Derivation of Exchange rate



Introduction

The production account is compiled for fourteen industries according to the International Standard Industrial Classification (ISIC Revision 3) adopted by the Zimbabwean economy. Under normal circumstances main sources of data are economic censuses carried out yearly for agriculture, manufacturing, mining and quarrying, construction, and, water and electricity; annual surveys for services industries (used to determine cost structures); central and local government accounts; sales taxes; and employment statistics on numbers of employees and earnings as well as annual reports of public enterprises. Of late, due to inadequate funding of statistics, major economic surveys were carried until 2005. Due to this and many other challenges that were being experienced in the economy, alternative methods based on using some proxy indicators have been adopted.

2.0 The Calculation of Gross Domestic Product 2000- 2005

2.1 Derivation of a weighted exchange rate

For 2005 the amount of goods imported using the official exchange rates and imported using parallel market exchange rate were used as weights for deriving unitary exchange rate. This rate was used to convert the 2005 current price GDP in the Zimbabwean Dollar terms to GDP in US dollar terms for that year.

2.2 Calculation of Gross Domestic Product

The detailed formula is described below:

• A weighted exchange rate was found using the following formula: 0.4* Official exchange rate + 0.6 * parallel exchange rate. The formula is adopted following the assumption that 40% of the transactions were done on the formal market and 60% were done on the parallel market.

• 2005 was used as a benchmark, so the weighted exchange rate for the year was used to divide the nominal GDP for the same year to come up with the GDP in US dollars

• To project backwards the following formula was used: [pic]*[pic]

Where y stands for the year, and k stands for constant.

This was done for all the years backwards

• For the years after 2005, the following formula was used:

[pic]*[pic]

This method assumes that the movement in the GDP deflator is the same as those in the unitary exchange rate. This in turn implies that the GDP deflation for the GDP in US dollar is one each year i.e. there is no GDP inflation in US dollars.

If the movements in CPI were equal to the movement to the GDP deflator then all the movements will be the same as movements in unitary exchange rates

If such a scenario arises where CPI movement is the same as movement of the GDP deflator and movement in unitary exchange rates, then there is no inflation in US dollar terms

3.0 Compilation GDP for 2009

3.1 Value added Tax Method

Value Added tax (VAT) is a fraction deductible from value addition. In Zimbabwe VAT constitute 15% of the taxable industries’ value addition. The total VAT collected for 2009 is equal to $370, 443,408.65

Therefore the total value addition for the industries is $370, 443,408.65*[pic][pic]= 2,469,622,720

This figure was allocated proportionally to the contribution of each industry to VAT

Non taxable industries estimates were derived from recent surveys and production accounts as given in the account overleaf:

|INDUSTRY |Normal Source of Data |PROPOSED SOLUTION |

| | | |

| |a) Production Account of Agriculture, forestry | |

|Agriculture, Hunting and Forestry|and Fishing |Recent Crop assessment data were used. This data was |

| | |complimented with data from Tobacco marketing |

| |b) Crop production on large scale commercial farms, |institutions. VAT data on agriculture services, |

| |c)Agricultural production on small scale commercial |forestry hunting and fishing was added to come up with |

| |farms, |the value addition for the whole industry. |

| | | |

| |d)Agriculture and livestock on communal lands | |

| | | |

| |c) Agricultural services, | |

| | | |

| |d) Changes in herds communal and commercial, e)Net | |

| |additions to capital stock in large scale commercial | |

| |farms, | |

| | | |

| |f) Production by Agricultural Estates, | |

| | | |

| |g) Volume and value of livestock slaughtering and | |

| |milk and butter fat prodn , | |

| | | |

| |h)Public Corporations GFCF (From Finance parastatal | |

| |bodies summary) Central Govt. GFCF (From Finance GFS)| |

|Mining and Quarrying |a) Census of Industrial Production tables (final | |

| |tables), |In Zimbabwe almost all the minerals that are produced |

| | |are exported the value addition should be close to the |

| |b) Mineral production volume index (1990 = 100), |value of mineral exports. The value addition is |

| | |246,083,507 and the value of exports is 345,406,196 |

| |c) Value of mineral production, |the difference between being intermediate consumption, |

