Instrumental Variables and Long-Run Economic Growth

Transcription

1 Instrumental Variables and Long-Run Economic Growth Gregory Casey Marc Klemp October 29, 2015 Abstract In the long-run growth literature, it is common to use historical or geographic instruments for contemporary endogenous regressors in instrumental variables (IV) regressions. We study the interpretation of these IV regressions in a simple, but general, framework that is consistent with the existing literature. We are interested in estimating the long-run effect of changing historical conditions. We develop an augmented estimator that accounts for persistence in the endogenous regressor in order to estimate this parameter of interest. We then apply our results to estimate the long-run effect of institutions on economic performance. Using several common measures of institutions, as well as a range of empirical strategies, we document a surprisingly small degree of persistence in institutional quality, implying that IV regressions overestimate long-run causal effects. In our preferred specification, we find that increasing institutional quality as measured by the standard constraints on the executive index in 1700 from the lowest to highest possible value of institutional quality increases 1990 income per capita by 1.2 standard deviations. Keywords Long-Run Economic Growth, IV, Institutions JEL Classification Codes C10, C30, O10, O40 We wish to thank Mette Ajrnæs, Kenneth Chay, Carl-Johan Dalgaard, Diego Focanti, Oded Galor, Philipp Ketz, Daniel le Maire, Stelios Michalopoulos, Ömer Özak, Sanjay Singh, Tim Squires, David Weil and participants at the Brown University Macro Lunch and University of Copenhagen Economic Growth Mini Workshop for valuable comments. The research of Klemp is funded by the Carlsberg Foundation and by the Danish Research Council reference no and reference no Gregory Casey (Gregory Casey@brown.edu): Department of Economics, Brown University, 64 Waterman St., Providence, RI 02912, USA. Marc Klemp (marc klemp@brown.edu): Department of Economics and Population Studies and Training Center, Brown University, 64 Waterman St., Providence, RI 02912, USA, and Department of Economics, University of Copenhagen, Øster Farimagsgade 5, building 26, DK-1353 Copenhagen K, Denmark.

2 1 Introduction A growing literature examines the determinants of economic development in the long-run. 1 In this literature, it is common to use historical or geographic instruments for contemporary endogenous regressors in instrumental variables (IV) regressions (e.g., Frankel and Romer, 1999; Acemoglu et al., 2001; Easterly, 2007). 2 In this paper, we study the interpretation of these IV regressions, develop a new estimator to estimate long-run causal effects, and apply our findings to generate updated estimates of the long-run impact of improving institutional quality. Despite the prominence of IV with historical instruments and contemporary endogenous regressors, specific interpretations are rarely attached to coefficient estimates. We provide a simple, but general, framework for interpreting these regressions that is consistent with existing literature. The regression coefficient is the long-run effect of the endogenous variable divided by the degree of persistence. So, a large regression coefficient can indicate either large long-run causal effects or low persistence. We define persistence as the causal effect of past values of the endogenous variable on present value. In other words, persistence measures the degree to which past improvements in the endogenous variable matter for today s level of the variable. Without knowing the degree of persistence, we cannot learn about the long-run causal effect of the endogenous variable. In some applications, including our investigation of institutions, this parameter is relevant to theory independently of its role in regression bias. We also argue that, under realistic conditions, the regression coefficient does not estimate the contemporary causal effect of the endogenous variable. If data on the endogenous variable was available at the time when the instrument first had an effect, we could simply use standard IV techniques to estimate the long-run causal effect. In most cases, however, such data does not exist. Using the intuition from our theoretical results, we develop an augmented estimator that estimates the long-run effect of the endogenous variable under common constraints of data availability. In particular, the new estimator corrects the bias of the conventional IV analysis by accounting for the degree of persistence in the endogenous variable. Our updated estimator uses multiple-equation GMM setting with a single instrument. One equation estimates the usual regression, while the other directly estimates the degree of persistence using observations of the endogenous variable at two intermediate points in time. Together, these equations allow us to extract an estimate of the long-run causal effect. We use our new results to generate updated estimates of the long-run impact of institutions on economic performance. We choose this application for several reasons. First, the work by Acemoglu et al. (2001) is likely the most prominent paper using this technique, and many important papers in the institutions literature followed suit (e.g., Easterly and Levine, 2003; Rodrik et al., 2004; Acemoglu et al., 2011). Moreover, unlike most papers using this empirical technique, Acemoglu et al. (2001) provide an explicit framework for interpreting their results and a discussion about 1 For an overview of the literature, see Spolaore and Wacziarg (2013) andnunn (2014). 2 This technique is still popular in many literatures, including: trade (Galor and Mountford, 2008; Giovanni and Levchenko, 2009; Do and Levchenko, 2007; Do et al., 2014); international migration (Andersen and Dalgaard, 2011; Alesina et al., 2013); institutions (Acemoglu et al., 2011, 2014; Naritomi et al., 2012; Auer, 2013); and culture (Tabellini, 2010; Gorodnichenko and Roland, 2011, 2013). 1

