INFLATION AND SEIGNIORAGE STUDIES IN AFRICA A Thesis presented to the Faculty of the Graduate School at the University of Missouri-Columbia In Partial Fulfillment of the Requirements for the Degree Master of Arts by JASON MUELLER Dr. Neil Raymon, Thesis Supervisor DECEMBER 2007
The undersigned, appointed by the dean of the Graduate School, have examined the thesis entitled INFLATION AND SEIGNIORAGE STUDIES IN AFRICA presented by Jason Mueller, a candidate for the degree of master of arts, and hereby certify that, in their opinion, it is worthy of acceptance. Professor Neil Raymon Professor Oksana Loginova Professor Douglas Moesel
ACKNOWLEDGEMENTS I would like to thank Dr. Neil Raymon for advising me on this paper and for giving me a good deal of advice and ideas. I would also like to thank the other members of my thesis committee, Dr. Oksana Loginova and Dr. Douglas Moesel, for their oversight. I would also like to thank Dr. Shawn Ni for his assistance in his writing and research class. ii
TABLE OF CONTENTS ACKNOWLEDGEMENTS... ii LIST OF TABLES... iv Chapter 1. INTRODUCTION... 1 2. LONG-TERM RELATIONSHIP ANALYSIS... 5 3. YEAR-BY-YEAR RELATIONSHIP ANALYSIS... 7 4. COUNTRY-BY-COUNTRY RELATIONSHIP ANALYSIS... 12 5. YEAR-BY-YEAR RELATIONSHIP ANALYSIS REVISED... 17 6. PANEL DATA RELATIONSHIP ANALYSIS... 20 7. SUMMARY AND CONCLUSIONS... 22 APPENDIX 1. DATA... 23 BIBLIOGRAPHY... 30 iii
LIST OF TABLES Table Page 1. Long-term Relationship... 5 2. Year-by-year Relationship... 7-10 3. Country-by-country Relationship... 12-15 4. Year-by-year Relationship Revised... 17-18 5. Panel Data Relationship... 20-21 6. Data... 23-29 iv
1. Introduction The link between seigniorage and inflation has been established and is estimated to be in the form of a Laffer curve in which the maximum amount of seigniorage occurs at a particular inflation rate and the smaller amounts of seigniorage occur at both high and low rates of inflation, presenting the dual equilibria that Bruno and Fischer analyzed in their 1990 paper Seigniorage, Operating Rules, and the High Inflation Trap. In that paper, Bruno and Fischer use a basic money-only model to demonstrate dual equilibria under both rational expectations and adaptive expectations. Another important study on inflation, seigniorage, and the Laffer curve is the 1995 paper Money Demand and Seigniorage-Maximizing Inflation by Easterly, Mauro, and Schmidt-Hebbel. This work develops a model of money, inflation, and seigniorage, and then uses data from eleven high-inflation countries in the time period 1960-1990 to calculate the theoretical seigniorage-maximizing inflation rate using several different equations and statistical methods. The seigniorage-maximizing rates they calculate range all the way from 42 percent to infinity. Yet another important paper on the inflation-seigniorage link is Kiguel and Neumeyer s work Seigniorage and Inflation: The Case of Argentina, which studies the inflationary events of Argentina from 1979 to 1989. This paper finds 1
that Argentina s revenue-maximizing inflation rates are around twenty to thirty percent per month, which are quite high. In this paper, I will analyze the Laffer curves formed by the seigniorage and inflation relationship for twenty-nine countries in Africa. The motivation for choosing Africa is that it is a region of the world that is not often studied in economics and that the countries do exhibit economic and governmental diversity; although many of the countries are poor, several are oil-rich countries and a few have healthy economies. The twenty-nine countries I chose were the countries for which reliable data exist for the period 1981 to 2005. This analysis will use the model developed by Ahmad Jafari-Samimi in Relationship Between Inflation and Seigniorage in Developing Countries: An Estimation of the Laffer Curve. The Jafari-Samimi model uses a quadratic equation to demonstrate the relationship between inflation and seigniorage. This equation is: R = α 0 + α 1 π + α 2 π 2 R is seigniorage as a percentage on GDP, π is the inflation rate, and the α i s are the coefficients, where, in order to produce the usual shape of the Laffer curve, α 0 should be positive, α 1 should be positive, and α 2 should be negative. For the purposes of statistical modeling, this equation will be used, except that an error term U should be added to the equation. 2
According to Easterly, Mauro, and Schmidt-Hebbel, seigniorage should be equal to inflation plus growth, times money holdings scaled to consumption (588), which in equation form is: S = (π + g) m / c. However, in the Jafari-Samimi model, seigniorage is defined by the equation R = mg y + mπ, where m is the ratio of real monetary base to GDP, g y is the growth rate of real GDP, and π is inflation (69). In my paper, I shall use the Jafari-Samimi definition and scale seigniorage to GDP and not consumption. The method of research I used was based on two sources: International Financial Statistics and the World Economic Outlook Database, both of which are issued by the International Monetary Fund. I used IFS to obtain money holdings data, specifically line 34 of the country reports. I used WEO to obtain nominal GDP figures, real GDP growth figures, and inflation figures. I then plugged in these numbers into the formulae I explained earlier and analyzed the results using SAS statistical software. The following sections will produce preliminary results from two equations, the R = α 0 + α 1 π + α 2 π 2 equation already mentioned, and the equation without an intercept R = α 1 π + α 2 π 2 3
