Country # Bond $Tot Amount (billion)
United States 23 12,946
Thailand 15 0,909
Norway 11 0,653
China (Mainland) 10 1,412
France 7 0,824
Japan 5 0,402
New Zealand 5 0,500
Sweden 4 1,025
India 2 1,000
Spain 2 0,390
United Kingdom 2 0,840
Bermuda 2 1,580
Switzerland 2 0,365
Netherlands 2 0,961
Belgium 1 0,721
Singapore 1 0,200
Portugal 1 0,061
Argentina 1 0,035
Latvia 1 0,030
Italy 1 0,001
Total 98 24,857
Table (7.3) Energy green bond issuer by country of incorporation
This table reports the annual average amount issued (in $B) as well as the number of energy green bond by country issued on an annual basis from 2012 until 2020.
Copenhagen Business School Master Thesis 15 Sept 2021
Vanilla bonds Green bonds
All 1217 98
Matched 91 91
Unmatched 1126 7
Table (7.4) Overview on the matching performance
is critical to report on the matching balance to demonstrate that the resulting estimate is approximately unbiased and relies little on extrapolation or correct outcome model spec-ification. To make sure the reader remembers the matchit object obtained by means of matching, a brief summary of the objective follows:
- method: 1:1 genetic matching without replacement - distance: Mahalanobis
- number of obs.: 1464 (original), 182 (matched) - target estimand: ATT
- covariates: maturity, coupon, issue.date, log.amount.issued.(usd), ticker.
As you can read, the matching method relies on a genetic algorithm. Such an algorithm is explained in 5.3. The “without replacement” attribute implies that control units, namely the vanilla bonds can only be matched to one treated unit each, forming a unique pair of bonds whose issuer is the same. Among the various method for measuring a spatial distance available, I have chosen the Mahalanobis distance. Furthermore, the Green bond group has lost 7 observations, after the matching process has been deployed, leaving the experiment with 91 pairs of bonds. Finally, the list of covariates includes, besides the four listed above, the “ticker” covariate which is meant to be identical for each of the matching pair, i.e., each pair of bonds contains a green and vanilla bond issued from the same issuer.
Table 7.4 shows the sample size before and after matching for both the treated and control groups. The matching procedure left 7 green bonds and 1126 control units unmatched.
Ideally, unmatched units would be those far from the treated units and would require greater extrapolation were they to have been retained.
We can visualize the distribution of propensity scores of those who were matched using a jitter plot in Figure 7.1. On the other hand, Figure 7.2 and Figure 7.3 provide a summary
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Figure (7.1) This is a table of the sample sizes before and after matching. We use a jitter-type plot to visualize the distribution of propensity scores of those who were matched. The matching procedure left 156 treated and 1126 control units unmatched. Ideally, unmatched units would be those far from the treated units and would require greater extrapolation were they to have been retained.We can visualize the distribution of propensity scores of those who were matched using jitter.
related to the balance of the full marginal distribution of a covariate, beyond just the mean and variance.
Figure 7.2 shows six eQQ plot related to three covariates, reported before and after the matching. As you can see, the matching algorithm has performed well in the case of the coupon variable, reaching a good balance. In the cases of the maturity and the issue date, the achieved balance is slightly worse than the coupon’s one, and, as we can see, t the observations fell out the 45 degrees line still. Similar conclusions can be drawn by looking at the Figure 7.3. However, in this case the imbalance between the treated and the control groups in regard to the issue date variable is much clearer.
After plotting the data, basic statistics related to the four covariates are reported. Ta-ble 7.5 shows the mean, the median and the standard deviation of the two experimental groups. Moreover, it also reports the result of a t-test that determines if there is a
signifi-Copenhagen Business School Master Thesis 15 Sept 2021
Figure (7.2) The y-axis displays the each value of the covariate for the treated units, and the x-axis displays the the value of the covariate at the corresponding quantile in the control group. When values fall on the 45 degree line, the groups are balanced. Above, we can see that issue.date remains somewhat imbalanced, but coupon and maturity have much better balance after matching than before.
Figure (7.3) Visual diagnostics such as eCDF plots, can be used to see exactly how the covariate distributions differ from each other, i.e., where in the distribution the greatest imbalances are (Ho et al., 2007).
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cant difference between the means of the two groups. A t-test looks at the t-statistic, the t-distribution values, and the degrees of freedom to determine the statistical significance.
This test is a fundamental proof to check whether the matching process has output two groups which are similar in the covariates chosen.
Table 7.5 shows the covariate balance for the matching characteristics. Although the issue date covariate results in being significantly different in the two groups, the remaining three covariates reports a difference in means which is not significantly different, confirming there is no significant difference between the green bonds and matched vanilla bonds from the same issuer.
Table 7.6 follows the same scheme applied for the previous table. It provides an answer to the question: “Is there a premium on corporate green bonds in the energy industry?”. On average, there is no appreciable difference between the yields of green versus vanilla bonds issued from the same issuer. The mean difference is small in economic terms (0,091%) and statistically insignificant (p-value = 0,695).
Copenhagen Business School Master Thesis 15 Sept 2021
Matching char-acteristic
Type Count Mean Median Std. Dev. P-value (diff.
in means)
maturity Green 91 08/2029 07/2027 2908 0,519
Vanilla 91 10/2028 07/2025 3006
issue date Green 91 07/2018 12/2018 417 0,0001
Vanilla 91 02/2017 10/2017 1040 log(issued
amount) in(usd)
Green 91 19,593 19,807 0,845 0,764
Vanilla 91 19,557 19,549 0,769
coupon Green 91 2,742 3,100 1,442 0,046
Vanilla 91 3,185 3,410 1,527
Table (7.5) Covariate balance for the within-issuer matching of green bonds to vanilla bonds. This table shows descriptive statistics studying green and matched vanilla bonds from the same issuer. The matching is described in Section 4.4.1. Log (amount issued) is the natural logarithm of the issuance amount. Maturity is the maturity of the bond.
Coupon is the coupon rate. Issue date is the issue date of the bond. The last column reports the p-value of the difference-in-means t-test. When the P-value is less than 0.05 (P¡0.05), the conclusion is that the two means are significantly different.
Matching Char-acteristics
Type Count Mean Median Std. Dev. P-value (diff.
in means)
yield at issue (in%)
Green 91 1,870 1,781 1,575 0,695
Vanilla 91 1,962 1,985 1,525 Table (7.6) Is there a premium on corporate green bonds?
The table above reports the mean and the median of the yield at issue for green bonds and matched vanilla bonds of the same issuer. The last column reports the diff. in means tests, along with the corresponding p-value. When the P-value is less than 0.05 (P¡0.05), the conclusion is that the two means are significantly different.
By design, this matching procedure provides for each green bond a matched brown bond Page 90 of 198
by the same issuer that is as similar as possible except for the “greenness”. In section 7.something, we will discuss the result of our analysis.