research papers on institutions

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• NATURE INDEX
• 29 April 2020

Leading research institutions 2020

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A researcher at the University of California, San Diego, prepares to launch a 3D-printed rocket. Credit: Erik Jepsen/UC San Diego

The Chinese Academy of Sciences (CAS) in Beijing has topped the Nature Index 2020 Annual Tables list as the most prolific producer of research published in the 82 selected journals tracked by the Index (see Graphic).

CAS’s Share of 1805.22 in 2019 was almost twice that of Harvard University in Cambridge, Massachusetts, which came in second. Research institutions from China, the United States, France, Germany and the United Kingdom feature among the ten most prolific institutions in the Index. See the 2020 Annual Tables Top 100 research institutions for 2019 .

(Share, formerly referred to in the Nature Index as Fractional Count (FC), is a measure of an entity’s contribution to articles in the 82 journals tracked by the index, calculated according to the proportion of its affiliated authors on an article relative to all authors on the article. When comparing data over time, Share values are adjusted to 2019 levels to account for the small annual variation in the total number of articles in the Nature Index journals. The Nature Index is one indicator of institutional research performance. See Editor’s note below.)

Source: Nature Index

Here is a selection of institutions from the top 25 of the Nature Index 2020 Annual Tables .

University of Science and Technology of China

Share: 455.82; Count: 1,231; Change in adjusted Share (2018–19): +25.6%; Place: 8th

Established by the Chinese Academy of Sciences (CAS) in 1958 in Beijing (then known as Peking), the University of Science and Technology of China (USTC) moved to its current location in Hefei, the capital of the eastern Chinese province of Anhui, in 1970.

Today, it employs about 16,000 students, including 1,900 PhD students, as well as 1,812 faculty members, 547 of which are professors.

Nature Index 2020 Annual Tables

The institution’s strongest subjects in the Nature Index are chemistry and physical sciences. USTC is a global collaborator, counting the Max Planck Society in Munich, Germany, the University of Oxford, UK, and Stanford University in California among its close partners.

In 2019, USTC researchers were part of an international team that discovered a stellar black hole with a mass 70 times greater than that of the Sun. The findings, published in Nature , were mentioned in more than 300 tweets and nearly 200 news stories, according to Altmetric.

University of Michigan, United States

Share: 343.45; Count: 939; Change in adjusted Share (2018–19): − 3.3%; Place: 19th

Placed first among public universities in the United States for research volume, according to the US National Science Foundation, the University of Michigan in Ann Arbor encompasses 260,000 square metres of lab space, which is accessed by students and staff in 227 centres and institutes across its campus.

With US$1.62 billion in research expenditure and more than 500 new invention reports in the fiscal year 2019, the University of Michigan is focused on innovative areas in research, including data science, precision health and bioscience. Its Global CO 2 Initiative, launched in 2018, aims to identify and pursue commercially sustainable approaches that reduce atmospheric CO 2 levels by 4 gigatons per year.

A 2019 study published in Science on honesty and selfishness across cultures, led by behavioural economist Alain Cohn, was covered by almost 300 online news outlets and reached more than 22 million people on Twitter, according to Altmetric. The study, which tested people’s willingness to return a dummy lost wallet, revealed a ‘high level’ of civic honesty.

University of California, San Diego, United States

Share: 340.85; Count: 1,048; Change in adjusted Share (2018–19): − 1.2%; Place: 20th

With US$1.35 billion in annual research funding, the University of California, San Diego, is a force in natural-sciences research, particularly in oceanography and the life sciences.

Its health-sciences group, which includes the School of Medicine and Skaggs School of Pharmacy and Pharmaceutical Sciences, brought in US$761 million in research funding in the fiscal year 2019, and Scripps Oceanography, one of the world’s oldest and largest centres for research in ocean and Earth science, won $180 million in funding.

The university also has a focus on innovation, with more than 2,500 active inventions, 1,870 US and foreign patents, and 31 start-ups launched in 2018 by faculty members, students and staff. One such start-up was CavoGene LifeSciences, which aims to develop gene therapies to treat neurodegenerative disease.

Zhejiang University, China

Share: 329.82; Count: 815; Change in adjusted Share (2018–19): +10.5%; Place: 23rd

Zhejiang University in Hangzhou, China, is part of the Chinese government’s Double First Class Plan, which aims to develop several world-class universities by 2050. It employs 3,741 full-time faculty members and partners with nearly 200 institutions around the world.

Zhejiang’s total research funding reached 4.56 billion yuan (US$644 million) in 2018, with 926 projects supported by the Chinese National Natural Science Fund and 1,838 Chinese invention patents issued. The university is home to materials scientist Dawei Di, who was listed as a top innovator under 35 by MIT Technology Review in 2019 for his work on organic light-emitting diodes and perovskite light-emitting diodes.

In 2019, Zheijiang researchers published a Science paper with an international team that proposed a method for boosting plant growth while reducing water use, which could contribute to more sustainable agriculture practices.

Northwestern University, United States

Share: 317.12; Count: 762; Change in adjusted Share (2018–19): − 7.6%; Place: 25th

Founded as a private research university in 1851, Northwestern University, based in Evanston, Illinois, now also has campuses in Chicago and Doha, Qatar, and employs 3,300 full-time research staff. It has an annual budget of US$2 billion and attracts more than US$700 million for sponsored research each year.

The fastest-rising institution in the United States in high-quality life-sciences research output, Northwestern University was also 14th in the world in chemistry in the Nature Index 2020 Annual Tables .

Its star researchers include mathematician Emmy Murphy, one of six recipients of the 2020 New Horizons Prize for her work in the field of topology — the study of geometric properties and relationships — and physicist John Joseph Carrasco and neuroscientist Andrew Miri, who in February were awarded prestigious Sloan Research Fellowships.

doi: https://doi.org/10.1038/d41586-020-01230-x

This article is part of Nature Index 2020 Annual Tables , an editorially independent supplement. Advertisers have no influence over the content.

Editor’s note: The Nature Index is one indicator of institutional research performance. The metrics of Count and Share used to order Nature Index listings are based on an institution’s or country’s publication output in 82 natural-science journals, selected on reputation by an independent panel of leading scientists in their fields. Nature Index recognizes that many other factors must be taken into account when considering research quality and institutional performance; Nature Index metrics alone should not be used to assess institutions or individuals. Nature Index data and methods are transparent and available under a creative commons licence at natureindex.com .

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Institutions and economic development: new measurements and evidence

• Open access
• Published: 08 March 2023
• Volume 65 , pages 1693–1728, ( 2023 )

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• Esther Acquah 1 ,
• Lorenzo Carbonari   ORCID: orcid.org/0000-0002-9862-8036 2 ,
• Alessio Farcomeni 2 &
• Giovanni Trovato 2  

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We propose a new set of indices to capture the multidimensionality of a country’s institutional setting. Our indices are obtained by employing a dimension reduction approach on the institutional variables provided by the Fraser Institute ( 2018 ). We estimate the impact that institutions have on the level and the growth rate of per capita GDP, using a large sample of countries over the period 1980–2015. To identify the causal effect of our institutional indices on a country’s GDP we employ the Generalized Propensity Score method. Institutions matter especially in low- and middle-income countries, and not all institutions are alike for economic development. We also document non-linearities in the causal effects that different institutions have on growth and the presence of threshold effects.

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1 Introduction

In their influential essay, Acemoglu et al. ( 2005 ) provide convincing arguments in favor of the idea that institutions cause economic prosperity by providing “ right” incentives and constraints to the economic agents. Along the path of economic development, Acemoglu and coauthors claim, institutions emerge as outcomes of social decisions. Particularly, economic institutions encouraging economic growth may arise “ when political institutions allocate power to groups with interests in broad-based property rights enforcement, when they create effective constraints on power-holders, and when there are relatively few rents to be captured by power-holders ”. This view traces back to North ( 1990 ), who defines institutions as “ the rules of the game in a society or, more formally, [...] the humanly devised constraints that shape human interaction ”. Consistently with this definition, the fundamental explanation of comparative growth should be sought in institutional differences. This is the perspective we adopt in this paper.

The attempt to understand cross-country differences in GDP dynamics through this lens is certainly not new. Footnote 1 We contribute in two ways. First, we provide new measures to describe a country’s institutional environment. Since the institutional setting is a multidimensional phenomenon and the array of connections between institutions and economic development is potentially extremely large, the first contribution of the paper is to propose a brand-new set of indices aimed at summarizing such multidimensionality. In our view, the term “institution” must be intended in a broad sense. Institutions affect the interactions among agents on many grounds. They operate formally, through the design of the rules of the game , but also informally, by shaping customs and social norms . The possibility for individuals and organizations—like corporations, public entities, financial institutions, etc.—to lead the society as a whole towards productive economic activities crucially depends on the incentives for these activities. Incentives that typically institutions provide. Building on the data provided by the Fraser Institute ( 2018 ), we focus on the following five measures: i) the size of the public sector, ii) the reliability and fairness of the legal system, iii) the degree of liquidity in the financial markets, iv) the degree of openness to international trade and v) the strength of regulation . Footnote 2 Our indices are obtained by employing a dimension reduction approach designed for panel data (Farcomeni et al. 2021 ) and rated on a 0–10 scale. Such a rating reflects the general idea that an institution is better the more it increases market freedom, protects private property rights, provides liquidity to the economy (with a beneficial effect on interest rates and capital accumulation), and promotes trade. These are considered the most important preconditions for a sustained economic development.

