Page 1

Contributions to Economic Analysis &

Policy

Volume 4, Issue 12005

Article 12

Adjustment Costs and Irreversibility as

Determinants of Investment: Evidence from

African Manufacturing

Arne Bigsten, G¨ oteborg University

Paul Collier, Oxford University

Stefan Dercon, Oxford University

Marcel Fafchamps, Oxford University

Bernard Gauthier, HEC Montr´ eal

Jan Willem Gunning, Free University, Amsterdam

Remco Oostendorp, Free University, Amsterdam

Catherine Pattillo, IMF

M˚ ans S¨ oderbom, Oxford University

Francis Teal, Oxford University

Copyright c ?2005 by the authors. All rights reserved. No part of this publication may be re-

produced, stored in a retrieval system, or transmitted, in any form or by any means, electronic,

mechanical, photocopying, recording, or otherwise, without the prior written permission of the

publisher, bepress, which has been given certain exclusive rights by the author. Contributions to

Economic Analysis & Policy is one of The B.E. Journals in Economic Analysis & Policy, pro-

duced by The Berkeley Electronic Press (bepress). http://www.bepress.com/bejeap.

Page 2

Adjustment Costs and Irreversibility as

Determinants of Investment: Evidence from

African Manufacturing∗

Arne Bigsten, Paul Collier, Stefan Dercon, Marcel Fafchamps, Bernard Gauthier,

Jan Willem Gunning, Remco Oostendorp, Catherine Pattillo, M˚ ans S¨ oderbom,

and Francis Teal

Abstract

In this paper we investigate if the predictions of three different models of capital adjustment

costs are consistent with the observed investment patterns among manufacturing firms in five

African countries. We document a high frequency of zero investment episodes, which is consis-

tent with both fixed adjustment costs and irreversibility and inconsistent with quadratic adjustment

costs. We model the decision to invest using a dynamic discrete choice model and find evidence of

irreversibility and not fixed costs. We finally model the investment rate as a function of the size of

the capital disequilibrium. The results confirm that irreversibility is an important factor affecting

the investment behaviour of African manufacturing firms. Some implications of this finding are

discussed.

KEYWORDS: investment, adjustment costs, irreversibility, hazard function, African manufactur-

ing

∗This paper draws on work undertaken as part of the Regional Programme on Enterprise Devel-

opment (RPED), organised by the World Bank and funded by the Swedish, French, Belgian, UK,

Canadian and Dutch governments. Support of the Dutch, UK, Canadian, and Belgian governments

for workshops of the group is gratefully acknowledged. We are grateful to Don Fullerton (Editor),

two anonymous referees, Mats Gran´ er, Richard Mash, Ali Tasiran, and seminar participants at

Oxford and G¨ oteborg University for comments on earlier drafts of the paper. The authors form

the ISA (Industrial Surveys in Africa) Group, which uses multi-country data sets to analyse the

microeconomics of industrial performance in Africa. The support of the Economic and Social Re-

search Council (UK) is gratefully acknowledged. The work was part of the program of the ESRC

Global Poverty Research Group. S¨ oderbom acknowledges financial support from the Leverhulme

Trust. The use of the data and the responsibility for the views expressed are those of the authors.

Correspondence: M˚ ans S¨ oderbom, Centre for the Study of African Economies, Department of

Economics, University of Oxford, Manor Road Building, Oxford OX1 3UQ, UK.

Page 3

1. INTRODUCTION

Adjustment costs are central to modern investment theory, and how adjustment

costs vary with investment has direct implications for the specification of the

investment equation. Under quadratic adjustment costs (QAC), which is the most

common functional form used in the literature, large investments are associated

with very high adjustment costs, so the firm has an incentive to spread out a given

adjustment of the capital stock over several periods. One implication of QAC is

thus that investment is a smooth and serially correlated process. However, some

authors have recently argued that it is more realistic to model the adjustment cost

as fixed and thus invariant to the size of the investment, rather than a quadratic.

