2593	42	1744	9.92E+09	2.40E+08	4689.02
2009	4363	299	6995	3.92E+10	2.50E+08	4753
2010	4493	311	5724	3.23E+10	3.10E+08	4817.83
2011	4734	129	8027	3.65E+10	4.30E+08	4883.53
2012	5815	314	6863	3.61E+10	5.20E+08	4930
2013	4690	231	11838	4.59E+10	6.80E+08	4977
2014	4537	161	12797	6.67E+10	7.30E+08	5025
2015	4634	314	12524	7.18E+10	7.00E+08	5073
2016	6125	190	12269	7.70E+10	8.00E+08	5120.85
2017	2784	44	11871	9.09E+10	8.40E+08	5200.31

Source: see Table 1 and Section 2.2.

Table 15

The higher education data of Fars Province

	grad	st	hei	prof	acprof	asprof
2005	9389
2006	7630	56424	50	131	206	758
2007	2917	24435	40	135	210	719
2008	31919	122192	79	131	209	741
2009	46360	205160	89	176	250	1216
2010	34540	231682	112	261	432	1531
2011	35482	254740	134	338	366	1457
2012	41715	264304	133	277	374	1608
2013	43878	260360	147	255	400	1696
2014	41755	270999	153	256	397	1748
2015	42641	264973	147	270	432	2072
2016	39137	233047	141	299	489	2282
2017		209156	143	358	807	2124
	lctu	aslctu	edust	bud	rgdp	rpop
2005				5.57E+09	8.00E+07	4280.67
2006	607	32	1785	5.63E+09	1.00E+08	4336.88
2007	676	10	1466	3.21E+09	1.30E+08	4387.8
2008	975	20	429	1.08E+10	1.50E+08	4439.24
2009	4268	308	2310	2.09E+10	1.60E+08	4491.19
2010	4690	377	2668	2.09E+10	2.00E+08	4543.66
2011	5015	333	5824	2.54E+10	2.80E+08	4596.66
2012	5841	526	3495	5.01E+10	3.50E+08	4647
2013	5349	368	8085	3.23E+10	4.90E+08	4697
2014	5219	382	8833	4.00E+10	5.90E+08	4748
2015	5552	779	9175	9.66E+10	5.90E+08	4799
2016	5552	313	8598	9.41E+10	6.70E+08	4851.27
2017	1937	51	10500	1.20E+11	7.00E+08	4903.8

Source: see Table 1 and Section 2.2.

Table 16

The higher education data of Gilan Province

	grad	st	hei	prof	acprof	asprof
2005	6045
2006	6992	32371	33	17	67	587
2007	2805	24083	40	17	79	614
2008	13151	55884	40	14	56	500
2009	24048	93845	43	25	67	769
2010	21025	111304	63	31	122	827
2011	18898	122923	69	40	120	943
2012	24154	134244	72	30	129	859
2013	24540	135234	83	41	167	1089
2014	26070	145713	84	44	166	1081
2015	28528	148968	86	64	233	1178
2016	27115	131858	87	102	254	1289
2017		123058	86	122	268	1103
	lctu	aslctu	edust	bud	rgdp	rpop
2005				2.15E+08	4.10E+07	2385.95
2006	487	51	977	2.20E+08	5.00E+07	2404.86
2007	487	232	1382	2.25E+08	6.60E+07	2418.47
2008	767	17	599	3.18E+08	8.20E+07	2432.86
2009	2189	84	1239	4.57E+08	9.10E+07	2448.04
2010	2072	83	1574	7.09E+08	1.00E+08	2464.04
2011	1990	96	3192	7.58E+08	1.30E+08	2480.87
2012	1934	106	3068	8.59E+08	1.60E+08	2490
2013	2040	82	5587	1.41E+09	2.30E+08	2500
2014	2112	67	6176	1.84E+09	2.50E+08	2510
2015	2275	131	6476	2.57E+09	2.70E+08	2520
2016	2162	27	7062	3.84E+09	3.00E+08	2530.7
2017	1386	25	6554	5.05E+09	3.20E+08	2550.66

Source: see Table 1 and Section 2.2.

Table 17

The higher education data of Golestan Province

	grad	st	hei	prof	acprof	asprof
2005	3090
2006	2463	23157	19	5	19	180
2007	3478	10567	16	12	38	206
2008	8667	31600	28	11	44	220
2009	11933	55708	28	12	57	375
2010	12965	69222	44	14	54	380
2011	11312	83110	50	41	62	432
2012	14964	88110	48	17	71	451
2013	15550	87609	55	24	103	476
2014	14683	90768	50	22	94	511
2015	15867	91220	54	31	118	629
2016	13110	82499	56	34	158	875
2017		75704	55	47	177	837
	lctu	aslctu	edust	bud	rgdp	rpop
2005				16020147	2.50E+07	1596.15
2006	203	3	549	16617814	2.90E+07	1617.09
2007	274	16	695	11581064	3.70E+07	1648.1
2008	633	13	445	12555441	4.50E+07	1679.59
2009	1328	153	1168	15437731	5.10E+07	1711.57
2010	1419	161	1221	21126864	5.80E+07	1744.04
2011	1681	230	2058	39011525	7.20E+07	1777.01
2012	1414	58	1856	63980064	9.20E+07	1795
2013	1072	46	4379	1.05E+08	1.30E+08	1814
2014	1150	59	4223	1.98E+08	1.40E+08	1832
2015	1068	51	4451	1.53E+08	1.50E+08	1850
2016	1168	34	4599	5.10E+08	1.70E+08	1868.82
2017	711	11	4208	7.87E+08	1.80E+08	1911.22

Source: see Table 1 and Section 2.2.