3 the role of past values of institutions; by combining the two, we arrive at our simple framework, making our new results immediately applicable to this example. Finally, given the prominence of the institutions literature, much effort has gone into collecting measures of institutional quality at different points in time. This data is essential in both steps of our empirical application. To complement our new estimator, we start by estimating the degree of institutional persistence in commonly used datasets, which allows us to utilize much more data and measure the degree of persistence with greater accuracy. Our analytic results demonstrate how to to combine these estimates of persistence with the existing results to calculate the long-run impact of improving institutions. Panel data suggests that improving institutions in 1850 from the worst observed score to the best observed score increases current institutional quality by less than 1% of a standard deviation, indicating that large IV regression coefficients may be caused by low institutional persistence rather than a high impact of institutions on economic growth. We then apply our new estimator to measure the long-run impact of institutions on economic performance. In our preferred specification, changing institutions in 1700 from the lowest possible score on the standard constraints to the executive measure (1) to the highest possible score (7) leads to a 1.2 standard deviation change in 1990 income per capita. This effect is less than half as large as the coefficient generated by the standard IV regression. Our results have important implications for the field of long-run economic growth. First, we provide an interpretation for IV regressions with historical instruments and contemporary endogenous regressors. We then provide an estimation procedure that enables researchers to estimate the long-run effect of various determinants of economic performance. We then measure the persistence of institutions. Finally, using our new analytic results and empirical technique, we generate updated estimates of the impact of institutions on long-run economic growth (see, e.g., Acemoglu et al., 2005; Banerjee and Iyer, 2005; Dell, 2010; Bruhn and Gallego, 2012). While our approach is applied to institutions, it is relevant for any historical estimates using IV with contemporary endogenous regressors. In Section 2, we present our framework and main analytic results. Section 3 measures the degree of persistence in commonly used measures of institutional quality. Section 4 applies our new results to directly estimate the long-run causal effect of improving historical institutions. Section 5 concludes. 2 Analytic Results 2.1 Interpreting IV regressions in the long-run growth literature In this section, we provide a general framework for interpreting instrumental variable regressions when the instrument precedes the endogenous regressor in time. To help fix ideas, we will focus on the example of institutions and economic growth, which will also be the subject of our empirical section. The framework is not specific to institutions and is relevant for any regression of this sort. 2

4 Equations (1) (4) present a very simple model of institutions and income where X t is institutions at time t, Y t is income, Z an exogenous determinant of historical institutions, and A is a variable, such as capital accumulation or technology, that is affected by past institutions and exerts a direct effect on contemporary income. We consider two periods, 0 for historical and 1 for contemporary. This is a simple generalization of the data generating process presented in Acemoglu et al. (2001). In particular, we add the existence of the A variable, which is consistent with the empirical findings and interpretation presented in their paper. 3 The basic framework is given by: X 0 = δ 0,0 + ψz + ε X,0 (1) X 1 = δ 0,1 + δ 1 X 0 + ε X,1 (2) A 1 = γ 0 + γ 1 X 0 + ε A,1 (3) Y 1 = β 0 + β 1 X 1 + β 2 A 1 + ε Y,1. (4) The contemporaneous relationship between institutions and income is given by Y 1 X 1 = β 1. The long-run effect of historical institutions on contemporary income per capita is η Y 1 X 0. The other key parameter in this set-up is δ 1, which measures the impact of a shock to historical institutions on contemporary institutions. If δ 1 > 1, then institutional quality diverges over time in response to a shock. If δ 1 < 1, then institutional quality converges over time, and shocks eventually die out. We refer to δ 1 as a a measure of persistence. Figure 1 provides a simple representation of this system. The existence of the A variable is a violation of the exclusion restriction in the classic case where the goal is to estimate β 1. At first, this appear to be a negative result, but we argue that η is the inherent parameter of interest in this setting: consider, the case in which current income depends only current institutions while past institutions have no (direct or indirect) effect on current institutions (i.e., institutions have no persistence). Trivially, improving historical institutions has no long-run impact on development in this setting even if β 1 is large. Thus, we learn nothing about long-run development from the regression. As we show below, we can still estimate this more inherently interesting parameter despite the existence of the A variable. Some algebra shows that η = (β 1 δ 1 + β 2 γ 1 ). The simple 2SLS regression of Y 1 on X 1 with Z as an instrument yields: plim ˆβ IV 1 = β 1 + β 2γ 1 δ 1 = η δ 1. (5) 3 In particular, Acemoglu et al. (2001) find that historical institutions exert an impact on contemporary income independently of contemporary institutions. Their interpretation of these results is in line with our equations: In some specifications, the overidentification tests using measures of early institutions reject at that 10-percent level (but not at the 5-percent level). There are in fact good reasons to expect institutions circa 1900 to have a direct effect on income today (and hence the overidentifying tests to reject our restrictions): these institutions should affect physical and human capital investments at the beginning of the century, and have some effect on current income levels through this channel ( fn 31, p. 1393). 3