Under fixed adjustment costs (FAC) the best policy for the firm is either to keep

the capital stock unchanged or to undertake a large investment (or alternatively a

disinvestment) concentrated to one or a few periods. Caballero and Engel (1999)

argue that FAC is more consistent with plant-level data, which often indicate that

investment is intermittent and lumpy rather than gradual (Doms and Dunne,

1998). Other authors have stressed the implications of investment being

irreversible (Dixit and Pindyck, 1994). The idea here is that once a firm has

acquired new capital, the associated cost is sunk (perhaps because there are no

second hand markets for fixed capital) and cannot be recovered should the firm

want to reverse the investment decision.

In this paper we use data on manufacturing firms in Cameroon, Ghana,

Kenya, Zambia and Zimbabwe to investigate if there is any evidence that

company investment in these countries is associated with QAC, FAC or

irreversibility (IRR). Very informally, these three adjustment cost models can be

thought of as representing different forms of ‘sand in the wheels’, which prevent

the firm from adjusting its capital stock fully and instantaneously in response to,

say, a demand shock. Firms in Sub-Saharan Africa (SSA) have to deal with quite

a lot of sand in the wheels: the infrastructure in these countries is typically poor,

the financial markets are underdeveloped and often badly functioning, and

secondary markets for capital goods are limited or completely absent. There is

also in these countries a legacy of interventionist industrial policies where many

manufacturing activities required licences and permits. It would thus seem

plausible that adjustment costs may be quite significant in Africa. Further, the size

distribution of firms in Africa is heavily skewed to the right, with a much higher

proportion of very small firms than elsewhere (see e.g. Tybout, 2000). To the

extent that small firms are especially strongly affected by adjustment costs, one

might expect to find quite clear evidence of such mechanisms in our sample. One

contribution of the paper is thus to confront new theories with data from an

environment which in many ways is ideal to look for empirical support of such

models.

Contributions to Economic Analysis & Policy

1Bigsten et al.: Adjustment Costs and Irreversibility

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A common finding in previous research on investment in Africa based on

firm-level data is that investment is quite hard to explain based on traditional

models. Bigsten et al. (1999) estimate accelerator models and Euler equations

based on a similar data set to that used in the current paper, and find that these

models explain at most 17% of the variation in the investment rate. Pattillo (1998)

further finds that proxies for uncertainty have some explanatory power in

investment regressions, which is consistent with models of investment under

irreversibility. In investigating whether QAC, FAC and IRR are important

determinants of investment, the paper thus contributes to improving the

understanding of the determinants of investment in Africa more broadly.

The paper is organised as follows. In Section 2 we discuss the theoretical

underpinnings and the empirical framework. In Section 3 we analyse the patterns

of investment and the extent to which investment is concentrated in intermittent

periods of large expenditures. In Section 4 we report results from various dynamic

discrete choice models which shed light on the dynamics of investment and the

nature of the adjustment costs. In Section 5 we analyse how firms respond to

contemporaneous imbalances in the capital stock. We provide conclusions in

Section 6.

2. ANALYTICAL FRAMEWORK

It is widely observed that firms do not immediately adjust their capital stocks in

response to shocks to the ‘fundamentals’ (e.g. demand). The conventional

explanation advanced in the literature is that capital investment is associated with

adjustment costs.1 The majority of previous empirical studies of investment

behaviour have assumed QAC, hence the adjustment cost function is continuously

differentiable and the marginal cost is constant in the investment rate. This model

implies that the firm adjusts to the long run equilibrium gradually, by making

continuous small adjustments every period. Over the last decade, however, the

literature concerned with the implications for investment of IRR and FAC has

grown rapidly. Under fixed costs there are increasing returns in the adjustment

cost function, and the firm therefore waits and invests infrequently, in large

lumps, in order to avoid paying the fixed costs in many periods. Similarly, partial

or total irreversibility implies a discontinuity in the marginal cost to investment,

1Adjustment costs are costs associated with the sale, purchase or productive implementation of

capital goods over and above the price of the goods. Such costs are associated with, for instance,

searching for and deciding upon the adequate piece of equipment to be purchased, scrapping the

obsolete machines, installing the new capital stock, reorganizing and training the workforce, etc.