Table 18

The higher education data of Hamedan Province

	grad	st	hei	prof	acprof	asprof
2005	5762
2006	5400	34112	28	19	59	440
2007	3553	20602	33	10	44	406
2008	11002	72207	41	20	50	359
2009	14797	81038	38	22	75	539
2010	21102	85712	47	28	104	640
2011	11617	96177	49	35	120	713
2012	17710	100805	49	30	110	652
2013	16356	97107	57	56	145	793
2014	16004	106362	54	60	148	827
2015	16378	101771	56	73	187	882
2016	15929	88427	50	83	215	955
2017		81467	55	85	227	1050
	lctu	aslctu	edust	bud	rgdp	rpop
2005				2.81E+08	2.60E+07	1698.96
2006	476	15	940	2.87E+08	3.20E+07	1703.27
2007	468	12	999	1.58E+08	4.20E+07	1714.26
2008	638	5	255	2.29E+08	4.90E+07	1725.26
2009	1117	140	1225	2.67E+08	5.80E+07	1736.26
2010	1227	196	1496	2.88E+08	6.80E+07	1747.26
2011	1485	112	1529	3.54E+08	9.10E+07	1758.27
2012	928	98	1561	4.65E+08	1.10E+08	1754
2013	951	52	3214	6.18E+08	1.60E+08	1750
2014	942	31	3344	1.02E+09	1.60E+08	1746
2015	910	93	3436	1.36E+09	1.70E+08	1742
2016	875	11	3327	2.15E+09	1.90E+08	1738.23
2017	804	3	3486	2.88E+09	2.00E+08	1761.54

Source: see Table 1 and Section 2.2.

Table 19

The higher education data of Hormozgan Province

	grad	st	hei	prof	acprof	asprof
2005	1882
2006	1816	14793	15	8	14	252
2007	904	8692	13	4	19	233
2008	4528	27215	19	3	20	231
2009	7715	52499	24	7	27	269
2010	9183	62456	35	5	22	295
2011	9191	68898	34	10	21	341
2012	10078	71995	38	8	17	292
2013	11180	81936	49	4	25	350
2014	12089	92196	53	19	49	509
2015	14520	95539	52	16	55	632
2016	14036	77659	50	14	76	737
2017		69535	46	14	75	540
	lctu	aslctu	edust	bud	rgdp	rpop
2005				17215769	3.60E+07	1367.9
2006	250	21	607	17848593	4.20E+07	1403.67
2007	202	7	692	17848812	5.10E+07	1437.2
2008	333		306	20225735	6.60E+07	1471.4
2009	835	192	576	1.12E+09	6.80E+07	1506.29
2010	888	216	1024	4.55E+09	8.80E+07	1541.88
2011	1070	158	1017	8.02E+09	1.40E+08	1578.18
2012	880	145	1102	1.74E+08	1.80E+08	1616
2013	1081	146	2404	3.14E+10	2.50E+08	1654
2014	1134	136	3092	2.63E+10	2.60E+08	1694
2015	1180	122	3521	8.18E+09	2.50E+08	1735
2016	1177	95	3354	1.79E+09	2.90E+08	1776.42
2017	601	14	3556	1.81E+09	3.10E+08	1804.97

Source: see Table 1 and Section 2.2.

Table 20

The higher education data of Ilam Province

	grad	st	hei	prof	acprof	asprof
2005	1094
2006	920	11457	9	0	0	111
2007	905	8433	13			75
2008	4417	21710	15			78
2009	5035	29298	16	5		101
2010	5803	40651	26		2	124
2011	5595	44444	23	18	3	162
2012	4614	44947	25	3	6	204
2013	6269	44641	27	3	16	234
2014	7449	45366	27	3	12	238
2015	9421	49013	29	4	40	305
2016	7553	39701	26	5	44	332
2017		35005	26	11	62	315
	lctu	aslctu	edust	bud	rgdp	rpop
2005				4677861.7	2.30E+07	539.459
2006	217	10	337	4902957	3.20E+07	545.787
2007	206	16	269	6320002	4.80E+07	548.122
2008	227	13	106	6998574	5.20E+07	550.471
2009	487	53	508	7912372	4.70E+07	552.833
2010	470	51	670	9949163	6.40E+07	555.209
2011	499	82	1123	14151249	8.20E+07	557.599
2012	478	56	856	19736961	6.60E+07	562
2013	442	35	2131	22870974	9.80E+07	566
2014	500	10	2234	27899278	1.00E+08	571
2015	427	23	2510	32505219	8.30E+07	575
2016	580	4	2446	64656637	9.40E+07	580.158
2017	335	1	2938	1.30E+08	9.80E+07	580.87

Source: see Table 1 and Section 2.2.

