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African Journal of Agricultural and Resource Economics Volume 10 Number 1 pages 1-
The flexible accelerator model of investment: An application to
Ugandan tea-processing firms
*Edgar E. Twine International Livestock Research Institute, c/o IITA East Africa Hub, Dar es Salaam, Tanzania. E-mail: [email protected]
Barnabas Kiiza Makerere University, Kampala, Uganda. E-mail: [email protected]
Bernard Bashaasha Makerere University, Kampala, Uganda. E-mail: [email protected]
Abstract
The study uses the flexible accelerator model to examine determinants of the level and growth of investment in machinery and equipment for a sample of tea-processing firms in Uganda. Using a dynamic panel data model, we find that, in the long run, the level of investment in machinery and equipment is positively influenced by the accelerator, firm-level liquidity, and a favourable investment climate in the country. Depreciation of the exchange rate negatively affects investment. We conclude that firm-level strategies that increase output and profitability, and a favourable investment policy climate, are imperative to the growth of the tea industry.
Key words : accelerator model; fixed asset investments; Ugandan tea-processing firms
1. Introduction
Investment or capital accumulation is widely regarded as important in raising output and income at both the firm and national level. The private sector in Uganda has responded to macroeconomic policy reforms with private investment increasing by 13% per year on average from 1986/1987 to 1997/ (Collier & Reinikka 2001). The sectors that have attracted most investment in recent years are manufacturing, agriculture, forestry, fishing, construction and services. Inflows of foreign direct investment into these sectors have positively influenced economic growth in the country (Obwona 1997). The formal and informal manufacturing sector has experienced an average growth rate of 6.6% per annum and constitutes about 10% of GDP. The manufacturing sector is characterised mainly by the production of simple basic consumer goods. Capital goods industries are still few in number, while textiles, apparel and especially agro-processing are seen as promising industries (Ministry of Finance, Planning and Economic Development 2003). The Ugandan government has for long believed that diversification and promotion of value-added agricultural production is crucial to achieving favourable terms of trade. But most of the country’s exports are still in raw form, with little or no value addition. This is in spite of the government’s Medium-Term Competitiveness Strategy (MTCS), which was aimed at creating a favourable environment for increased private investment (Ministry of Finance, Planning and Economic Development 2000), and the Marketing and Agro-Processing Strategy (MAPS), which outlined priority areas for public sector intervention in agricultural marketing and agro- processing (Ministry of Finance, Planning and Economic Development and Ministry of Agriculture,
Animal Industry and Fisheries 2003). Therefore it is important for policy makers to understand the mechanisms through which government policy would systematically have an impact on private investment in agro-processing.
Tea is one of Uganda’s major export commodities and its processing requires substantially larger investment than coffee and grain processing. Competitiveness of the tea sector would benefit from growth in investment in processing because production of high-grade tea is hampered by inadequate sorting machines, low withering capacity and a lack of adequate space for sorting, bulking and packing. This study focuses on value addition in a sample of tea manufacturing firms by exploring the current rate of investment in tea-processing machinery and equipment. Machinery includes rotavens, fermenters, dryers, boilers, pre-sorters, vibroscreens and lathe machines. Equipment includes weighing scales, thermometers, density meters, infrared moisture detectors and hygrometers.
Past studies, such as those by Reinikka and Svensson (1999; 2001) and Darku (2001), on investment behaviour by private firms have been based on a sample of firms from different sectors, without accounting for unobservable sector-specific factors. Other studies, such as that by Jenkins (1998), use only macroeconomic time series data to study private investment. This paper deviates from these studies by using firm-level panel data to examine the factors that have an impact on the level and growth of investment in machinery and equipment in a single sector. In addition, the paper provides further evidence of the appropriateness of the flexible accelerator model in studying investment behaviour.
2. Models of investment behaviour: A synopsis
Investment models usually distinguish two separate elements in the investment process: the determination of a desired capital stock and the specification of an adjustment process by which the gap between existing and desired capital stock is filled (Spyros 1983). Baddeley (2002) has provided a detailed description of the four theoretical models of investment behaviour, namely the accelerator theory, the neoclassical theory of Jorgenson, the q-theory of Tobin, and the option theory. These models typically introduce the effects of determining factors such as output, finance and prices through the desired capital stock, and the adjustment of capital to the desired level is considered an independent process.
