On Reform Intensity under Uncertainty

JOURNAL OF COMPARATIVE ECONOMICS 25, 297–321 (1997)ARTICLE NO. JE971482

On Reform Intensity under Uncertainty1

Simon Johnson

Sloan School of Management, Massachusetts Institute of Technology,Cambridge, Massachusetts 02142

Panos Kouvelis

Olin School of Business, Washington University, St. Louis, Missouri 63130

and

Vikas Sinha

IBM, Armonk, New York 10504

Received October 28, 1996; revised August 19, 1997

Johnson, Simon, Kouvelis, Panos, and Sinha, Vikas—On Reform Intensity underUncertainty

We model policy reform as a way to affect the stochastic process of relative returns thatfirms face when switching from old to new activities. This stochastic process has an Itoprocess component that is noncontrollable and policy reforms result in jumps in relativereturns that arrive according to a Poisson process. The intensity of policy reform dependson the arrival rate and magnitude of jumps. We use a single firm model to understand thereaction of the firm to such a stochastic process and the usual hysteresis results in switchingbetween old and new activities. Aggregation to the level of all firms leads to an appropriatedefinition of the government payoff function, and we use this to obtain the optimal levelof reform. The results are as follows: there exists an optimal level of radical reform thatovercomes the hysteresis behavior of firms; if such a level is not desirable, then the intensityof policy reform is not at an extreme point; and this gradual level of optimal reform islower if uncertainty is higher. J. Comp. Econom., December 1997, 25(3), pp. 297–321.Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massa-chusetts 02142; Olin School of Business, Washington University, St. Louis, Missouri 63130;and IBM, Armonk, New York 10504. q 1997 Academic Press

Journal of Economic Literature Classification Numbers: C61, E63, P20.

1 Generous financial support was provided by the Center for International Business Educationand Research at the Fuqua School of Business.

0147-5967/97 $25.00Copyright q 1997 by Academic PressAll rights of reproduction in any form reserved.

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298 JOHNSON, KOUVELIS, AND SINHA

1. INTRODUCTION

The real options literature uses the concepts of option pricing to analyzefirms’ investment decisions, and has been developed in economics by Abeland Eberly (1994, 1995a, 1995b), Abel et al. (1995), Dixit (1989a, 1989b,1995), McDonald and Siegel (1986), and Pindyck (1993a).2 More recently,these same tools have been used to study government policy issues. Pindyck(1993b) analyzes the introduction of a new environmental policy as an optimalstopping problem, while Metcalf and Hassett (1993) show how uncertaintyabout government tax policy can reduce investment. These ideas are used inthe models of reform proposed by Rodrik (1991) and Laban and Wolf (1993).

These option pricing models share the important characteristic that a moreradical policy can slow down actual change by increasing uncertainty inthe environment and consequently raising the option value of waiting. Theimplication is that investors prefer to wait until some uncertainty is resolved,so reducing uncertainty should be an important government goal. As Dewatri-pont and Roland (1995) argue, this type of model provides an importantrationale for reforming gradually rather than rapidly.3

These models assume that the government takes as given the stochasticprocess that characterizes the market environment faced by firms, e.g., profits,prices, costs, but such an assumption seems restrictive. We develop a morecomprehensive model in which the government implements reform throughcontrolling the stochastic process faced by firms. In this model, radical reformincreases uncertainty. Nonetheless, the government’s optimal policy can beto adopt a radical breakthrough level of reform because, in this case, theimmediate benefits of change outweigh the option value of waiting. Thisoptimal reform intensity is higher if firms have a higher discount rate and ifthe trend growth in return on new opportunities is slower. If this breakthroughlevel is not desirable, the optimal intensity of policy reform is not at anextreme point. This gradual level of optimal reform is lower when uncertaintyis higher.

This result is relevant to the active debate on the relative merits of radicaland gradual reform policies in formerly planned countries. In an early influen-tial article, Lipton and Sachs (1990) argued for radical reform in Poland, and

2 The economics literature is reviewed by Pindyck (1991). There have also been importantcontributions in the operations research and applied finance literatures, such as Cohen and Lee(1989), Hodder and Triantis (1993), Huchzermeier and Cohen (1993), Kogut and Kulatilaka(1994), and Trigeorgis (1993).

3 This result is often implicit in the models. For example, Laban and Wolf (1993) do notstudy the optimal intensity of reform explicitly, but the gradualism result is apparent from theirProposition 3. They do discuss the need for a big push, but this is in terms of investors’expectations, which are given exogenously.