Table 21

The higher education data of Kerman Province

	grad	st	hei	prof	acprof	asprof
2005	7729
2006	5652	44990	42	40	83	623
2007	3111	31063	43	32	58	498
2008	15726	76686	53	58	46	530
2009	30808	120229	60	66	72	727
2010	23421	145237	82	83	157	926
2011	19439	158067	86	100	185	1029
2012	23498	161657	84	82	205	1142
2013	28678	167117	103	111	237	1318
2014	24081	173486	98	112	251	1422
2015	26151	171125	98	135	258	1645
2016	26251	156887	100	178	302	1905
2017		143033	100	193	345	1583
	lctu	aslctu	edust	bud	rgdp	rpop
2005				2.33E+09	4.90E+07	2584.96
2006	840	42	988	2.36E+09	6.90E+07	2652.41
2007	753	34	1000	8.95E+08	8.60E+07	2707.35
2008	866	32	263	2.80E+09	8.90E+07	2763.45
2009	1839	104	1672	3.95E+09	1.00E+08	2820.74
2010	1891	161	2411	5.17E+09	1.40E+08	2879.25
2011	2320	178	4303	7.89E+09	1.70E+08	2938.99
2012	1992	235	3436	8.54E+09	2.30E+08	2983
2013	1809	153	9485	1.36E+10	3.50E+08	3028
2014	2000	190	7531	1.58E+10	3.70E+08	3073
2015	2038	168	8490	1.92E+10	3.60E+08	3119
2016	2021	111	8993	2.17E+10	4.10E+08	3164.72
2017	1295	30	8047	2.55E+10	4.30E+08	3233.94

Source: see Table 1 and Section 2.2.

Table 22

The higher education data of Kermanshah

	grad	st	hei	prof	acprof	asprof
2005	4030
2006	2665	33330	27	19	23	355
2007	2330	15641	16	1	14	232
2008	8320	61277	38	7	18	253
2009	15142	70509	34	10	29	261
2010	9443	77917	42	9	41	426
2011	8891	82927	43	16	58	461
2012	12897	91720	43	28	69	518
2013	12235	95158	55	34	86	582
2014	14658	102009	52	37	97	673
2015	16911	102882	59	49	128	778
2016	16174	92457	55	55	140	816
2017		81518	53	51	172	901
	lctu	aslctu	edust	bud	rgdp	rpop
2005				58324142	2.80E+07	1867.61
2006	373	48	1171	59993240	3.40E+07	1879.39
2007	494	48	1254	59993344	4.30E+07	1892.06
2008	540	34	638	2.52E+08	5.40E+07	1904.97
2009	1127	78	1360	3.54E+08	6.30E+07	1918.14
2010	1304	67	1065	5.46E+08	8.10E+07	1931.55
2011	1138	77	1861	8.83E+08	1.10E+08	1945.23
2012	1056	106	1429	1.10E+09	1.40E+08	1946
2013	1086	101	3260	1.35E+09	1.70E+08	1948
2014	1099	52	3271	1.85E+09	3.70E+08	1949
2015	1269	70	4045	1.51E+09	3.60E+08	1951
2016	1220	64	4198	3.60E+09	4.00E+08	1952.43
2017	484	25	4397	4.27E+09	4.20E+08	1975.79

Source: see Table 1 and Section 2.2.

Table 23

The higher education data of Khuzestan Province

	grad	st	hei	prof	acprof	asprof
2005	6592
2006	6362	42938	35	75	126	641
2007	3000	24581	35	68	96	549
2008	24046	84059	60	49	85	432
2009	30278	205261	61	110	182	942
2010	32926	223145	72	115	245	1238
2011	28579	234814	111	162	313	1352
2012	35846	251685	120	126	252	1204
2013	39081	253454	133	119	294	1348
2014	38679	262316	125	115	269	1485
2015	44811	267118	139	149	316	1754
2016	42288	244757	137	254	479	2109
2017		218731	129	206	349	1901
	lctu	aslctu	edust	bud	rgdp	rpop
2005				1.98E+09	3.70E+08	4218.37
2006	740	40	1284	2.01E+09	4.50E+08	4274.98
2007	605	33	1221	2.38E+09	6.00E+08	4325.44
2008	745	20	460	2.41E+09	6.50E+08	4376.35
2009	3778	603	1646	3.63E+09	5.70E+08	4427.69
2010	4041	649	1948	4.90E+09	7.70E+08	4479.48
2011	4531	474	3438	6.41E+09	1.00E+09	4531.72
2012	5170	461	1710	7.59E+09	9.10E+08	4567
2013	4685	357	5187	1.27E+10	1.30E+09	4603
2014	6139	394	5166	1.51E+10	2.30E+09	4639
2015	6425	448	6408	1.92E+10	1.80E+09	4675
2016	6409	314	6308	2.50E+10	2.00E+09	4710.51
2017	2086	56	7744	2.91E+10	2.10E+09	4776.9

Source: see Table 1 and Section 2.2.