for which I will also obtain the rate of inflation that produces the most seigniorage and that maximum amount of seigniorage. By optimizing the equation using simple calculus, setting the first derivative to zero, and solving for inflation, the optimal rate of inflation (π*) is found to be equal to α 1 /(2α 2 ). The maximum amount of seigniorage is found by plugging the optimal inflation rate back into the initial equation and is equal to α 2 1 /(4α 2 ). Section 2 will analyze the long-term Laffer curve for African countries by using the long-term average rates of inflation and seigniorage. Section 3 will analyze the year-by-year Laffer curves for African countries to examine the shortrun effects of inflation and seigniorage on the Laffer curve. Section 4 will use country-by-country analysis of the various Laffer curves. Section 5 will revisit the year-by-year Laffer curves using revised data based on the results of Section 4. Section 6 will analyze all the data using various panel data techniques. Section 7 will sum up the results and conclude. 4
2. Long-term Relationship Analysis This section uses average inflation and seigniorage rates for twenty-nine African countries from 1981 to 2005 to analyze the long-run Laffer curve produced by inflation and seigniorage. The twenty-nine countries are: Algeria, Benin, Botswana, Burkina Faso, Burundi, Cameroon, Central African Republic, Chad, Republic of Congo, Cote d Ivoire, Egypt, Ethiopia, Gambia, Ghana, Kenya, Lesotho, Libya, Malawi, Mauritius, Morocco, Niger, Nigeria, Rwanda, Senegal, Sierra Leone, South Africa, Swaziland, Tanzania, and Togo. (Note: in all tables, * is significance at 10 percent, ** is significance at 5 percent, and *** is significance at 1 percent.) Table 1. Long-term Relationship Average With Average Without Stat α 0 (value) 0.64387 α 0 (t-statistic) 1.19 α 1 (value) 0.18806 0.2697 α 1 (t-statistic) 2.47** 8.06*** α 2 (value) -0.00199-0.0037 α 2 (t-statistic) -1.12-3.42*** R 2 0.4799 0.8412 Optimal INF 36.44594595 Max R 4.914735811 In this long-term data set, the model without the intercept looks to be quite significant (as the values for both α 1 and α 2 are both significant at one percent and have the expected sign), while the model with the intercept appears to be only slightly significant (as the value for α 1 is significant at five percent, but all 5
coefficients have the expected signs). As for how the data from the model without the intercept compare with the optimal inflation rate and the theoretical maximum rate of seigniorage, three out of the twenty-nine countries (Algeria, Egypt, and Sierra Leone) have average seigniorage rates that are actually higher than the theoretical predicted maximum and one country (Sierra Leone) has an average inflation rate that is higher than the optimum. 6
3. Year-by-year Relationship Analysis This section analyzes year-by-year data to check the short-term relationship between inflation and seigniorage. The years I am using are 1981 through 2005. Table 2. Year-by-year Relationship 1981 With 1981 Without 1982 With 1982 Without 1983 With 1983 Without Stat α 0 (value) 0.58064 0.97521 0.03305 α 0 (t-statistic) 0.87 0.83 0.05 α 1 (value) 0.1641 0.21207 0.16768 0.26843 0.27624 0.27809 α 1 (t-statistic) 2.6** 7.01*** 1.25 4.71*** 5.02*** 7.68*** α 2 (value) -0.00050683-0.00093324-0.0007859-0.00268-0.00137-0.00138 α 2 (t-statistic) -0.83-2.59** -0.26-1.33-3.36*** -4.55*** R 2 0.6174 0.8073 0.2124 0.672 0.6483 0.7947 Optimal INF 113.6202906 50.08022388 100.7572464 Max R 12.04772751 6.721517248 14.00979132 1984 With 1984 Without 1985 With 1985 Without 1986 With 1986 Without Stat α 0 (value) 0.33005 1.20962 0.89428 α 0 (t-statistic) 0.32 1.7 1.71* α 1 (value) 0.27734 0.30846 0.19153 0.28162 0.20877 0.24778 α 1 (t-statistic) 2.43** 5.13*** 2.63** 5.44*** 4.85*** 6.55*** α 2 (value) -0.00285-0.00336-0.0009361-0.00196-0.00076023-0.00103 α 2 (t-statistic) -1.2-1.94* -0.87-2.14** -1.85* -2.62** R 2 0.3269 0.6754 0.4371 0.6932 0.7015 0.788 Optimal INF 45.90178571 71.84183673 120.2815534 Max R 7.079432411 10.11604903 14.90168165 7