5 First stage Z X 0 X 1 Y 1 A 1 Figure 1: Causal diagram of equations (1) (4) and the first stage in a conventional 2SLS regression. Rectangular nodes represent observed variables and circular nodes represent unobserved variables. The dotted line represent the first stage in a conventional 2SLS estimation. Thus, the resulting coefficient is consistent for the parameter of interest divided by the institutional persistence term, δ 1. This has an intuitive interpretation in that a one unit change in X 1 is associated with a 1 δ 1 unit change in X 0. The 2SLS coefficient overestimates η when institutional quality converges over time, i.e. δ 1 < 1, and underestimates the effect when institutional quality diverges over time, i.e. δ 1 > 1. The two are equal only in the knife-edge case where δ 1 = 1. We refer to this condition as institutions being perfectly persistent. In light of these results, it is apparent that a large 2SLS coefficient does not imply a large long-run effect of institutions on economic performance. The regression measures the long-term impact of improving historical institutions enough to raise contemporary institutions by one unit. Thus, a large regressions coefficient may indicate an important impact of institutions on economic performance or that the regression is picking up a very large change in past institutions. To understand the long-run impact of institutions, we need to know how large of a change in institutions is reflected in the regression coefficient. The algebra also indicates that, in the presence of an A variable, it is not possible to recover the contemporaneous relationship between institutions and income per capita, β 1. These results suggest that we could recover η by multiplying the IV coefficient by δ 1 or by including X 0, rather than X 1, in the regression. In most applications, including that of Acemoglu et al. (2001), we do not observe X 0. Thus, we need to combine the cross-sectional regression with an estimate of δ 1. In the next subsection, we demonstrate how to use GMM to combine cross-sectional income regressions with measures of institutional persistence in order to estimate η. 4 4 Appendix section A.1 provides results without the A variable. This is a special case of the framework we provide. IV In this case, the relationship between the regression coefficient and η is identical in that η = plim ˆβ 1 δ 1. Similarly, IV γ 1 = 0 plim ˆβ 1 = β 1. Thus, the IV regression accurately estimates Y 1 X 1. 4

6 2.2 Estimating η In this section, we demonstrate how to estimate η when X 0 is not observed. This is often the case when using historical or geographic instruments. In order to estimate δ 1 without X 0, we make use of institutions measured at intermediate points in time. Thus, our framework here extends that of the previous section by allowing for more than two time periods. Let X t be institutions at time t, Y t be income at time t, and Z be an exogenous shock to institutions at time H that differs across countries. Once again, A captures other channels through which past institutions affect current income per capita. Let C be the point at which we measure income per capita, S be the point where institutions are first measured, and T a second time institutions are measured. Finally, Q = T S. In our application, the length of a period t is 1 year. X t = δ 0,t + δ 1 X t 1 + ɛ X,t, t = 1... C, t H (6) X H = δ 0,H + δ 1 X H 1 + ψz + ɛ X,H (7) A C = γ 0 + γ 1 X H + ɛ A, (8) Y C = β 0 + β 1 X C + β 2 A C + ɛ Y. (9) Institutions follow a simple law of motion given by (6). Then, in some year H, institutions are shocked by Z. In our particular example, they are shocked by the arrival of Europeans, which interacts with the disease environment to affect settler mortality and historical institutions. After the shock, institutions continue to follow the original law of motion. In addition to affecting contemporary (time C) institutions, historical institutions also affect contemporary income per capita via (human or physical) capital accumulation, trade, technology, culture, etc. We model this effect in a simple reduced-form manner by specifying a variable A C, which describes the relationship between institutions in year H and contemporary income per capita. Our key assumption is that δ 1 is constant over time. This allows us to infer the relationship between historical and contemporary institutions even when we can only observe institutions at intermediate points in time. 5 We start by solving for the relationship between values of X T and X T Q. This will be important because we will use the relationship between X T and X T Q to estimate the degree of institutional persistence. To do so, we simply apply (6) recursively: X T = δ 0,T + δ 1 X T 1 + ɛ X,T (10) = (Q 1 k=0 δ1δ k ) 0,T k + δ Q 1 X T Q + (Q 1 δ1ɛ k ) X,T k. (11) k=0 5 This results can be generalized to any known functional form for the evolution of δ 1. Based on our results presented in section 3, we believe that a constant δ 1 is consistent with available data. 5

7 Now consider the IV regression: X T,i = a 0 + a 1 X T Q,i + a 2,i (12) where i denotes a country and Z i is an instrument for X T Q,i. There is no violation of the exclusion restriction in this case and, according to (11), the estimation yields: plim â 1 = δ Q 1. (13) Now we turn to the relationship between income on institutional quality. A little algebra yields: Y C = β 0 + (β 1 δ C H 1 + β 2 γ 1 )X H + ɛ, (14) where β 0 = ( β 0,C + β C H 1 1 k=0 δ1 kδ ) 0,T k + β2 γ 0 and ɛ = ( β Q 1 1 it is immediate that η H Y C X H k=0 δk 1 ɛ ) X,T k + ɛ Y,C + β2 ɛ A. Now, = (β 1 δ1 C H + β 2 γ 1 ). Now Consider the standard IV regression: Y C = b 0 + b 1 X C,i + b 2,i. (15) where i denotes a country and Z i is an instrument for X C. Similar to our results from section 2, this regression yields: and plim ˆb 1 = β 1δ C H 1 + β 2 γ 1 δ C H 1 = η H δ C H 1. (16) To solve for η H, we simply combine the results from estimating equations (12) and (15) : â 1 = δ Q 1 (17) 1 Q δ 1 = â1 (18) η H ˆb1 = δ1 C H (19) η H = ˆb 1 δ1 C H (20) C H Q = ˆb 1 â1. (21) Our new estimator is given by equation (21). To construct confidence intervals around our estimates of η H, we estimate equations (12) and (15) jointly via GMM and apply the delta method to generate point estimates and standard errors for the nonlinear transformation yielding the expression for η H in equation (21). 6

