APPENDIX TO “DETERMINANTS OF MINING
INVESTMENT: A CASE STUDY OF ZIMBABWE”
Lyman Mlambo, Institute of Mining Research, University of Zimbabwe
Theoretical Literature Review on Determinants of Investment
The following two sections briefly look at the main theories of investment. It is from theories of investment that we identify the major factors that determine investment. The two theories 1looked at here are Keynes’ theory and the accelerator model.
2Keynes’ Theory of Investment
Pentecost (2000, p.119) identifies two main components to the theory: (1) the role of expectations; and (2) supply price of capital goods. He views the value of a piece of capital equipment as the net present value of income that will be derived from the use of that equipment, that is, income over and above its purchase cost. That is, value or demand price of machine (V) is given by:
nmRI3ttNPV！？ (1) ；；tt;；;；1？i1？it！！m？10t
where n = the whole life of the piece of equipment
m = the whole investment period (that is the time it takes to set up the investment equipment).
This may be one year or more.
i = discount rate (normally, the rate of interest)
R = net receipts from use of machine in period/year t.
A net present value of zero indicates that the project is not profitable, while any positive NPV shows that the project (or having the asset) is profitable.
It can be observed that the first term in the RHS is the total income/net receipts from the use of the equipment over its lifespan (n), and that the second term is the total cost of having the equipment operational or its purchase price or cost.
The rate of discount which ensures that NPV is equal to zero, or that total net receipts over the asset life equals the cost of the asset, is of great interest and it is called the internal rate of
return (IRR). It is what Keynes calls the marginal efficiency of capital(MEC) and is actually
the expected rate of return from a capital asset (Shapiro, 1974). IRR is the discount rate that ensures that net receipts cover the initial cost.
The market interest rate is a measure of the cost of loanable funds hence may be used to discount future money to present value because it represents the time value of money. A lower interest rate will mean that future receipts of a project are not heavily discounted, and
1 Two other theories are identified in the literature – neo-classical theory and Tobin’s Q-theory (see
Dzawanda 1994 and Pentecost 2000). However, apparently what we get from the neo-classical theory is the emphasis on the importance of real rate of interest in the calculation of user cost. From Tobin the emphasis is on the financial market as an alternative investment to investment in real markets. 2 Based on Pentecost (2000), NEPC Handout, and Shapiro (1974). 3 This formulation is from NEPC Investment Profitability Analysis’ handouts. For a more detailed treatment of this theory read Pentecost (2000) and Shapiro (1974)
when their present value is compared with initial project costs, the NPV will be higher than with a higher rate of interest.
Therefore, a comparison of the MEC to the current market rate of interest, r, indicates
whether or not an investment may be profitable. It would be profitable if r < MEC and vice versa. That is, if the interest rate in the market is lower that the one that would give a profit of zero, then investment profitability is positive. Thus, once MEC is given, r determines whether
or not the good will be purchased though it does not determine the MEC of that good (Shapiro, 1974, p.163).
IRR (MEC) may be computed by a trial and error method (where one tries several discount
rates until the appropriate one is found) or some short-cut method (adhoc method) (NEPC
Handout on Investment Profitability Analysis).
Anything that makes the businessman expect more income flow from use of a capital good, assuming the capital good does not change its price, will raise its MEC. Also a fall in the price of the capital good (by reducing costs hence increasing NPV) with expected income unchanged will raise its MEC. A decrease in r affect MEC though it would make the purchase of the good more profitable if r falls below MEC from a position of MEC<r (Shapiro, 1974, p.163).
If a firm has a given set of possible investment projects and assuming it has the money available or can borrow to invest, each year it will invest in the projects whose MEC are higher than the current market rate of interest. As the market rate of interest falls, ceteris
paribus, new additional projects with lower MECs are undertaken. The optimal level of capital stock in any given year is that where the least (last) profitable of all the projects has MEC equal to the current of interest, otherwise, the capital stock is not optimal. When MEC = rate of interest there is no need for net investments (Shapiro, 1974, pp.164-165).
Therefore, all things the same, a change in either interest rate or MEC affects net investment. When interest rate falls more projects will be undertaken and vice versa. When MEC falls (due to change in business conditions) less projects will be undertaken at the same rate of interest (many projects become less profitable) and vice versa.
The Keynesian investment function can then be summarised by:
I！；？；i (2) 01
；where captures exogenous shifts in (business) expectations (Pentecost, 2000, p.124). Thus, 0
both MEC and interest rate affect investment.
The Accelerator theory of investment
The flexible accelerator model assumes the existence of an equilibrium, optimal, desired, or
long-run stock of capital required to produce a given output for a given technology, rate of interest, and so forth (Gujarati (1988, p.519).
Further derivation follows equation (3).