Table 24

The higher education data of Kohgiluyeh and Buyer Ahmad Province

	grad	st	hei	prof	acprof	asprof
2005	1642
2006	773	9385	8	0	0	105
2007	1003	5444	14			134
2008	4271	11177	14		3	147
2009	7205	36964	15		7	287
2010	4850	43640	18		11	238
2011	6352	47492	25	1	18	250
2012	6726	50748	23	2	17	253
2013	7507	53654	32	3	20	282
2014	7572	48207	27	3	18	289
2015	8794	57724	33	5	48	333
2016	8246	49743	32	11	69	363
2017		41209	27	18	91	419
	lctu	aslctu	edust	bud	rgdp	rpop
2005				5265326.1	1.00E+08	624.564
2006	156	0	269	5512545	1.20E+08	634.299
2007	185	6	126	8733679	1.20E+08	638.984
2008	228		103	9985606	1.30E+08	643.757
2009	796	34	195	12613400	1.10E+08	648.621
2010	634	43	485	12675544	1.50E+08	653.577
2011	730	30	1323	16067901	1.90E+08	658.629
2012	828	41	747	20725137	1.40E+08	669
2013	828	36	2200	36753111	2.10E+08	680
2014	964	21	2179	42664061	1.90E+08	691
2015	839	28	2688	49658348	1.50E+08	702
2016	746	13	2630	88362414	1.70E+08	713.052
2017	259	9	2919	1.48E+08	1.70E+08	712.992

Source: see Table 1 and Section 2.2.

Table 25

The higher education data of Kordestan Province

	grad	st	hei	prof	acprof	asprof
2005	2214
2006	3380	19476	16	0	3	131
2007	1688	8353	13	1	2	154
2008	5296	40944	24	3	2	147
2009	7847	46165	23	2	14	215
2010	7042	51810	26	2	19	205
2011	6813	56755	25	2	26	322
2012	9487	63860	29	3	28	344
2013	8445	64465	40	5	38	416
2014	10796	68162	35	2	27	433
2015	10822	70107	39	10	67	507
2016	10409	62916	39	17	97	561
2017		54747	36	23	108	562
	lctu	aslctu	edust	bud	rgdp	rpop
2005				17952712	1.70E+07	1429.33
2006	230	20	416	18606957	2.20E+07	1440.16
2007	348	18	355	1.72E+08	2.80E+07	1450.26
2008	494	17	209	29023152	3.40E+07	1460.66
2009	423	13	955	67610560	3.90E+07	1471.35
2010	391	40	967	98280281	4.70E+07	1482.35
2011	480	66	1845	1.58E+08	6.40E+07	1493.65
2012	438	61	1123	2.04E+08	7.60E+07	1514
2013	414	25	2543	3.32E+08	1.10E+08	1535
2014	411	49	2729	4.36E+08	1.10E+08	1557
2015	513	53	3251	5.57E+08	1.20E+08	1580
2016	525	56	3148	8.12E+08	1.30E+08	1603.01
2017	483	21	3119	1.05E+09	1.40E+08	1602.02

Source: see Table 1 and Section 2.2.

Table 26

The higher education data of Lorestan Province

	grad	st	hei	prof	acprof	asprof
2005	1956
2006	2759	21150	16	0	3	172
2007	2036	17514	24		4	190
2008	9294	36016	30	2	4	224
2009	14496	75031	29	2	10	319
2010	14474	83537	45	3	18	380
2011	10737	89952	48	8	21	454
2012	12828	96912	51	10	42	638
2013	15833	99977	59	25	44	537
2014	15243	105030	61	21	57	495
2015	16943	109519	59	15	75	611
2016	16601	92204	56	55	90	649
2017		84654	55	37	99	722
	lctu	aslctu	edust	bud	rgdp	rpop
2005				13653374	2.20E+07	1701.59
2006	260	8	378	14179798	2.90E+07	1716.53
2007	271	2	620	10582487	3.40E+07	1724.13
2008	543		367	39444069	4.00E+07	1731.7
2009	1510	61	864	31777033	4.60E+07	1739.24
2010	1473	85	1435	28120419	5.90E+07	1746.76
2011	1713	331	2014	40519176	7.20E+07	1754.24
2012	2029	131	1486	63521074	9.40E+07	1756
2013	1599	96	2646	1.09E+08	1.30E+08	1757
2014	1513	26	3722	2.84E+08	1.40E+08	1758
2015	1564	30	4034	4.10E+08	1.40E+08	1759
2016	1620	178	3566	8.23E+08	1.60E+08	1760.65
2017	680	20	4380	1.16E+09	1.70E+08	1775.1

Source: see Table 1 and Section 2.2.