8 3 Application Part 1: Measuring institutional persistence To begin our empirical application, we use a variety of data sources and methods to estimate the persistence of institutions in panel data. When compared to the cross-sectional application of our augmented estimator, the approach uses significantly more data, allowing us to measure persistence with far greater precision. Our analytic results from section 2 demonstrate that this parameter dictates how to update standard IV regressions to estimate the long-run impact of improving institutions. We document a surprisingly low degree of persistence in our measures of institutions, suggesting that long-run causal effect of institutions on economic development is small. Independently of our results in section 2, the degree of institutional persistence has important important implications for the theory of divergent paths of development (Acemoglu et al., 2005, 2008). In section 4, we will continue our application by applying our new estimator to the institutions literature. In that case we find a non-negligible, but still moderate, effect of institutions on income per capita. The difference occurs because the IV regression yield a higher, but much less precise, estimate of institutional persistence. 3.1 Data Our first main measure of institutional quality, Constraints on the Executive, comes from the Polity IV dataset, which is standard in the literature. Constraints on the Executive measures the limits to executive power and is measured on a 7 point scale that increases in the level of constraints. This is the preferred measure of institutional quality identified in the IV literature (Glaeser et al., 2004; Acemoglu et al., 2005). In the appendix, we also use the Democracy and Autocracy measures. Democracy captures constraints on the executive and the ability of citizens to express preferences about leaders. It is measured on an 11 point scale. Autocracy captures constraints on the executive and several measures of openness of political participation. It is also measured on an 11 point scale. A major advantage of this dataset is the length of the time series. In particular, for a set of 25 countries, we have institutional data from The cross section increases to 125 countries in later years. For a smaller set of XX countries, we even have data from Our second major measure of institutional quality is the Political Rights Index (PRI) from Freedom House. The original data is available from It is also measured on a 1-7 scale. Ranging from a score of 1 (very high political rights) to 7 (few or no political rights). We use the augmented data from Acemoglu et al. (2008), which adds data for 1960 and 1965 and normalizes the data to a [0, 1] scale. The scale is increasing in institutional quality. Our last major measure of institutional quality is the Vanhanen Index of Democratization, which measures democracy in independent countries from (Vanhanen, 2000). The Vanhanen index has two key components. The first is the share of non-majority parties in the most recent parliamentary or presidential round of voting. In particular, this competition variable is calculated as 100-(share of voting for the largest party). The second component, the participation variable, 7

9 7 Average over countries Year Figure 2: This figure depicts the average level of Constraint on the Executive plotted against time for countries with available data for the 150-year period.. measures the fraction of the total population that voted in the most recent election. Importantly, this includes children, non-citizens and others without voting rights. The index is the product of these two measures divided by 100. The Vanhanen Index provides a useful complement to the more commonly used measures because it is more continuous and does not suffer from issues of truncation. Any linear regression using Polity IV or Freedom House measures implicitly assumes that the difference between a 2 and a 3 in an index is the same as a difference between a 3 and a 4. Since the Vanhanen Index is not categorical, this is not an issue. Moreover, no country allows children or non-citizens to vote, and no country has an infinitesimally small ruling party. So, the measure is only truncated from below. Figures 2 4 provides the means for each of these variables over time. 6 The sample is restricted to the countries with data over the entire period. For all of the variables, the mean remains relatively constant until the wave of democratization starting in Note that this change in mean institutional quality does not imply that the degree of institutional persistence changed in 1965, since the change in institutions could be driven by factors common to all countries. Throughout our analysis, we show that our results hold before 1965 and are robust to allowing the degree of institutional persistence to shift in Regression Specification To measure the persistence of institutions, we employ the time-series of analog of equation (2): 6 Figures A.7 A.9 in the appendix depicts the data for the sample of colonized countries only and establish similar patterns of the variables over time. 8

10 .6 Average over countries Year Figure 3: This figure depicts the average level of the Freedom House PRI plotted against time for countries with available data for the 150-year period.. 20 Average over countries Year Figure 4: This figure depicts the average level of the Vanhanen Index plotted against time for countries with available data for the 150-year period.. 9