We are aware that some of our institutional indices are constructed starting from variables which, at best, can only be taken as proxies for institutions. While the legal system and the regulatory environment are intuitively identifiable as institutions per se, it might not be the same for other indices like, for instance, the size of the public sector. This measure, however, can be intended as a proxy for the welfare state, which is an institution itself or an aggregation of institutions, implicitly assuming that the larger is the public sector, the more developed is the welfare state. An assumption that seems to be supported by the data. Footnote 3 Similarly, well-functioning financial market and trade openness are informative about not only the appropriateness of the policies undertaken to pursue these goals but also about the soundness of the institutions which conceive and implement those policies.

As a second contribution, we use these indicators to assess their joint and separate role on GDP. We do this by explicitly taking into account the unobserved heterogeneity among countries. Using an optimal clustering method, we split our sample of 80 countries over the period 1980–2015, into two groups, “high-income” and “low- and middle-income” countries. By doing this we allow for heterogeneous effects of institutions among clusters. Then, applying the restrictions provided by an augmented version of the Solow model, including a role for institutions, we first estimate a Gaussian mixed-effects model to empirically prove the positive association between GDP (levels and growth rate) and our institutional indices. Finally, we employ the Generalized Propensity Score method proposed by Hirano and Imbens ( 2004 ) to properly address the issues of endogeneity and omitted variable bias and to identify the causal effect of institutions on GDP.

Our estimates show that the obtained institutional indices vary across the two groups of countries. We show that improvements in some institutions (i.e., larger values of our institutional indices) may cause both higher levels and growth rates of the long-run per capita GDP. Such effects appear stronger for those countries which have been classified as “low- and middle-income”, where, comparatively, markets are more dysfunctional and bureaucracies typically less efficient. Specifically, we document the important role played by the legal system in determining the long-run level of GDP in “low- and middle-income” countries. This has an important policy implication. In countries where basic institutions are often lacking, market-friendly policies may not yield desired results or may even be counterproductive. In such a context, reforms should aim at establishing a reliable legal system and protecting property rights.

Differently from the large body of the literature on the topic, Footnote 4 which focuses on the linear association between some institutional indices and GDP (levels and growth rate), a final important feature of our analysis is that it looks at and finds non-linear causal effects. Institutions affect GDP directly and indirectly, trough their interaction with cluster membership. Improvements in institutions always determine a positive level effect on per capita GDP. Our estimates document an interesting non-linear causal effect of (our proxy for) welfare state on GDP: the positive impact of this indicator tends to increase up to some limit (being smaller in the group of “low- and middle-income” countries) and then starts to decline (more sharply in the group of “low- and middle-income” countries). Also, all our institutional indicators display non-linear effects (despite not always statistically significant) on GDP growth. As a further check for non-linearity, we carry on a threshold analysis based on the augmented Solow model. This exercise confirms the presence of thresholds effects in the two groups of countries.

Our work relates closely to the empirical literature on the link between institutions and GDP dynamics, which has significantly increased over the last three decades as we have listed above. In general, a positive and direct relationship between institutions and GDP levels/growth rates is found. Estimates, however, substantially vary in terms of magnitude across different samples and/or specifications. Moreover, most of the papers rely only on few variables to capture institutional quality and/or do not provide any causal evidence on the relationship between institutions and GDP dynamics. Since the literature is vast, here we focus our attention to those studies which, like ours, build upon Mankiw et al. ( 1992 ) (MRW, hereafter).

Using a large sample of countries over the period 1975–1990, Dawson ( 1998 ) find that one standard deviation increase of an initial value of the “economic freedom” index above the mean provides a 3.78 percentage point higher growth rate in the subsequent 15-year sample period, holding the level of freedom fixed over the period. Taking data from 97 countries over the period 1974–89, Knach and Keefer ( 1995 ) introduce two institutional variables into an MRW regression, meant to capture the security of property rights and the enforcement of contracts, and find that an increase of one standard deviation in their “rule of law” index leads to an increase in the GDP growth rate by 0.504 of its standard deviation. In a subsequent paper, Keefer and Knack ( 1997 ) also show that whenever good institutions are absent convergence tends to be slower.

Analyzing a sample of 127 countries over the period 1950–1994, Hall and Jones ( 1999 ) show that differences in capital accumulation, productivity, and therefore output per worker are fundamentally related to differences in “social infrastructure” across countries. The positive impact of the “rule of law” on GDP growth has been found by Barro ( 1997 ), for a panel of 100 countries over the period 1960–1990, while Rodrik et al. ( 2004 ), using the data set of Acemoglu et al. ( 2001 ), find institutions to be crucial in determining the long-run level of a country’s income. Their estimates indicate that a one standard deviation increase in institutional quality produces a two log-points rise in per capita incomes. For a panel of 56 countries over the period 1981–2010, Nawaz ( 2015 ) find that the impact on GDP growth of various institutional variables is relatively larger in “high-income” countries as compared to the “low- and middle-income” ones.

Using a large sample of countries over the period 1960–2000, Minier ( 2007 ) focuses on the indirect effect of (political) institutions on growth, by introducing parameter heterogeneity into a growth regression. In such a frame, there are typically multiple growth regimes and threshold effects, which are ultimately affected by institutional quality. Minier’s estimates shed light on the interesting link between institutions and trade. Specifically, the weaker are the institutions of a country (proxied by several policy-related variables), the more it suffers from trade openness. Footnote 5

While most studies present a linear linkage between institutions and growth, there is also an empirical growth literature that deals with the non-linearities in the canonical cross-country growth regression. Footnote 6 For instance, using data on 100 countries over the years 1995–2018, Li and Kumbhakar ( 2022 ) propose a quantile regression model in which countries are grouped according to their growth rates, finding a positive effect of economic freedom on per capita GDP growth. In particular, they show that countries that fall into the 20th-50th percentiles of per capita GDP have a positive and significant effect of economic freedom on growth, whereas the effect is not significant below or above these percentiles. Our work belongs to this strand of the literature, examining whether the (causal) relationship between institutions and growth is subject to non-linearities after constructing optimal institutional indices.

The rest of the paper is organized as follows. Section  2 outlines and discusses the methodology proposed to derive the set of institutional indices and the empirical model to assess the role of institutions in explaining GDP dynamics. Section  3 describes the data set. Section  4 presents the estimates, with some comments. Section  5 is a conclusion.

2 Model and methodology

2.1 institutional indices.

Our first goal is to compute time-dependent summaries of indicators of interest. The main purpose of creating these institutional and policy indices is to identify unidimensional latent variables to summarize multidimensional indicators that, to some extent, are measuring similar characteristics from a different perspective. These latent variables can then be used for ranking and identifying different levels ( doses ) of the characteristics of interest (e.g., the reliability and fairness of the legal system). Notice that the resulting summaries are optimal from a specific mathematical perspective. However, they can only give a partial point of view on the information contained in the data.

There are different methods available for dimension reduction. The most widely used (e.g., principal component analysis) is anyway restricted to cross-sectional data and would not be appropriate for multidimensional measurements (in our case: a collection of indices that are deemed to measure different aspects of the same unidimensional latent trait) that are repeatedly measured over time (Hall et al. 2006 ). Among the different possible approaches proposed by the literature (e.g., Chen and Buja 2009 ; Maruotti et al. 2017 ), we opt for a methodology based on the specification of a latent Markov model (Bartolucci et al. 2013 , 2014 ) for the latent trait, as in e.g. Xia et al. ( 2016 ) or Vogelsmeier et al. ( 2019 ). Specifically, we employ the methodology proposed by Farcomeni et al. ( 2021 ), whose main advantage is that it allows us to explicitly consider dependence arising from measurements on the same agent that is repeated over time.

Formally, let \(X_{itm}\) denote the m -th indicator for country i at time t . Let also \(U_{it}\) denote an unobserved discrete latent variable and \(w_m\) be the weight of latent class separation for \(m=1,\ldots ,M\) . We assume \(Z_{it} = \sum _{m=1}^M w_m X_{itm}\) follows a latent Markov model according to which \(Z_{it}\) is independent of \(Z_{is}\) conditionally on \(U_{it}\) , which follows a homogeneous first-order Markov chain. Additionally, conditional on \(U_{it}=j\) we assume \(Z_{it}\) is Gaussian with mean \(\xi _j(w)\) . The optimal weights \({\hat{w}}_m\) for \(m=1,\ldots ,M\) optimize latent class separation, that is, maximize

under the constraint \(\sum _m w_m^2=1\) , where \(p_{tj}(w) = \Pr (U_{it} = j)\) and \({\bar{\xi }}_t(w)=\sum _j p_{tj}(w){{\hat{\xi }}}_j(w)\) . In words, we set weights so that the latent means (the means of each subgroup as identified by \(U_{it}\) ) are as far from each other as possible.