The largest share of adjustment costs is likely to consist of opportunity costs of foregone output

during the period of adjustment (Hamermesh and Pfann, 1996).

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which creates an inaction range within which fluctuations in marginal returns are

insufficient for investment to respond. In models of IRR and FAC, firms refrain

from adjusting their capital stock until the underlying disequilibrium reaches a

certain threshold level, dictated by parameters related to demand and the degree

of irreversibility, inter alia.2In contrast, under QAC there is no region of inaction,

so investment in this model is continuous and gradual.

With QAC it is straightforward to derive an investment equation that is a

linear function of the explanatory variables, e.g. Tobin’s Q model (Hayashi,

1982). This is probably the main reason why this formulation has been so popular

over the last two decades. In contrast, under IRR or FAC it is very difficult if not

impossible to obtain a closed form analytical solution for investment without

making several potentially strong assumptions, e.g. about technology,

expectations formations and the underlying stochastic process. In what follows we

provide a broad and fairly general characterisation of investment behaviour under

QAC, FAC and IRR.

Drawing on Hamermesh and Pfann (1996), the first row of Figure 1 shows

how the capital stock evolves over time, where the first column refers to QAC, the

second to IRR and the third FAC. The line with o-symbols depicts how capital

would change if there were no adjustment costs (i.e. without sand in the wheels),

and the line without symbols shows the capital evolution under the three different

adjustment cost models.3Under no adjustment costs, changes in capital track

changes in the fundamentals. Under QAC, shown in column 1, the capital stock is

continuously adjusted but always less so than under no adjustment costs. Under

IRR, illustrated in column 2, there are periods where optimal capital does not

vary, even though the fundamentals are changing. Inaction occurs because the

firm does not wish to add to the capital stock if in the near future its demand for

capital might decrease, since in that case the investment cannot be reversed.

Finally, the third column illustrates the dynamics of capital with FAC. Only large

changes in the fundamentals lead the firm to change capital, and when this

happens the resulting investment is large.

2 See e.g. Dixit and Pindyck (1994).

3 For simplicity, it is assumed that agents have perfect foresight and that capital does not

depreciate. However, the general mechanisms demonstrated in Figure 1 are not altered by

adopting more realistic assumptions regarding expectation formations and capital depreciation.

Contributions to Economic Analysis & Policy

3Bigsten et al.: Adjustment Costs and Irreversibility

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Figure 1. Adjustment Costs and Investment Patterns

i) Quadratic Adjustment

Costs (QAC)

ii) Irreversibility (IRR)iii) Fixed Adjustment

Costs (FAC)

Actual and Desired K

time

Desired Actual

0

5

15

Desired

time

Desired Actual

0

5

15

Desired

time

Desired Actual

0

5

15

(I/K)

time

0

-.013

.013

time

0

-.038

.038

time

0

-.7

.7

I(t+1)/K(t)

log K(t)/K*(t+1)

-1

1

-1

-.5

0

.5

1

log K(t)/K*(t+1)

-1

1

-1

-.5

0

.5

1

log K(t)/K*(t+1)

-1

1

-1

-.5

0

.5

1

Note: The upper row of the figure is adopted from Hamermesh and Pfann (1996), the middle row

is derived from the upper row, and the lower row is adopted from Goolsbee and Gross (2000).

The second row of Figure 1 graphs the dynamics of the investment rate

(defined as investment divided by capital), derived from the path of capital, under

the three models. This row relates to one of two dimensions of investment

behaviour we will examine, namely how the probability of investment depends on

past investments. The figure shows the smooth path of continuous investment

under QAC, and the periods of inaction interrupted by periods of investment

under IRR and FAC. Cooper, Haltiwanger and Power (1999) formulate a machine

replacement problem and demonstrate how the solution to the firm’s optimisation

problem can be characterised by a hazard function, which is the rate at which

machines are replaced conditional on the time since the previous replacement. In

particular, Cooper et al. show that under FAC the hazard function exhibits

positive duration dependence, i.e. that the hazard of replacement is increasing in