Table 27

The higher education data of Markazi Province

	grad	st	hei	prof	acprof	asprof
2005	3053
2006	2075	29865	26	9	30	293
2007	1076	12324	16	9	21	261
2008	12449	59959	35	20	23	290
2009	20580	109403	41	20	68	707
2010	18548	113793	53	14	44	684
2011	18811	117618	64	21	60	805
2012	23228	119836	63	19	61	883
2013	21170	112428	67	23	85	947
2014	20070	112369	61	27	81	1022
2015	21219	112687	67	30	130	1123
2016	17853	95208	62	44	119	1210
2017		85571	56	37	110	911
	lctu	aslctu	edust	bud	rgdp	rpop
2005				29986969	3.80E+07	1337.83
2006	361	46	932	30970432	4.90E+07	1351.26
2007	229	9	809	30970590	6.00E+07	1363.28
2008	722	46	233	19604963	6.90E+07	1375.56
2009	2930	409	932	32288973	7.60E+07	1388.09
2010	2861	391	1644	35652564	9.20E+07	1400.89
2011	2769	244	2265	43210243	1.30E+08	1413.96
2012	3374	713	1642	65841577	1.70E+08	1417
2013	2735	616	2892	1.12E+08	2.10E+08	1420
2014	2932	641	3671	1.76E+08	2.80E+08	1423
2015	2944	646	3561	2.13E+08	2.70E+08	1426
2016	3028	645	3329	2.92E+08	3.10E+08	1429.47
2017	980	23	4221	3.80E+08	3.20E+08	1450.55

Source: see Table 1 and Section 2.2.

Table 28

The higher education data of Mazandaran Province

	grad	st	hei	prof	acprof	asprof
2005	10415
2006	11778	69104	66	35	91	849
2007	8824	58511	98	44	90	949
2008	24056	131831	95	54	103	972
2009	55755	182737	104	77	142	1235
2010	39548	219023	131	58	165	1339
2011	37033	240336	147	61	179	1537
2012	43136	254361	137	83	251	1502
2013	47334	250133	149	78	268	1688
2014	47352	241244	139	105	288	1921
2015	48842	244890	139	170	440	2079
2016	46062	222033	150	194	486	2232
2017		211262	149	211	538	1950
	lctu	aslctu	edust	bud	rgdp	rpop
2005				8.13E+08	6.40E+07	2887.2
2006	1420	99	2100	8.27E+08	7.60E+07	2922.43
2007	1847	89	3018	1.07E+09	9.70E+07	2952.47
2008	2739	77	901	1.21E+09	1.30E+08	2982.65
2009	4361	178	3561	4.21E+09	1.40E+08	3012.95
2010	4330	309	4208	5.86E+09	1.70E+08	3043.38
2011	5571	252	5634	7.89E+09	2.10E+08	3073.94
2012	4150	141	7200	7.14E+09	2.60E+08	3115
2013	3282	96	9670	1.34E+10	3.60E+08	3157
2014	3637	93	11225	2.35E+10	3.80E+08	3198
2015	3955	265	12004	3.71E+10	4.20E+08	3241
2016	3922	57	11752	6.94E+10	4.70E+08	3283.58
2017	2092	19	11772	8.88E+10	5.00E+08	3303.25

Source: see Table 1 and Section 2.2.

Table 29

The higher education data of North Khorasan Province

	grad	st	hei	prof	acprof	asprof
2005	697
2006	922	7241	7	0	0	5
2007	613	2823	6			8
2008	4613	17543	14			12
2009	5287	27785	14	2	3	77
2010	5118	33086	20	2	3	83
2011	4941	35169	20		2	97
2012	6201	41681	21	0	3	97
2013	6731	41263	23	0	3	144
2014	7558	44781	25	0	5	186
2015	8951	44992	28	3	10	306
2016	8156	41034	27	14	35	387
2017		36997	27	14	31	452
	lctu	aslctu	edust	bud	rgdp	rpop
2005				3940532	1.20E+07	802.729
2006	22	0	229	4129524.2	1.60E+07	811.572
2007	63		385	4325733.7	1.90E+07	822.479
2008	195		191	4529366.5	2.30E+07	833.545
2009	519	22	431	4740632.7	2.60E+07	844.773
2010	554	32	523	4959746.2	2.70E+07	856.165
2011	589	41	1170	5186924.8	3.60E+07	867.727
2012	676	83	767	5422390.7	4.50E+07	867
2013	602	50	1756	5540532	6.40E+07	866
2014	619	44	2307	5604027	6.50E+07	865
2015	646	43	2461	10601815	7.00E+07	864
2016	766	19	2288	24306036	7.90E+07	863.092
2017	425	0	2468	20461610	8.40E+07	885.053

Source: see Table 1 and Section 2.2.