1987 With 1987 Without 1988 With 1988 Without 1989 With 1989 Without Stat α 0 (value) 0.28743 1.28865 0.84236 α 0 (t-statistic) 0.74 4*** 2.15** α 1 (value) 0.20125 0.2162 0.12822 0.20538 0.15183 0.19931 α 1 (t-statistic) 5.86*** 7.88*** 2.91* 4.09*** 3.84*** 5.7*** α 2 (value) -0.0007983-0.00090589-0.00048974-0.00137-0.00041343-0.00086418 α 2 (t-statistic) -2.53** -3.26*** -0.37-0.84-0.78-1.66 R 2 0.7742 0.844 0.5491 0.7206 0.682 0.7816 Optimal INF 119.3301615 74.95620438 115.3174107 Max R 12.89959046 7.697252628 11.49195657 Stat 1990 With 1990 Without 1991 With 1991 Without 1992 With 1992 Without α 0 (value) -0.43561 0.64665 0.0105 α 0 (t-statistic) -0.47 0.98 0.02 α 1 (value) 0.27703 0.25091 0.19957 0.23782 0.21272 0.21355 α 1 (t-statistic) 3.39*** 4.22*** 3.7*** 6.39*** 3.53*** 4.37*** α 2 (value) -0.00112-0.00088533-0.00090168-0.00119-0.00202-0.00204 α 2 (t-statistic) -1.21-1.14-1.83* -3.04*** -1.35-1.49 R 2 0.5799 0.6726 0.5581 0.7433 0.601 0.7329 Optimal INF 141.7042233 99.92436975 52.34068627 Max R 17.77750333 11.88200681 5.588676777 1993 With 1993 Without 1994 With 1994 Without 1995 With 1995 Without Stat α 0 (value) 0.48529 0.60175 0.42454 α 0 (t-statistic) 1.18 0.5 0.78 α 1 (value) 0.13971 0.17804 0.19357 0.23035 0.15314 0.18644 α 1 (t-statistic) 3.09*** 5.65*** 2.25** 5.28*** 3.02*** 6.86*** α 2 (value) -0.000402-0.00093155-0.00103-0.00146-0.00050637-0.00090876 α 2 (t-statistic) -0.5-1.38-0.87-1.85* -0.73-1.98* R 2 0.6587 0.8168 0.5045 0.8196 0.7345 0.8755 Optimal INF 95.56116151 78.8869863 102.5793389 Max R 8.506854597 9.085808647 9.56244597 8
1996 With 1996 Without 1997 With 1997 Without 1998 With 1998 Without Stat α 0 (value) 1.22563 0.85516 0.74176 α 0 (t-statistic) 2.69** 3.67*** 3.4*** α 1 (value) 0.06657 0.21062 0.10378 0.19191 0.12949 0.2048 α 1 (t-statistic) 0.94 4.07*** 3.4*** 8.41*** 3.1*** 4.9*** α 2 (value) 0.00085815-0.00213-0.00062173-0.00179-0.00095877-0.00209 α 2 (t-statistic) 0.41-1.07-1.31-4.19*** -1.13-2.28** R 2 0.2296 0.6022 0.6013 0.8195 0.5016 0.6399 Optimal INF 49.4413146 53.6061453 48.9952153 Max R 5.20666484 5.14377767 5.01711005 1999 With 1999 Without 2000 With 2000 Without 2001 With 2001 Without Stat α 0 (value) 0.5822 0.50011 0.91121 α 0 (t-statistic) 4.46*** 2.66** 3.6*** α 1 (value) 0.1271 0.20319 0.13575 0.18767 0.13866 0.18895 α 1 (t-statistic) 4.46*** 6.82*** 3.88*** 5.83*** 3.45*** 4.18*** α 2 (value) -0.00153-0.00328-0.00073916-0.00172-0.00319-0.00224 α 2 (t-statistic) -1.7-3.11*** -0.76-1.74* -1.4-0.82 R 2 0.7001 0.8068 0.6972 0.7997 0.3436 0.542 Optimal INF 30.97408537 54.55523256 42.1763393 Max R 3.146812203 5.119190247 3.98460965 2002 With 2002 Without 2003 With 2003 Without 2004 With 2004 Without Stat α 0 (value) 0.6446 0.84883 1.21497 α 0 (t-statistic) 2.74** 2.98*** 3.55*** α 1 (value) 0.11726 0.15212 0.10761 0.15702 0.10631 0.39052 α 1 (t-statistic) 2.01* 4.18*** 2.05* 2.4** 0.89 3.71*** α 2 (value) 0.00000916-0.00224 0.00399 0.0021 0.0002597-0.0137 α 2 (t-statistic) 0-0.82 1.58 0.38 0.03-1.6 R 2 0.3596 0.542 0.6072 0.6362 0.2204 0.6614 Optimal INF 33.95535714-37.38571429 14.25255474 Max R 2.582644464-2.935152429 2.782953839 9
Stat 2005 With 2005 Without α 0 (value) 1.07247 α 0 (t-statistic) 1.95* α 1 (value) 0.08363 0.42328 α 1 (t-statistic) 0.44 5.14*** α 2 (value) 0.00262-0.01608 α 2 (t-statistic) 0.23-2.44** R 2 0.2533 0.7399 Optimal INF 13.16169154 Max R 2.785540398 For the model without the intercept, the α 1 coefficient is very significant (with 24 of the 25 values being significant at one percent with the other value being significant at five percent and with all values being positive as expected) and the α 2 coefficient being quite significant as well (with five values being significant at one percent, another five values being significant at five percent, and another four values being significant at ten percent, with all but one value [2003] being negative as expected). The model with the intercept is much less significant, as the α 0 coefficient has three values that are significant at one percent, another two values that are significant at five percent, and another two values that are significant at ten percent, with all but one value [1990] being positive as expected. The α 1 coefficient has fourteen values that are significant at one percent, another four values that are significant at five percent, and another three values that are significant at ten percent, with all values being positive as expected. The α 2 coefficient has only one value that is significant at one percent, another value that is significant at five percent, and another two values that are significant at ten percent, with five values [1996, 2002, 2003, 10
2004, and 2005] being positive instead of the expected negative values. Once again, the model without the intercept looks to be quite significant, while the model with the intercept appears to be only slightly significant. As for how the data from the model without the intercept compare with the optimal inflation rate and the theoretical maximum rate of seigniorage, the twenty-four years that fit the theoretical model have a total of thirty-five instances of exceeding the theoretical maximum seigniorage rate (for an average of 1.458 countries per year and about five percent of the countries) and 12 instances of exceeding the optimum inflation rate (for an average of.5 countries per year and about 1.7 percent of the countries). 11
