rafmacalaba/datause-encoder-data huggingface dataset:
# **Introduction**

Taxes are the main source of government revenue in most countries and provide funding for public investments in human capital, infrastructure, and social insurance. Increasing tax revenues is thus a major policy goal in many low- and lower-middle-income countries that collect a low share of their GDP as tax revenues. In 2019, for example, the average tax-to-GDP ratio was 12 percent for low-income countries, 18 percent for lower-middle-income countries, 21 percent for uppermiddle-income countries, and 30 percent for high-income countries (UNU-WIDER Government Revenue Dataset 2022). Tax-to-GDP ratios among lower-income countries, in fact, resemble those of modern high-income countries at similar stages of development: among 18 developed countries with available historical data, tax-to-GDP ratios in 1919 averaged 12 percent (Besley and Persson 2019; Mitchell 2007). To account for why developing countries tax so little, Besley and Persson (2014) argued that low taxation is an outgrowth of deeper economic and institutional factors constraining development, concluding that “the most important challenge is taking steps that encourage development, rather than special measures focused exclusively on improving the tax system.” This view might suggest that tax capacity should expand with economic development. However, over the last 30 years, the relationship between GDP growth and taxation levels among low- and lower-middle-income countries has remained essentially flat. Figure 1 plots the relationship between percentage changes from 1990-2000 to 2010-2019 in GDP per capita and tax revenues as a share of GDP for such countries. This pattern suggests economic growth does not automatically generate increases in tax revenue, a point Besley and Persson (2014) also note. Rather, governments must invest in improving the tax system to take advantage of expansions in the tax base that result from increased economic activity.

Improving a tax system requires investments in the ability of the tax administration to carry out its three core tasks: identifying taxpayers, determining how much they owe, and bringing these liabilities into state coffers (Cotton and Dark 2017). Following the framework in Okunogbe (2021), we will refer to these three dimensions of tax capacity as identification, detection and collection capacity. Identification capacity is the ability to uniquely identify individuals (as well as assets or entities) that are liable to taxation through comprehensive registries and databases. Detection capacity entails verifying the amounts of tax liability, often utilizing data from third parties. Collection capacity is the ability to ensure the payment of liabilities. It involves the use of billing 2
Flores, CA, and OA Mitnik. 2013. “Comparing Treatments across Labor Markets: An Assessment of Nonexperimental Multiple-Treatment Strategies.” _Review Of Economics And Statistics_ , no. 4451.

- Glazerman, S, A Protik, B Teh, J Bruch, and J Max. 2013. _Transfer Incentives for HighPerforming Teachers: Final Results from a Multisite Randomized Experiment_ .

- Glennerster, Rachel, and Kudzai Takavarasha. 2013. _Running Randomized Evaluations: A Practical Guide_ . Edited by Princetone University Press.

- Glewwe, Paul, Michael Kremer, and Sylvie Moulin. 2009. “Many Children Left behind? Textbooks and Test Scores in Kenya.” _American Economic Journal: Applied Economics_ 1 (1): 112–35.

- Hollands, Fiona, M., Yilin Pan, Robert Shand, M. Levin, Henry, R. Belfield, Clive, Michael Kieffer, Brooks Bowden, A., and Barbara Hanisch-cerda. 2013. _Improving Early Literacy: Cost-Effectiveness Analysis of Effective Reading Programs_ .

- Hotz, V. Joseph, Guido W. Imbens, and Julie H. Mortimer. 2005. “Predicting the Efficacy of Future Training Programs Using Past Experiences at Other Locations.” _Journal of Econometrics_ 125 (1-2): 241–70. doi:10.1016/j.jeconom.2004.04.009.

- Jain, Rahul, Michael Grabner, and Eberechukwu Onukwugha. 2011. “Sensitivity Analysis in Cost-Effectiveness Studies: From Guidelines to Practice.” _PharmacoEconomics_ 29 (4): 297–314. doi:10.2165/11584630-000000000-00000.

- J-PAL. 2014a. “Student_Learning_cea-Data-Full-Workbook-1”. Jameel Abdul Poverty Action Lab.

———. 2014b. _Learning: What Works_ . Policy Bulletin.

Kremer, Michael, Conner Brannen, and Rachel Glennerster. 2013. “The Challenge of Education and Learning in the Developing World.” _Science (New York, N.Y.)_ 340 (6130): 297–300. doi:10.1126/science.1235350.