| |d) Central Govt. GFCF (From Finance GFS) |29% of gross output |

|Manufacturing |a) Census of Industrial Production tables (final |Value added tax was used. Value addition was |

| |tables), |496,936,835 plus around 20% informal sector |

| |b) Index of volume of production of the | |

| |manufacturing industries(1990=100) | |

|Electricity and Water |a) Census of Industrial Production tables (final), b)|Production accounts from ZESA holdings and Zimbabwe |

| |Electrical energy produced in Zimbabwe, |National water authority were used. |

| |c) Central Govt. GFCF (From Finance GFS), ZESA report| |

| |for GFCF (Finance section) | |

|Construction |a) Census of Industrial Production tables (Prodn |Percentage change in Imports for building and |

| |section) |construction Material was used to project 2008 figure. |

| |b) Construction work done by the public and private |The taxation data was very minimal |

| |sectors (prodn sect) | |

| |c) B roll earnings ( from company returns) | |

| |employment section, | |

| |d) Construction earnings (from employment section), | |

| |e) Central Govt. GFCF ( From Finance GFS) | |

| | | |

| | | |

|Distribution, hotels and |a) Turnover figures from the taxes department (Prodn |Tax data was used . Data for hotel occupants was |

|Restaurants |Section), |readily available from ZTA be readily available |

| |b) Retail trade value index (Prodn Section), | |

| |c) Hotel bed occupancy ( migration statistics), | |

| |d) National Accounts questionnaire analysis( Output | |

| |and GFCF), | |

| |e) Classification of functions of govt. (other | |

| |economic activities, central, local), | |

| |f) Parastatal bodies Summary (Finance Section), | |

| |g) Central Govt. GFCF (From Finance GFS), | |

| |h) Census of Distribution (preliminary figures) | |

|Transport and Communication |a) NRZ, PTC, AZ, figures (finance section parastatals| |

| |summary), Load tonne Km NRZ for the above from |Taxation data was used. |

| |Production section, Load tonne Km flown AZ for the | |

| |above from Production section, | |

| |b) CMED & Civil Aviation ( Finance section), | |

| |c) Consumer price index ( Code 17500), | |

| |d) Number of vehicles registered (production | |

| |Section/Min. of transport), NRZ own account | |

| |production ( Production Section), | |

| |e) PTC own production ( production Section), PTC | |

| |earnings code 7200 (employment section), PTC revenue | |

| |annual report ( Finance section), | |

| |f) National Accounts Questionnaire Analysis both | |

| |output and GFCF, | |

| |g) Parastatal bodies Summary (Finance Section), | |

| |h) Central Govt GFCF ( From Finance GFS) | |

| | |Taxation data was used |

|Finance and Insurance |a) Report of the Commissioner of Insurance and | |

| |Provident Funds(Min of Fin), | |

| |b) Finance statistics report (Finance Section), | |

| |c) Imputed banking charges | |

|Real Estate |a) Number of electricity connections from ZESA annual|Electricity new connections data was used |

| |report, | |

| |b) Rental income (estimated by national accounts), | |

| |c) Earnings from the employment section | |

|Domestic Services |Number of employees (all industries) from Employment|VAT data was used |

| |section, | |

| | | |

| | | |

| | | |

|Public Administration |a) Classification of Functions of Government figures |Data on industry employees and earnings from SSB was |

| |from finance section, |used, and also data on Governments Accounts |

| |b) Public Administration a) Earnings figures from | |

| |Employment section, | |

| |b) Numbers employed in public administration, | |

| |c) Gross fixed capital formation (GFS Finance | |

| |Section) | |

|Education |a) Classification of Functions of Government figures |Government accounts data was used. VAT data was also |

| |from finance section, |used for private education institutions |

| |b) Education Earnings figures from Employment | |

| |section, | |

| |c) Numbers employed in Education, | |

| |d) Gross fixed capital formation (GFS Finance | |

| |Section), | |

| |e) GFCF non profit making bodies ( Finance Section) | |

|Health |a) Classification of Functions of Government figures |Government accounts data was used. For private health |