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299REFORM INTENSITY UNDER UNCERTAINTY

much of the informal literature has followed this lead.4 After five years, thereis strong evidence that radical reform works well under some conditions. Thebest performing ex-communist countries are the radical reformers: Polandand the Czech Republic in Eastern Europe and the Baltics in the formerSoviet Union (Aslund, 1994a; Hansson, 1994; Aslund et al., 1996). Ukrainehad extremely poor performance with slow and partial reform through mid-1994, and its situation has improved significantly since the introduction ofmore radical reform in October 1994 (European Bank for Reconstruction andDevelopment, 1995).

In contrast, however, most formal models have emphasized the disad-vantages of moving too fast. Models such as Dewatripont and Roland(1992a, 1992b, 1995), Murrell and Wang (1993), Aghion and Blanchard(1994) and Aghion et al. (1994) assume convex adjustment costs thatreduce the optimal pace of reform.5 Informal arguments against radicalreform are provided by Amsden et al. (1994), Murrell (1992, 1993, 1995),Portes (1994), and Roland (1994).

The virtues of a ‘‘big bang’’ price liberalization are clear in earliermodels by Murphy et al. (1992) and Gates et al. (1996), but these papersassume that the economy begins with pervasive price controls; thus, theydo not apply to most reforming economies after 1992. Critical mass effectsfor government policy are present in Roland and Verdier (1994), but thisis a nonstochastic model.

While our model does not attempt to resolve the debate over the optimalintensity of reform, it extends some of the arguments in favor of rapid reformto a general stochastic context. In particular, it also demonstrates that, becauseit resolves uncertainty, rapid macroeconomic stabilization may be best forrestructuring even if that restructuring takes a considerable length of time. Inour general stochastic framework, the optimal reform is usually radical be-cause this is the only way the government can overcome the tendency offirms to wait for uncertainty to be resolved. Thus, this paper strengthens thecase for initiating and continuing radical reform in East Europe and the formerSoviet Union. At the same time, however, the paper shows that gradual reformcan be optimal under the right conditions, particularly when there is lowuncertainty about the direction of change. China is probably closer to thissecond case.

4 Leading proponents of radical reform include Anders Aslund and Stanley Fischer. See, forexample, Aslund (1994a) and (1994b), Fischer and Gelb (1991), and Fischer (1994).

5 The precise mechanism varies. For example, all three Dewatripont and Roland papers assumefaster reform leads to more layoffs and a greater political backlash. In Aghion and Blanchard(1994) faster reform increases unemployment, which raises the fiscal burden on new private sectorfirms and slows their development. In Murrell and Wang (1993), private sector development isconstrained by the availability of institutions that cannot grow fast and may even be disruptedby radical reform.

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Our most important contribution is to clarify that even though enterpriseand financial restructuring obviously take a considerable amount of time,rapid reform can be optimal. In our model switching to new activities doesnot mean complete or instantaneous restructuring, but rather a change ofmode of operation from old to new, i.e., beginning the process of restructuring.By making faster change more costly, we are implicitly assuming that gradu-alist micro-level change has advantages. Our model shows, however, that eventhough micro change takes time, fast macro-level reform can have importantadvantages because it resolves uncertainty.

Our modified real options model has three important elements. First, wemodel explicitly the way firms switch between old and new activities; wecall this a change in activity mode. Switching between modes is costly and,in general, firms can switch from old to new activities but also back to oldactivities. This assumption is designed to capture how firms in formerlycommunist countries can restructure when the economic environmentchanges. Our results are unaffected by whether the switching cost is fixed orconvex in the magnitude of the policy change; i.e., higher if firms are requiredto make larger adjustments.

Second, we assume that the firms’ environment is uncertain in the sensethat the relative return on the new activity is a stochastic process. Becauseof the switching cost and the relative return uncertainty, there is an optionvalue to waiting and a hysteresis band of inaction in switching betweenactivities. As in all models of this type, greater uncertainty widens the hystere-sis band.6

Third, the government chooses the intensity of the reforms but cannotdetermine the exact changes in the stochastic process of relative returns whichthe firm faces. More specifically, policy reform changes the firm’s environ-ment as follows. The firm’s relative return process evolves according to anIto process,7 and policy interventions controlled by the government occuraccording to a Poisson process and induce jumps in the relative return process.A more rapid reform is a faster arrival rate and deeper reform is a largerjump when policy change occurs. As far as we are aware, this is a new wayto model policy reform.8

6 This part of the model draws on the recent real options literature, in particular as developedin Dixit (1989a, 1989b, 1989c) and reviewed in Dixit and Pindyck (1994). The hysteresis bandis an area of inaction in which the decision-maker continues in the existing mode of operation.This is suboptimal in terms looking only at current payoffs but optimal once adjustment costsare taken into consideration.