11 INST c,t = α c + ν t + δ 1 INST c,t 1 + ɛ c,t (22) where INST is a measure of institutional quality, ν t is a time fixed effect, and α c is a country fixedeffect. As demonstrated in Section 2, the relevant measure of institutional persistence is δ 1. This simple specification is consistent with the growing literature that examines the determinants of institutional quality (e.g., Acemoglu et al, 2008, 2009). We use the three main measures of institutions discussed in the previous section. In the appendix, we show that the results are unchanged if we use the components of the Vanhanen Index of Democracy or the Democracy/Autocracy variables from Polity IV. In each specification, we report the p-value of the simple t-test for δ 1 = 1. To properly measure the persistence of institutional quality, we need to correct for two main types of omitted variables. First, we need to control for changes in institutional quality that are common to all countries. We do so by including time fixed-effects. There may also be countryspecific factors that lead to higher institutions in all time periods, but do not affect the persistence in institutions following a shock. To control for omitted variables of this type, we include country fixed-effects. The existing literature has shown the importance of country fixed effects in eliminating spurious correlation (Acemoglu et al., 2008, 2009). We do not include any country-specific time-varying control variables for two reasons. First, we are interested in the persistence of institutions through any intervening channel. For example, if institutions increase income and higher income leads to better institutions in the next period, then we want to capture this effect in our measure of persistence. 7 Of course, not controlling for other factors may create a problem of omitted variables. Omitted variables, however, are likely to affect past and current institutions in the same direction, biasing our estimate of δ 1 upward. Without a more complete theory of institutional persistence, it is not possible to decide a priori which variables are channels of institutional persistence and which are omitted variables. Moreover, as discussed in Section 4.4, the existing literature estimates related panel regressions with control variables and always finds that δ 1 < 1. In our main sample, we use the data in 1, 5, 10, 30, and 100 year intervals and run regressions on the entire unbalanced sample. We take single observations instead of aggregating across years to follow the existing literature (Acemoglu et al., 2008, 2009). In the appendix, we also demonstrate that our results hold in the sample of only former colonies and the sample of the 25 countries for which we have data from We also account for measurement error by applying the Arellano-Bond GMM estimator. This technique also corrects for Nickell bias. Another source of bias may come from the truncation of some of the key measures of institutional quality, namely the Polity IV and Freedom House measures. To demonstrate that truncation is not driving our results, we always present our results with the less commonly used Vanhanen Index of Democracy. While this measure theoretically has an upper bound, it is not achieved within the sample. Benhabib et al. (2011) use this measure specifically to overcome the truncation issue of the more standard measures. 7 This result is shown formally in section A3 of the appendix. 10

12 Another potential concern is that the panel variation in institutional quality does not represent large fundamental shocks that are more likely to be persistent. In Section 4, we estimate institutional persistence using settler mortality as an instrument, which was a quantitatively important shock. Our point estimates in that section have much less statistical power, but also suggest that δ 1 < 1. These results are also not subject to measurement error or Nickell bias. Also, under the data generating process specified for our GMM estimation, the use of instruments will also allow for measures of institutional persistence that account for channels through which institutions persist, but remove bias from omitted variables Main Results Table 1 estimates (22) using yearly data on the entire unbalanced panel. Results are presented with and without year fixed effects. In all cases, the coefficient is significantly less than 1 at the 1% level. The high R-squared values from these regressions suggest that past institutions account for most of the variation in current institutions at the yearly level. The inclusion of year fixed effects has very little effect on the R-squared, but does lower the estimate of δ 1 for all three of our main variables. We also report the results of the Phillips-Perron unit root test which is testing the null hypothesis that a variable is perfectly persistent, i.e., that it has a unit root. This unit root test is robust to general forms of heteroskedasticity in the error term, and does not require a specified lag length for the test regression. Table 2 repeats this analysis at 5 year intervals. The results are qualitatively similar, though year fixed effects matter more in this specification. At 5 year intervals, we are able to present results using the Arellano-Bond difference GMM estimator, using twice lagged levels of the independent variable as the instrument. This procedure corrects for both Nickell bias and measurement error. We find lower estimates for δ 1 in this specification. 9 Tables 3 and 4 extend these results to 10 and 30 year intervals, respectively. These longer time periods should alleviate concerns of measurement error and are more appropriate for capturing the long-run trends in institutional quality that we are interested in measuring. They are, however, more susceptible to Nickell bias. So, we place greater emphasis on the GMM results in this setting. The null hypothesis of δ 1 = 1 is rejected in all specifications at the 5% level and usually at the 1% level. We cannot include the freedom house measure in the 30 year specification because there is insufficient data to include country fixed effects. Finally, table 5 reports results at 100 years. The results are consistent, though we only have data for Constraints on the Executive at this time frame. We now move to quantifying these effects in terms relevant for long-run economic growth. We prefer to focus on the 10-year estimates because they represent a reasonable trade-off between having 8 This result is shown formally in appendix section A.3. 9 Given the length of the panel, Stata could not estimate the GMM estimator for yearly data. In the future, we plan to utilize greater computing resources to estimate GMM for yearly data. 11