The resulting summary is a linear combination of the initial dimensions which optimizes the separation of clusters of agents (e.g., countries that have a more or a less reliable legal system). Weights can be used for the interpretation and assessment of the importance of the original variables. A limitation is a Gaussian assumption for \(Z_{it}\) , which might not hold in practice if any \(X_{ith}\) is severely skewed, or if H is small.

Our methodology identifies five groups of indicators, which we summarize separately, creating treatment variables \(z_1\) to \(z_5\) (see Tables  11 and  12 in the Appendix for detailed descriptions) and jointly (treatment variable z ). Finally, we normalize and scale the resulting indicators on a score of 0 (e.g., no reliability and fairness of the legal system) to 10 (e.g., highest reliability and fairness of the legal system). Footnote 7

2.2 The augmented Solow model

The rest of the paper is aimed at quantifying the causal effect of the institutional indices derived above on GDP levels and growth rates. To do this, we extend the canonical MRW’s setting to account for a direct impact of institutions on the Total Factor Productivity (TFP) [see, e.g. Nawaz and Khawaja ( 2019 )]. Footnote 8

For a country i at time t , we assume that the aggregate output is obtained through the following linearly homogeneous production function:

where Y is the level of real GDP, K is the stock of physical capital, H is the stock of human capital, A is the Harrod-neutral technological progress and L is the labor force. We assume that the labor force and technology grow at the exogenously given rates n and g , respectively. For the sake of simplicity, we also assume that both forms of capital depreciate at the same constant rate \(\delta \) . Let now \(\ln \left( \frac{Y_{it}}{L_{it}}\right) ^*\) denote the (natural logarithm of the) level of per capita GDP in the long-run, such that

where \(s_k\) and \(s_h\) indicate the exogenous fractions of total income invested in physical capital and human capital, respectively. Notice that the term A is a reduced form to capture the large set of factors, other than inputs, that affect the steady-state level of GDP, such as resource endowments, climate, and institutions. Specifically, as in Dawson ( 1998 ), the notion that institutions affect productivity can be easily incorporated in the model by assuming A to be a function of institutions ( z ). Therefore, differently from MRW, in which \(\ln (A)_{it}=\alpha +\epsilon _{it}\) , with \(\epsilon _i \sim N(0,1)\) representing a country-specific shock, in our set-up, we assume: \(\ln (A)_{it}=f(z_{it})+\epsilon _{it}\) . Footnote 9 Using this, we obtain the following empirical equation:

where \(\psi _0+\psi _1f(z_{it})\) is the TFP, \(\psi _1\) captures the effect of institutions on per capita GDP, \(\psi _2\equiv \left( \frac{\alpha }{1-\alpha -\beta }\right) \) , \(\psi _3\equiv \left( \frac{\beta }{1-\alpha -\beta }\right) \) and \(\psi _4\equiv -\left( \frac{\alpha +\beta }{1-\alpha -\beta }\right) \) . This specification implies that differences in institutions have a homogeneous effect on the level of productivity across countries ( \(\psi _1\) ). The growth of per capita income can be then expressed as a function of the determinants of the steady-state and the initial level of income, i.e

where \({Y_0}/{L_0}\) is the per capita income at some initial time and \(\lambda \) indicates the speed of conditional convergence toward the steady-state. Plugging ( 3 ) into ( 4 ) we finally get the following empirical equation:

where \(\zeta _0\equiv (1-e^{\lambda t})\psi _0\) , \(\zeta _1\equiv (1-e^{-\lambda t})\psi _1f(z_{it})\) , \(\zeta _2\equiv (1-e^{-\lambda t})\frac{\alpha }{1-\alpha -\beta }\) , \(\zeta _3\equiv (1-e^{-\lambda t})\frac{\beta }{1-\alpha -\beta }\) , \(\zeta _4\equiv -(1-e^{-\lambda t})\frac{\alpha +\beta }{1-\alpha -\beta }\) and \(\zeta _4\equiv -(1-e^{-\lambda t})\) .

2.3 Estimation method

We first divide countries into groups according to a model-based clustering method. To do so, we restrict to the (log of) GDP in 1980 and compare twenty possible Gaussian mixture models, combining \(k=1,\ldots ,9\) groups with homogeneous or heterogeneous cluster-specific variance. The resulting optimal clustering is then used as a control, being a possible proxy for residual unobserved heterogeneity.

We then estimate Gaussian mixed-effects models in which we include fixed effects for treatment ( z , \(z_1, \ldots , z_5\) ), its square, interactions with cluster indicators, and control variables. For each endpoint \(x_{it}\) this leads to the equation

The model above reduces to ( 3 ) where the augmented Solow model is year and cluster ( \(c_i\) ) specific, with \(f(z_{it}) = (\eta _1 z_{it} + \eta _2 z_{it}^2 + \eta _3 c_i + \eta _4 z_{it}c_i + \eta _5 z_{it}^2c_i)/\psi _1\) . Footnote 10

Subsequently, we put forward a causal analysis using a Generalized Propensity Score (GPS) method (Hirano and Imbens 2004 ). This is a generalization of the propensity score method for continuous treatments. Accordingly, we estimate a fixed-effect model to predict each treatment using controls and a country-specific intercept, as

where y denotes the log of real per capita GDP, \(\ln \left( {Y}/{L}\right) \) . The resulting predicted treatment \({{\hat{z}}}_{it}\) and its square is then included in a regression model to predict the outcome \(x_{it}\) , which is either the log-GDP or its growth rate, as in

together with the treatment, its square, and interactions of treatment and GPS with cluster indicators. The resulting predicted dose-response surface can be used to assess causal relationships between the treatment and endpoint, as discussed in Hirano and Imbens ( 2004 ) and references therein.

We note that a limitation of the GPS method is that it requires a selection-on-observables assumption, unlike Instrumental Variables (IV), Difference-in-Differences (DiD), and similar methods. The latter is not simply applicable in our context anyway as reliable IV are not available for our setting; and complex dose-response relationships are not amenable to assumptions underlying the DiD method. Similar reasoning about these assumptions applies for instance to panel cointegration methods and Generalized Method of Moments (GMM) estimation.

To construct our sample, we merge information from three different sources. Our final sample contains country-level data for 80 countries from 1980 to 2015 taken over every fifth year. Footnote 11 Our main dependent variable is the real per capita GDP ( y ) taken from The World Bank ( 2018 ). We used this variable to construct our second dependent variable, which is the 5 years average growth rate of the real per capita GDP ( Growth ). This leaves us with seven data points for each country while at the same time controlling for initial income ( \(y_{t-1}\) ) which starts from 1980. Data on the total population used in constructing effective labor ( \(n+g+\delta \) ) and the investment share ( I / GDP ) that are seen to affect GDP dynamics were also taken from The World Bank ( 2018 ). The rate of human capital accumulation has been proxied by the Human Capital Index ( HC ) taken from the PWT ( 2018 ).

Finally, the variables used in the construction of our optimal institutional indices were taken from the Fraser Institute ( 2018 ) database. Footnote 12 The optimal summary index ( z ) and the optimal sub-indices ( \(z_i\) , \(i=1,\dots ,5\) ) have been obtained by applying the methodology proposed in Sect.  2.1 . Specifically, the summary index, z is constructed from the sub-indices Public sector size \((z_1)\) , Reliability and fairness of the legal system \((z_2)\) , Liquidity market openness \((z_3)\) , Degree of (trade) protectionism \((z_4)\) , and Regulation \((z_5)\) . As part of our investigation, we will conduct several robustness analyses with the five optimal sub-indices of institutions ( \(z_1\) to \(z_5\) ) as alternative treatments to the overall institutional variable z . A detailed description of the Fraser Institute ( 2018 ) variables used to construct our treatment indices and the variables employed in our regressions can be found in Tables  11 and  12 in the Appendix.

Table  1 presents the summary statistics of key variables used in the analysis. Overall, there are 560 observations across 80 countries for 7-year periods taken every fifth year. On average, the natural logarithm of real per capita GDP is about 8.56 (equivalent to 5218 (in millions of US Dollars)), and countries’ GDP growth rates are approximately 0.08. The average institutional index is approximately 7.1 (score out of 10). The analysis also includes the binary variable ‘ cluster ’, which is 1 for “high-income” countries and zero otherwise. Footnote 13 Table  2 reports the correlation matrix among key variables.

4.1 Regime Membership

To partially remove effects of initial conditions, we classify countries with respect to their initial per capita GDP in 1980 ( \(y_{0}\) ). Clearly some countries will move to other clusters and others will persist in their initial cluster. By adjusting we remove confounding due to the initial status of each country. Using the Bayesian Information Criterion (BIC) and as suggested by the Classification Trimmed Likelihood (CTL) curves (Garcia-Escudero et al. 2011 ; Farcomeni and Greco 2015 ) presented in Fig.  1 , we identify two clusters. The figure shows the objective function at convergence for the different number of clusters and increasing trimming levels \(\alpha \) . The curves for \(k=2,3,4\) clusters almost overlap, while there is a gap for \(k=1\) versus \(k=2\) , indicating that the optimal number of groups is \(k=2\) .