The formulation of the accelerator model can be traced back at least to Clark (1917). Clark (1917: 234) explained that demand for capital “varies, not with the volume of demand for the finished product, but rather with the acceleration of that demand”. Because of Clark’s focus on quantity as opposed to price, his model is regarded as being ‘Keynesian’ in spirit and has been referred to as the rigid (simple) accelerator model of investment (Akkina & Celebi 2002). The rigid accelerator model explains investment as a function of output growth only and assumes that the desired stock of capital is attained in each time period. But because the model ignores the influence on investment of uncertainty, profits, financial factors and other variables, it has over time been reformulated into the so-called flexible accelerator model of investment (Goodwin 1948; Chenery 1952; Koyck 1954; Lucas 1967; Gould 1968; Treadway 1971). The model is flexible in the sense that it allows investment to vary with other relevant variables, including those related to uncertainty and market imperfections. This is especially important when analysing investment behaviour in developing economies [see, for instance, Wai and Wong (1982), Dehn (2000), Erden and Holcombe (2005), and Shih et al. (2007)]. Another important feature of the flexible version is that adjustment to the desired capital stock is not considered to be instantaneous.
invest in a tangible asset. The investment opportunity may accrue to the firm as a result of the firm’s ownership of patents, unutilised resources/capacity, reputation, and managerial competencies (Dixit & Pindyck 1994). There are different types of real options, the most common of which are: option to defer, time to build option, option to alter operating scale, option to abandon, option to switch, growth options, and multiple interacting options (Trigeorgis 1993). Dixit (1992) uses the option to defer an investment to demonstrate that uncertainty and irreversibility have an effect on the value of a firm’s real options. In fact, the option to defer exists as a result of uncertainty. Also known as the option to wait, a deferral option is an American call option where one has the right to delay the start of an investment project (Copeland & Antikarov 2001). The money needed to start the project is referred to as the exercise price. According to Dixit (1992), investments may involve sunk costs, and the economic environment is often characterised by uncertainty. Moreover, a postponed investment opportunity is not necessarily a missed opportunity. Thus there is a benefit to waiting for more and better information, implying that the option to wait has a positive value.
The three common real options models include the Black-Scholes option pricing model (Black & Scholes 1973), the binomial option pricing model (Cox et al. 1979), and the Dixit-Pindyck model (Dixit & Pindyck 1994). Although these models are not econometric in nature and therefore would not be applicable to this study, their empirical application has been helpful in emphasising the need for econometric models to account for uncertainty in investment behaviour.
3. Conceptual framework and empirical model
In this study we employed the flexible accelerator model, in which capital is adjusted toward its desired level and therefore the firm’s net investment is proportional to the change in desired capital (Latruffe 2004). The model is essentially a partial adjustment model and, just like the adaptive expectations model, it is a theoretical justification of the Koyck model^2 (Gujarati 2003). Under the partial adjustment process, capital stock is adjusted only toward a proportion of its desired stock, since the adjustment is not instantaneous. We assume that there is an optimal or desired equilibrium amount of capital stock needed to produce a given output under a given state of technology and rate of interest. The demand for capital increases when the demand for output accelerates, hence the name accelerator model (Latruffe 2004). Following Reinikka and Svensson (2001), we take the cost of instantaneous net investment as given by C ( I ), where I is net investment and C is a cost function, with C ( 0 ) 0 and,
since desired capital is the stock of capital that a firm would hold if adjustment costs were momentarily
removed (Chun & Mun 2005), C '^ ( I ), C "^ ( I ) 0 for all I 0 .Firms are assumed to maximise profit^3 ,
where the profit function, ( t , K ), is concave in capital stock. That is, (^) k '^ ( t , K ) 0 and
" k^ ( t , K ) 0 , where t is time. We also assume that firms take product and factor prices as given. At
constant relative prices, investment is given by:
I (^) t ( K * K t ) (1)
(^2) The Koyck model is obtained by algebraically converting a distributed-lag model into an autoregressive model. The adaptive expectations model can be combined with the partial adjustment model to obtain an autoregressive model, with the first and second lags of the dependent variable as explanatory variables. (^3) In deriving the model, Bigsten et al. (1997) and Gunning and Mengistae (2001) assume firms maximise profit with a value
function of the form Vt ( Kt )max ( Kt , Lt , It ) t 1 Et V t 1 ( Kt ), where Lt is labour, t 1 is the firm’s discount
factor, and the expectations operator Et is conditional on information available at time t.
