(i) Presentation of the Results of Model Fittings
_
The following statistics are presented for the estimated equation: (R2) coefficient of multiple determination adjusted for degrees of freedom; (F) F statistics together with the position regarding its significance; (DW) Durbin-Watson statistics. We present in parentheses under the respective coefficients the t-ratios for the estimated regression coefficients. For those equations which include the lagged endogenous variable among the predetermined variables as well as those which are characterised by the presence of autocorrelation, we apply two forms of modified maximum likelihood (Cachrane and Hildreth) estimation techniques and include in the table of results for the relevant cases, the coefficient for the estimated lagged disturbance Ut-1 with the respective estimate of p, the autocorrelation parameter. We also show, for each estimated equation, the relative estimation method.
The coefficients are given to four decimal places, other statistics (t,F,DW,R2,p) are given to three places and, in accordance with normal practice, the level of significance for each t-ratio for the estimated regression coefficients is indicated.
The estimated equations are the results of numerous trials regarding the optimal form of the functions as well as the variables that give as a group the most desirable qualities of a satisfactory model fitting.
In order to allow for a thorough study of the effects of the Dutch Disease on the various sectors of the economy, the same variables have been retained in respect of the fitted equations for Blocks 1,2 and 4. Unless otherwise rejected due to the presence of autocorrelation, corresponding equations in these three blocks have been estimated jointly using two-stage least-squares (2SLS).
(ii) Model Performance
BLOCK 1
Eight out of ten fitted regressions have the value of R2 in the region of 0.9. The utilities equation's R2 is 0.789 and construction bears the lowest value of R of 0.542. The value of the "F" statistics is significant at five percent level of significance and the value of the DW `d' statistic indicates the absence of autocorrelation in each one of the ten fitted regressions. From the statistical and econometric point of view, therefore, all the fitted regressions provide good fits to the situations (data)under analysis.
All the fitted equations in respect of the block under consideration satisfy the economic criteria except the one in respect of agriculture. That is to say, the evidence that emerges from the empirical equations is compatible with the model specifications which are based on economic theory for the situation under consideration.
As for the agriculture-fitted regression the coefficients corresponding to rain and fixed capital formation do not satisfy the economic criterion. The valid explanation for this situation is the presence of the Dutch Disease which is discussed in the previous section. Thus the results show that there has been disinvestment in the agricultural sector. The results also confirm the inadequacy of rainfall in Botswana's agricultural production. That is, the average rainfall during the post-independence period has not been high enough to support adequate agricultural production (ceteris paribus). This means that to raise arable agriculture to the level that can sustain meaningful economic development the country must adopt, in suitable areas, irrigation systems. Relying on rain-fed agriculture is one of the major factors responsible for poor agricultural output.
It is also important to note at this juncture that values of coefficients corresponding to the variable fixed capital formation differ significantly between sectors. This situation supports the rejection of the hypothesis of a uniform production process justifying one production function for the entire economy. The production characteristics vary from sector to sector, and sectoral production functions help to capture these differences.
BLOCK 2
Labour Inputs (Man-hours)
From the statistical and econometric criteria point of view the ten fitted regressions for labour inputs give satisfactory fits.
Eight out of the ten fitted regressions satisfy the criteria demanded by economic theory regarding the signs of the coefficients as well as relative significances as narrated in the previous section. Two sectors have negative and significant output coefficients. These are agriculture and trade. A negative and significant output regression coefficient for agriculture is brought about by the Dutch Disease, which has resulted in the drain of resources from agriculture to sectors producing non-traded goods and partly due to the fact that agricultural employment in Botswana, like in most countries in Sub-Saharan Africa, is essentially residual where those not employed in the formal sector remain (Lipumba et al, 1988). Therefore, as output in agriculture slumped, employment (in the traditional farming sub-sector) continued increasing and productivity declined. The negative output coefficient in the trade equation requires further study both from the accuracy of data point of view and that of the economic situation.