We are then left with a predictable grouping reported in Table  3 . This leads to the variable ‘ cluster ’, the indicator of being a “high-income” country (Cluster 2). Overall, there are 23 “high-income” countries out of the 80 countries in our sample. Footnote 14

4.2 Estimates

4.2.1 institutions and gdp level.

Table  4 reports the results of the model for GDP level using the Main institutional index (Model 1) and the five sub-indices (Models 2–6).

In the analysis conducted on the whole sample, we find that the effect on the long-run level of income of our aggregate institutional index ( z ) is essentially null in “low- and middle- income” countries (0.001) while it is positive (despite not statistically significant) in “high-income” countries (0.046). Parameter estimates for physical capital (0.102) and human capital (0.587), which are both statistically significant, are in line with the recent empirical literature based on MRW. Footnote 15

The results presented in the remaining five alternative specifications (models 2–6) employ a set of covariates including one sub-index in each estimation. For “low- and middle-income” countries, the sub-index Reliability and fairness of the legal system (model 3) positively (0.058) and significantly ( \(p\) value \(<0.001\) ) affects the level of income in the long-run while we find a negative impact of the Liquidity market openness (model 4) sub-index ( \(-\) 0.035, with a \(p\) value \(<0.005\) ). Footnote 16

4.2.2 Institutions and GDP growth

The analysis conducted on the whole sample shows that improvements in the main institutional index ( z ) foster economic development in “low- and middle-income” countries.

Table  5 reports the estimates of the growth regression model. The index z is found to have a positive impact (0.030 with a \(p\) value \(<0.01\) ) on the 5-year average real per capita GDP growth rate (model 1). The effect is not conclusive for “high-income” countries since the parameter for the interaction \(z \times cluster\) is not statistically significant. The coefficients for physical capital (0.159) and human capital (0.182) are in line with the literature based on MRW while the coefficient for the lagged value of GDP ( \(-\) 0.061) indicates that there is a slight tendency toward convergence in our sample.

The results for the baseline growth regression when using the five alternative synthetic sub-indices taken in isolation are reported in models 2–6 of the table. There is evidence of Public sector size ( \(z_1\) ) being harmful to growth for “low- and middle-income” countries ( \(-\) 0.025, \(p\) value \(<0.05\) ) while the GDP growth effect of the Degree of (trade) protectionism ( \(z_4\) ) is negative in “high-income” countries ( \(-\) 0.070, \(p\) value \(<0.01\) ).

4.2.3 Estimates with all five sub-indices of institutions

Results in Table  6 present estimates for using all the five sub-indices of institutions ( \(z_i: i=1,\ldots , 5\) ) as regressors together with the other covariates. From model 1 of the table, we find a positive and statistically significant impact on GDP (0.056, \(p\) value \(<0.01\) ) of the sub-index Reliability and fairness of the legal system in “low- and middle-income” countries.

In the growth specification (model 2), the sub-indices that have statistically significant effects are Public sector size for “low- and middle-income” countries ( \(-\) 0.027, \(p\) value \(<0.05\) ) and the Degree of (trade) protectionism ( \(z_4\) ) for “high-income” countries ( \(-\) 0.054, \(p\) value \(<0.05\) ).

4.3 Generalized Propensity Score Analysis

We use the Generalized Propensity Score (GPS) estimator to evaluate the causal effect of each treatment on GDP dynamics. Tables  7 and  8 report the estimates while Figs.  2 and  3 present dose-response curves for “high-income” (solid line) and “low- and middle-income” (dotted line) countries in models 1–6.

From Table  7 and Fig.  2 , we see that with the partial exception of Public sector size ( \(z_1\) ) (see the second plot of Fig.  2 in which the dotted lines do not always lie above the solid ones), an improvement in institutions causes a more pronounced level effect on GDP in “high-income” countries.

Dose-response: causal effect of institutions on GDP level. Note : The treatments used in the various panels are (1)—Main institutional index ( z ), (2)—Public sector size ( \(z_1\) ), (3)—Reliability and fairness of the legal system ( \(z_2\) ), (4)—Liquidity market openness ( \(z_3\) ), (5)—Degree of (trade) protectionism ( \(z_4\) ), (6)—Regulation ( \(z_5\) )

Estimates in Table  8 and dose-response curves in Fig.  3 exhibit some form of non-linearity in the causal effect of institutions on growth. Footnote 17 The overall index ( z ) and sub-indices—with the exception of \(z_4\) for “low- and middle-income” countries—display a concave pattern.

The non-linear relationship in the causal effect of Public sector size ( \(z_1\) ) on GDP growth rate is reminiscent of Barro ( 1990 ). Public provision of infrastructure, rule of law, and protection of property rights is particularly important for growth in the early phases of the economic development. In Panel (2) of Fig.  3 , the dotted curve lays above the solid one for \(z_1\ge 5\) , suggesting that, to exert a positive effect on growth in “low- and middle-income” countries, the size of the public sector cannot be too low. However, as it gets too large, distortionary effects due to high taxes and public borrowing, as well as diminishing returns to public capital may emerge. Footnote 18

The non-monotonic effect of the strength of regulation ( \(z_5\) ) on GDP growth in the cluster of “high-income” countries seems to capture the stylized fact that a heavier regulatory burden tends to reduce productivity growth in OECD countries. Footnote 19

Trade protectionism ( \(z_4\) ) appears to be an important source of growth in “low- and middle-income” countries. Despite far from been conclusive, this result is consistent with the correlation between protectionist or inward-oriented trade strategies and growth in the so-called “first era of globalization”. Footnote 20

Dose-response: causal effect of institutions on GDP growth. Note : See notes under Fig.  2

4.4 Sub-sample Analysis

With the copious number of studies revealing institutional lapses in developing countries, Tables  15 ,  16 , and  17 as well as Tables  18 and  19 (all of them in the Appendix) report results of the analysis conducted on a restricted sub-sample of “low- and middle-income” countries when using the mixed effect and GPS approaches, respectively. Footnote 21 Notice that in this sub-sample analysis, we do not include the interaction \(z -cluster\) , since it is not identifiable in the sub-sample. The reason is that we stratified by cluster and this variable is a constant in each sub-sample.

From the results presented in Tables  15 and  16 , we find no significant effect of institutions on GDP level but a positive linear effect (0.027, \(p\) value \(<0.01\) ) on its growth rate. In terms of the sub-indices, we observe a non-linear relationship between GDP dynamics and Public sector size ( \(z_1\) ) as well as Degree of (trade) protectionism ( \(z_6\) ), such that increases in the sub-indices causes higher income and faster growth only if they do not exceed values around 4. There is also a significant non-linear relationship between GDP growth and Liquidity market openness ( \(z_4\) ) but the effect is weak ( \(-\) 0.001, \(p\) value \(< 0.10\) ) and decreases at higher values of the index.

Such non-linearities appear even clearer from the dose-response curves shown in Figs.  4 and  5 . The beneficial effect on GDP due to improvements in institutions ( z ) emerges only for higher values of the index ( \(z>5\) ), as shown in Panel (1) of Fig.  4 . Almost the opposite instead occurs when we assess the causal impact of z on GDP growth, with a dose-response plot showing a concave pattern, as illustrated in Panel (1) of Fig.  5 .

4.5 Threshold Effects

We have documented that improvements in a country’s institutional indices produce different effects on GDP (levels and growth rates), depending on whether the country belongs to the “high-income” or the “low- and middle-income” cluster. The analysis presented in Sect.  4.3 provides evidence about the possible non-linear causal effects of institutions on GDP dynamics. Those estimates, however, pertain to the reduced form regressions ( 7 ) and ( 8 ) which go beyond the standard (log-)linear growth model. To reconcile the issue of non-linear effects with the canonical growth model, we carry on a threshold analysis which incorporates all the restrictions provided by the augmented Solow model presented in Sect.  2.2 .

To test for the presence of potential threshold effects within the various classifications provided in Table  3 , we employ the dynamic panel threshold strategy proposed by Seo and Shin ( 2016 ), which allows for non-linear asymmetric dynamics, unobserved heterogeneity, and treats economic institutions as an endogenous variable. Footnote 22 For the sake of space, we restrict our attention to the relationship between the main institutional index, ( z ) and the GDP growth rate.

The model considered is of the form:

where \(y_{it}\) is the natural logarithm of real per capita GDP, \(z_{it}\) is our optimal measure of institutions (transition variable) and \(x_{it}\) is a set of covariates including natural logarithms of total population, human and physical capital. Also, \(\gamma \) is the threshold parameter and the error term, \(\epsilon _{it}\) . We used lagged values of political institutions as one of the instruments that lead to the selection of economic institutions together with the other exogenous covariates in an attempt to address the issue of endogeneity. The use of this instrument is motivated by the hierarchy of institutions hypothesis introduced by Acemoglu et al. ( 2005 ) where political institutions have been documented to set the stage for their economic institutional counterparts which affect economic outcomes of a country. Footnote 23 From equation ( 9 ), the hypothesis of interest is the null, \(H_0: \delta = 0\) as against the alternative \(H_1: \delta \ne 0\) .