where K * is the desired capital stock, K (^) t is actual capital stock in the current period, and is a
coefficient of adjustment, such that 0 1. Investment is taken to be proportional to the gap
between the desired and actual capital stock. That is, investment will be large if the desired capital
stock is much larger than the current capital stock. If the expected future demand for output is Q * , then
Kt Q t where 0 1. That is, desired capital stock is proportional to expected demand for
output, implying a fixed proportions technology^4 , and is determined by relative prices. Equation (1)
is rewritten as
It ( Q * t Kt 1 ) (2)
Demand expectations are assumed to be linear functions of current output, and thus
It ( Qt Kt 1 ) (3)
where 0 1. First-differencing of equation (3), and noting that I (^) t 1 Kt 1 Kt 2 , implies that
It 1 Q ( 1 ) It 1 (4)
where 1 and Q is change in output. Equation (4) is the traditional flexible accelerator model,
where fluctuations in sales induce investment.
Investment in the previous period can have either a positive or negative effect on current investment, depending on its magnitude, returns and the cost of adjusting the stock of capital. According to Lamont (2000), lagged investment captures the effect of investment lags such as delivery lags, planning lags and construction lags, which may cause actual investment to be negatively correlated with current returns. In addition, lags may prevent firms from immediately adjusting investment when, for instance, the discount rate changes. Therefore variations in expected investment are a large part of the variations in actual investment, a phenomenon that causes this year’s investment to be chosen in the previous year.
Tybout (1983) observes that, when firms finance all investment from profits and retained earnings, they behave according to equation (4). But, due to binding shortages, they invest using current profits. Current profits represent the importance of a firm’s internal liquidity. Given Uganda’s weak financial sector it is assumed that firms do not have adequate access to credit and therefore use current profits to invest. Thus
It C ^1 ( t ) (5)
If investment is constrained by availability of and/or access to financial resources, it is expected that its level will increase with firm age, At (Bigsten et al. 1997; Gunning & Mengistae 2001). Age is a
measure of experience accumulated by the firm. In addition to affecting access to finance, experience
(^4) This and the assumption of constant relative prices rule out the role of factor prices in the characterisation of optimal investment behaviour.
government). The ratio of M2 to GDP is used as a proxy for the size of formal financial market infrastructure or financial depth in the economy (Long 1990; Izumida 1992). We hypothesise that an increase in the financial depth of an economy positively affects a firm’s investment behaviour by widening the options for investment finance.
4. Data and estimation
The data used for the study were obtained from a sample of five randomly selected tea-processing firms for a fourteen-year period from 1990 to 2003. This represents 22% of the total number of tea- processing firms in Uganda. The data consists of detailed audited accounts information on several variables, including firm profits in Uganda Shillings (USh), value of output of processed tea (sales) in USh, firm age in years, firm size as number of employees in each firm, and stock of machinery and equipment in USh. Investment is then computed as the difference in capital stock between the current
period and previous period ( Kt Kt 1 ), while investment rate is computed as the ratio of investment to
capital stock in the previous period, { ( Kt Kt 1 )/ Kt 1 }. The value of output of processed tea is used as
a proxy for output. In addition, macroeconomic variables for the same time period, including consumer price index (CPI), real exchange rate, interest rate, inflation rate, index of industrial production, GDP and M2, were obtained from the archives of the research department of the central bank of Uganda. All variables were transformed into real form using the consumer price index and 1990 as the base year. Summary statistics of the variables are provided in Table 1.