Table 30

The higher education data of Qazvin Province

	grad	st	hei	prof	acprof	asprof
2005	2829
2006	3712	26590	27	11	25	545
2007	7355	22650	37	2	23	430
2008	13760	48436	34	4	20	403
2009	21948	85099	42	50	48	625
2010	17391	99103	56	49	66	679
2011	19128	115137	77	29	103	869
2012	24010	122865	71	32	83	691
2013	21925	129391	81	32	104	909
2014	23775	133944	74	32	107	974
2015	24075	126061	70	49	172	1109
2016	21223	107337	63	59	174	1117
2017		89219	53	40	181	964
	lctu	aslctu	edust	bud	rgdp	rpop
2005				1.36E+08	2.60E+07	1124.7
2006	394	3	918	1.39E+08	3.30E+07	1143.2
2007	1047	41	918	1.12E+08	4.00E+07	1154.69
2008	1326	33	240	1.24E+08	5.30E+07	1166.28
2009	2401	146	1229	1.47E+08	5.80E+07	1177.95
2010	2369	146	1731	1.68E+08	6.50E+07	1189.71
2011	2810	148	2142	1.83E+08	8.70E+07	1201.56
2012	2321	106	2404	2.14E+08	1.10E+08	1216
2013	2217	75	3808	2.45E+08	1.60E+08	1230
2014	2424	91	3963	2.53E+08	2.10E+08	1244
2015	2326	101	4223	2.55E+08	2.10E+08	1259
2016	2184	113	4470	3.08E+08	2.40E+08	1273.76
2017	779	26	4310	3.28E+08	2.50E+08	1283.67

Source: see Table 1 and Section 2.2.

Table 31

The higher education data of Qom Province

	grad	st	hei	prof	acprof	asprof
2005	2012
2006	2023	14315	12	12	22	227
2007	1331	9775	19	49	60	395
2008	3472	31906	26	15	43	283
2009	6238	40373	24	17	66	442
2010	7017	44298	31	16	46	417
2011	6519	50708	32	54	90	616
2012	8062	57653	34	26	79	578
2013	8938	60693	36	26	86	744
2014	9634	66212	41	32	103	746
2015	13071	73528	44	40	140	893
2016	11285	71784	44	43	179	911
2017		66735	46	50	247	951
	lctu	aslctu	edust	bud	rgdp	rpop
2005				43994.08	1.80E+07	1026.84
2006	232	2	432	49711	2.10E+07	1046.74
2007	526	13	310	170368	2.80E+07	1066.98
2008	579	5	304	318434	3.30E+07	1087.59
2009	605	10	988	19738926	3.70E+07	1108.57
2010	584	9	1259	27912880	4.50E+07	1129.93
2011	789	20	1785	39819403	6.00E+07	1151.67
2012	466	23	1693	58030551	7.80E+07	1179
2013	416	5	2264	89200020	1.00E+08	1206
2014	380	3	2993	1.80E+08	1.20E+08	1234
2015	454	10	3337	1.74E+08	1.40E+08	1263
2016	487	0	2862	2.46E+08	1.60E+08	1292.28
2017	444	7	3036	3.98E+08	1.70E+08	1305.3

Source: see Table 1 and Section 2.2.

Table 32

The higher education data of Razavi Khorasan Province

	grad	st	hei	prof	acprof	asprof
2005	12571
2006	12330	84124	83	94	350	485
2007	10693	54092	82	140	272	843
2008	29678	143986	104	168	296	1072
2009	55377	207476	126	223	348	1346
2010	36548	232268	158	256	473	1416
2011	33571	245218	145	237	449	1579
2012	42798	270601	151	269	469	1633
2013	43472	269257	169	304	558	1845
2014	42282	299168	173	348	547	2093
2015	49872	302725	179	394	670	2369
2016	49302	269630	175	441	752	2551
2017		254734	171	388	678	2273
	lctu	aslctu	edust	bud	rgdp	rpop
2005				6.09E+09	9.30E+07	5500.88
2006	1017	39	2773	6.16E+09	1.20E+08	5593.08
2007	1469	173	2678	2.39E+09	1.50E+08	5671.76
2008	2932	62	1312	6.12E+09	1.70E+08	5751.23
2009	3811	152	4606	2.24E+10	2.10E+08	5831.49
2010	4064	193	5037	2.22E+10	2.60E+08	5912.55
2011	3903	225	7519	2.63E+10	3.40E+08	5994.4
2012	3360	338	7915	2.87E+10	4.00E+08	6080
2013	3074	182	11466	3.13E+10	5.70E+08	6167
2014	3355	195	12880	3.80E+10	6.30E+08	6255
2015	3480	260	13673	4.18E+10	6.60E+08	6344
2016	3621	153	13593	4.45E+10	7.50E+08	6434.5
2017	1718	29	11821	6.46E+10	7.90E+08	6507.17

Source: see Table 1 and Section 2.2.