Using the first difference generalized method of moments estimator (FD-GMM), Models 1, 2, and 3 of Table  9 presents the results with the full sample of 80 countries, “high-income”, and “low- and middle-income” countries, respectively. To have comparable results, we report the estimated coefficients for countries below ( \(\phi \) ) and above ( \(\tau \) ) the estimated threshold effects in each cluster, respectively.

Following the old “rule of thumb” (see Steiger and Stock 1997 ; Stock and Yogo 2002 ) which says for the weak identification surrounding the instrumental variable not to be considered a problem, the \(F\) -statistics should be at least 10, we found the \(F\) -statistic to be above 10 for “high-income” countries and close to the 10 for “low- and middle-income” countries and the overall sample. In general, the estimated threshold effects ( \({\hat{\gamma }}\) ) are statistically significantly different from zero and similar to those reported in Acquah ( 2021 ) who used the original institutional indices from the Fraser Institute ( 2018 ) in a similar estimation approach. Particularly, for economic institutions to influence GDP growth, it must on average develop to a point of 6, 8, and 7 (out of a score of 10) for the full sample of 80, “high-income” and “low- and middle-income” countries, respectively. Since the threshold variable is unit-free, we interpret the estimated long-run effect of institutions towards GDP growth in reference to the estimated threshold parameter ( \({\hat{\gamma }}\) ) as a way of providing some understanding into the gains or losses of institutions for countries whose institutional developments are below ( \({\hat{\phi }}_{\triangle q}\) ) and above ( \({\hat{\tau }}_{\triangle q}\) ) the estimated threshold effect in what follows. From Table  9 , we observe a significant difference in the parameter estimates of countries above and below the estimated threshold effect when using our institutional index. Above the estimated threshold effect of 8 (out of 10), changes (if the change persists for 5 years) in our institutional index leads to an increase in the growth rate of “high-income” countries by 0.4 percentage points (Model 2). The corresponding effect is positive for “low- and middle-income” countries but statistically not significant and negative in the overall sample. Interestingly, below the threshold of 7 (out of 10), improvements in the institutional measure are associated with an increase in the GDP growth rate by 0.026 percentage points for the “low- and middle-income” countries (Model 3). The coefficient estimates of the other variables are equally different in magnitude and/or signs for the sample above and below the threshold effect in Models 1–3.

4.6 Instrumental Variables

In this section, we assess how our institutional measures perform in comparison to the most frequently used proxy for institution, namely the Rule of law index , within a framework that puts the joint role of institutions and human capital center stage. Footnote 24 To do this we estimate a more parsimonious model in which both our institutional measures and human capital are simultaneously treated as endogenous and instrumented using historical variables. Specifically, we use i) the mortality rate of European settlers in former colonies to instrument country’s institutional quality, as in Acemoglu et al. ( 2001 ), and ii) the presence of Protestant missionary activity to instrument human capital in the former colonies, as in Acemoglu et al. ( 2014 ). Footnote 25

Because the empirical model is identical to that in Acemoglu et al. ( 2014 ), we shall be brief. The dependent variable is the (log of the) current level of GDP. Table  10 presents a comparison between the estimates of the main model in Acemoglu et al. ( 2014 ), in which the Rule of law index is used as a proxy for institutions and the (average) Years of Schooling as a proxy for human capital, and two models using our institutional measures, i.e., the Public sector size \(z_1\) (Model 1) and the Reliability and fairness of the legal system \(z_2\) (Model 2), respectively. Footnote 26 The bottom half of the table provides the first stages for the two endogenous variables. The differences in the variables used and the estimation technique justify the differences in the magnitude of the parameters.

As in Acemoglu et al. ( 2014 ), the coefficient on human capital is positive and significant ( \(p\) value \(<0.001\) ) while the coefficient on our institutional measure is positive and barely significant ( \(p\) value \(<0.10\) ) in both Models 1 and 2. First stage estimates are in line with those in Acemoglu et al. ( 2014 ) and document a negative association between settlers mortality and institutions, which is statistically significant only in Model 2, and between settlers mortality and human capital, which is instead always statistically significant. These results survive to several robustness checks. Footnote 27

Overall, the IV regressions, in which both institutions and human capital are instrumented using historical sources of variation, show a positive effect of the two variables on the current level of GDP. The effect of Public sector size (Model 1) and the Reliability and fairness of the legal system (Model 2), however, tends to be lower in magnitude and less precisely estimated than the one of the (log of) Human Capital Index. This result is in line with Glaeser et al. ( 2004 ) and the literature that suggests that human capital is a more basic source of economic prosperity than political institutions.

5 Concluding remarks

This paper contributes to the debate on the nexus among institutions and economic development in two ways. It provides a new set of indices to capture a country’s institutional environment and it empirically investigates whether there is any causality running from institutions to economic development.

Building on Fraser Institute ( 2018 ), we propose a dimension reduction approach to obtain a new set of indices to summarize the multidimensionality of a country’s institutional setting. To identify the causal effect of these brand-new institutional indices on GDP (levels and growth rate) we employ the Generalized Propensity Score estimation approach. Using a large sample of countries over the period 1980–2015, our analysis documents the positive and statistically significant impact that improvements in institutions have on the growth rate of per capita GDP, in the economies that, according to our classification, belong to the cluster of “low- and middle-income”. Moreover, we find a sizable effect of human capital on GDP dynamics.

Our causal analysis also shows non-linearities in the effects that different institutions have on income and growth. The empirical model used to test causality takes into account the role of physical and human capital and lets institutions interact with cluster membership. The sub-index that captures the extent of welfare state, which we term Public sector size ( \(z_{1}\) ), displays a concave pattern in both regression models. Improvements of this index produce gains in terms of higher income and faster growth especially in less advanced economies, provided that the value of the sub-index is not too high. Despite not always statistically significant, improvements in all the other considered institutions cause a positive level effect that is larger for “low- and middle-income” countries.

The Mixed-Effect Model also stresses reliability and fairness of the legal system as a crucial driver for economic development. This result is reminiscent of La Porta et al. ( 2008 ) and has several policy implications. Specifically, our analysis reveals that the design and the implementation of legal reforms appear to be particularly important in “low- and middle-income” countries. Policy interventions aimed at improving this institution are complex. Such interventions pertain to i) drafting and enacting of laws and regulations, ii) enforcing laws and regulations, and iii) resolving and settling disputes. Like many economists, political scientists, and legal scholars have pointed out, however, legal reforms in a society emerge as an equilibrium outcome, thus reflecting the balance between different interests of different social groups. Footnote 28 Moreover, the so-called “legal transplant” has rarely turned out to be successful. Footnote 29

Finally, we document interesting threshold effects which support the existence of non-linearities. Again, higher values in our institutional indices, which typically translate into advances in institutional quality, are particularly important for those countries which are below the estimated threshold and belong to the cluster of “low- and middle-income” countries.

See the list of studies mentioned below.

As noted in the literature, these sub-dimensions of institutions equally capture policy variables such as the size of the public sector in terms of government expenditure and taxes (see, for instance, De Haan et al. 2006 ). We will use these indices irrespective of whether they are institutional measures or policies aside from the main institutional index obtained with the dimension reduction analysis.

The World Bank documents that, over the period 2000–2019, the total tax revenue (% of GDP) has a correlation of 0.46 with the government expenditure on education (% of GDP), of 0.33 with the domestic general government health expenditure per capita) and of 0.28 with the coverage of social insurance programs (% of population). Moreover, in countries with a large public sector (such as China, France, Finland, Italy, Norway and Singapore), central governments are generally full or majority owners of important state-owned enterprises, which play a crucial role for GDP growth through their technological dynamism and export successes (see, e.g., Chang et al. 2007 ).

See, e.g., Ali ( 1997 ), Dawson ( 1998 ), Dawson ( 2003 ), Hall and Jones ( 1999 ), De Haan and Sturm ( 2000 ), Ali and Crain ( 2001 ), Acemoglu et al. ( 2005 ), De Haan et al. ( 2006 ), Cebula ( 2011 ), Cebula and Mixon ( 2012 ), Iqbal and Daly ( 2014 ) and Hussain and Haque ( 2016 ).

In Sect.  4.5 , we explore the possible existence of non-linearities between institutions and economic growth. The main difference between Minier’s work and ours is that we focus on our brand-new institutional indices while using political institutions as the variable that controls the selection of economic institutions which may affect growth.

See, e.g., Barro ( 1996 ), Liu and Stengos ( 1999 ), Cohen-Cole et al. ( 2012 ), Li and Kumbhakar ( 2022 ) and, for a survey, Cohen-Cole et al. ( 2005 ).

Generally, we can say that higher values of our indices correspond to improvements in the quality of the institutions to which the indices refer. In the causal analysis conducted in the Sect.  4.3 we show, however, that, for some institutions, too high values of the index referring to them may lead to a negative effect on GDP dynamics. This potential negative effect suggests to avoid reference to a notion of institutions quality for our indices.

Manca ( 2010 ) provides evidence that countries endowed with better institutions have higher TFP growth rates and faster rates of technology adoption.