The dynamic panel data model used in this study presents complications in estimation, primarily because of the presence of a stochastic explanatory variable; in both the fixed and random effects setting, the lagged dependent variable may be correlated with the error term, with or without serial correlation in the latter (Greene 2008). For instance, in the Koyck and adaptive expectations models, the lagged dependent variable is correlated with the final error term because it (the lagged dependent variable) is contemporaneously correlated with a lagged original error term that is a component of the final one. As such, ordinary least squares (OLS) estimates of these models will be both biased and inconsistent. In our partial adjustment model, however, the lagged dependent variable is not contemporaneously correlated with either the final or original error term. Therefore, OLS estimates will be consistent, but biased in small samples (Gujarati 2003) such as ours, since the stochastic variable and error term are not independent for all observations. Greene (2008) observes that, for relatively small time periods of say five to 15, the bias in estimation of the coefficient on the lagged dependent variable ranges between 15 and 60%. Moreover, in the presence of serial correlation, the estimator becomes inefficient as well. The challenge in this analysis is to determine and apply an estimator to our dynamic panel data model that will reduce the inefficiency of our parameter estimates.
Table 1: Summary statistics of variables used in the model, 1990 to 2003 Variable Mean Std. Dev. Output (billion Shillings) 1.629 1. Capital stock (million Shillings) 894.543 749. Profit (million Shillings) 34.160 271. Firm age*^ (Years) 33.8 4. Inflation rate 8.19 10. Exchange rate 90.54 14. Interest rate 20.92 1. Ratio of M2 to GDP 0.241 0. Ratio of IIP to GDP 3.41E-11 1.94E-
- Average age in 2003 Source: Survey data
Several estimators of dynamic panel data models have been proposed in the literature. Recently, Kao and Chiang (2000) derived the dynamic OLS (DOLS) estimator, which they found to be superior to both the OLS and the fully modified OLS (FMOLS) estimators. These estimators require that the variables in the panel be co-integrated, which, according to Pedroni’s (1999) co-integration test, is not the case with our data. Anderson and Hsiao (1981, 1982) propose a general approach based on instrumental variables. Their relatively computationally simple estimator controls for heterogeneity in both the fixed and random effects cases, using either the twice-lagged levels or twice-lagged first differences of the dependent variable.^5 But it has been shown that there in fact are a potentially large number of instruments that can be accommodated by this estimator, including all values of the exogenous variables (Ahn & Schmidt 1995; Arellano & Bond 1991; Arellano & Bover 1995). Consequently, Arellano and Bond (1991) and Arellano and Bover (1995) used the general approach to develop a GMM estimator that is more efficient. The estimator was further improved by Blundell and Bond (1998). For these reasons, we applied and compared the results of both the fixed effects Anderson-Hsiao (AH) estimator and the Arellano-Bover/Blundell-Bond (AB/BB) consistent GMM estimator, which allows for serial correlation in the errors.
5. Results
5.1 Investment rate
The average investment rate was found to be 18% for all tea-processing firms in the sample. This rate lies between the 1996/1997 average rate of 23% for Ugandan firms (including manufacturing, commercial agriculture, agro-processing, fishing, construction and tourism) that invested and 12% for all firms – those that did and did not invest (Reinikka & Svensson 2001). The average investment rate for tea-processing firms in Uganda can also be compared with rates of investment in African countries, which at the median value have generally been low relative to those of Europe and India. Investment rates in manufacturing for the different countries were found to be less than 10%, implying that small maintenance and replacement investments were an important part of investment activity (Bigsten 1997; Naude et al. 2000). Investment rates for South African manufacturing firms were found to be 17% and 10% for large and small firms respectively, which were low but also comparable with those for other African countries.
(^5) Arellano (1989) and Kiviet (1995) find the estimator based on levels as instruments to have a variance that is smaller than that for the estimator based on differences.
raising external funds, firms have sufficient reason to use internal funds to finance investment. In the long run, if taken as retained earnings, profits play a key role in funding investment. Based on the importance of profit in investment behaviour, we find results from the AB/BB estimator to be more plausible than those obtained from the AH estimator.
The equation estimated with the AH estimator includes the ratio of M2 to GDP, i.e. [M2/GDP], while the one estimated using the AB/BB estimator includes the ratio of the index of industrial production to GDP, [IIP/GDP]. Both variables are positive and significant, as expected a priori. That the ratio of M to GDP is significant means that a larger financial market infrastructure leads to higher investments by the firms. The index of industrial production may be indicative of the positive influence of favourable investment policies for the manufacturing sector that have been pursued by the country through the Uganda Investment Authority (UIA). Growth in gross domestic investment signifies a favourable investment climate for individual firms.