4. Country-by-country Relationship Analysis This section analyzes the relationship between inflation and seigniorage country-by-country. I am using the data from 1981 to 2005 for each country. Table 3. Country-by-country Relationship Algeria Botswana Botswana Algeria With Without Benin With Benin WithoutWith Without Stat α 0 (value) 2.26631 0.50945 1.83193 α 0 (t-statistic) 2.01* 3.78*** 1.57 α 1 (value) 0.32767 0.57157 0.24046 0.31202-0.1047 0.26173 α 1 (t-statistic) 2.14** 5.77*** 6.96*** 8.59*** -0.44 4.7*** α 2 (value) 0.00093244-0.00365-0.00060873-0.00175 0.00639-0.01077 α 2 (t-statistic) 0.27-1.29-0.94-2.43** 0.54-2.2** R 2 0.7034 0.8625 0.9499 0.9425 0.0219 0.8435 Optimal INF 78.29726027 89.14857143 12.15088208 Max R 22.37618253 13.90806863 1.590125183 Burkina Burkina Faso Burundi Cameroon Cameroon Faso With Without Burundi WithWithout With Without Stat α 0 (value) 0.74081 0.81277 0.06237 α 0 (t-statistic) 4.28*** 3.66*** 0.38 α 1 (value) 0.08845 0.23428 0.07287 0.16231 0.19748 0.20498 α 1 (t-statistic) 1.62 4.16*** 2.25** 6.13*** 5.6*** 7.16*** α 2 (value) 0.00174-0.00245 0.00095523-0.001-0.00359-0.00377 α 2 (t-statistic) 0.87-1.06 0.97-0.98-2.86*** -3.28*** R 2 0.6459 0.7188 0.7362 0.8821 0.7283 0.8311 Optimal INF 47.8122449 81.155 27.18567639 Max R 5.600726367 6.586134025 2.786259973 12
Central African Republic Central African Republic Chad With Chad Without Stat With Without α 0 (value) 0.05393 0.80493 α 0 (t-statistic) 0.24 3.59*** α 1 (value) 0.18865 0.19162 0.12822 0.14068 α 1 (t-statistic) 4.47*** 4.84*** 5.29*** 4.76*** α 2 (value) 0.00103 0.001-0.0011 0.00026506 α 2 (t-statistic) 0.94 0.93-0.92 0.19 R 2 0.8509 0.8715 0.6312 0.6855 Optimal INF -95.81-265.3738776 Max R -9.1795561-18.66639855 Republic of Republic of Cote d Ivoire Egypt Congo With Congo Without Cote d Ivoire Without With Egypt Without Stat With α 0 (value) 0.65246 0.00096039 0.17368 α 0 (t-statistic) 7.16*** 0 0.13 α 1 (value) 0.02037 0.0302 0.24135 0.24157 0.38928 0.41664 α 1 (t-statistic) 1.52 1.27 4.18*** 8.49*** 1.7 4.11*** α 2 (value) 0.00353 0.00462-0.00017651-0.00018224 0.00239 0.00154 α 2 (t-statistic) 5.48*** 4.14** -0.1-0.17 0.29 0.31 R 2 0.7941 0.7211 0.8867 0.9325 0.7254 0.896 Optimal INF -3.268398268 662.7798507-135.2727273 Max R -0.049352814 80.05386427-28.18001455 Ethiopia With Ethiopia Without Gambia Without Ghana Without Gambia With Ghana With Stat α 0 (value) 0.99107 0.39255 0.22897 α 0 (t-statistic) 2.87*** 0.77 0.61 α 1 (value) 0.12515 0.15873 0.23331 0.27499 0.14849 0.15384 α 1 (t-statistic) 2.88*** 3.31*** 3.53*** 7.39*** 8.32*** 21.71*** α 2 (value) 0.00093765 0.00099626-0.00156-0.00226-0.00043975-0.00050266 α 2 (t-statistic) 0.74 0.69-1.17-2.33** -3.52*** -7.35*** R 2 0.6049 0.6828 0.6688 0.8559 0.941 0.9818 Optimal INF -79.66293939 60.8384956 153.025902 Max R -6.322449185 8.36498895 11.7707524 13
Lesotho Kenya With Kenya Without Lesotho With Without Libya With Libya Without Stat α 0 (value) 0.57942 0.4098 1.45778 α 0 (t-statistic) 2.69** 0.43 1.61 α 1 (value) 0.09219 0.15218 0.1719 0.245 0.28522 0.29538 α 1 (t-statistic) 3.73*** 12.68*** 0.99 5.59*** 2.5** 2.51** α 2 (value) 0.00040317-0.00058719 0.00212-0.00075709-0.01026 0.00237 α 2 (t-statistic) 0.89-1.97* 0.29-0.25-0.76 0.21 R 2 0.9259 0.9665 0.6584 0.9385 0.2387 0.4081 Optimal INF 129.5832695 161.803749-62.3164557 Max R 9.859990974 19.8209592-9.203517342 Malawi Without Mauritius With Mauritius Without Morocco With Morocco Without Malawi With Stat α 0 (value) 0.45164 1.12014 2.15041 α 0 (t-statistic) 1.58 2.37** 2.03* α 1 (value) 0.07408 0.10394 0.07579 0.3513 0.33784 1.08117 α 1 (t-statistic) 3.51*** 10.62*** 0.62 7.95*** 0.8 4.9*** α 2 (value) 0.00054809 0.00019798 0.00185-0.01215-0.01554-0.06433 α 2 (t-statistic) 1.96* 1.12 0.27-3.21*** -0.48-2.85*** R 2 0.9434 0.9749 0.3833 0.9067 0.0687 0.6809 Optimal INF -262.501263 14.4567901 8.40331105 Max R -13.6421906 2.53933519 4.54270391 Niger With Nigeria Niger Without Nigeria With Without Rwanda With Rwanda Without Stat α 0 (value) 0.10695 0.63103 0.10284 α 0 (t-statistic) 0.83 1.59 0.28 α 1 (value) 0.08962 0.0931 0.12336 0.165 0.17813 0.18726 α 1 (t-statistic) 2.94*** 3.11*** 4*** 9.78*** 3.65*** 5.36*** α 2 (value) 0.0006788 0.00086672 0.00005184-0.00044605-0.00188-0.00201 α 2 (t-statistic) 0.78 0.78 0.12-1.47-2.28** -2.94*** R 2 0.7752 0.798 0.9021 0.9615 0.5041 0.686 Optimal INF -53.7082333 184.9568434 46.58208955 Max R -2.50011826 15.25893958 4.361481045 14