the time since previous replacement. The reason is that in periods soon after an

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investment has been made, the productivity gains from an additional investment

are small, while the cost is fixed, hence the present value of benefits is unlikely to

exceed the costs. As time passes the likelihood of net gain (and thus investment)

increases, as the productivity of the available leading edge technology begins to

exceed that of the existing capital. In contrast, under QAC the firm spreads out a

given adjustment over periods which yields positive serial correlation in

investment. This is clear from the left figure in the second row in Figure 1, where

investment rates of similar magnitudes occur in bunches. This translates into

negative duration dependence and thus a downward sloping hazard function: the

probability of (a large) investment in period t is higher if there was (a large)

investment in period t-1 than if there was not. Under IRR, the dynamic adjustment

pattern is similar to that under QAC in that the probability of investing will be

higher if a firm has invested in the recent past, thus yielding negative duration

dependence and a downward sloping hazard. This can be seen in the centre figure

in the second row. One important difference compared to QAC, however, is the

prevalence of periods of investment inactivity under IRR.

For the three adjustment cost structures, the third row of Figure 1 depicts

the average investment rate as a function of the capital imbalance, i.e. the

mandated investment, defined as the difference between desired and actual capital

(from Goolsbee and Gross, 2000). Caballero and Engel (1999) show how, in a

framework with stochastic FAC, average investment is an increasing, nonlinear

function of mandated investment. This is depicted in the right picture in the third

row, showing a region of inaction and a nonlinear function, where large

deviations of actual from desired capital lead to proportionately larger changes in

investment than small deviations. The relationship is linear under QAC (as firms

close a constant part of the gap between desired and actual capital each period),

and linear outside a region of inaction under IRR.

To summarize, over time both IRR and QAC yield positive

autocorrelation in investment. This implies that the likelihood of investment in the

current period is higher if the firm has invested recently, than if it has not. In other

words, the hazard of investment falls with the length of investment inactivity, and

so the investment process exhibits negative duration dependence. In contrast, with

FAC the hazard rises with the length if investment inactivity, yielding positive

duration dependence. Furthermore, in the imbalance state, both IRR and FAC lead

to an inaction range, whereas QAC does not. Hence, we can distinguish between

FAC on the one hand and IRR and QAC on the other, based on duration

dependence analysis; and between QAC on the one hand and FAC and IRR on the

other, based on an analysis of how actual investment responds to underlying

imbalances. In order to differentiate between the three models it is thus necessary

to examine adjustment in both the imbalance state and over time. This is the

Contributions to Economic Analysis & Policy

5Bigsten et al.: Adjustment Costs and Irreversibility

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premise for the econometric analysis below. First we examine if descriptive

statistics tell us anything about the nature of adjustment costs.

3. DATA AND DESCRIPTIVE STATISTICS

This paper uses survey firm level data from Cameroon, Ghana, Kenya, Zambia

and Zimbabwe, collected as part of the Regional Programme on Enterprise

Development (RPED) organised by the World Bank. The contemporaneous data

span the following periods: Cameroon, 1993-95; Ghana, 1991-93; Kenya, Zambia

and Zimbabwe, 1992-94. Retrospective information enables us to construct longer

time series than three years for certain variables, including investment. A total of

1208 firms have been surveyed at least once. We have discarded firms with too

few observations over time and a few outliers, yielding a sample size of 821

firms, which we will refer to as the “full sample” throughout the analysis. All

financial variables (e.g. investment and capital) have been converted to real 1991

U.S. dollars to ensure comparability across countries and over time periods. For

details about sample selection and construction of variables, see Appendix.4

In Table 1 we report proportions of positive investments during a one-year

period, by country and for four size classes.5 For the pooled sample, the overall

proportion with positive investment in the lower right corner is 0.42, which means

that 58% of the observations are zero investment episodes. The particularly low

investment propensity in Cameroon and Ghana and the high propensity in

Zimbabwe can largely be attributed to differences in the size distribution of firms,

as the propensity to invest is positively related to firm size. In Table 2 we report

proportions of firms ever selling capital goods during the sample period.6All

countries have an extremely low incidence of major disinvestment. Less than 2%

of all sampled firms ever have a disinvestment rate in excess of 10%.