In almost each one of the ten fitted equations under discussion, the lagged endogenous variable coefficient is statistically significant (at five percent level of significance), confirming the conventional partial-adjustment behaviour of labour inputs to output. This situation is an indirect indication of the relevance of the hypothesis that factor intensities are revealed by employment behaviour in Botswana's state of production. That is, the observed changes in measured labour inputs are proportional to the desired changes. Although the variable Q/W is not statistically significant in most equations, its "t" values are fairly high in several equations. This variable measures the ratio of the price of capital to the wage rate. The price of capital changes with import prices (inflation). For the period under consideration, nominal wages in Botswana were a policy variable as explained in the previous sections. They depended on, among other things, the levels at which the government fixed public servants' wages. A sudden rise in this coefficient implies that the government was failing to raise wages in lien with the price of capital. A fall in the ratio implies that the government was raising money wages faster than the price of capital and consequently inflation. A constant ratio implies that wages and inflation underwent changes at the same rate. A significant ratio implies that the desired inputs of labour were being chosen so as to minimise the cost of producing expected output in a long-run equilibrium. The fairly significant values of the relevant ratio in Botswana's labour inputs fitted regressions imply that the requirement of cost minimization, i.e., that the ratio of marginal products of labour be equated to the ratio of price of capital to wage rate, was almost satisfied.
The revised wages and employment policy is meant to do away with government intervention in the labour market and subsequently to bring about efficiency in manpower allocation. The consequences of this course of action are that wages in the labour market would be determined by the supply and the demand for labour in the country. In this case the desired inputs of labour and capital would be presumed to be chosen so as to minimize the cost of producing expected output in long-run equilibrium (Hickman et al, 1976). Assuming that there is no monopsony in factor markets, then cost minimization would require that the ratio of marginal products of labour and capital be equated to the ratio of their expected prices. In the short-run it would be possible to test this axiom using the relevant estimated production, labour and investment functions.
The results also indicate that output is statistically significant in all the fitted regressions except in agriculture and trade, in which it appears with wrong arithmetic signs for reasons already discussed.
Employment
The two fitted regressions satisfy both the econometric criteria and those required by economic theory. The output elasticity of formal employment is equal to 3.8314. This value is relatively higher than those established by Lipumba et al for Tanzania. Apparently, in Botswana employment levels in the formal sectors have kept pace with output levels. The elasticity with respect to fixed capital formation is also fairly high - in the region of 0.9. However, the fact that this value is less than one implies that a proportional increase in fixed capital formation would be accompanied by a relatively lower proportional increase in formal employment.
Unemployment is one of the major problems in Botswana. Employment projections in the current National Development Plan (NDP 6)are based on the following assumptions:
- That the average employment coefficient in a sector, that is to say, the amount of labour required to produce a given amount of output, does not diminish. For if this were to occur, it would decrease the sector's demand for labour.
- That there is no significant substitution of capital for labour.
- That the cost of labour relative to the cost of other production inputs remains constant.
The fitted regression for formal employment provides evidence for the validity of the first assumption. As for the second assumption concerning the issue of substitution, Mhozya (1987) establishes the elasticity of substitution between any pairs of inputs in the entire Botswana economy to be around 1.467, implying a fairly significant substitution of capital for labour. Computations of the relevant factor from our output functions in this study confirm the relevant value and support the hypothesis that production processes are becoming more and more capital intensive.
Regarding the employment function of traditional agriculture and the informal sectors, the results indicate that the best fit regression is of an autoregressive nature. Previous period level of employment in the relevant sector determines the level of employment in the current period (ceteris paribus) and output produced does not explain the amount of labour hired to a large extent.
BLOCK 3 CONSUMPTION (ON GDP)
The two fitted regressions under this block satisfy all the statistical, econometric and economic theory criteria. The marginal propensity to consume is 0.5731. This value is relatively lower than those which have been established by Limpumba et al in the case of Tanzania. This coefficient is even lower for service consumption. These values, however, are relatively very high when compared to those of developed countries, (Hickman et al, 1976). The values are typical of medium-income countries. The results thus support the hypothesis that as incomes increase the marginal propensity to consume falls. Botswana is today a middle-income country.
BLOCK 4 FIXED INVESTMENT
All the ten fitted equations satisfy the statistical and econometric criteria. In the agriculture and utilities, fitted regressions output coefficients bear wrong arithmetic signs. These are apparently not statistically significant.
The estimated coefficients in respect of factor on GDP vary significantly between 0.9512 (for construction) and 0.0975 (for manufacturing). This suggests lack of uniformity in the characteristics of fixed investment between sectors in the country in as far as the output explanatory variable is concerned. Furthermore, in almost all the ten equations the lagged endogenous variable coefficient is statistically significant with the value being around 0.5. This means that the partial Adjustment behaviour is relevant to Botswana.