Senegal Sierra Leone Sierra Leone South South Africa Senegal With Without With Without Africa WithWithout Stat α 0 (value) 0.53884 0.61286 0.69141 α 0 (t-statistic) 3.87*** 0.93 1.75* α 1 (value) 0.18315 0.24203 0.0943 0.11573 0.26952 0.4046 α 1 (t-statistic) 5.69*** 6.73*** 3.03*** 5.54*** 3.08*** 9.53*** α 2 (value) -0.0014-0.00256 0.00020122 0.00005438-0.00835-0.01414 α 2 (t-statistic) -1.42-2.16** 0.75 0.25-1.91* -4.74*** R 2 0.8291 0.848 0.8836 0.947 0.5458 0.9502 Optimal INF 47.27148438-1064.086061 14.30693069 Max R 5.720558682-61.57333992 2.894292079 Swaziland Tanzania Tanzania Swaziland Without With Without Togo With Togo Without Stat With α 0 (value) -0.09491-0.28609 0.19713 α 0 (t-statistic) -0.15-0.3 0.91 α 1 (value) 0.13014 0.11266 0.24502 0.21535 0.22019 0.243 α 1 (t-statistic) 1.06 3.46*** 2.14** 3.91*** 4.32*** 5.49*** α 2 (value) 0.00080381 0.00152-0.00111-0.00048802-0.00043468-0.00081947 α 2 (t-statistic) 0.15 0.66-0.41-0.28-0.39-0.8 R 2 0.6156 0.9028 0.7379 0.918 0.8483 0.8763 Optimal INF -37.05921053 220.6364493 148.2665625 Max R -2.087545329 23.75702968 18.01438735 For the model without the intercept, the α 1 coefficient is very significant (with 27 of the 29 values being significant at one percent and another value being significant at five percent and with all values being positive as expected) and the α 2 coefficient being quite significant as well (with six values being significant at one percent, another five values being significant at five percent, and another value being significant at ten percent, with all but ten values [Central African Republic, Chad, Republic of Congo, Egypt, Ethiopia, Libya, Malawi, Niger, Sierra Leone, and Swaziland] being negative as expected). The model with the intercept is much less significant, as the α 0 coefficient has seven values that are 15
significant at one percent, another two values that are significant at five percent, and another three values that are significant at ten percent, with all but two values (Swaziland and Tanzania) being positive as expected. The α 1 coefficient has seventeen values that are significant at one percent and another four values that are significant at five percent with all but one value (Botswana) being positive as expected. The α 2 coefficient has three values that are significant at one percent, another value that is significant at five percent, and another two values that are significant at ten percent, with sixteen values being positive instead of the expected negative values. Once again, the model without the intercept looks to be quite significant (but with only nineteen of the twenty-nine countries having the correct sign for the α 2 coefficient), while the model with the intercept appears to be only slightly significant, with more than half of the α 2 coefficients having the wrong sign. As for how the data from the model without the intercept compare with the optimal inflation rate and the theoretical maximum rate of seigniorage, the nineteen countries that fit the theoretical model have a total of thirty-two instances of exceeding the theoretical maximum seigniorage rate (for an average of 1.684 instances per country and about 6.7 percent of the possible instances) and seventeen instances of exceeding the optimum inflation rate (for an average of.8947 instances per country and about 3.58 percent of the possible instances). 16
5. Year-by-Year Relationship Analysis Revised In this section, I have redone the year-by-year analysis using only the nineteen countries that conformed to the expected results in the country-bycountry analysis and only using the model without the intercept. Once again, I am using the years 1981 through 2005, as well as calculating the long-term averages as in Section 2 of this paper. Table 4. Year-by-year Relationship Revised Stat Average Revised 1981 Revised 1982 Revised 1983 Revised 1984 Revised α 1 (value) 0.29924 0.24671 0.34797 0.27704 0.36819 α 1 (t-statistic) 6.04*** 6.9*** 2.58** 6.13*** 3.22*** α 2 (value) -0.00539-0.00127-0.00809-0.00136-0.00771 α 2 (t-statistic) -2.51** -3.21*** -1.04-3.93*** -1.46 R 2 0.8438 0.8786 0.702 0.8014 0.6645 Optimal INF 27.75881262 97.12992126 21.50618047 101.8529412 23.87743191 Max R 4.153273544 11.98146144 3.741752809 14.10866941 4.395715827 Stat 1985 Revised 1986 Revised 1987 Revised 1988 Revised 1989 Revised 1990 Revised α 1 (value) 0.29123 0.27654 0.15256 0.31262 0.30668 0.03291 α 1 (t-statistic) 2.88** 4.61*** 2.78** 5.45*** 4.5*** 0.27 α 2 (value) -0.00153-0.0024 0.00099609-0.00431-0.0043 0.0062 α 2 (t-statistic) -0.43-1.62 0.5-2.31** -2.24** 1.94* R 2 0.6925 0.7959 0.8221 0.8509 0.7593 0.7307 Optimal INF 95.17320261 57.6125-76.57942555 36.26682135 35.66046512-2.654032258 Max R 13.8586459 7.966080375-5.841478581 5.668866845 5.468175721-0.043672101 Stat 1991 Revised 1992 Revised 1993 Revised 1994 Revised 1995 Revised 1996 Revised α 1 (value) 0.22126 0.22546 0.17657 0.24338 0.21694 0.28718 α 1 (t-statistic) 3.26*** 4.17*** 5.41*** 4.23*** 6.04*** 4.47*** α 2 (value) -0.00184-0.0017-0.00081058-0.00166-0.00135-0.00468 α 2 (t-statistic) -0.73-1.15-1.26-1.62-2.09* -2.01* R 2 0.7356 0.8049 0.8959 0.8131 0.885 0.7161 Optimal INF 60.125 66.31176471 108.915838 73.30722892 80.34814815 30.68162393 Max R 6.65162875 7.475325235 9.615634762 8.920756687 8.71536363 4.40557438 17