Having found that a significant share of the firms refrain from investing

during an entire year, we proceed by examining whether firms compensate by

making relatively large (lumpy) investments once they decide to act. In Tables 3

and 4 we define seven categories of investment rates ranging from just above zero

4 All surveys deliberately oversampled large firms. In recognition, we control for differences

between firm size categories in most of the empirical analysis.

5 For Table 1 we use data from two years before the first survey year, in addition to

contemporaneous data from the three survey years. This means that each firm has at least 3

observations and at most 5 observations, and the period covered is in effect 1989-1995.

6 The sample period refers to the three years with contemporaneous data.

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Table 1. Pooled Investment Propensities, by Country and Firm Size

Employment, LCameroonGhana KenyaZimbabwe ZambiaTotal

1≤ L ≤5

0.21

78

0.31

80

0.44

180

0.53

51

0.29

132

0.36

521

5< L ≤20

0.29

143

0.44

167

0.40

193

0.51

122

0.29

177

0.38

802

20< L ≤100

0.24

147

0.48

153

0.41

280

0.63

177

0.28

228

0.40

985

L >1000.38

146

0.20

363

0.44

264

0.71

543

0.38

189

0.46

1505

Total0.29

514

0.32

763

0.42

917

0.66

893

0.31

726

0.42

3813

Notes: The top number in each cell is the proportion of firms with positive investments during one

year. The bottom number in each cell is the number of observations. The table is based on data

from the full sample of 821 firms.

to more than 40%, and show the contribution of each category to each country’s

total investment. We also show in these tables the proportions of the non-zero

investments that belong to each of the seven categories (i.e. these proportions sum

to unity in a given column). That is, 38% of the non-zero investments in the

pooled sample are in the category 0<(I/K) ≤0.05, 19% are in the category

0.05<(I/K)≤0.10, and so on. Table 3 provides a breakdown by country, while

Table 4 distinguishes between two size categories. Table 3 shows that the largest

proportion of the observations (firms in a given year) have investment rates less

than 10%, suggesting that small maintenance and replacement investments are an

important part of investment activity.7 However, for 14% of the observations in

the pooled sample, when there is investment, the investment rate is over 40%, and

these observations make up 26% of the total investment in the sample. Adding

7 Nilsen and Schiantarelli (2003) note that while the large fraction of observations with small

positive investment rates may seem inconsistent with non-convex adjustment costs, it is

reasonable if we assume that adjustment costs for replacement investment are very small, and

fixed costs are relevant only for expansion investment.

Contributions to Economic Analysis & Policy

7Bigsten et al.: Adjustment Costs and Irreversibility

Page 10

Table 2. Proportions of Firms Selling Equipment

Any Disinvestment

Large

(L>20)

Disinvestment rate >10%

Small

(L≤20)

(L>20)

Small

(L≤20)

AllLarge All

Cameroon 0.07

60

0.13

53

0.10

113

0.00

60

0.00

53

0.00

113

Ghana0.04

70

0.08

67

0.06

137

0.01

70

0.03

67

0.02

137

Kenya0.05

83

0.15

96

0.10

179

0.00

83

0.03

96

0.02

179

Zimbabwe0.15

41

0.36

122

0.31

163

0.05

41

0.01

122

0.02

163

Zambia0.07

59

0.12

61

0.09

120

0.00

59

0.02

61

0.01

120

All 0.07

313

0.19

399

0.14

712

0.01

313

0.02

399

0.01

712

Notes: The top number in each cell is the proportion of firms ever selling capital (left part of the

table), or ever recording a disinvestment rate larger than 10% (right part of the table), during the

three years over which the firms were surveyed. The bottom number in each cell is the number of

observations. Due to incomplete observations, calculations are based on data for 712 of the 821

firms in the full sample.

over the three categories with the highest investment rates, it can also be observed

that 27% of the observations in the pooled sub-sample of non-zero investments

have investment rates larger than 20%. This suggests that disequilibria in capital

stocks may be substantial for a non-negligible number of firms, and provides

some evidence for the lumpiness of investment. Table 4 shows that this result is

more pronounced for small firms: 32% of the observations of investing small

firms have investment rates larger than 20%, compared to 25% for large firms.8

8 These percentages are obtained by adding the proportions of non-zero investments across the

three highest investment categories.

