Institutions and economic development: new measurements and evidence

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, maximizeunder 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).⁷

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)].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 thatwhere \(s_k\) 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: \(\ln (A)_{it}=f(z_{it})+\epsilon _{it}\).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.ewhere \({Y_0}/{L_0}\) 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 \(\zeta _4\equiv -(1-e^{-\lambda t})\).

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 equationThe model above reduces to (3) where the augmented Solow model is year and cluster (\(c_i\)) specific, with \(f(z_{it}) = (\eta _1 z_{it} + \eta _2 z_{it}^2 + \eta _3 c_i + \eta _4 z_{it}c_i + \eta _5 z_{it}^2c_i)/\psi _1\).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, aswhere 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 intogether 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 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.¹⁴

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.

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.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.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.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”.²⁰

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.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.

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.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.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.

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.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).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.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.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.