Stat 1997 Revised 1998 Revised 1999 Revised 2000 Revised 2001 Revised 2002 Revised α 1 (value) 0.23096 0.24004 0.19662 0.22319 0.32613 0.22402 α 1 (t-statistic) 5.9*** 2.35** 3.86*** 5.8*** 3.47*** 2.65** α 2 (value) -0.00372-0.00534-0.00293-0.00215-0.00825-0.00212 α 2 (t-statistic) -1.91* -0.6-0.91-1.86* -1.41-0.3 R 2 0.8895 0.5262 0.7794 0.8483 0.6378 0.7962 Optimal INF 31.04301075 22.47565543 33.55290102 51.90465116 19.76545455 52.83490566 Max R 3.584846882 2.697528165 3.2985857 5.792299547 3.223053845 5.918037783 Stat 2003 Revised 2004 Revised 2005 Revised α 1 (value) 0.32784 0.41292 0.41694 α 1 (t-statistic) 2.88** 3.66*** 4.49*** α 2 (value) -0.00389-0.01394-0.01817 α 2 (t-statistic) -0.69-1.46-2.18** R 2 0.7381 0.7494 0.7463 Optimal INF 42.13881748 14.81061693 11.47330765 Max R 6.907394961 3.057799971 2.391840446 In this long-term data set, the model looks to be quite significant (as the value for α 1 is significant at one percent, the value for α 2 is significant at five percent, and both coefficients have the expected signs). As for how the data from the model without the intercept compare with the optimal inflation rate and the theoretical maximum rate of seigniorage, three out of the nineteen countries (Algeria, Ghana, and Tanzania) have average seigniorage rates that are actually higher than the theoretical predicted maximum and one country (Ghana) has an average inflation rate that is higher than the optimum. For the year-by-year analysis, the α 1 coefficient is very significant (with eighteen values being significant at one percent and another six values being significant at five percent, with all values being positive as expected) and the α 2 coefficient being significant as well (with two values being significant at one percent, another three values being significant at five percent, and another five 18
values being significant at ten percent, with all but two values [1987 and 1990] being negative as expected). Once again, the model looks to be relatively significant, but not as significant as the year-by-year analysis done earlier in this paper. As for how the data from the model without the intercept compare with the optimal inflation rate and the theoretical maximum rate of seigniorage, the twenty-three years that fit the theoretical model have a total of thirty-seven instances of exceeding the theoretical maximum seigniorage rate (for an average of 1.61 countries per year and about 8.47 percent of possible instances) and fourteen instances of exceeding the optimum inflation rate (for an average of.61 countries per year and about 3.2 percent of possible instances). 19
6. Panel Data Relationship Analysis In this section, I will use various panel data methods to analyze the data; the methods I use are the seven methods supported by SAS: one-way fixed effects, two-way fixed effects, one-way random effects, two-way random effects, the Fuller and Battese method, the Parks method, and the Da Silva method. Each method was used with and without an intercept. Note: since the two-way random effects produces the same results as the Fuller and Battese method, the Fuller and Battese method will not be listed in the chart. Table 5. Panel Data Relationship One-way Fixed One-way Two-way Two-way One-way One-way Effects Fixed Effects Fixed EffectsFixed Effects Random Random Effects With Without With Without Effects With Without Stat α 0 (value) 0.413899 0.562138 0.584773 α 0 (t-statistic) 1.39 1.42 2.69*** α 1 (value) 0.17484 0.17484 0.176039 0.176039 0.173802 0.178964 α 1 (t-statistic) 21.98*** 21.98*** 20.33*** 20.33*** 22.11*** 23.49*** α 2 (value) -0.00052-0.00052-0.00054-0.00054-0.00052-0.00056 α 2 (t-statistic) -6.21*** -6.21*** -6.20*** -6.20*** -6.25*** -6.80*** R 2 0.7196 0.8364 0.7356 0.8457 0.6000 0.6194 Optimal INF 168.1153846 162.9990741 159.7892857 Max R 14.69664692 14.347097 14.29826486 20
Two-way Random Two-way Random EffectsParks Da Silva Parks Method Method Da Silva Method Effects With Without Method With Without With Without Stat α 0 (value) 0.583228 0.753328 0.656077 α 0 (t-statistic) 2.63*** 35.30*** 2.97*** α 1 (value) 0.174152 0.180013 0.155883 0.179274 0.165987 0.170521 α 1 (t-statistic) 21.63*** 23.16*** 312.28*** 268.03*** 22.68*** 23.77*** α 2 (value) -0.00053-0.00057-0.00041-0.00058-0.00048-0.00051 α 2 (t-statistic) -6.29*** -6.92*** -49.42*** -55.41*** -6.44*** -6.98*** R 2 0.5876 0.6094 0.9980 0.9966 0.5770 0.5872 Optimal INF 157.9061404 154.5465517 167.177451 Max R 14.21257902 13.85308926 14.25363306 All coefficient values are significant at one percent except for the intercept values for one-way and two-way fixed effects; also, all coefficient values have their expected signs. The data from all these methods are very significant. As for how the data from the model without the intercept compare with the optimal inflation rate and the theoretical maximum rate of seigniorage, there are no values of inflation higher than the optimal rates of any of the panel data methods, and there are only four instances (out of a possible 725) of seigniorage that are higher than the lowest maximum rate of seigniorage set by any of the panel data methods. 21