13 Table 1: Degree of Persistence of Institutions 1-Year Data Constraint on Executive Freedom House Measure of Democracy Vanhanen Index of Democracy OLS OLS OLS OLS OLS OLS (1) (2) (3) (4) (5) (6) First Lag of Constraint on the Executive (0.005) (0.007) First Lag of Freedom House Measure of Democracy (0.016) (0.016) First Lag of Vanhanen Index of Democratization (0.007) (0.011) Year FE No Yes No Yes No Yes Number of Observations 14,117 14,117 4,245 4,245 12,012 12,012 Number of Countries Adjusted R Signif. of main coeff.=1 test Signif. of unit root test (P-P) This table establishes that the degree of persistence of institutions is below one, accounting for year fixed effects. The estimation is performed with both OLS as well as the GMM estimator by Arellano and Bond (1991) where institutions are instrumented using a double lag. Robust standard errors are shown in the parentheses. *** Significant at the 1 percent level. ** Significant at the 5 percent level. * Significant at the 10 percent level. Table 2: Degree of Persistence of Institutions 5-Year Data Constraint on Executive Freedom House Measure of Democracy Vanhanen Index of Democracy OLS OLS GMM OLS OLS GMM OLS OLS GMM (1) (2) (3) (4) (5) (6) (7) (8) (9) First Lag of Constraint on the Executive (0.027) (0.033) (0.044) First Lag of Freedom House Measure of Democracy (0.049) (0.052) (0.107) First Lag of Vanhanen Index of Democratization (0.024) (0.036) (0.045) Year FE No Yes Yes No Yes Yes No Yes Yes Number of Observations 2,625 2,625 2, ,324 2,324 2,145 Number of Countries Adjusted R Signif. of main coeff.=1 test Signif. of unit root test (P-P) This table establishes that the degree of persistence of institutions is below one, accounting for year fixed effects. The estimation is performed with both OLS as well as the GMM estimator by Arellano and Bond (1991) where institutions are instrumented using a double lag. Robust standard errors are shown in the parentheses. *** Significant at the 1 percent level. ** Significant at the 5 percent level. * Significant at the 10 percent level. 12

14 Table 3: Degree of Persistence of Institutions 10-Year Data Constraint on Executive Freedom House Measure of Democracy Vanhanen Index of Democracy OLS OLS GMM OLS OLS GMM OLS OLS GMM (1) (2) (3) (4) (5) (6) (7) (8) (9) First Lag of Constraint on the Executive (0.048) (0.052) (0.070) First Lag of Freedom House Measure of Democracy (0.088) (0.088) (0.201) First Lag of Vanhanen Index of Democratization (0.038) (0.056) (0.107) Year FE No Yes Yes No Yes Yes No Yes Yes Number of Observations 1,258 1,258 1, ,113 1, Number of Countries Adjusted R Signif. of main coeff.=1 test Signif. of unit root test (P-P) This table establishes that the degree of persistence of institutions is below one, accounting for year fixed effects. The estimation is performed with both OLS as well as the GMM estimator by Arellano and Bond (1991) where institutions are instrumented using a double lag. Robust standard errors are shown in the parentheses. *** Significant at the 1 percent level. ** Significant at the 5 percent level. * Significant at the 10 percent level. Table 4: Degree of Persistence of Institutions 30-Year Data Constraint on Executive Vanhanen Index of Democracy OLS OLS GMM OLS OLS GMM (1) (2) (3) (4) (5) (6) First Lag of Constraint on the Executive (0.077) (0.072) (0.162) First Lag of Vanhanen Index of Democratization (0.089) (0.109) (0.223) Year FE No Yes Yes No Yes Yes Number of Observations Number of Countries Adjusted R Signif. of main coeff.=1 test Signif. of unit root test (P-P) This table establishes that the degree of persistence of institutions is below one, accounting for year fixed effects. The estimation is performed with both OLS as well as the GMM estimator by Arellano and Bond (1991) where institutions are instrumented using a double lag. Robust standard errors are shown in the parentheses. *** Significant at the 1 percent level. ** Significant at the 5 percent level. * Significant at the 10 percent level. 13

15 Table 5: Degree of Persistence of Institutions 100-Year Data Constraint on Executive (1) (2) (3) OLS OLS GMM First Lag of Constraint on the Executive (AJR 2005) (0.144) (0.142) (0.304) Year FE No Yes Yes Number of Observations Number of Countries Adjusted R Signif. of unit root test 1 Signif. of main coeff.=1 test more observations per country and still capturing long-run trends. 10 It is easiest to interpret the Vanhanen index because it does not have an upper bound. In 1850, the range in the Vanhanen index was With our estimates of δ 1, we can calculate the long run impact on current institutions of positive shock that improved a country s 1850 institutions from 0 to 7.38 on the Vanhanen scale. Let j denote the country without the shock and j denote the country with the shock. We take 2000 as current data because that is the most recent year available in the Vanhanen dataset. Using the results from column (8) which include year fixed effects, but are more conservative that the GMM estimates we get: INST j,2000 INST j,2000 = = =.001. (23) Thus, this shock only raises institutions by.001 on the Vanhanen scale in the long run. comparison, the standard deviation in the Vanhanen scale for 2000 is We can perform the same analysis for constraints on the executive. The maximum difference in this measure is 6. Using the same logic and the results from column 2, we get: INST j,2013 INST j,2013 = = = 1.53x10 5. (24) The standard deviation for constraints on the executive in 2013 is Thus, the data suggest that improving institutions in 1850 has a very small effect on institutions today. In our GMM application, we will focus on the sub-sample of former colonies in order to use settler mortality as an instrument for institutional quality. Thus, tables A.1-A.4 in the appendix present results for this subsample. The results are qualitatively unchanged. In every case, the null For 10 Since many colonies did not become independent until the 1960s, they do not have multiple observations in the 30-year specification. 14