As in Dawson ( 1998 ), this specification implies that differences in institutions have a “fixed effect” on the level of productivity across countries.

Notice that non-linear (i.e., quadratic) effects are needed in ( 6 ) as they are found to be significant in the data. Hence, omitting them would lead to bias in the other parameter estimates.

The sample is consistent across estimations and consists of a balanced panel, as required by the threshold analysis presented in Sect.  4.5 . We exclude from the analysis all the countries for which data are missing. South Korea has been excluded from the final sample because the time patterns for all institutional indices greatly deviate from the relative sample averages. Including South Korea implies less precise estimates and a downsizing of the parameters referred to the institutional indices. This appears incongruous, since South Korea is a well documented example of a growth enhancing interaction between institutions and private sector (see, e.g. Glaeser et al. 2004 ). For the sake of completeness, Tables  13 and  14 , in the Appendix, report the results of the models for GDP level and growth rate presented in the next section, including South Korea. All the remaining estimates are available upon request.

For a detailed description of the raw data, see Gwartney and Lawson ( 2003 ).

See Section 4.1 for details.

As a robustness check, we run our classification using the average GDP, obtaining basically the same cluster composition (i.e., only Cyprus and Portugal move from a cluster to another). This does not affect the main message of our estimates.

See, e.g., Bucci et al. ( 2022 ), for a study on non-OECD countries, and Bucci et al. ( 2019 ), for a study on OECD countries.

This index is meant to capture the relative tightness (low values of the index) or ease of monetary policy (high values of the index). See Table  11 in the Appendix for further details.

Our aim is to contribute to the empirical literature pointing out that non-linearities matter for understanding economic growth. For a discussion on the relationship between policy evaluation and growth non-linearities see, e.g., Cohen-Cole et al. ( 2012 )

The tendency toward a negative growth effect of a large public sector in rich countries is in line with the empirical literature on the topic (see, e.g., Fölster and Henrekson 1999 ).

See, e.g., Loayza et al. ( 2005 ), Bassanini and Ernst ( 2006 ) and Barone and Cingano ( 2011 ).

See, e.g., Schularick and Solomou ( 2011 ).

Estimates from the sample excluding countries such as Chile, Malaysia, Portugal, and Uruguay from the sample are available upon request. These four countries were in the high-income group according to the World Bank income classification as of the year 2015.

Acquah ( 2021 ) follows a similar exercise (refer for further details on the methodology).

See Acquah ( 2021 ) and references therein for a detailed discussion of this point.

We thank an anonymous referee for this suggestion.

By instrumenting country’s institutional quality with the the mortality rate of European settlers in former colonies, Acemoglu et al. ( 2001 ) provide a well known argument in favor of a virtuous link between institutions and economic prosperity. The gist of their argument is that where Europeans faced high settler mortality rates, they established extractive institutions that are ultimately associated with a low economic development. At the opposite, where European colonialists faced low mortality rates, they established inclusive institutions that fostered a sustained economic development. Acemoglu et al. ( 2014 ) establish a causal relationship among the presence of Protestant missionary activity and long-run differences in human capital in the former colonies. Their argument is that, “ conditional on the continent, the identity of the colonizer, and the quality of institutions, much of the variation in Protestant missionary activity was determined by idiosyncratic factors and need not be correlated with the potential for future economic development. Because Protestant missionaries played an important role in setting up schools, partly motivated by their desire to encourage reading of the Scriptures, this may have had a durable impact on schooling ”. For a discussion on the underlying mechanisms through which these historical variables may have affected the current quality of institutions, the reader can refer to the above mentioned paper. For a detailed description of the historical variables see the Appendix of Acemoglu et al. ( 2014 ).

The estimates obtained using the main institutional index and the sub-indices \(z_3-z_5\) are in line with those presented in Table  10 but less precise. They are omitted to save space and are available upon request. Importantly, the effect of human capital is always positive and statistically significant.

The full 2SLS models estimates are available upon request.

See, e.g., Besley and Ghatak ( 2009 ).

See, e.g., Aldashev ( 2009 ).

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Esther Acquah

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Lorenzo Carbonari, Alessio Farcomeni & Giovanni Trovato

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“We switch now to one of the typical ultimate causes of growth. Institutions do matter—no doubt about it. But: how much? Through what channels? These are much more difficult questions to answer”. Crafts and Toniolo ( 2010 ).

Appendix A Variable description

See Tables 11 and 12 .

Appendix B Estimates, including South Korea

See Tables 13 and 14 .

Appendix C Sub-sample analysis

1.1 c.1 sub-sample estimates.

The following results are estimates when using the sub-sample of 57 “low- and middle- income” countries.

See Tables 15 , 16 , 17 , 18 , 19 and Figs. 4 , 5 .

Dose-response, sub-sample analysis: causal effect of institutions on GDP level. Note : The various plots are the dose-response curves when using the generalized propensity score estimator to evaluate the causal effect of each treatment on GDP level for low-/ middle-income from models 1–6. The various treatment are (1)—Main institutional index ( z ), (2)—Public sector size ( \(z_1\) ), (3)—Reliability and fairness of the legal system ( \(z_2\) ), (4)—Liquidity market openness ( \(z_3\) ), (5)—Degree of (trade) protectionism ( \(z_4\) ), (6)—Regulation ( \(z_5\) )

Dose-response, sub-sample analysis: causal effect of institutions on GDP growth. Note : The various plots are the dose-response curves when using a generalized propensity score estimator to evaluate the causal effect of each treatment on GDP growth for low-/ middle-income from models 1–6. See notes under Fig.  4

Appendix D Alternative methods for construction of institutional indeces

In this appendix we give further motivation for the use of the methodology proposed in Farcomeni et al. ( 2021 ) for dimension reduction and automatic construction of institutional indices. Naive alternatives involve either (i) classical Principal Component Analysis (PCA) after treating the data as pooled cross sectional data and (ii) using all Fraser Institute variables directly as separate predictors.

The first route would not be completely scientifically sound as simple pooling would ignore dependence in the data (i.e., the fact that groups of measurements refer to the same nation at different years, and are therefore positively dependent). The consequence would be that the resulting unidimensional summary would not be internally valid. On this point see also Ando and Bai ( 2017 ) and references therein. The second route would involve an explosion of the number of parameters (e.g., when all areas are considered together, twenty four predictors would be included in the model instead of just one). This would make interpretation very cumbersome.

In the following we give also empirical evidence of the fact that the naive alternative routes would not be good choices, by comparing the leave-one-out predictions for the Gaussian mixed-effects models. Namely, we omit each measurement in turn, estimate three models (the one that uses our proposed indices, the one that uses PCA-based indices, and the one that uses institutional indicators directly), predict the omitted measurement. The final model summary is the Sum of Squared Errors (SSE) for predictions, that is, the sum of squared differences between the predictions and each omitted measurement. As could be expected, our proposal overall leads to an advantage in terms of predictive performance, as the average SSE for the six models (five areas plus all areas together) involved for each outcome are always smaller with our proposal (Table  20 ). It shall be mentioned that this applies separately for all models when comparing with raw indicators, while some models actually have a small advantage when comparing our proposal with PCA.

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Acquah, E., Carbonari, L., Farcomeni, A. et al. Institutions and economic development: new measurements and evidence. Empir Econ 65 , 1693–1728 (2023). https://doi.org/10.1007/s00181-023-02395-w

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DOI : https://doi.org/10.1007/s00181-023-02395-w

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To understand their financial position, universities need to understand the long-term implications of their operating revenues and costs in relation to the financial assets they have available. Standard budgeting procedures that focus on one or two years at a time and use generally accepted accounting principles (GAAP) do not do this. We present an alternative framework that discounts cash flow forecasts over the infinite future and compares the present value of operating obligations to the value of the university’s endowment net of any debt it has issued. We illustrate the potential of this framework using recent data from Harvard’s Faculty of Arts and Sciences (FAS).

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Diving Deeper into Postsecondary Value, IHEP Research Series Explores Equity and Economic Outcomes

Washington, DC (May 29, 2024) –   Higher education has long been recognized as a key driver of economic opportunity, but new research, spearheaded by the Institute for Higher Education Policy (IHEP), is diving deeper into questions of postsecondary value and equity. The “Elevating Equitable Value: Investigating Economic Outcomes of Postsecondary Education” series, informed by data from the Equitable Value Explorer tool along with state-level data, surveys, and additional sources, is exploring pressing questions about postsecondary value. Research released today by Trellis Strategies, the American Association of State Colleges and Universities (AASCU), Wayne State University, and the Research Institute at Dallas College completes the seven-paper series.  

“Earning a college degree can change the trajectory of students’ lives, their families, and their communities, for generations to come, but the benefits are not evenly distributed,” said IHEP President Mamie Voight . “By unpacking the nuances of value delivery across different contexts, this research strengthens the evidence-base showing that college is worth the investment. It also can inform policymakers and institutions about targeted strategies to improve the returns on postsecondary education for all students.”  