BLOCK 5 GOVERNMENT SECTOR
All the three equations representing the main sources of government revenue satisfy the statistical, econometric and economic theory criteria. All the marginal values estimated in the three equations are statistically significant (at 0.1 percent level of significance). The fact that the import marginal value is statistically significant implies that the customs revenue sharing formula is effective in the process of apportioning customs revenues in as far as Botswana is concerned.
The marginal rate of non-traditional GDP with respect to tax revenue agrees in value with those that have been established in other developing countries (the Tanzanian value, for example, is equal to 0.1361). Mining revenue contributes significantly to government revenue originating from rent, royalties and dividends. This is reflected in the value of its marginal rate, which is higher than those with respect to imports and non-traditional agriculture GDP. It is well-known that the long-term interest rate affects dividends received by government on its shareholdings in mining companies. Factors of significance to government revenue are the Shashe project and the diamond mines administered by Debswana (Lewis et al, 1983). The estimated coefficient in respect of the long-term interest rate variable unfortunately bears a negative sign which is also statistically significant. This is probably due to, among other things, the stagnation in interest rates.
BLOCK 6 PRICES AND SECTORAL LABOUR PRODUCTIVITY
Money supply does not appear in the best fit equation of the Consumer Price Index(CPI) implying that inflation in Botswana is to a large extent due to rises in the prices of imported goods and also due to the country's labour productivity. The estimated elasticities of import prices for the current year are 0.5522 and 0.8732 in respect of the CPI and the GDP, respectively. For the past year the value is 0.3059 in respect of the CPI, confirming the fact that import prices have very strong effects on overall Botswana prices. The fact that the current year import price coefficient is statistically significant in both the CPI and GDP equations implies that domestic prices respond effectively and instantaneously to imported inflation (within one year). Furthermore, as in the Tanzanian case (Limpumba, 1988), these results confirm the fact that the incomes policy on wages and salaries has succeeded in controlling inflation transmission via wages. The wage variable was tried and found to be statistically quite insignificant. There is also the absence of stickiness in almost all the equations except the agriculture deflator. This means that the responses to input prices and labour productivity changes for the nine sectors, excluding agriculture, are immediate.
On the other hand, unemployment has continued increasing in recent years. The incomes Policy, it appears, has not allowed for the smooth creation of additional jobs in the country. This is due to the fact that the policy uses government wages and salaries as a yardstick and basis for the determination of wages and salaries of all workers, including those in parastatals and semi-Government institutions. Government wages and salaries, however, may not be in line with the required levels as dictated by the demand and supply of labour in the market. It appears that for Botswana, where most of the inflation originates from without, an incomes policy simply brings about distortion in the equilibrium between the demand and supply of labour, resulting in unemployment.
BLOCK 7 MONETARY SECTOR
The links between money and prices in the model are shown in Fig. 1. The specifications and relative results of Block 6 show that the main determinants of prices are the import prices which reflect the prices of inputs and the labour productivities. Real money balances, do not appear in the expenditure functions of Blocks 3 and 4. As already mentioned, financial markets are not yet well-established in Botswana. For economies with well-established financial markets, the demand and supply of money determine the money stock and interest rates. Interest rates affect real expenditures in the consumption sectors and influence output and employment through the multiplier process. Labour demand directly affects money wages and, consequently, average unit costs and prices. At the same time, production levels influence prices via capacity utilization and the unit costs. It appears that this neat flow of causation is not relevant in the case of Botswana (just as it does not apply in most other countries operating without well-established financial markets).
The results represent the best fit empirical functions in respect of currency in circulation and total deposits respectively. In the case of currency in circulation, GDP turns out to be the most statistically significant variable. The average interest rates variable is also fairly significant. The level of prices variable is apparently weak in explaining the endogenous variable under consideration (currency in circulation). The value of the adjustment coefficient (one minus the coefficient of the lagged endogenous variable) is in the region of 0.64, and from the point of view of fulfilling the statistical, econometric and economic theory criteria, the fitted equation is quite satisfactory. The fitted equation for total deposits contains three explanatory variables. In this fitted equation also GDP is the most important explanatory variable.