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Table 3. Distribution of Investment Rates and Contribution to Aggregate

CAM GHAKEN ZIMZAN All

A. Sample distributions of non-zero investments, by country and pooled

0 < (I/K) ≤ 0.05

0.05 < (I/K) ≤ 0.10

0.10 < (I/K) ≤ 0.20

0.20 < (I/K) ≤ 0.30

0.30 < (I/K) ≤ 0.40

0.40 < (I/K)

0.27

0.16

0.19

0.12

0.04

0.23

0.41

0.16

0.16

0.09

0.05

0.13

0.40

0.20

0.16

0.06

0.04

0.14

0.36

0.22

0.17

0.07

0.07

0.12

0.46

0.15

0.12

0.08

0.02

0.17

0.38

0.19

0.16

0.08

0.05

0.14

B. Share of total investment, by country and pooled†

0 < (I/K) ≤ 0.05

0.05 < (I/K) ≤ 0.10

0.10 < (I/K) ≤ 0.20

0.20 < (I/K) ≤ 0.30

0.30 < (I/K) ≤ 0.40

0.40 < (I/K)

30%

28%

17%

9%

1%

16%

12%

9%

43%

15%

12%

9%

22%

23%

16%

11%

5%

24%

16%

12%

24%

13%

9%

26%

19%

6%

21%

6%

3%

45%

17%

13%

24%

13%

8%

26%

Observations 5147639178937263813

Note: The table is based on data from the full sample of 821 firms.

†Total investment is the aggregate investment expenditure over time in each country sub-sample

(and pooled for the column “All”).

Furthermore, the proportion of large firms making the lowest replacement and

maintenance investments is larger than that of small firms (40% and 34%,

respectively, of the non-zero investments fall into the lowest category for the two

size groups).

Tables 3 and 4 show that there is a relatively large fraction of large

investment rates in the sample. This could be consistent with either a few firms

always making large investments, or alternatively that many firms occasionally

having large investments. Hence these data cannot be used to determine how

important are investment spikes for individual firms. To further assess the extent

to which firms make infrequent but relatively large investments, we follow the

method initiated by Doms and Dunne (1998). We rank each firm’s investment

rates over time from the highest year (rank 1) to the lowest year (rank 5), and

Contributions to Economic Analysis & Policy

9Bigsten et al.: Adjustment Costs and Irreversibility

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Table 4. Distribution of Investment Rates and Contribution to Aggregate by Size

Employment ≤ 20

Employment > 20

A. Sample distributions of non-zero investments

0 < (I/K) ≤ 0.05

0.05 < (I/K) ≤ 0.10

0.10 < (I/K) ≤ 0.20

0.20 < (I/K) ≤ 0.30

0.30 < (I/K) ≤ 0.40

0.40 < (I/K)

0.34

0.18

0.17

0.09

0.05

0.17

0.40

0.20

0.15

0.07

0.05

0.13

B. Share of total investment†

0 < (I/K) ≤ 0.05

0.05 < (I/K) ≤ 0.10

0.10 < (I/K) ≤ 0.20

0.20 < (I/K) ≤ 0.30

0.30 < (I/K) ≤ 0.40

0.40 < (I/K)

6%

9%

12%

9%

6%

58%

18%

13%

24%

13%

8%

25%

Observations 13232490

Note: The table is based on data from the full sample of 821 firms.