16 hypothesis of δ 1 = 1 is rejected in all specifications at the 5% level, and it is almost always rejected at the 1% level. Tables A.5-A.8 in the appendix presents our results using the balanced panel from We only have data on 25 countries in this setting. In almost all specifications across these four tables, the null hypothesis is rejected at the 1% level. Two exceptions occur when using the Vanhanen data aggregated to 30 year intervals (table A.8). Without year fixed the p-value from the test is.33, though the coefficient is.782. When adding fixed effects, the p-value drops to When using GMM, which is more important in the 30 year specification, the null is rejected at 1% and the point estimate is actually negative. For further robustness, we repeat all our results with the democracy and autocracy measures from Polity IV and the components of the Vanhanen Index. Figures A.13-A.16 present these results for yearly data. The null of δ 1 = 1 is rejected at the 1% level in all specifications. We find the same qualitative results for longer time periods. 3.4 Does the level of Persistence Change over Time? In Section 5, we combine an estimate of institutional persistence with an IV regression of contemporary income on institutional quality to extract an estimate of the historical effect of institutions. A key assumption in this analysis is that institutional persistence is constant over time. In this section, we explore whether this is true in the data. We use two different approaches. First, we include an interaction term to account for the wave of democratization starting in Figures 1 and 3 shows a wave of democratization starting in It is possible that this wave could include a change in the degree of institutional persistence. The results are presented in tables A.9-A.12. The results strongly suggest that institutions become less persistent after 1965 when using constraints on the executive. The evidence is less clear for the Vanhanen index, but generally points in this direction. Importantly, we can reject the null that δ 1 = 1 in the pre-1965 specification at the 1% level in almost every specification across the four tables. The exceptions occur when using the Vanhanen index and 30 year data (Table A.12). Without year fixed effect, the pre-1960 persistence term is above one, but not significantly so. Once including fixed effects, the coefficient drop to.818, but is not significantly difference from 1 at conventional levels. When using GMM to account for nickel bias, the coefficient falls further to.467, and we can reject the null at the 10% level. In every specification, we find that institutions become less persistent after this wave of democratization. To be conservative, we will use estimates of institutional persistence before 1965 in our preferred specifications in Section 5. We can repeat our counterfactual experiment from above to test how the shift in 1965 affects the magnitude of improving historical institutions. For the Vanhanen Index results in column 5 of table A.11, we have: INST j,2000 INST j,2000 = ( ) = =.002. (25) 15

17 While the results is somewhat larger than in the previous section, the effect of historical institutions is still moderate in the data. For constraints on the executive, the related result is: INST j,2000 INST j,2000 = ( ) = = 3.41x10 5. Again, the effect is larger than in the previous section, but still very small compared to the standard deviation. We also examine whether institutional persistence in constant over time by running rolling regressions (Figures 5 and 6) for the two of the main dependent variables of interest that are available for more than 50 years, (i.e., Constraint on the Executive and the Vanhanen Index of Democracy). We run the 10-year regressions on 50-year rolling sample windows. 11 (26) In particular, we run a regression starting in each year between 1850 and 1963 and plot the estimate and its 95 percent confidence interval against the initial year of the rolling window. The coefficient on lagged institutions appears relatively stable in each case. Moreover, the 95% confidence interval almost always excludes 1, confirming the robustness of the finding that the degree of persistence of these measures of institutions is below Comparison with Previous Literature Though our results show surprisingly little institutional persistence, they are consistent with the existing literature. As described above, we do not include any control variables because we want to capture the full degree of persistence in institutions. A growing literature, however, looks at the determinants of institutions, mostly focusing on whether increase in income can lead to more democracy (the Modernization Hypothesis ). While it is not the goal of these papers to measure institutional persistence, the lag of institutions is always included as a control. In every case we have found in the literature, the coefficient is significantly less than one (Acemoglu et al., 2008, 2009; Benhabib et al., 2011; Heid et al., 2012; Cervellati et al., 2014). 4 Application Part 2: Estimating the long-run effect of institutions In this section, we apply our new estimator from section 2.2 to measure the long-run effect of institutions on economic development. To do so, we simultaneously estimate two equations via GMM. First, we estimate the cross-sectional relationship between contemporary institutions and contemporary income per capita via equation (12). Second, we estimate the persistence of institutions via equation (15). Then, we combine the results of these equations to extract the long-run effect of improving institutions using equation (21). 11 Additional figures for the alternative measures of institutions, i.e., democracy, autocracy, and the Vanhanen index of political competition, can be found in the appendix figures A.4-A.6. 16

18 1 Coefficient Estimate Initial year of the rolling window Figure 5: This figure depicts the coefficient from panel regressions of Constraint on the Executive on its 10-year lagged value in over period with a 50-year regression window and a step size of 1 years, estimated with OLS. The regressions account for year fixed effects. Robust standard errors are used for the calculation of the confidence band. 17