- Levin, Henry, M., Clive Belfied, Fiona Hollands, Brooks Bowden, A., Henan Chang, Robert Shand, Yilin Pan, and Barbara Hanisch-cerda. 2012. _Cost-Effectiveness Analysis of Interventions That Improve High School Completion_ .

- Levin, Henry, M., and J. McEwan, Patrick. 2001. _Cost-Effectiveness Analysis: Methods and Applications_ . Vol. 21. Thousand Oaks, CA: Sage.

- McEwan, Patrick J. 2012. “Cost-Effectiveness Analysis of Education and Health Interventions in Developing Countries.” _Journal of Development Effectiveness_ 4 (2): 189–213. doi:10.1080/19439342.2011.649044.

15
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continued -

|Country/Date,|Survey Name|Execudng Agoney|Geogrphial<br>Covegp|Number of<br>Households|
|---|---|---|---|---|
|Uruguay<br>Second half 1989|Encuesta Nacional de<br>Hogarm (NH)|Direccion Goneral de<br>Estadistica y Consos|Urban|21,473|
|Venezuela<br>Second half 1981|Encuosta<br>do Hogares<br>por Muesta (EHM)|Oficina Centrl do<br>Estadisdca e Informatica|National|4S,421|
|Venezuela<br>Second half 1989|Encuasado Hogares<br>por Muestra (EHM)|Oficina Cental do<br>Estadistica e Informatica|Nadonal|61,385|
J.C. Duque, N. Lozano-Gracia, J.E. Patino, P. Restrepo / LCR Flagship Report on Cities and 31 Productivity ( _exchange_index_ and _perimeter_ index_ ) as instruments for actual urban form (the results without outliers are reported in Table A6). We present in Tables A4 and A5 the estimates of the first stage, with and without outliers.<sup>11</sup> We began by discussing the instruments diagnostic test reported at the bottom of Table 8. Regarding the relevance of the instruments, the first stage of regressions results show that the instruments for actual urban form have considerable explanatory power. The explanatory power is tested using the F-tests, and we found values above 10 indicating that these instruments are strongly related to actual urban form. In fact, the results from estimating the first stage, reported in Tables A4 and A5, show that the potential urban form is a highly significant and positive predictor of the actual urban form, for the _exchange_ index_ as well as the _perimeter_ index_ . To further inspect the relevance of the instruments we carried out the Kleibergen-Paap test of under-identification (Kleibergen and Paap, 2006), which tests whether the model is identified, where identification requires that the excluded instruments are correlated with the endogenous regressor. The values of this test for the two models indicate that the test rejects the null hypothesis of under-identification at a 5% level of significance, suggesting that the instruments are relevant. We also perform a weak instrument test to test whether the instruments are correlated with the endogenous regressors, but only weakly. Since we allow intra-group correlation, the relevant statistic in this case is the Kleibergen and Paap (2006) rank Wald F statistic. The results reveal that the statistic values are higher than the Stock and Yogo (2005) critical values, rejecting the null hypothesis of weak instruments.

11 Table A2 shows the descriptive statistics of the variables.
Caribbean States (Antigua and Barbuda, Dominica, Grenada, St. Kitts and Nevis, St. Lucia, and, St. Vincent and the Grenadines) all depend on trade taxes for more than 25 percent of current government revenue. Dominica and St. Vincent rely on such taxes for more than 40 percent of their current tax revenues.<sup>12</sup> At the same time, since 2000 many countries in the region have been grappling with difficult fiscal and public debt situations. In Antigua and Barbuda for instance, public debt in 2003 accounted for 142 percent of GDP; in the same year, this ratio reached 171 percent in St Kitts and Nevis, and 150 percent in Jamaica. Although some countries in the region have embarked on a sustained process of fiscal adjustment and public sector reform, fiscal imbalances remain high in many of them.

Large fiscal deficits and high ratios of public debt act of course as major constraints on the ability of most countries of the region to cut tariffs. Indeed, in an analysis of the fiscal effects of tariff reduction for the Caribbean Community, Peters (2005) concluded that Caribbean countries are likely to experience short-run revenue shortfall as a consequence of trade liberalization. Indications are that the shortfall could be as much as a 45 percent decline in customs duties. Such a large effect could be mitigated in a variety of ways—most notably by lowering tax exemptions, enhancing indirect tax systems (by implementing a broad based tax such as the VAT) and by improving tax collection and administration (with regard in particular to the personal income tax). However, developing non trade-based, fiscal revenue structures which are broad based and capable of generating revenues on a sustainable basis is likely to take significant time. Thus, to avoid possible adverse effects of revenue losses on productive government spending (as noted earlier), temporary financing in the form of increased aid may be necessary to increase incentives to implement and sustain trade reform in the Caribbean.

