14 With both estimation methods, the vast majority (over 90%) of ODC observations lie below the lower threshold and have a negative financial openness coefficient. For emerging and industrial economies, a much higher fraction of observations lie between the lower and upper thresholds and have a positive financial openness coefficient: about two-fifths for emerging economies and four-fifths for industrial countries (relative to the GMM-based threshold). Thus, the threshold level seems plausible and of practical relevance for developing countries contemplating capital account liberalization. In the remaining discussion, we focus on the lower threshold, which is the relevant one for developing and emerging economies.<sup>14</sup> Since the threshold we have derived is static, it is interesting to see how different groups of countries are doing relative to this threshold over time.<sup>15</sup> In 1975-79, the proportion of countries in each group above the GMM-based lower threshold (private credit to GDP ratio of 0.50) was as follows: industrial countries—62 percent; emerging markets—25 percent; and ODCs—2 percent. By 2000-04, the proportions had increased to 100 percent, 48 percent and 14 percent, respectively. Figure 3 shows how the credit to GDP ratio has changed for each of the emerging market countries from 1985-89 to 2000-04, and how these levels match up against the estimated FE and GMM thresholds. For most of the emerging markets, the data points lie above the 45-degree line, implying increases in financial depth over time by this measure. The fraction of emerging markets above the GMM threshold rises from 25% in 1975-79 to 48% in 2000-04, while the number above the FE threshold goes from 0% to 38%. It is worth noting that a country like China comes out looking very good by this measure despite the weaknesses in its financial sector, which is dominated by state-owned banks. This is a useful reminder of the potential pitfalls of using a particular uni-dimensional measure of financial development. And of course the worldwide crisis that first hit the U.S. and then spread to other industrial countries has shown that financial depth is not equivalent to financial stability.

# _V.2.2 Robustness of financial depth threshold_

We test the sensitivity of our baseline results for the financial depth threshold in a number of ways. First, we use a different set of basic controls and redo the regressions in Table 2. We retain log initial income and the education variable, and add the following controls— trade openness, CPI inflation, and the logarithm of the number of phone lines per capita (a proxy for the level of infrastructure). We do not present the results here, but they were quite similar in terms of the signs and magnitudes of the coefficients of interest. The implied upper and lower thresholds from the FE specification with quadratic interactions are private credit to GDP ratios of 63 percent and 148 percent, respectively (compared to 71 percent and 137 percent based on the results in Table 2). For the GMM specification the results are such that, while the estimated overall financial openness coefficient retains an inverted U- shape, it remains positive and does not cut the x-axis.

> 14 The upper threshold is an artifact of the quadratic specification. We experimented with the inclusion of higher order polynomials of the threshold variable (and corresponding interactions with financial openness). The coefficients on the higher order terms were usually not statistically significant but their magnitudes generally showed a flattening out of (rather than a decline in) the implied marginal effect of financial openness on growth at high levels of the threshold variable. This is another reason why we focus on the lower threshold. 15 An important issue here is whether the thresholds themselves change over time. This is not an easy question to address in an empirical framework that uses cross-country data and, therefore, comes up against obvious data limitations. We leave this for future work and note that our exercise here is meant only to be illustrative of the empirical content of the thresholds concept.