| |from finance section, |institutions VAT data was used. |

| |b) Earnings figures from Employment section, | |

| |c) Numbers employed in Health, Gross fixed capital | |

| |formation (GFS Finance Section), GFCF non profit | |

| |making bodies ( Finance Section), | |

| | | |

| | | |

| | | |

| |a)Classification of Functions of Government figures |Vat data was used. |

|Other Services |from finance section, | |

| |b) Earnings figures from Employment section, | |

| |c) Numbers employed in other services, | |

| |d) Gross fixed capital formation (GFS Finance | |

| |Section), | |

| |e) GFCF non profit making bodies ( Finance Section), | |

| |Parastatal bodies Summary (Finance Section), | |

| |f)National accounts Questionnaire analysis (GFCF) | |

3.2 Rough Check on the validity of the GDP figure

Under normal circumstance the taxable industries constitute 53 % of GDP at factor cost

GDP at factor cost is therefore equal to 2,469,622,720 *[pic] = 4,659,665,509

If we add net the value of net tax which is 758,540,227

The figure comes to $ 5,366,048,433

3.3 Expenditure Tables

The figures are still very preliminary:

|Private Expenditure |Income and Expenditure survey (ICES) and |Calculated as a residual |

| |As a residual | |

|Consumption Expenditure by Non |Boosted Output figures from the survey results (Finance Section) |Data for the survey was used |

|Profit Making Bodies | | |

| | | |

| | | |

| |a) Central Government intermediate consumption by commodity, |COFOG data was used |

|General Government consumption |b) Local Government intermediate consumption total, | |

|expenditure |c) Fees sales and recoveries for both central and local government, | |

|GCF |ICES data, Agriculture Production Account, CIP, COFOG |COFOG data was used for government. |

| | |Imports of Building and construction |

| | |materials will be used, car parts and|

| | |plant and machinery as well |

|GFCF |ICES data, Agriculture Production Account, CIP, COFOG |Imports of Building and construction |

| | |materials will be used, car parts and|

| | |plant and machinery as well |

|Changes in stock |GMB, oil refinery company, sugar refinery, tobacco sales floors, |Data was obtained from GMB, GMB, oil|

| |agriculture production account |refinery company, sugar refinery, |

| | |tobacco sales floors and changes in |

| | |lives stocks were imputed |

|Exports and Imports |Customs and Exercise data | |

| |Reserve Bank BOP data |Customs and exercise data was used, |

| | |BOP data was used |

|Property income paid and |Reserve Bank BOP data |BOP data was used |

|received from abroad | | |

4.0 Calculation of CPI in United States Dollars

4.1 Introduction

The Central Statistical Office of Zimbabwe produces a consumer price index (CPI) and the month on month and year on year rates of inflation for the whole country once every month. The CPI is based on price observations from across the country covering both urban and rural outlets and weights obtained from the latest Income Consumption and Expenditure Survey (ICES)

As the economic situation characterized by hyperinflation deteriorated in 2007 and 2008 many products became scarce or unavailable in the country. The number of observations per month of the prices of the products used for computing the CPI similarly decreased. Under normal circumstances on average, close to 1500 observations of prices of all products were made every month. However, less than 500 observations per month were being made in the last half of 2008.

The period was also characterized by an increase in the number of domestic transactions that were conducted in foreign currency. This began unofficially, as parallel or black market activities, then there was a mixture of both official (some shops were licensed to sell in foreign currency) and unofficial domestic transactions in foreign currency, until early in 2009 all transactions were permitted to be conducted in foreign currency.

It thus became necessary to construct a CPI of transactions in foreign currency. Although the office had begun observing prices both in foreign and local currency from the middle of 2008, there were very few recorded observations of prices in foreign currency until December 2008 when a total of 283 observations were recorded.

This paper describes how the challenges of constructing a new foreign currency based CPI, without conducting an ICES and faced with having to start with a few products that were available and accommodating an increasing number of products as they reappeared in the market, were handled. The techniques employed were similar to those used when the number of products available in the market was decreasing.