> 12By contrast, taxes on international trade account for only 7 percent of current revenues for Trinidad and Tobago and 9 percent for Barbados.  See World Bank (2008, Chapter 2) for more details.

16
**Table 4 Informal employees as percentage of all employees, by European region and worker category, 2008-2009**

||**_South_**|**_ES, PT, GR_**|**_East_**|**_West_**|**_North_**|**_Total_**|**_%_**<br>**_N obs._**<br>|
|---|---|---|---|---|---|---|---|
|Total|21.1|14.2|5.3|7.1|2.7|8.6|26247|
|Male|19.2|12.8|5.4|7.0|2.6|8.2|12839|
|Female|22.9|15.6|5.1|7.2|2.7|8.9|13405|
|Education||||||||
|Less than secondary|20.9|14.9|9.0|12.9|5.3|14.5|5049|
|Secondary|24.5|17.6|5.1|6.8|3.2|8.4|12758|
|Tertiary|16.6|8.6|4.2|3.4|1.4|5.7|8407|
|Students (all levels)|30.5|20.2|21.3|16.0|12.7|19.7|1000|
|Age||||||||
|15-24|29.5|21.6|14.9|13.8|8.1|17.0|2378|
|25-54|18.5|12.9|4.1|5.6|1.9|7.1|19653|
|55-64|26.5|13.1|5.2|8.6|2.4|9.0|3673|
|65+|33.9|36.4|8.0|23.7|6.9|15.7|489|
|Disability or illness affects life|28.2|19.7|5.8|6.8|4.0|8.0|3840|
|Origin||||||||
|Native majority|15.7|12.2|4.2|7.1|2.8|6.9|19999|
|Native minority|30.3|16.1|10.7|6.0|1.8|14.0|1770|
|2<sup>nd</sup>generation immigrant|31.1|14.4|6.7|6.2|2.1|12.6|2092|
|Immigrant:|||||||2386|
|_Working rights due to nationality_<sup>a</sup>|30.0|16.5|6.5|8.7|1.9|15.0|1650|
|_No working rights due to nationality_|33.5|33.7|5.9|6.0|0.0|14.3|736|
|<br>_From CEE of FSU_|37.1|55.4|7.1|11.9|1.4|18.9|1049|
|<br>_From developing countries_|23.6|16.2|1.9|6.8|0.0|13.0|728|
|_From developed countries_|28.8|20.8|0.0|5.2|2.3|8.6|609|
|Occupation||||||||
|Highly skilled non-manual|17.2|8.6|3.0|3.9|1.2|5.1|10986|
|Low skilled non-manual|20.9|12.4|6.8|9.0|3.8|10.7|6909|
|Skilled manual|21.9|13.6|5.6|8.5|3.8|9.0|5479|
|Elementary|30.3|28.6|9.7|14.6|8.0|16.8|2319|
|Establishment siz|e|||||||
|1-9|31.2|25.7|10.6|13.2|4.9|16.2|6501|
|10-24|15.5|9.5|5.5|7.7|2.6|7.8|5549|
|25-99|16.5|4.1|2.5|5.7|1.4|5.5|6445|
|100+|14.9|6.3|1.7|2.7|1.9|4.1|6893|
|NA|21.1|6.5|10.3|17.6|29.0|13.4|859|
|Economic activity||||||||
|Agriculture & Forestry|31.1|27.7|7.1|14.3|5.6|13.3|623|
|Manufacturing and Mining|15.8|9.5|3.1|5.1|2.1|5.6|4341|
|Construction|27.1|19.7|11.4|10.0|5.5|13.7|1863|
|Trade & Auto Repair|24.5|13.9|7.7|9.1|3.3|11.0|3292|
|Hotels & Restaurants|29.7|22.1|10.4|22.2|6.1|19.7|996|
|Transport|23.0|12.5|3.5|6.6|4.3|7.6|1271|
|<br>Finances|17.1|2.4|3.4|3.1|1.8|6.0|824|
|Business Services|15.1|9.2|6.5|6.8|1.4|7.8|2243|
|Public utilities|22.2|7.4|2.3|10.1|0.0|6.3|335|
|Post & Telecom|8.4|7.2|3.8|3.7|0.0|4.5|443|
|Public Administration|14.5|5.4|2.6|4.3|1.1|6.1|2055|
|Education|18.7|7.5|2.1|4.8|2.0|6.1|2644|
|Health & Social Care|10.8|9.1|2.1|4.8|1.9|4.1|2808|
|<br>Personal & HH Services|<br>39.5|<br>38.6|<br>8.3|<br>13.3|<br>5.2|<br>17.7|<br>1471|

_Notes:_ For Italy and Austria, results refer to 2006 and 2007, respectively. Countries weighted equally (i.e. a respondent from any country is equally likely to be sampled.<sup>a</sup> Country-specific (and year-specific) rules on free movement of labor within EU are taken into account. _Source:_ Calculation with ESS data.