Table 33

The higher education data of Semnan Province

	grad	st	hei	prof	acprof	asprof
2005	3807
2006	3596	26992	25	2	20	431
2007	3161	22665	35	2	14	398
2008	8481	51808	32	2	27	454
2009	18777	82182	42	7	64	684
2010	13258	83647	49	12	80	828
2011	11422	94193	57	18	109	1179
2012	15204	103697	56	39	138	1235
2013	15697	100526	61	36	135	1125
2014	16509	109737	78	47	173	1165
2015	16690	108297	63	68	275	1592
2016	16056	98807	59	68	290	1456
2017		88924	60	58	245	1089
	lctu	aslctu	edust	bud	rgdp	rpop
2005				46128.879	1.50E+07	580.452
2006	455	11	735	52061	1.90E+07	589.233
2007	528	16	657	41305565	2.30E+07	597.296
2008	893	4	298	14473932	3.00E+07	605.462
2009	1789	39	1274	1.25E+09	3.30E+07	613.733
2010	1974	56	1734	1.59E+09	4.40E+07	622.111
2011	2046	66	1699	2.21E+09	5.80E+07	630.596
2012	1715	104	1784	3.29E+09	6.80E+07	644
2013	1505	82	2713	3.92E+09	9.50E+07	658
2014	1475	81	3398	6.52E+09	1.00E+08	673
2015	1572	90	3521	7.02E+09	1.10E+08	687
2016	1522	78	3190	1.06E+10	1.20E+08	702.36
2017	883	5	3382	1.17E+10	1.30E+08	704.349

Source: see Table 1 and Section 2.2.

Table 34

The higher education data of Sistan and Baluchestan Province

	grad	st	hei	prof	acprof	asprof
2005	4365
2006	4352	41373	28	7	19	433
2007	3902	41548	45	6	27	426
2008	9054	53953	30	2	31	495
2009	15105	80926	35	4	33	568
2010	10418	83164	45	13	70	675
2011	10976	86055	44	14	64	638
2012	12844	92727	47	21	105	502
2013	13249	95807	52	21	105	537
2014	14754	97952	50	22	114	587
2015	16738	110915	58	28	152	676
2016	15072	101822	65	35	164	775
2017		96217	60	59	184	824
	lctu	aslctu	edust	bud	rgdp	rpop
2005				1.23E+08	2.00E+07	2334.74
2006	758	14	694	1.26E+08	2.30E+07	2405.74
2007	752	25	463	9.37E+08	2.80E+07	2431.13
2008	855	6	156	2.02E+08	3.50E+07	2456.68
2009	1477	44	489	3.51E+08	4.10E+07	2482.41
2010	1212	76	1275	9.02E+08	6.00E+07	2508.29
2011	1174	118	2123	1.91E+09	7.80E+07	2534.33
2012	1199	64	1407	2.52E+09	1.00E+08	2581
2013	1230	51	2080	5.20E+09	1.30E+08	2629
2014	1334	45	2703	7.35E+09	1.50E+08	2677
2015	1444	119	2718	8.81E+09	1.60E+08	2725
2016	1354	49	2952	1.09E+10	1.90E+08	2775.01
2017	1095	22	2930	1.17E+10	1.90E+08	2786.41

Source: see Table 1 and Section 2.2.

Table 35

The higher education data of South Khorasan Province

	grad	st	hei	prof	acprof	asprof
2005	2384
2006	549	12421	13	3	5	98
2007	1630	8154	6	5	9	159
2008	4419	27825	18	2	10	177
2009	5100	33423	19	3	9	216
2010	5037	36778	24	3	24	249
2011	5058	42743	24	6	30	284
2012	7165	45655	22	5	58	483
2013	6459	44325	24	4	53	348
2014	7798	47561	27	6	98	480
2015	8083	50381	31	17	119	625
2016	8068	45478	31	27	188	681
2017		44475	34	34	136	492
	lctu	aslctu	edust	bud	rgdp	rpop
2005				22847989	9.00E+06	625.624
2006	204	61	490	23640350	1.20E+07	702.827
2007	214	7	529	12588694	1.60E+07	708.559
2008	302	4	362	26317321	1.90E+07	714.36
2009	590	84	749	36198655	2.20E+07	720.231
2010	581	103	881	39540624	2.30E+07	726.175
2011	518	36	1548	42905592	3.00E+07	732.192
2012	620	81	1154	48632052	3.90E+07	739
2013	599	48	1456	90392188	5.30E+07	747
2014	649	41	2063	1.39E+08	5.80E+07	754
2015	724	49	2226	1.82E+08	6.80E+07	761
2016	734	56	2281	2.79E+08	7.70E+07	768.898
2017	409	8	2244	3.68E+08	8.10E+07	785.061

Source: see Table 1 and Section 2.2.