†Total investment is the aggregate investment expenditure over time in each sub-sample defined

by firm size.

compute the average investment rates for each rank and the share of each rank in

a firm’s total investments.9 Table 5 shows that the average investment rate of the

highest rank year is almost three times higher than that of the second highest year,

and seven times higher than that of rank 3. The investments associated with the

largest investment rate for each firm represents 50% of total investments, which

further underlines the considerable importance of lumpy investments at the firm

level for aggregate investments.10We have also looked at the mean investment

rate for each rank separately for small and large firms. These results, which are

9 Only firms with at least five years of observations were included in these computations.

10 The average investment rates are for a five year period. Our results are similar to other studies.

Doms and Dunne (1998) find that 50% of total investment over a 16 year period is contributed by

the highest three ranks; Nilsen and Schiantarelli (2003) report that 46% of total investment over a

14 year period is accounted for by the highest three ranks; and Gelos and Isgut (2001) find that

investment episodes in the highest three ranks account for 58% of total investment in the Mexican

sample (11 years) and 61% in the Colombian sample (eight years).

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Table 5. Ranked Investment Rates, Persistence, and Share of Total

Rank GhanaKenya Zimbabwe ZambiaAll

1 Mean (I/K)0.27

0.04

0.50

0.27

0.06

0.45

0.32

0.09

0.49

0.31

0.04

0.80

0.29

0.06

0.50

(High) Adjacent (I/K)

Share of Total

2 Mean (I/K)

Adjacent (I/K)

Share of Total

0.08

0.10

0.33

0.12

0.09

0.29

0.15

0.15

0.25

0.09

0.09

0.15

0.12

0.11

0.25

3 Mean (I/K)

Adjacent (I/K)

Share of Total

0.01

0.10

0.17

0.05

0.11

0.18

0.07

0.11

0.11

0.02

0.09

0.04

0.04

0.11

0.12

4Mean (I/K)

Adjacent (I/K)

Share of Total

0.00

0.07

0.00

0.02

0.09

0.06

0.03

0.10

0.10

0.01

0.10

0.01

0.02

0.09

0.09

5 Mean (I/K)0.00

0.06

0.00

0.01

0.10

0.03

0.01

0.13

0.06

0.00

0.11

0.00

0.01

0.10

0.05

(Low) Adjacent (I/K)

Share of Total

Observations97 123 14769 436

Notes: Only firms with at least five observations on investments, and who invested at least once,

were included. The Cameroonian sub-sample has too few firms with sufficient information to

compute statistics of the type reported in the table, and therefore we confine attention to the other

four countries in this particular case. Mean (I/K) are average investment rates across firms for each

given rank; Adjacent (I/K) are average investment rates in the year(s) after and/or before the rank;

Share of Total are shares contributed to aggregate investment by each rank, where aggregate

investment has been calculated as explained in the note below Table 3.

not reported to conserve space, indicate that the highest ranked investment rate

accounts for a larger share of total investments for small firms than for large

firms, consistent with other evidence that investment tends to be lumpier for small

firms. That zero investment episodes and lumpy investment appear to be more

important for small firms appears plausible: indivisibility of capital goods is

probably more important for smaller firms, and the intermittent, lumpy character

of investment could be smoothed in large firms by the aggregation of different

types of production processes that occur.

Contributions to Economic Analysis & Policy

11Bigsten et al.: Adjustment Costs and Irreversibility

Page 14

To document the degree of persistence in investments, we have calculated

the average investment rates one year before and after observations for each rank.

These calculations, shown in Table 5, ‘adjacent (I/K)’, also lend further support to

the notion that investment is lumpy, since the average investment rates in the

years immediately before and after the firm’s highest investment are

conspicuously low. The mean investment rate in the years before and after the

highest rank is on average less than one fourth of the investment in the year of the

highest rank. In contrast to the highest rank, however, there does seem to be some

degree of persistence for the lower ranks.

To summarise, the data discussed in this section suggest that investment

activity takes the form of quite large adjustments concentrated in a few periods.

These descriptive statistics are consistent with an adjustment cost technology

featuring non-convexities, possibly due to fixed costs.

4. ECONOMETRIC ANALYSIS OF INVESTMENT DYNAMICS

The fixed cost model developed by Cooper et al. (1999) predicts that the

probability of investing increases with the time since the last investment. That is,

using the terminology of transition data econometrics, the Cooper et al. model

predicts an upward sloping hazard function. Under both IRR and QAC, however,

investment will be positively serially correlated, and the hazard function will

consequently be downward sloping: the probability of investing in time t is higher

if there has been investment in time t-1 than if there has not.