52
are much more straightforward to interpret. Since the marginal effects of a multinomial logit model depend on the values of the explanatory variables, one must decide at which values to report them. As is common in the literature, the table shows the average marginal effects. In other words, Table 3 provides insights into the determinants of the sectoral choice of individuals with average characteristics. The delta method is used to compute standard errors.

Table 3 Marginal effects from selection regressions

|||Inactiv|e|Pu|blic se|ctor|Pri|vate se|ctor|
|---|---|---|---|---|---|---|---|---|---|
||Estimat|e|S.E.|Estimat|e|S.E.|Estimat|e|S.E.|
|_Socio-demographic characteristics_||||||||||
|Urban|0.030|*|(0.017)|0.055|***|(0.008)|-0.085|***|(0.018)|
|Female|0.385|***|(0.029)|-0.149|***|(0.014)|-0.236|***|(0.023)|
|Bhutanese|-0.156|**|(0.070)|0.233|***|(0.048)|-0.078||(0.048)|
|Potential experience|-0.090|***|(0.003)|0.026|***|(0.002)|0.064|***|(0.003)|
|Potential experience squared|0.001|***|(0.000)|-0.000|***|(0.000)|-0.001|***|(0.000)|
|_Education_||||||||||
|Primary education|-0.180|***|(0.038)|0.100|***|(0.014)|0.079|**|(0.034)|
|Lower secondary education|-0.212|***|(0.039)|0.127|***|(0.014)|0.084|**|(0.036)|
|<br>Middle secondary education|-0.410|***|<br>(0.039)|0.187|***|<br>(0.018)|0.219|***|<br>(0.037)|
|Higher secondary education|-0.566|***|(0.036)|0.281|***|(0.020)|0.286|***|(0.037)|
|Lower tertiary education|-0.692|***|(0.042)|0.323|***|(0.019)|0.369|***|(0.039)|
|<br>Higher tertiary education|-0.829|***|<br>(0.258)|0.368|***|<br>(0.077)|0.461|**|<br>(0.191)|
|_Selection variables_||||||||||
|Wealth index|0.024|***|(0.009)|0.003||(0.007)|-0.026|***|(0.007)|
|Prop. of individuals in<br>household aged 14 or under|-0.101|*|(0.057)|0.100|***|(0.018)|0.002||(0.054)|
|Prop. of individuals in||||||||||
|household aged 66 or over|0.165||(0.104)|-0.128|***|(0.048)|-0.036||(0.096)|
|Prop. of individuals in<br>household in public sector|0.231|***|(0.038)|-0.010||(0.017)|-0.221|***|(0.032)|
|Prop. of individuals in<br>household inprivate sector|0.079|***|(0.019)|-0.103|***|(0.014)|0.024|*|(0.014)|

_Notes_ . (1) The symbols *, ** and *** indicate significance at the 10%, 5% and 1% levels, respectively. (2) Weights have been used for the estimation. (3) The reported standard errors have been calculated using the delta method. (4) Location variables are not depicted.

In many ways, the multinomial logit estimates of Table 3 confirm the descriptive evidence of Table 2. For instance, they confirm that urban workers are more likely to work in the public rather than in the private sector, _ceteris paribus_ . Additionally, they provide some evidence that city dwellers are more likely to be inactive. Moreover, the multinomial logit estimates confirm that relatively welleducated individuals are more likely to self-select into public sector jobs. Well-educated individuals are also much less likely to be inactive. Other results of the multinomial logit estimates could not have