7. Summary and Conclusions In summary, the results show that the model without the intercept is quite significant, while the model with the intercept appears to be only slightly significant. Jafari-Simimi concludes that the lack of an intercept implies that seigniorage comes from the inflation tax alone and that the few instances of inflation higher than the optimal rate imply that governments do not try to maximize revenue through the inflation tax (75). I agree with his conclusions. My conclusion is that the Laffer curve does hold in the model without an intercept, as demonstrated by the multiple data sets and methods used to analyze them. 22
Appendix Table 6. Data (INF = Inflation, R = Seigniorage) Country 1981 INF 1981 R 1982 INF 1982 R 1983 INF 1983 R 1984 INF 1984 R Algeria 6.6 4.91 5.3 7.06 12.7 11.83 10.7 11.14 Benin 0.8 0.53 4.1 1.36-6.1-1.69 10.3 2.19 Botswana 3.9 2.49 12.7 3.08 8.3 2.27 6.5 1.42 Burkina Faso 6.5 0.90 13.4 1.42 2.7 0.15 7.5 0.99 Burundi 11 3.19 8 0.79 5.3 1.19 25 3.04 Cameroon 4.6 2.76 13.4 2.54 13.5 2.58 16.6 2.73 Central African Republic 14.7 5.38 13.2 1.62 14.6 1.52 2.6 2.16 Chad 8.1-0.39 6.5 1.57 11.6 3.57 20.3 4.34 R. Congo 0.8 0.55 3.5 1.18 3.5 1.03 3.5 1.10 Cote d'ivoire 7.8 2.32 5.7 1.11 8.4 1.12 4.1 0.41 Egypt 9.6 5.26 15.6 10.78 16.7 11.29 19.6 12.32 Ethiopia 5.4 0.62 5.2 0.74-0.2 0.92 9 0.93 Gambia 4.1-0.87 12.7 5.60 15.4 4.78 24.7 2.76 Ghana 100.2 11.92 16.8 1.22 142.4 11.89 6 1.38 Kenya 11.8 1.74 20.7 2.74 11.4 1.32 10.3 1.23 Lesotho 11.3 1.83 19 3.93 9.6 1.09 12.6 4.46 Libya 13.7 0.26 12 1.07 11.5 4.88 10.6 4.60 Malawi 9 0.39 12.5 1.57 18.6 1.98 11.9 1.56 Mauritius 15.5 1.36 12.9 2.87 4.9 1.55 7 1.19 Morocco 13.2 3.42 6.7 4.72 12.5 3.67 7.5 3.46 Niger 23.6 2.97-0.4 0.19 6.6 0.26 0.5-2.00 Nigeria 17.3 1.71 7.1 1.26 38.7 6.67 22.6 4.10 Rwanda 3.1 0.48 18.4 1.24 1.8 0.60 5.9 1.41 Senegal 11.3 3.10 15.9 4.38 12.4 1.27 9.7 2.17 Sierra Leone 25.4 2.86 44.7 6.77 83.1 12.72 52.3 7.40 South Africa 13.7 2.96 13.5 2.08 11.3 1.67 13.1 3.85 Swaziland 14.4 3.12 11.5 1.35 10.6 1.24 18.6 2.54 Tanzania 26.3 7.74 23.4 6.51 34.5 9.03 27.6 6.42 Togo 11 2.36 16.6 4.42-0.2-1.57-3.1 0.88 23
Country 1985 INF 1985 R 1986 INF 1986 R 1987 INF 1987 R 1988 INF 1988 R Algeria 12.5 12.55 11.9 8.08 3.2 1.79 8.6 4.86 Benin 1.2 1.02 0.4 0.53-1.3-0.45 3.4 1.10 Botswana 10.4 1.56 10.8 1.74 8.1 1.93 10.4 2.57 Burkina Faso 1 1.23-3.5 0.55 3 0.36 2.2 1.04 Burundi -5.5 0.81 4.4 1.06 5 1.45 5.4 1.39 Cameroon 3.7 1.16 8.5 1.47 18.9 1.47-1.9-1.00 Central African Republic 10.5 1.93 2.4 1.30-7 -2.52-3.9-0.29 Chad 5.1 2.28-16 -1.87-4.7-0.21 14.9 3.27 R. Congo 3.5 1.15 3.5 0.94 3.5 0.95-13 1.29 Cote d'ivoire 4.4 1.61 8.3 2.63 7.5 1.38 4.1 0.99 Egypt 11.4 8.50 28 14.55 25.1 10.41 10 4.68 Ethiopia 20.5 1.26-11.8-0.34-4.7 1.42 6.9 1.25 Gambia 25.5 6.03 52.3 8.39 15.3 2.41 12.4 1.84 Ghana 19.5 2.61 33.3 3.94 34.2 4.18 26.6 3.78 Kenya 13 1.54 10.3 1.80 13 1.90 4.8 1.00 Lesotho 19.4 5.07 10.1 2.24 11.8 2.81 15 5.02 Libya 6.2 3.06 3.7-0.30 3.8 1.49 3.8 4.36 Malawi 11.1 1.35 13.9 1.38 35.5 4.31 26.4 3.78 Mauritius 7.1 1.81 2.8 1.69 1.2 1.84 8.3 2.42 Morocco 9.5 4.67 4.4 3.67 2.4-0.03 1.5 3.62 Niger -5 0.34-4.2 0.28 0.2 0.03-4.6 0.28 Nigeria 1.1 1.56 13.6 1.79 9.7 0.74 39 6.72 Rwanda -1.9 0.19 2.4 0.72 2.9 0.24 2.3 0.24 Senegal 11.7 2.18 4.1 1.13-5.2 0.13-2.1-0.39 Sierra Leone 74.5 9.96 116.3 14.87 116.8 12.89 38.3 4.48 South Africa 18.4 2.88 18.2 2.83 14.7 3.08 12.1 3.11 Swaziland 18.2 2.11 8.9 2.38 16.3 3.26 17.8 2.21 Tanzania 39.2 9.57 28.5 8.05 32.3 8.85 30.8 4.65 Togo 4.6 2.12 1.4 1.15-0.5-0.73 0.7 1.54 24
Country 1989 INF 1989 R 1990 INF 1990 R 1991 INF 1991 R 1992 INF 1992 R Algeria 10.7 9.18 47.4 23.75 25.5 9.15 28 10.38 Benin -0.2-0.53 1.1 2.10 2.1 1.39 5.9 2.00 Botswana 11.3 1.88 12 1.56 12.6 1.54 16.5 1.34 Burkina Faso 1.6 0.48-1.4-0.25-0.9 1.01-0.2 0.00 Burundi 12 1.56 10.7 1.70 8.3 1.69 3.5 0.56 Cameroon 0-0.20-0.7-0.76-0.2-0.45 0.8-0.20 Central African Republic 0.6 0.31-1.1-0.66-0.8-0.37 0-0.43 Chad -4.8-0.44 3.4 1.00 2.1 1.91-6.8-0.63 R. Congo -11.6 1.23 1.5 0.40 7.4 1.43-2.7-0.02 Cote d'ivoire 0.1 0.51 0.1-0.18 1.7 0.29 3.6 0.55 Egypt 16.7 5.76 21.4 6.46 20.7 5.81 9.7 2.22 Ethiopia 11 1.92 5 1.60 45 8.47 2.1-1.66 Gambia 8.4 1.70 10.5 2.03 11.6 1.96 4.2 1.23 Ghana 30.5 4.13 35.9 3.75 10.3 1.36 13.3 2.38 Kenya 7.6 1.10 41.4 4.50 14.5 1.58 33.7 4.17 Lesotho 14.3 3.88 15.8 3.41 14.1 2.93 18.4 3.33 Libya 6.6 2.58 10.8-5.11 11.7 12.05 9.4 4.76 Malawi -1 0.03 23.2 2.95 7.4 1.65 36.1 3.36 Mauritius 14.4 2.91 10.4 2.33 8.6 2.36 6.4 2.55 Morocco 5.6 2.52 7.5 3.91 8.2 5.13 3.9-0.04 Niger 1.6 0.33-2.6-0.45-6.9-0.54-2.6-1.05 Nigeria 44.7 5.67 2.7 1.99 23 2.88 48.8 6.46 Rwanda 0.7-0.37 6 0.50 21.4 1.30 14.5 1.76 Senegal 0.8 0.71-0.9-0.21-0.7 0.26-0.5 0.10 Sierra Leone 85.5 11.11 98.3 14.47 115.4 11.70 34.8 2.33 South Africa 15.5 3.08 14.7 2.50 16.3 2.76 9.7 1.45 Swaziland 8.6 1.64 11 1.77 9.6 1.03 8.6 0.92 Tanzania 36.9 5.38 18.6 3.48 37.8 5.10 20.7 2.89 Togo -3 0.15 1.5 1.14 5 0.82-2.1-0.62 25