5.3 Determinants of growth in investment
Table 3 summarises the results of the short-run investment model. From the AH estimator, we find that the accelerator model does not explain investment behaviour in the short run. However, the model appears to hold when estimated using the more efficient AB/BB estimator. Change in sales represents demand-influenced forces and has an implication for capacity expansion, whereby an increase in sales may result in the need for more tea-processing capacity, hence inducing further acquisition of capital. Change in lagged investment is investment growth in the previous period. From both estimators we obtain a negative and significant coefficient, suggesting that investment growth in the previous period has a negative influence on investment growth in the current period. We posit that investment growth in the previous period increases the supply capacity of tea firms, which in turn dampens investment growth in the subsequent period. Growth in macroeconomic factors does not seem to affect investment in the short run.
5.4 Elasticities
To better understand the importance of the significant variables in our model, we provide their elasticities in Table 4 with respect to the level of investment. The magnitudes of the elasticities obtained from the AH estimator are twice those obtained from the AB/BB estimator. From both estimators it is clear that, in the long run, investment is mostly responsive to foreign exchange rates; from the AB/BB estimator, a 1% depreciation of the Uganda shilling would lead to an 8% decline in the level of investment, whereas a 1% growth in output would increase the level of investment by about 0.5%. The estimated elasticity with respect to profit is small.
Table 3: Determinants of growth in investment by tea firms Anderson-Hsiao Arellano-Bover/Blundell-Bond Variable Coefficient z-statistic p-value Coefficient z-statistic p-value Constant 8.75E + 07 (6.50E + 07)
1.35 0.178 9.27E + 08 (1.63E + 09)
0.57 0.
ΔOutput -0. (0.242)
-0.54 0.589 0. (0.152)
1.75 0.
ΔInvestment t-1 -0. (0.117)
-3.40 0.001 -0. (0.135)
-2.64 0.
ΔProfit -0. (0.280)
-0.54 0.588 0. (0.202)
1.18 0.
Age -2.80E + 08 (4.77E + 08)
-0.59 0.
ΔForex. rate - (7583905)
-1.14 0.255 -1.02E + 07 (6768567)
-1.50 0.
ΔInterest rate 566. (3314.292)
0.17 0.864 -561. (1996.042)
-0.28 0.
ΔInflation rate 608. (1205.169)
0.50 0.614 2120. (2787.433)
0.76 0.
Δ [IIP/GDP] 1522. (1303.077)
1.17 0.
Δ [M2/GDP] 1106. (2804.206)
0.39 0.
Number of obs. = 65; Number of groups = 5; Wald Chi-Sq (7) = 60.99; Prob > Chi-Sq = 0.
Number of obs. = 60; Number of groups = 5; Wald Chi-Sq (8) = 13.66; Prob > Chi-Sq = 0. Dependent variable is change in investment. Figures in parentheses are standard errors
Table 4: Elasticities of significant variables in the long-run model Anderson-Hsiao Arellano-Bover/Blundell-Bond ΔOutput 0.86 0. Profit 0. Forex. rate -16.34 -8. [IIP/GDP] 9.7E- [M2/GDP] 1.3E-
6. Conclusions
This study has found that the average investment rate in machinery and equipment by Ugandan tea- processing firms is about 18% and is relatively close to the average investment rates for all Ugandan firms, as revealed elsewhere. Also, the study has found the flexible accelerator model to be appropriate in explaining the investment behaviour of Ugandan tea-processing firms when estimated using the Arellano-Bover/Blundell-Bond estimator as opposed to the Anderson-Hsiao estimator. In the long run, the level of investment in fixed assets is positively and significantly influenced by change in output, level of firm level liquidity, and a favourable investment climate in the country. In addition, long-run investment in fixed assets by these firms is negatively but significantly affected by the level of depreciation of the real exchange rate.
The long-run results are consistent with the short-run horizon findings with respect to the effect of the accelerator. But economy-wide variables are found not to be important in the short run. Increased investment in agro-processing machinery and equipment in the tea industry may lead to improved value-addition and productivity, which in turn should boost the competitiveness of processed tea exports. At the firm level, policy incentives specific to the growth of the tea sector may be put in place to target key constraints to investment in fixed assets by firms, such as level of gross sales and net
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