- 18 -
Table 7: Boys’ enrollment spillover effects, by girls’ age

||boy|s’ enroll|ment|
|---|---|---|---|
||ay|_@|3)|
|girls’ scholarship program|0.02|0.01|0.02|
|older girl in HH of secondary school age|(0.03)<br>[.54]|(0.04)<br>[.71]<br>-0.01**<br>(0.01)|(0.03)<br>[1.00]|
|younger girl in HH of secondary school age||[.03]<br>-0.01<br>(0.02)||
|||[1.00]||
|older girl in HH enrolled in secondary school|||0.14|
||||(0.04)|
||||[.13]|
|younger girl in HH enrolled in secondary school|||0.10|
||||(0.05)<br>29]|
|older girl inHH ofsecondary school age*program||0.03<br>[.41]||
|younger girl in HH of secondary school age*program||-0.004<br>(0.04)<br>.99)||
|older girl inHH enrolled in secondary school*program|||0.07<br>(0.02)|
||||[.14]|
|younger girl in HH enrolled in secondary school*program|||0.08<br>(0.06)|
||||34]|
|N|4,718|4,718|4,718|
|R-squared|0.12|0.12|0.14|
|programspillovereffect(oldergirlinHH)||0.04|=—-0.10***|
|||(0.04)|(0.04)|
|||[64]|[.00]|
|programspillovereffect(youngergirlinHH)||0.02|0.10|
|||(0.03)|(0.06)|
|||[42]|[.13]|
|meanoutcome|0.60|0.60|0.60|

Sample is boys of secondary school age (13-18), Regions 2-6, Gambia Integrated Household Survey 1992/1998/2003/2010. “Older” girls include those of same age as boy. Program spillover effect is sum of program and program’ girl in HH coefficients. Standard errors in parenthesis, clustered by region. p-values in brackets, calculated from 200 iterations of wild-t cluster bootstrap of Cameron et al (2008) with Webb (2013) 6-point distribution of weights. Starred significance levels are based on these p-values. * significant at 10%; ** significant at 5%; *** significant at 1%.
<u>Table 3: Relative Importance of Major Variables in Inflation Starts</u>

|||||Perc|ent Dueto<sup>b</sup>|||
|---|---|---|---|---|---|---|---|
|Country||Probability<sup>a</sup>|GAP|FP|DEMOC|BS|CF|
|A. EPISODES||||||||
|Argentina|1987|0.16|0.27|0.73|-0.19|-0.06|0.25|
|Brazil|1986|0.49|0.32|0.16|-0.03|0.41|0.15|
||1992|0.02|-0.51|-0.32|-0.24|0.04|0.04|
|Colombia|1984|0.03|-0.04|-0.37|-0.53|0.24|-0.30|
|India|1990|0.12|0.00|0.25|-0.28|0.62|0.41|
|Indonesia|1986|0.09|-0.23|-0.54|1.31|-0.03|0.48|
||1997|0.17|0.19|0.47|0.60|-0.27|0.01|
|Israel|1983|0.19|-0.07|-0.26|-0.24|1.99|-0.42|
|Korea|1986|0.16|0.36|-0.08|0.64|-0.35|0.43|
|Malaysia|1987|0.11|-0.27|-0.15|0.18|0.46|0.78|
|Mexico|1985|0.19|0.09|-0.11|0.45|0.35|0.23|
||1990|0.07|1.74|-1.52|1.67|-0.39|-0.50|
|Peru|1980|0.10|0.02|0.63|-0.15|-0.19|0.68|
||1987|0.16|1.15|-0.63|-0.08|0.28|0.29|
|Philippines|1983|0.20|0.04|0.56|0.51|-0.12|0.01|
||1987|0.16|0.41|0.40|-0.19|-0.11|0.49|
|South Africa|1984|0.10|1.47|-0.74|-0.16|0.21|0.22|
|Thailand|1986|0.20|-0.31|0.65|0.26|0.06|0.34|
|Turkey|1983|0.12|0.24|0.61|-0.12|-0.19|0.46|
||1987|0.17|0.61|0.33|-0.08|0.00|0.14|
||1990|0.06|5.45|-3.20|-2.54|-0.43|1.72|
||2001|0.15|-1.04|0.58|-0.20|1.36|0.29|
|Venezuela|1984|0.06|0.99|4.42|-2.34|-5.55|3.48|
||1992|0.06|2.58|-0.45|-1.01|-0.21|0.09|
|B. AVERAGES||||||||
||1980|0.10|0.02|0.63|-0.15|-0.19|0.68|
||1983|0.17|0.07|0.30|0.05|0.56|0.02|
||1984|0.06|0.81|1.11|-1.01|-1.70|1.13|
||1985|0.19|0.09|-0.11|0.45|0.35|0.23|
||1986|0.24|0.03|0.05|0.54|0.02|0.35|
||1987|0.15|0.44|0.13|-0.07|0.11|0.39|
||1990|0.08|2.39|-1.49|-0.38|-0.06|0.54|
||1992|0.04|1.03|-0.39|-0.62|-0.09|0.06|
||1997|0.17|0.19|0.47|0.60|-0.27|0.01|
||2001|0.15|-1.04|0.58|-0.20|1.36|0.29|

a Probability figures are the fitted values from Model 6. b Figures presented are the percentage differences between point probability estimate and the baseline probability, where the baseline probability = 1 − _F_ ( _X_ β) = 0.050.