Table 36

The higher education data of West Azerbaijan Province

	grad	st	hei	prof	acprof	asprof
2005	5748
2006	5960	37705	30	11	46	332
2007	3678	22432	31	16	55	352
2008	11847	73841	41	20	66	394
2009	20265	95819	48	29	80	501
2010	17174	104919	62	32	110	580
2011	14626	120870	66	41	111	688
2012	21572	127448	68	100	164	949
2013	21542	131596	73	109	193	1035
2014	20712	139729	76	109	248	1087
2015	24178	138644	78	112	295	1209
2016	24417	128856	82	122	359	1333
2017		116097	79	145	226	1140
	lctu	aslctu	edust	bud	rgdp	rpop
2005				3.44E+08	3.70E+07	2832.9
2006	341	13	910	3.51E+08	4.70E+07	2873.46
2007	341	9	753	3.33E+08	5.60E+07	2913.63
2008	666	6	496	3.95E+08	6.80E+07	2954.41
2009	1456	80	1465	9.35E+08	8.50E+07	2995.82
2010	1399	132	1663	1.08E+09	9.40E+07	3037.87
2011	2020	147	3268	1.34E+09	1.30E+08	3080.58
2012	1597	142	2079	1.77E+09	1.60E+08	3117
2013	1689	96	5223	2.30E+09	2.20E+08	3153
2014	1896	62	5496	3.83E+09	2.40E+08	3190
2015	1796	149	5729	3.90E+09	2.50E+08	3227
2016	1889	45	5652	5.22E+09	2.90E+08	3265.22
2017	1078	54	6208	5.75E+09	3.10E+08	3309.57

Source: see Table 1 and Section 2.2.

Table 37

The higher education data of Yazd Province

	grad	st	hei	prof	acprof	asprof
2005	5261
2006	4898	33448	30	12	17	241
2007	3227	22154	33	7	34	358
2008	12023	52618	35	22	34	370
2009	21918	82735	47	13	60	547
2010	14476	83188	53	18	97	676
2011	12851	88094	47	25	111	714
2012	15905	91703	48	19	108	698
2013	15398	87495	55	42	147	872
2014	13161	94679	54	27	147	845
2015	14728	94076	56	52	198	992
2016	15355	83836	57	58	249	1154
2017		81367	57	73	210	991
	lctu	aslctu	edust	bud	rgdp	rpop
2005				1.21E+08	2.30E+07	972.075
2006	328	8	795	1.24E+08	3.00E+07	924.411
2007	551	71	995	1.61E+08	3.90E+07	939.973
2008	792		932	1.98E+08	4.80E+07	955.786
2009	1457	123	2029	3.23E+08	5.50E+07	971.854
2010	1361	80	2401	4.97E+08	8.00E+07	988.18
2011	1452	144	2227	7.42E+08	1.00E+08	1004.77
2012	1316	164	2587	9.18E+08	1.50E+08	1030
2013	2366	147	3580	1.90E+09	2.00E+08	1056
2014	1174	105	4074	2.40E+09	2.20E+08	1083
2015	1115	317	4540	6.72E+09	2.20E+08	1110
2016	1234	115	4404	9.24E+09	2.50E+08	1138.53
2017	548	13	4557	1.12E+10	2.60E+08	1132.61

Source: see Table 1 and Section 2.2.

Table 38

The higher education data of Zanjan Province

	grad	st	hei	prof	acprof	asprof
2005	2430
2006	3656	18375	18	21	14	253
2007	1211	11442	20	15	25	310
2008	6666	33994	23	9	21	338
2009	9993	59116	25	49	55	523
2010	11743	63545	34	20	41	517
2011	9907	71804	44	27	74	761
2012	14083	76371	39	32	62	593
2013	11408	73393	41	54	79	680
2014	12856	75274	38	64	93	752
2015	13523	71305	41	66	118	907
2016	13069	60258	39	58	145	939
2017		54842	36	45	182	819
	lctu	aslctu	edust	bud	rgdp	rpop
2005				14764908	1.70E+07	957.235
2006	322	7	626	15325081	2.10E+07	964.601
2007	292	7	564	5567575	2.50E+07	974.399
2008	591	21	96	29823792	3.10E+07	984.406
2009	1420	82	1044	50324931	3.50E+07	994.627
2010	1427	120	1339	69855066	4.30E+07	1005.07
2011	1882	23	2289	1.28E+08	5.40E+07	1015.73
2012	1687	68	1210	1.95E+08	7.00E+07	1024
2013	1359	38	2959	3.51E+08	9.60E+07	1032
2014	1416	36	3009	6.52E+08	1.20E+08	1040
2015	1522	44	3132	9.08E+08	1.40E+08	1049
2016	1089	36	2970	1.39E+09	1.60E+08	1057.46
2017	529	7	3052	1.81E+09	1.60E+08	1068.62

Source: see Table 1 and Section 2.2.

References

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Higher education in Iran: An investigation of its expansion during 2005–2015 period using a control function approach

Abstract

Keywords

1. Introduction

1.1.1 The system and behaviour

2. Materials and methods

2.1 Empirical methodology

2.1.1 Control function approach

Table 1 Variables, abbreviations, and sources

Table 8 Comparing OP, LP and wooldridge results with panel data model (4) results

Footnotes

Acknowledgments

Appendix

References

Table 1
Variables, abbreviations, and sources

Table 8
Comparing OP, LP and wooldridge results with panel data model (4) results