*K！；Q (3) t1t
*KQwhere is desired mining capital stock in period t, and is current mining output in tt
4The capital adjustment process is defined by the following equation:
*;；K？K！，K？K (4) tt？1tt？1
where , being , is the coefficient of adjustment. ，0，，：1
*;；K！，K？1？，K (5) ttt？1
Substituting (3) into (5) and simplifying gives:
5;；K！，；Q？1？，K (6) t1tt？1
The net investment function as strictly based on relationship (4) becomes:
nK？K！I！，；Q？，K (7) tt？1t1tt？1
(If we assume that replacement investment in period t is a positive proportion of previous 6period’s level of capital, gross investment is given by (See Dzawanda 1994):
gI！K？K？(K (8) ttt？1t？1
g;；I！K？1？(K (9) ttt？1
Substituting (7) into (8):
g;；I！，；Q？(？，K (10) t1t？1t？1
Lagging (10) once and multiplying the result by (1？)we get: (
g(1？()I！，；Q？(1？()((？，)K (11) t？11t？1t？2
Subtracting (11) from (10) gives:
g;；I！K？1？(KBut from (9), . Therefore: t？1t？1t？2
4 Pentecost, 2000, p.124; Gujarati, 1988; Dzawanda, 1994. 5 Both Pentecost (2000) and Dzawanda (1994) apparently make a mistake in deriving equation 9. 6 The rest of the derivation here follows this reference.
ggI！，；Q？，；(1？()Q？(1？，)I (12) 11？1？1tttt
Adding a constant for autonomous investment and an error term , gross investment is ；u0t
finally specified as a function of current output, lagged output and lagged investment:
gggg;；I！IQ,Q,I！；？，；Q？，；(1？()Q？(1？，)I？u (13) tttt？1t？101t1t？1t？1t
Model (14) can then be estimated. The coefficients of current output, lagged output and lagged investment as explanators of mining investment can be tested for significance. Notice that from this estimation we can also find the values of the coefficient of adjustment () and ，
(the depreciation rate ().
Mineral Reserves estimate Year
Gold 84 000 000 t 1990s
Asbestos 560 000 000 t 1993
Nickel 114 000 000 t 1980
Coal 2 000 000 000 t 1992
Copper 350 000 000 t 1988
Chrome 608 000 000 t 2001
Iron ore 100 000 000 t 1973
Cobalt 8 000 t 1987
Platinum 136 000 000 t 1988
Aluminium 2 000 000 t 1983
Estimated Results from a Flexible Accelerator Model for Zimbabwe
This study estimated model (13), reproduced below, using the data for Zimbabwe Mining sector from 1977 to 1997. Data from 1998 to 2009 could not be used because they are either not available or unreliable. The data was obtained from Reserve Bank of Zimbabwe (1998) and CSO(2001).
gggg;；I！IQ,Q,I！；？，；Q？，；(1？()Q？(1？，)I？u (13) tttt？1t？101t1t？1t？1t
The above model is both an autoregressive model and a distributed lag model. To take care of autoressiveness we use the instrumental variable technique, and the ad hoc method is used to
deal with the problem of distributed lags. First, we regress gross mining investment against mining sector current and lagged outputs, from which we get estimates of investment. These estimates are lagged to get an instrumental variable for the lagged investment variable.
Model without lagged output variable
Model with lagged output variable, uncorrected for autocorrelation
According to the ad hoc method of estimating a distributed lag model, we begin with current output and then regress with lagged output included. In this sequential regression if the coefficient of any lag of the concerned variable changes sign and/ or the coefficient becomes insignificant one takes the last stable result. Note that since the variable Q is the one being lagged we may view Q as being with lag zero. We note in the above regressions that in (15) the coefficient of Q changes sign which makes (15) unstable. A further analysis of (15) will show that and that , since they are respectively computed from the results as 6.5 ，，1，0；
and -0.08. The results would also imply a negative rate of depreciation. These values are meaningless since they mean that in any year miners actual capital is 6 times more than they would desire in the long run and that the proportion of desired capital to output is negative. Note that the qualitative results in (15) will not change even after correcting the regression for autocorrelation. For these reasons model (15) is rejected as unsuitable.
Therefore, (this is the coefficient of adjustment, which we may equate to 1 since ，！1.1271
；！0.302-0.1271 is not significantly different from zero), and (which is the proportion of 1
desired capital to output). The value of the proportion of desired capital to output indicates that when output increases by 100% (doubles) desired capital stock increases by 30%. When we combine this result with that on coefficient of adjustment the result is that actual capital must also increase by about 30% (approximately equal to 34%). All that this shows is that current output is very significant in determination of investment and that desired capital is approximately the same as the desired stock.
for investment estimation
Year Q Q-1 I
1977 238 230.5 66
1978 252 237.5 59
1979 315 252.2 83
1980 415 314.8 83
1981 394 414.8 133
1982 383 393.5 94
1983 470 383 86
1984 546 470.5 81
1985 629 546.5 35
1986 699 629.5 57
1987 816 699.4 123
1988 986 815.6 200
1989 1144 985.7 144
1990 1346 1144 166
1991 1863 1346 273
1992 2485 1863 512
1993 3086 2485 518
1994 4327 3086 785
1995 5412 4327 2000 1996 6110 5412 2370 1997 6630 6110 1552