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Several papers in the series explored how institutional policy and practice can ensure all students benefit from a college degree. Research by Trellis Strategies underscores the connection between student financial well-being during college and future economic returns. A ten-percentage-point decrease in the number of students experiencing financial instability during college was correlated with higher economic returns to students, especially at four-year public schools. The authors highlight the importance of programs that expand access to emergency aid, promote financial literacy, and enhance transparency around college costs and financial aid options.  

A study by the American Association of State Colleges and Universities (AASCU) found that all 33 institutions participating in their Student Success Equity Intensive program had earnings that exceeded the Postsecondary Value Commission’s minimum economic return threshold, but equity gaps persist. Institutions serving a larger proportion of Black, Latinx, and Indigenous students or Pell Grant recipients saw a smaller economic return – the amount by which earnings exceed those of a typical high school graduate, plus the cost of their education  – demonstrating the need for continued efforts to promote student success and the financial value of college degrees.  

Another key finding shows a strong link between faculty composition and student outcomes. Research by Frederick Tucker of the City University of New York reveals that institutions with more tenured or tenure-track faculty, alongside a smaller proportion of full-time adjuncts, see stronger economic returns for students. This is particularly true at Minority-Serving Institutions (MSIs) and colleges serving a large share of Pell Grant recipients.  

How Does Postsecondary Value Differ By and Within States?

The research in this series adds to our growing understanding of how certain states are delivering value. For example, a project by Wayne State University found that while postsecondary education generally leads to higher earnings in Michigan, disparities exist. Public, four-year universities in the state provided the highest economic return, exceeding the minimum threshold by over $22,000, while most other types of institutions in the state offered a smaller but still positive return. Michigan ranked high nationally in terms of the amount that students’ earnings typically exceed the minimum economic return threshold,  despite having a moderate ranking in median post-college earnings.  

The Research Institute at Dallas College’s analysis paired data from the Equitable Value Explorer with state longitudinal data to measure the economic return at more than 500 Hispanic-Serving Institutions (HSIs) nationwide, in addition to outcomes for all Hispanic students in Texas. Overall, economic returns were positive for Hispanic students, but disparities persisted even within Hispanic communities, particularly for immigrants, those from low-income backgrounds and women.   

What is the Role of Geography in the Postsecondary Value Equation?

Location plays a significant role in education options and economic returns. Two papers in the series examined the geographic dimension of value. The American Institutes for Research’s study found that community college students generally earn more after college than those with only a high school diploma in their region. However, community colleges serving a higher percentage of underrepresented students tend to deliver a lower economic value, underscoring the need for additional support to ensure these institutions can effectively serve their students.  

Boston College researchers’ analysis of rural-serving institutions (RSIs) found that while median post-college earnings may be slightly lower compared to urban and suburban institutions, RSIs are typically more affordable. The majority of RSIs still provide a positive economic return for students after factoring in these relatively low education costs, highlighting their vital role in expanding access to higher education in underserved areas.  

IHEP is expanding and strengthening the community of researchers, practitioners and advocates exploring postsecondary value through an equity lens, by providing the tools necessary for researchers, associations, and institutions to tackle these critical questions. For more information about the Equitable Value Explorer, please visit: https://equity.postsecondaryvalue.org/     

Supporting the Whole Student Through Holistic Advising: Reflections on ED’s Raise The Bar Summit

Investing in Student Success: IHEP’s Federal Funding Priorities for FY25

At what point do we decide AI’s risks outweigh its promise?

In June 2015, Sam Altman told a tech conference, “I think that AI will probably, most likely, sort of lead to the end of the world. But in the meantime, there will be great companies created with serious machine learning.”

His comments echoed a certain postapocalyptic New Yorker cartoon , but Altman, then the president of the startup accelerator Y Combinator, did not appear to be joking. In the next breath, he announced that he’d just funded a new venture focused on “AI safety research.” That company was OpenAI, now best known as the creator of ChatGPT.

The simultaneous cheerleading and doomsaying about AI has only gotten louder in the years since. Charles Jones , a professor of economics at Stanford Graduate School of Business and senior fellow at the Stanford Institute for Economic Policy Research (SIEPR), has been watching with interest as developers and investors like Altman grapple with the dilemma at the heart of this rapidly advancing technology. “They acknowledge this double-edged sword aspect of AI: It could be more important than electricity or the internet, but it does seem like it could potentially be more dangerous than nuclear weapons,” he says.

Out of curiosity, Jones, an expert on modeling economic growth, did some back-of-the-envelope math on the relationship between AI-fueled productivity and existential risk. What he found surprised him. It formed the basis of a new paper in which he presents some models for assessing AI’s tradeoffs. While these models can’t predict when or if advanced artificial intelligence will slip its leash, they demonstrate how variables such as economic growth, existential risk, and risk tolerance will shape the future of AI — and humanity.

There are still a lot of unknowns here, as Jones is quick to emphasize. We can’t put a number on the likelihood that AI will birth a new age of prosperity or kill us all. Jones acknowledges that both of those outcomes may prove unlikely, but also notes that they may be correlated. “It does seem that the same world where this fantastic intelligence helps us innovate and raise growth rates a lot also may be the world where these existential risks are real as well,” he says. “Maybe those two things go together.”

Rise of the machines

Jones’ model starts with the assumption that AI could generate unprecedented economic growth. Just as people coming up with new ideas have driven the past few centuries of progress, AI-generated ideas could fuel the next wave of innovation. The big difference is that AI does not need years of education before it can produce breakthrough research or innovations. “The fact that it’s a computer program means you can just spin up a million instances of it,” Jones says. “And then you’ve got a million really, really smart researchers answering a question for you.”

Once scale laws kick in and AI’s capabilities increase exponentially, we could be looking at an economic expansion unlike any in history. Taking one of the most optimistic forecasts, Jones calculates that if AI spurs a 10 percent annual growth rate, global incomes will increase more than 50-fold over 40 years. In comparison, real per capita GDP in the U.S. doubled in the past 40 years.

Now for the downside: Let’s assume that such phenomenal growth comes with a 1 percent chance that AI will end the world in any given year. At what point would we decide that all this increased productivity is not worth the attendant danger? To estimate this, Jones built a simple model that uses the log utility curve, a common representation of consumer preferences, to represent aversion to risk. When he ran those numbers, he found that people would accept a substantial chance that AI would end humanity in the next 40 years.

“The surprising thing here is that people with log preferences in the simple model are willing to take a one-in-three chance of killing everyone to get a 50-fold increase in consumption,” Jones says. Yet even these risk-takers have a limit: When the existential risk from AI doubles, the ideal outcome under log utility is never letting AI run at all.

In scenarios where people have lower risk tolerance, they would accept slower growth in exchange for reduced risk. That raises the question of whose interests will guide the evolution of AI. “If the entrepreneurs who are designing these AIs are very tolerant of risk, they may not have the average person’s risk tolerance, and so they may be more willing to take these gambles,” Jones says.

However, his paper also suggests that it may not be wealthy countries like the U.S. that will be most willing to risk AI running amok. “Getting an extra thousand dollars is really valuable when you’re poor and less valuable when you’re rich,” he explains. Likewise, if AI brings huge bumps in living standards in poorer nations, it could make them more tolerant of its risks.

Healthy, wealthy… and wise?

Jones also built a more complex model that considers the possibility that AI will help us live healthier, longer lives. “In addition to inventing safer nuclear power, faster computer chips, and better solar panels, AI might also cure cancer and heart disease,” he says. Those kinds of breakthroughs would further complicate our relationship with this double-edged tech. If the average life expectancy doubled, even the most risk-averse people would be much more willing to take their chances with AI risk. “The surprise here is that cutting mortality in half suddenly turns your willingness to accept existential risk from 4 percent to 25 percent or even more,” Jones explains. In other words, people would be much more willing to gamble if the prize was a chance to live to 200.

The models also suggest that AI could mitigate the economic effects of falling birth rates , another subject Jones has recently written about. “If machines can create ideas, then the slowing of population growth may not be such a problem,” he says.

Jones’ models provide insights into the wildest visions of AI, such as the singularity — the fabled moment when technological growth becomes infinite. He found that, in practical terms, accelerated growth might be hard to distinguish from the singularity. “If growth rates were to go to 10 percent a year, that would be just as good as a singularity,” he says. “We’re all going to be as rich as Bill Gates.”

Overall, Jones cautions that none of his results are predictive or prescriptive. Instead, they’re meant to help refine our thinking about the double-edged sword of AI. As we rush toward a future where AI can’t be turned off, efforts to quantify and limit the potential for disaster will become even more essential. “Any investments in reducing that risk are really valuable,” Jones says.

This story was originally published May 29, 2024 by Stanford GSB Insights.

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Yale Is Lead Institution in the ‘All of Us’ Research Consortium

The consortium has received a large grant from the national institutes of health.

Researchers at Yale University have been awarded a $5.6 million grant for the first year of a five-year project to establish the Coast-to-Coast Consortium (C2C) and further their pioneering efforts with the National Institutes of Health's (NIH) All of Us Research Program. Yale will lead the new consortium to further participant enrollment and engagement efforts across seven organizations.

The award is designated to facilitate participant engagement, enrollment, data collection, and retention. C2C will build on the foundation set by the California Precision Medicine Consortium (CAPMC), established in 2018, which enrolled more than 65,500 participants to the program.