18
Bank 2018). In some areas of the coast, aquifers are also subject to increasing salinity intrusion (Ayers et al., 2016; Khan et al., 2014). Additionally, shallow groundwater levels in the northwestern, north central, and southwestern areas of the country are declining over time, particularly affecting public water supplies during the dry season when there is notable groundwater abstraction for irrigation (Shamsudduha et al., 2009; Shamsudduha et al., 2012).

Nevertheless, Bangladesh’s progress in providing nearly universal access to “improved” drinking water supply can mostly be credited to its abundance of groundwater sources. According to the 2011 Bangladesh Census, there are 31 million households that have access to primarily groundwater supplies via tubewells, tapwater and other water wells such as dugwells (BBS, 2015). The current number of privately-owned tubewells is approximately 17 million, compared to a previous estimate of 6 million to 11 million in the early 1990s (BGS and DPHE, 2001). In addition to these private wells, an additional 1.6 million public tubewells have been installed by the Department of Public Health Engineering of Bangladesh in order to provide As-safe drinking water supply in rural areas of which about 20% are considered deep (>150 mbgl) wells (DPHE, 2016). Consequently, sourcing groundwater from deep aquifers, has become an effective and popular mitigation strategy for drinking-water supply over the last couple of decades for both As and even salinity water quality issues (Burgess et al., 2010; van Geen et al., 2016). However, there is concern of potential contamination of deep groundwater due to ingress of As and salinity from shallow depths (Shamsudduha et al., 2018). Contrary to these hydrological concerns, from ethical consideration (i.e., positive impacts outweigh the negative consequences of long-term exposure to arsenic), Ravenscroft and others (Ravenscroft et al., 2013) advocate that the development of deep groundwater in Bangladesh is needed. Although it may lead to unsustainable exploitation over the long-term, it will lessen the burden of crippling disease and death from As and salinity contamination of shallow groundwater and surface water while also benefiting future generations by improving public health, education and economic conditions.

Assessment of groundwater risks in Bangladesh has been conducted in isolation. To date, integrated, multi-hazard groundwater risk mapping has not been conducted at the national scale to guide water resources officials and policy makers in Bangladesh. As the new era of the United Nation’s Sustainable Development Goals (SDGs) has begun, Bangladesh needs to look beyond improved access to ‘improved and safe drinking water supply’ in order to address water quality (SDG 6.3: _improve water quality by reducing pollution_ ) and water sustainability 3
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# V. COUPhMATIVI IAVLYSIS OF r NOKIAL NODRL AD SOCIUTZ NDDgL UWSULTS

The model described earlier was programed using Turbo Basic on an IBM PC AT. First, the case assumed by Schwartz was used as a che_k. The eztensions possible with this model were then incorporated and priced, Checks were made by taking extreme cases where we know the expected result.

The basic case assumed by Schwartz is that of a company having issued **a** zero coupon with face value F=lO0, maturing in five years. At maturily date the bondholder has the right to buy a certain commodity bundle with initial value P And price volatility av and is correlated with the commodity price movement with correlation coefficient P.

Table 1 shows the price of the bond for various values of the covariance between the commodity price and the value of the firm as well as various values of the firm and the commodity bundle. The average difference in the prices obtained from the two models is about 0.3Z with the maximum being 0.9X and the minimum being 0. This is after 10 iterations of the binomial model. In the limit the binomial model tends towards the Schwartz model. The advantage is not just simplicity, the binomial method enables us to incorporate senior debt, payouts by the firm before the maturity of the bond (in terms of coupons and dividends), interim coupons or options linked to the comodity bond and the risk of default thereof, stochastic interest rates, Caps, etc. This can be done in a simple and intuitive mdanner; which is isportant because few bonds are identically structured and deriving the corresponding differential equation as well as solving it, even if computationally feasible, may be uneconomical. The following observations can be made from the results in Table 1.