Commercial banks, being profit-maximizing enterprises, would not opt for incurring the opportunity costs of holding excess cash. In the past, this has been the case in Botswana. The main reasons have been lack of demand for credit by borrowers, the high risk of lending money to some sectors, and the level of interest rates on the various types of loans. These facts are confirmed by the results of the fitted regression for excess reserves in which none of the above mentioned factors is statistically significant (neither at 0.1 level of significance nor at 5 percent level). Interest rates also determine the level of credit to the public by commercial banks. The results indicate that the rate of interest on loans is the most significant variable in this regard. The rates of interest have recently been changed to be in lien with the position in the money market, in which case they (interest rates) are bound to remain significant in this regard in future.
BLOCK 8 EXTERNAL TRADE
Producer Prices
Botswana's major exports are made up of beef and mineral products. Of the mineral products, diamonds account for about 75 percent to total export value. The BCL company which carries out the mining of copper-nickel at Selibe-Phikwe has not done very well (EIU, The Economist Intelligent Unit Annual Supplement, 1984). In the early years of production it was besieged by a succession of technical problems. This was followed by low metal prices due to world recession. These factors have caused the mine to operate at a loss and to accumulate significant and large arrears in debt payments to the principal shareholders. This explains why the variable representing BCL margins has a negative sign and is apparently not statistically significant.
The foreign exchange variable represents in this case the number of U.S. dollars per Pula. This means that the lower the value of the exchange rate the higher the number of Pulas per dollar. This explains why this variable carries a negative sign in the fitted regressions. Data for the export price of beef were difficult to come by. Records were obtained for a number of years and the rest were interpolated and extrapolated, and hence the poor performance of the variable in the equation describing producer price of beef. The consumer price index is nevertheless the most important determining factor for the relevant price.
PRODUCTION OF EXPORT COMMODITIES
The results indicate that beef production responds positively to own price increases. However, it does not respond to the price of the seemingly competing agricultural products. Statistics indicate that throughout the pre-independence period beef has enjoyed better price relative to arable agricultural products prices.
As for the metals, the results show very high and statistically significant labour coefficients. The inclusion of the time trend in the equations reduces the capital coefficient to almost nil and statistically insignificant. The capital coefficients in the omitted variable equations (when the time variable is excluded) are, however, relatively high and statistically significant. The positive and significant time trend reflects, for diamonds, the spectacular increase in production in the early eighties due to the opening of Jwaneng mine.
IMPORTS
Botswana is one of the few countries in Africa which operate with an open economy. There are almost no restrictions on foreign exchange for the amount of goods one can import in the country, subject only to the rules and regulations of the Common Customs Union. Imports of consumer goods are therefore not constrained by the supply of foreign exchange (a situation which is relevant in most other SADCC countries).
Foreign exchange obtained from the previous years' exports would therefore, normally, be expected not to be crucial in determining the level of imports of consumer goods in the current year in this case. This situation is confirmed by the insignificance of the relevant variable in the equation representing imports of consumer goods. As expected,the coefficient with respect to the index of food production is very high (0.83). Botswana is not food-sufficient and in the last decade had to import a significant proportion of its food-stuff requirements due to the recurrence of droughts.
The results also indicate that elasticities on the demand variables are either trivial or low. The variable GDP does not appear in the best-fit equations and the elasticity in respect of fixed capital formation in the equation for imports of capital goods is only 0.33.
BLOCK 9 INCOMES, TAXES AND WAGES
The results of the equation representing urban household personal income indicate that this factor is best explained or modelled using an equation of an autoregressive nature. The coefficient with respect to real non-traditional agriculture GDP is not statistically significant. It means that personal income that accrues to a particular household in the current year is determined, to a large extent, by the previous years' earned income.
In the rural household income equation, however, traditional agriculture GDP significantly determines the level of personal income. This is probably due to the fact that in rural Botswana (just as in most rural parts of any developing country) agriculture is the major source of income.
In urban areas, however,the majority of citizens supplement their incomes by conducting businesses outside their regular employment in rural areas, and some of this income is of traditional agriculture in kind (e.g. cattle-post).
In the private corporate profits equation, the unemployment rate is included to capture the possible decline in the corporate share of private output usually observed during business contractions. This factor has a very high and statistically significant elasticity in the relevant equation signifying the extent of effects of unemployment on the overall private corporate profits brought about by the Dutch Disease.
The results also indicate that personal taxes are best modelled by an autoregressive type of a relation in which the previous period level of taxes determines the current period level of personal taxes. As for corporate taxes the government corporate tax rate is the main determining factor, as expected.