In order to test and distinguish between these hypotheses, we use

econometric methods for transition data analysis. A potential difficulty in the

analysis of transition data is that failure to control for time invariant heterogeneity

in explanatory factors across firms will result in inconsistent estimates, typically

biasing the slope of the estimated hazard function downwards. Therefore we will

pay close attention to unobserved heterogeneity, which, following Cooper et al.,

we will model by a semiparametric random effects approach. In contrast to

Cooper et al. we recognise the endogeneity of the initial conditions, which if

ignored can give inconsistent results.

To obtain an estimable representation of the investment decision, we

define a dummy variable yit equal to one if there is investment and zero if not, and

specify the model as follows:

++⋅+⋅

=

otherwise0

where β is a vector of coefficients associated with observed vector of exogenous

variables xit, δ is a vector of coefficients associated with a vector of duration

dummies Dit, vi is a firm-specific random effect that is unobserved to the

(1)

≥

0 if1

iti it it

it

uvDx

y

δβ

,

12Vol. 4 [2005], No. 1, Article 12

http://www.bepress.com/bejeap/contributions/vol4/iss1/art12

Page 15

econometrician, uit is a serially uncorrelated logistic disturbance term, and i and t

are firm and time indices, respectively. The jth element of the vector

) ...(

21

Jit it itit

dddD =

is equal to one if the firm last invested in period t-j and zero

otherwise.11 With this definition of Dit the coefficients δ1,…,δJ determine the

shape of the hazard: if the coefficients on the dummies for long durations are

larger than those on short duration dummies, then the hazard function is upward

sloping, and vice versa. This specification, which is similar to that adopted by

Cooper et al., is quite flexible. Clerides et al. (1998) show that a similar approach

can be used for the estimation of dynamic discrete choice models more general

than single-spell duration models.

The assumption that the disturbance term is logistically distributed yields

the logit model, implying that the probability of observing any investment,

conditional on the random effect, is equal to

(2)

({{

exp1

+⋅+⋅−+=

it itit

vDxH

δβ

To integrate the random effect out of the likelihood function, we assume that v

follows a discrete multinomial distribution with M points of support. Hence, the

support points and the probabilities, which determine the entire distribution of the

heterogeneity, are parameters to be estimated.12 Because of the dynamics there is

an initial conditions problem in that all past investment outcomes, including the

condition at the first point of observation, will be correlated with the random

effect. This implies that the likelihood will involve the conditional density of the

random effect, rather than the unconditional density.13

Taking the above into account, the resulting individual likelihood can be

written

(

∑∏

= =

m

St

1

)}}1

−

i

.

(3)

)

()()()

()

−

=⋅−⋅=

M

T

S

imi

it

y

m it

it

y

m it

S

ii

yeveHeHyL

0

1

0

Pr,1, Pr

,

11 Hence d1it = yi,t-1 and, for j>1,

(

1

)

∏

=

q

−

−−

−=

1

1

,,

j

qt i

y

jt i

y

jit

d

.

12 This approach was suggested by Heckman and Singer (1984), and has subsequently been used

in various microeconometric analyses of, for instance, dynamic discrete choice (Moon and

Stotsky, 1993; Blau and Gilleskie, 2001; Cooper et al., 1999), duration data (Blau, 1994; Ham and

LaLonde, 1996), and count data (Deb and Trivedi, 1997). One of the merits of this strategy is

flexibility: Monte Carlo evidence indicates that this approach compares favourably to standard

MLE correctly assuming normality, and that it performs better than MLE assuming normality

when this is incorrect (Mroz and Guilkey, 1995; Mroz, 1999).

13 Indeed, based on the unconditional density, maximum likelihood estimates will not be

consistent unless the initial conditions are truly independent of the random effect or T is very large

(see e.g. Hsiao, 1986, pp. 169-172).

Contributions to Economic Analysis & Policy

13Bigsten et al.: Adjustment Costs and Irreversibility