Country 1993 INF 1993 R 1994 INF 1994 R 1995 INF 1995 R 1996 INF 1996 R Algeria 16.1 5.30 38.5 12.28 21.8 6.64 15.1 4.34 Benin 2.9 1.62 54 11.75 3.1 1.36 6.9 1.76 Botswana 12.7 1.02 9.8 0.88 10.8 0.96 9.6 0.91 Burkina Faso 2.7 0.84 29.1 4.92 3.9 1.73 6.9 3.09 Burundi 15.5 1.28 13.2 1.61 19.2 1.75 37.4 4.88 Cameroon -4.1-0.55 33.8 2.92 16.2 1.33 4.6 0.58 Central African Republic -4.8-1.01 44.7 10.63 5 1.97 4.6-0.79 Chad 31.4 3.23 15.3 1.90 10 1.09 10.5 1.75 R. Congo 0-0.13 19.4 1.90 28.8 4.19 5.5 1.16 Cote d'ivoire 2.5 0.36 32.2 7.58 7.7 2.55 3.5 1.95 Egypt 15 3.94 6.4 2.32 9.7 2.89 8.2 2.54 Ethiopia 4.7 3.60 6.3 2.22 14.8 4.08-9 0.73 Gambia 5.1 1.55 5 1.03 4 0.08 2.3 0.98 Ghana 27.7 3.88 34.2 5.00 70.8 8.93 26.1 3.29 Kenya 54.7 7.10 6.6 1.15 6.9 1.26 10.7 1.69 Lesotho 6 1.44 10.2 2.07 9.3 2.04 8.6 2.60 Libya 7.5 5.08 10.7 5.55 8.3 1.35 0.9 2.34 Malawi 18.3 3.13 66 8.16 74.9 9.18 6.7 1.31 Mauritius 15 3.38 6 1.53 6 1.44 7.4 1.02 Morocco 5.9 2.03 5.7 6.62 4.1-1.08 3.9 6.49 Niger 3.5 0.62 40.6 4.72 6.2 0.94 3.6 0.62 Nigeria 61.3 7.95 76.8 10.95 51.6 5.71 14.3 1.73 Rwanda 12.5 0.39 64.4 2.47 38.4 8.82 8.7 2.29 Senegal 0.5 0.22 37.5 5.32 5.5 1.42 2.4 0.58 Sierra Leone 26.7 2.15 17.7 1.53 34.5 1.86 6.4-1.13 South Africa 9.5 1.90 10 2.59 6.9 2.04 9.3 3.25 Swaziland 13.2 1.34 13.8 1.35 10.1 0.95 5.8 0.70 Tanzania 26.1 3.76 38 5.68 26.8 4.31 15.5 2.38 Togo 2.4-1.62 48.5 9.78 6.4 2.40 4.9 1.89 26
Country 1997 INF 1997 R 1998 INF 1998 R 1999 INF 1999 R 2000 INF 2000 R Algeria 6 1.73 3.9 2.60 1.2 1.21 0.1 0.58 Benin 2.4 1.18 5.6 1.22-3.2 0.37 9.8 3.20 Botswana 7.8 0.97 6.4 1.19 8.4 1.07 8.5 1.01 Burkina Faso 1.8 1.52 1 1.31 0.7 1.12 2.4 0.61 Burundi 26.6 3.80-1 0.46 20.7 3.00 14.1 1.77 Cameroon 7 0.92 2.2 0.59 2.2 0.58-0.7 0.33 Central African Republic 0.4 1.50-3 0.13-4.2-0.09 8.1 1.48 Chad 0.6 0.76 3.5 1.02 3.3 0.27 13 1.40 R. Congo 16.3 1.93-2.7 0.13 4.1 0.19-3.3 0.58 Cote d'ivoire 5.2 1.72 2 1.05 1.5 0.51 3.6-0.16 Egypt 4.8 2.03 4.5 2.45 2.9 1.73 2.5 1.44 Ethiopia 2.6 1.11 2.3-0.30 12.3 3.36 0.3 1.27 Gambia 0.3 0.78 4.8 1.58 1.7 1.18 0.2 1.04 Ghana 22.1 3.29 15.8 2.46 13.8 1.88 40.5 5.60 Kenya 12 1.44 0.7 0.44 10.5 1.56 11.8 1.52 Lesotho 7.9 2.60 9.7 0.99 6.3 1.02 6 1.40 Libya 3.3 3.39 3.8 1.47 1.7 1.24-6.6-1.27 Malawi 15.2 1.59 53.1 4.98 28.2 2.69 35.4 3.40 Mauritius 5.1 1.14 9 2.17 5.3 1.14 4.6 1.36 Morocco 1.5-0.33 2.2 4.63 0.9 0.72 1.7 1.92 Niger 4.1 0.47 3.4 0.67-1.9-0.14 4.7 0.20 Nigeria 10.2 1.28 11.9 1.43 0.2 0.20 14.5 2.76 Rwanda 16.6 3.04-6 0.26 2.1 0.89 5.8 1.06 Senegal 1.9 0.63 0.9 0.91 0.5 0.94 1.3 0.63 Sierra Leone 66.9 4.94-5.7-0.55 36.7 3.18-3.1 0.07 South Africa 6.2 2.22 9 2.73 2.2 1.47 7.2 3.29 Swaziland 7.8 0.86 4.9 0.52 9.1 0.99 6.4 0.62 Tanzania 15.4 1.98 11.3 1.47 7 1.03 5.5 1.01 Togo 3 0.89-1.4-0.54 4.5 1.09-2.5-0.67 27
Country 2001 INF 2001 R 2002 INF 2002 R 2003 INF 2003 R 2004 INF 2004 R Algeria 7.5 2.93-1.5 1.00 4 3.38 2 2.56 Benin 2.3 1.86 1.2 1.07 0.8 0.93 2.6 0.90 Botswana 5.8 0.71 10.6 1.12 6.4 0.89 7.9 1.30 Burkina Faso 1 0.97 3.9 0.91 3.2 2.04 0.7 0.74 Burundi 3.9 0.87 3.5 1.36 10.7 1.77 11.8 3.43 Cameroon 4.8 0.94 4.3 0.89-0.1 0.38 1 0.47 Central African Republic 2.5 0.39 9.1 1.11-1.3-1.09-0.3 0.14 Chad 0.7 1.37 12.6 2.69-11.9 0.30 2.1 2.69 R. Congo 8.3 1.41-2.8 0.23 6.4 0.83 1.1 0.52 Cote d'ivoire 4.8 0.82 4.4 0.61-0.1-0.26 4.4 0.95 Egypt 2.2 1.07 2.7 1.18 4 1.68 11.7 2.73 Ethiopia -11.4-0.78-1 0.05 23.5 5.40 1.7 4.04 Gambia 8.1 2.39 13 2.34 17.6 7.02 8 3.87 Ghana 21.3 3.37 15.2 3.24 23.6 4.67 11.8 2.99 Kenya 1.6 0.77 4.2 0.65 8.3 1.88 16.3 3.40 Lesotho 9.2 2.20 9.8 2.51 5.8 1.66 5 1.72 Libya -10.3-1.67-7.3-1.96-1.3 1.30-3.5 0.38 Malawi 22.1 1.60 10.9 0.88 9.8 1.05 13.7 1.68 Mauritius 5.2 1.16 5.7 0.96 3.9 1.47 5.6 2.06 Morocco 1.7 5.44 1.4 2.87 1.8 4.95 0.5 3.75 Niger 3.2 0.75 0.6 0.23-1.5 0.29 3.7 0.34 Nigeria 16.5 3.00 12.2 2.30 23.8 5.61 10.1 2.23 Rwanda -0.2 0.55 6.2 1.33 7.7 0.78 10.2 1.35 Senegal 3.9 1.27 1.5 0.33-1.4 1.11 1.7 1.57 Sierra Leone 3.4 2.56-3.1 3.06 11.3 2.62 14.4 2.59 South Africa 4.7 1.27 12.4 2.71 0.2 0.57 3.5 1.45 Swaziland 10.8 0.83 11.5 0.92 4.6 0.54 3.2 0.37 Tanzania 4.9 1.03 4.4 1.18 4.6 1.07 4.1 1.15 Togo 6.8 0.74 1.6 0.20-1.7 0.56 3.9 1.17 28
Country 2005 INF 2005 R AVERAGE INF AVERAGE R Algeria 1.7 2.19 11.98 6.457 Benin 3.7 1.28 4.55 1.518 Botswana 11.3 1.13 9.58 1.462 Burkina Faso 4.5 1.38 3.75 1.162 Burundi 1.2 0.43 10.80 1.794 Cameroon 3.5 0.51 6.08 0.879 Central African Republic 1.7 0.61 4.33 0.996 Chad 1.8 0.73 5.30 1.343 R. Congo 3.2 1.36 3.51 1.021 Cote d'ivoire 2.5 0.70 5.20 1.245 Egypt 4.7 1.73 11.35 5.030 Ethiopia 13 6.13 6.14 1.922 Gambia 1.8 1.74 10.76 2.538 Ghana 14.8 3.13 32.27 4.171 Kenya 7.6 2.14 13.78 1.984 Lesotho 3.5 1.29 10.75 2.541 Libya 3 2.28 4.56 2.126 Malawi 16.6 1.75 23.02 2.629 Mauritius 1.9 1.02 7.21 1.789 Morocco 2.1 3.23 4.65 3.199 Niger 4.2 1.27 3.22 0.465 Nigeria 11.6 2.24 23.33 3.558 Rwanda 5.6 1.25 9.98 1.311 Senegal 1.4 1.41 4.56 1.247 Sierra Leone 13.1 2.47 44.18 5.476 South Africa 3.6 1.65 10.24 2.376 Swaziland 6.3 0.67 10.46 1.369 Tanzania 5 1.45 21.01 4.207 Togo 5.5 1.12 4.55 1.147 29
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