The normal method of calculating the CPI and rates of inflation in Zimbabwe

i) Index

Every month prices of about 385 products are observed from outlets across the country in both rural and urban areas. The work is organized by province and for each province a geometric mean price for each item is calculated every month. The mean price is calculated for those items for which there are matching observations of prices, outlet by outlet in the current and previous month. A geometric mean price ratio of current to previous month prices is also calculated for each item, each province. National weighted mean prices and weighted mean price ratios are calculated from the provincial mean prices and mean price ratios, respectively, using expenditure weights obtained from the ICES.

The Laspeyres formula is used for calculating the price index. The month on month rate of inflation is obtained by dividing the current by the previous month’s index and expressing the change as a percentage while the year on year rate of inflation is obtained by similarly comparing the figures for the current month with those of the same month in the previous year.

The calculation of the index is done at the lowest subclass level of aggregation. The class index is then obtained as a weighted mean of its subclass indices. The weight of the sub class is equal to the sum of the weights of the individual elementary aggregate items that comprise the sub-class.

We have

[pic][pic] = [pic][pic]

= [pic] [pic]

= [pic]

= [pic]

= [pic]

In the above [pic] is the price of an item in the current month, the national weighted mean price as described above;

[pic]is the price in the base or reference period;

[pic]is the quantity of the product consumed in the base period and generally,

[pic] is the price of the item in the sth month.

[pic] = [pic] is the weight of item or its expenditure share during the period the Income, Consumption and Expenditure Survey (ICES) was conducted.

For the above derivation the ICES period is taken as though it is also the reference period for the prices.

The formula for It is applied at the smallest sub-class level for which prices are observed from the outlets, for example the bread sub-class. In this instance wo refers to the share of each type of bread in the total household expenditure as at the time of the ICES.

The index for bread for any month t is thus given by

[pic]

[pic] for white bread, 2 for brown bread and 3 for biscuits.

For computational purposes [pic] is taken as a weight[pic].

Hence [pic], in the above example.

The index for the next level of aggregation is obtained as a weighted arithmetic mean of the indices of the subclasses in the class. The process is repeated in a similar manner up to the all items index.

ii) Rate of Inflation

The month on month rate of inflation is obtained as It/It– 1 = Rtm.

The year on year rate of inflation is obtained as It/It–1 = Rty

Rtm and Rty are the month on month and the year on year rates of inflation, respectively.

Due to non availability of products we obtained

[pic]

[pic] [pic]

We then obtained [pic] for t = 2,3,……

I1 = [pic]

Compare [pic] [pic]

and [pic] for a sub-group like bread.

[pic]

= [pic]

= [pic]

= [pic]

= [pic]

= [pic]

= [pic]

= [pic]

The index for a subgroup for a month is calculated using the Laspeyers formula.

[pic][pic]

For computational purposes this is written as follows:_

[pic] = [pic]

= [pic] [pic]

= [pic]

= [pic] [pic][pic]

The rate of inflation for the subgroup for the month is given by[pic].

Milk, cheese and eggs consists of the items sour milk, fresh milk, sterilized milk, powdered milk, full cream and powdered milk for babies.

The formulae for Ik and Rt could not be used in Zimbabwe when the US dollar based consumer price index was introduced with the reference December 2008 = 100 but still using the weights derived from the 2001 Income, Consumption and Expenditure Survey (ICES). The reason was that there were items that were not available in the market as at December 2008. Infact from a possible 1400 observations of all items across the country only 280 odd were made in December 2008. The products became increasingly available as the months progressed in 2009.

When a product was not observed at all it was dropped, together with its corresponding weight, from the calculation of the index for its group and the all items index. For January 2009 only those items whose prices had been observed both in December 2008 and January 2009 were included in the calculation of the index. Since the index had December 2008 = 100, for January 2009 the index and the month on month rate of inflation were the same.

An item whose price had not been observed in December 2008, had to have its prices observed for at least two consecutive month before it was included in the calculation of the index and rate of inflation.

The usual computational technique of calculating [pic] as described above, could not be applied directly because it required knowledge or an estimate of

[pic], which did not exist because pio did not exist.

However an index with the previous month = 100 including all items whose prices had been observed both in the current and previous month. The month indices are also the month on month rates of inflation.

By chaining such indices, an estimate of the index for the current month with December 2008 = 100 was obtained.

Hence [pic].

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