This award follows the All of Us program's recent achievement of returning personalized health-related DNA results to more than 100,000 participants. Returning results to participants involves examining a specific set of genes that are associated with certain serious health conditions, such as hereditary cancers and heart disease. Through this process, the program observed 32,500 DNA variants. More than 7,000 of these variants had never been observed among people who had previously had genetic testing, allowing participants to act upon information that never was available before. The program is not only advancing individual health outcomes but also contributing to global genomic medicine research efforts.

Lucila Ohno-Machado, MD, PhD, MBA , deputy dean for biomedical informatics and the chair of biomedical informatics and data science at Yale School of Medicine, a key figure in Yale's participation in the All of Us initiative, underscored the significance of this milestone. "The All of Us Program provides an unprecedented opportunity to include diverse populations in large-scale genomic research. By including individuals from historically underrepresented communities, we can uncover insights into genetic variations that may have been overlooked in the past, ultimately leading to more equitable healthcare for all."

Yale collaborates with C2C, including the University of California, San Diego; the University of California, Davis; the University of California, San Francisco; Cedars-Sinai Medical Center, the University of Southern California, and the Puerto Rico Consortium for Clinical Investigation, in its research efforts. C2C represents a diverse and dynamic network committed to advancing biomedical research and innovation.

Since its inception, the All of Us team at Yale has enrolled more than 500 local participants in the program, with an impressive 81% representation of underrepresented racial or ethnic minorities. This diversity not only enriches the dataset but also ensures that research findings are applicable and beneficial to all populations.

Recruitment for All of Us is ongoing. Volunteers must be at least 18 years old and can represent any gender, race, ethnicity, or cultural background. Participants are invited to an initial in-person visit of 30 minutes to an hour, with regular online updates regarding health and lifestyle in subsequent months and years.

With continuing efforts to expand participation, the All of Us Research Program continues to make strides toward its goal of creating a diverse and comprehensive dataset that will drive transformative biomedical research discoveries for all populations, reflecting Yale's unwavering dedication to pioneering research and promoting equitable healthcare.

More than 800,000 individuals have joined the program to contribute to this research effort. Participants can share a wide range of data from biosamples, survey responses, physical measurements, electronic health records (EHRs), and wearable devices. These data are made broadly available to registered researchers through the program’s Researcher Workbench, fostering biomedical research discoveries and promoting health equity.

More than 75% of All of Us participants self-identify with communities historically underrepresented in medical research, while about 45% identify with a racial or ethnic minority group.

To learn more and enroll, visit the All of Us Yale website at JoinAllofUs.org/Yale .

The All of Us Research Program’s Coast-to-Coast Consortium at Yale University is funded by the National Institutes of Health award OT2OD037644.

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• Lucila Ohno-Machado, MD, MBA, PhD Waldemar von Zedtwitz Professor of Medicine and Biomedical Informatics and Data Science; Deputy Dean for Biomedical Informatics; Chair, Department of Biomedical Informatics and Data Science

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Modular, scalable hardware architecture for a quantum computer

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Quantum computers hold the promise of being able to quickly solve extremely complex problems that might take the world’s most powerful supercomputer decades to crack.

But achieving that performance involves building a system with millions of interconnected building blocks called qubits. Making and controlling so many qubits in a hardware architecture is an enormous challenge that scientists around the world are striving to meet.

Toward this goal, researchers at MIT and MITRE have demonstrated a scalable, modular hardware platform that integrates thousands of interconnected qubits onto a customized integrated circuit. This “quantum-system-on-chip” (QSoC) architecture enables the researchers to precisely tune and control a dense array of qubits. Multiple chips could be connected using optical networking to create a large-scale quantum communication network.

By tuning qubits across 11 frequency channels, this QSoC architecture allows for a new proposed protocol of “entanglement multiplexing” for large-scale quantum computing.

The team spent years perfecting an intricate process for manufacturing two-dimensional arrays of atom-sized qubit microchiplets and transferring thousands of them onto a carefully prepared complementary metal-oxide semiconductor (CMOS) chip. This transfer can be performed in a single step.

“We will need a large number of qubits, and great control over them, to really leverage the power of a quantum system and make it useful. We are proposing a brand new architecture and a fabrication technology that can support the scalability requirements of a hardware system for a quantum computer,” says Linsen Li, an electrical engineering and computer science (EECS) graduate student and lead author of a paper on this architecture.

Li’s co-authors include Ruonan Han, an associate professor in EECS, leader of the Terahertz Integrated Electronics Group, and member of the Research Laboratory of Electronics (RLE); senior author Dirk Englund, professor of EECS, principal investigator of the Quantum Photonics and Artificial Intelligence Group and of RLE; as well as others at MIT, Cornell University, the Delft Institute of Technology, the U.S. Army Research Laboratory, and the MITRE Corporation. The paper appears today in Nature .

Diamond microchiplets

While there are many types of qubits, the researchers chose to use diamond color centers because of their scalability advantages. They previously used such qubits to produce integrated quantum chips with photonic circuitry.

Qubits made from diamond color centers are “artificial atoms” that carry quantum information. Because diamond color centers are solid-state systems, the qubit manufacturing is compatible with modern semiconductor fabrication processes. They are also compact and have relatively long coherence times, which refers to the amount of time a qubit’s state remains stable, due to the clean environment provided by the diamond material.

In addition, diamond color centers have photonic interfaces which allows them to be remotely entangled, or connected, with other qubits that aren’t adjacent to them.

“The conventional assumption in the field is that the inhomogeneity of the diamond color center is a drawback compared to identical quantum memory like ions and neutral atoms. However, we turn this challenge into an advantage by embracing the diversity of the artificial atoms: Each atom has its own spectral frequency. This allows us to communicate with individual atoms by voltage tuning them into resonance with a laser, much like tuning the dial on a tiny radio,” says Englund.

This is especially difficult because the researchers must achieve this at a large scale to compensate for the qubit inhomogeneity in a large system.

To communicate across qubits, they need to have multiple such “quantum radios” dialed into the same channel. Achieving this condition becomes near-certain when scaling to thousands of qubits. To this end, the researchers surmounted that challenge by integrating a large array of diamond color center qubits onto a CMOS chip which provides the control dials. The chip can be incorporated with built-in digital logic that rapidly and automatically reconfigures the voltages, enabling the qubits to reach full connectivity.

“This compensates for the in-homogenous nature of the system. With the CMOS platform, we can quickly and dynamically tune all the qubit frequencies,” Li explains.

Lock-and-release fabrication

To build this QSoC, the researchers developed a fabrication process to transfer diamond color center “microchiplets” onto a CMOS backplane at a large scale.

They started by fabricating an array of diamond color center microchiplets from a solid block of diamond. They also designed and fabricated nanoscale optical antennas that enable more efficient collection of the photons emitted by these color center qubits in free space.

Then, they designed and mapped out the chip from the semiconductor foundry. Working in the MIT.nano cleanroom, they post-processed a CMOS chip to add microscale sockets that match up with the diamond microchiplet array.

They built an in-house transfer setup in the lab and applied a lock-and-release process to integrate the two layers by locking the diamond microchiplets into the sockets on the CMOS chip. Since the diamond microchiplets are weakly bonded to the diamond surface, when they release the bulk diamond horizontally, the microchiplets stay in the sockets.

“Because we can control the fabrication of both the diamond and the CMOS chip, we can make a complementary pattern. In this way, we can transfer thousands of diamond chiplets into their corresponding sockets all at the same time,” Li says.

The researchers demonstrated a 500-micron by 500-micron area transfer for an array with 1,024 diamond nanoantennas, but they could use larger diamond arrays and a larger CMOS chip to further scale up the system. In fact, they found that with more qubits, tuning the frequencies actually requires less voltage for this architecture.

“In this case, if you have more qubits, our architecture will work even better,” Li says.

The team tested many nanostructures before they determined the ideal microchiplet array for the lock-and-release process. However, making quantum microchiplets is no easy task, and the process took years to perfect.

“We have iterated and developed the recipe to fabricate these diamond nanostructures in MIT cleanroom, but it is a very complicated process. It took 19 steps of nanofabrication to get the diamond quantum microchiplets, and the steps were not straightforward,” he adds.

Alongside their QSoC, the researchers developed an approach to characterize the system and measure its performance on a large scale. To do this, they built a custom cryo-optical metrology setup.

Using this technique, they demonstrated an entire chip with over 4,000 qubits that could be tuned to the same frequency while maintaining their spin and optical properties. They also built a digital twin simulation that connects the experiment with digitized modeling, which helps them understand the root causes of the observed phenomenon and determine how to efficiently implement the architecture.

In the future, the researchers could boost the performance of their system by refining the materials they used to make qubits or developing more precise control processes. They could also apply this architecture to other solid-state quantum systems.

This work was supported by the MITRE Corporation Quantum Moonshot Program, the U.S. National Science Foundation, the U.S. Army Research Office, the Center for Quantum Networks, and the European Union’s Horizon 2020 Research and Innovation Program.

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• Electronics
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