19 1 Coefficient Estimate Initial year of the rolling window Figure 6: This figure depicts the coefficient from panel regressions of the Vanhanen Index of Democracy on its 10-year lagged value in over period with a 50-year regression window and a step size of 1 years, estimated with OLS. The regressions account for year fixed effects. Robust standard errors are used for the calculation of the confidence band. 18

20 Both equations are estimated using settler mortality as an instrument, following Acemoglu et al. (2001). Since these are cross-sectional estimates, we cannot include country fixed-effects. As a result, we may have a violation of the exclusion restriction if settler mortality is correlated with other country-specific factors such as the disease environment or geography. To mitigate these concerns, we include controls for the log of the absolute value of latitude and World Bank region fixed effects. Several studies have suggested that settler mortality is correlated with other contemporary variables, such as education or trade (e.g., Dollar and Kraay, 2003; Glaeser et al., 2004). For our results to be valid, we need only assume that settler mortality affected these other variables through historical institutions. Using the notation from Section 2, education or trade could serve as the A variable in our framework. Importantly, this procedure also provides another estimate of the level of persistence in institutions. Unlike the earlier panel methods, these new results follow from a large exogenous shock to institutional quality (the differential institutions set up by European colonizers). This mitigates our prior concern that low persistence in the panel was due to the fact that we were not observing major changes in institutions. The use of instrumental variables also allows us to correct for issues of measurement error and omitted variables. The trade-off is that we have many fewer observations, which severely limits our statistical power, and we cannot control for all geographic covariates via fixed effects. In Section A.3 of the appendix, we demonstrate how using IV allows us to separate channels through which institutions might persist from omitted variables that are correlated with both past and future institutions. In Section A.2 of the appendix, we also discuss the degree to which historical IV s correct for reverse causality. 4.1 Data As the measure of institutions, we use Constraint on the Executive from the Polity IV dataset discussed earlier. This measure is used in Acemoglu et al. (2001) and both the authors and critics have agreed that this is the preferred measure of institutions when compared to other measures used in the literature (Glaeser et al., 2004; Acemoglu and Johnson, 2005). We use institutions in 1990 as our contemporary measure, again following Acemoglu et al. (2001). We also use institutions in 1900 and 1960 to measure persistence. 12 Following recommendations by Albouy (2012) and Acemoglu et al. (2012), we use the log of potential settler mortality capped at values of potential settler mortality of 250 per 1000 as the instrument. 13 Unfortunately, it is not clear exactly when settler mortality should first affect institutions. We use Since these are cross-sectional estimates, we cannot include country fixed-effects. As a result, we may have a violation of the exclusion restriction if Settler Mortality is 12 Our panel data results suggest that settler mortality should have less and less predictive power for institutions as we move forward in time. Consistent with this intuition, we find that settler mortality is a weak instrument for institutions in Thus, we restrict our attention to the impact of historical institutions on the log of income per capita in The uncapped settler mortality variable is obtained directly from AJR (2001). 19

21 Table 6: Summary Statistics Average P25 P50 P75 S.D. Log GDP per capita in 1990s Constraint on Executive in 1990s Constraint on Executive in 1960s Constraint on Executive in Log Capped European Settler Mortality Log Absolute Latitude Observations 56 correlated with other country-specific factors such as disease environment of geography. To mitigate these concerns we include controls for the log of the absolute value of latitude and World Bank region fixed effects. 14 The measure of economic development is the natural logarithm of the gross domestic product per capita in 1990, again from Acemoglu et al. (2001). Summary statistics are provided in table Estimation Results Columns 1, 4, and 7 present results from estimating equation (15). For each of these income regressions, we provide two separate methods of estimating δ 1. In columns 2, 5, and 8, we use the persistence of institutions between 1900 and 1960 estimated via equation (12). In the remaining columns, we use the persistence of institutions between 1900 and According to our results from Section 3.3, the results using 1960 should be more conservative, which is consistent with what we observe here. Panel 1 presents the regression results. Panel 2 presents the implied estimates of η assuming that settler mortality first affects institutions in In also presents several tests of the null hypothesis that δ 1 < 1. Columns 1-3 present results without using any controls. The first stage F-statistics indicate that we have strong instruments in all regressions. The point estimates in column 2 and 3 once again indicate that δ 1 < 1, though we do not have enough statistical power to reject this null hypothesis of δ 1 = 1 at statistically significant levels. Given that this result is consistent with panel data, where we have considerably more power, we take this as further evidence for our earlier findings. The point estimates here indicate a higher degree of persistence than those found in section The latitude variable is the latitude of a country s approximate geodesic centroid obtained from CIA s World Factbook. The regional dummies indicate the Sub-Saharan Africa, Middle East & North Africa, South Asia, East Asia and Pacific, and the North America regions, as defined by the World Bank. There are no observations from the Europe & Central Asia region and the Latin America & Caribbean region is the background region. 15 Given the small number of observations and low statistical power, it is possible to construct specifications with δ 1 > 1, especially when including many covariates. In parsimonious specifications and those including World Bank 20