7 An Ito process is generalized Brownian motion in which drift and variance parameters canbe functions of both state and time. See Dixit and Pindyck (1994) for development of importantspecial cases such as geometric Brownian motion. We present the relevant equations in theSection 3.

8 The best presentation of existing theory on this point is in Dixit (1991).

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In this framework, the government faces a trade-off: a more intense policyraises the return in the new activity but also increases uncertainty and mightalso raise adjustment costs. However, our framework clearly shows that thereis generally a global optimum in which reforms are above a high thresholdlevel. This level does not depend on uncertainty but depends on the growthof relative returns of the activities and on the discount rate.

Our model also cautions against assuming that radical reform is alwaysoptimal, irrespective of initial conditions. In particular, it remains possiblethat China’s initial conditions were such that gradual reform was optimal.More generally, the optimal speed of reform is an unresolved issue in severalliteratures including the reform of trade regimes and organizational change.This paper offers a useful way to formalize aspects of these problems.

Section 2 discusses the nature of post-communist reform in more detail,and provides the key stylized facts which motivate our model. Section 3develops the single firm model and emphasizes links with the existing realoptions literature. Section 4 allows multiple firms and models the determinantsof optimal government policy. Section 5 uses the model to reinterpret post-communist economic reforms and to draw more general lessons. Section 6concludes.

2. POST-COMMUNIST REFORM

Under central planning, state enterprises were large and extremely hierar-chical.9 Managers were pushed to achieve centrally set targets that typicallyrequired obtaining the maximum possible physical output from available re-sources. There was little or no emphasis on maximizing profits or efficiencyand scant concern for controlling costs. Superiors wielded absolute and arbi-trary control through extensive use of administrative allocations and rationingschemes. Communist Party political control was pervasive. Not surprisingly,managers spent much of their time lobbying the government and trying tofind additional supplies.10

In this environment, the principal aspects of firm activity in a marketeconomy, e.g., marketing, finance, and operations, could hardly be recognized.Planning relieved firms of the responsibility for seeking out new customersor, for that matter, exhibiting much concern about existing customers asdistinct from ministerial superiors. Prices, which for the most part were fixed

9 Although there are still discussions about precisely how planned economies worked, theimportant aspects are clear. We provide only a brief summary here, drawing on the standardreferences of Berliner (1957), Kornai (1992), and Nove (1982).

10 Kornai’s famous ‘‘soft budget constraint’’ represents partly the negotiation between manag-ers and their superiors. Managers were always lobbying for more resources. See also the discus-sion in Lawrence and Vlachoutsicos (1990).

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by the government, did not play a major role in allocating resources. Underthese circumstances, there was no reason to market a firm’s products andcorporate finance was primarily just bookkeeping. At the same time, it madesense to arrange production and related operations to minimize the firm’svulnerability to supply disruptions. This could be achieved, for example, bycarrying large inventories.

The manner in which state enterprises operated was sensible given theeconomic and political environment that they faced (Ericson, 1991). However,the economic transformations that accompanied the end of communism haveput great pressure on firms to create new strategies for survival. Firms thatare now more or less on their own have suddenly discovered the importanceof maximizing profits.11

Recent empirical work in various reforming countries reveals similar is-sues.12 One of the first imperatives facing these enterprises is the need tochange their product mix in order to focus on activities in which they havesome form of advantage over their competitors. New effort must thereforebe devoted to marketing, to researching opportunities, and to identifyingpotential customers. Implementing a new strategy often requires a supportivereorganization of operations designed to shorten the production cycle, improvequality controls, and smooth the flow of work. This reorganization may inturn depend on a restructuring of management, focused on reducing hierarchyand eliminating administrative layers.13 In general, therefore, managers informerly planned economies face the task of overhauling at least six interre-lated attributes of their firms: product strategy, marketing, operations, internalorganization, compensation system, and financing arrangements. Thesechanges are typically discrete and may take several possible values, reflectingdifferent degrees of convergence toward the model represented by a firm ina market economy. Economic transition involves firms deciding when tomove from an old to a new way of organizing production.

Not all firms choose to make these changes immediately. For example, arecent study by Johnson et al. (1996) examined the different strategies at twoshipyards after the end of communism. At the Gdansk shipyard, managementhas based its reform strategy largely on the perceived successes of the enter-prise in the past. In the 1970s, the shipyard produced 30 ships per year using17,000 workers. It had an inefficient vertically integrated production system

11 There is some debate about the extent to which firms care about profits, particularly whenproperty rights are unclear. All that matters for our models is that the change in environmentcreates an incentive to change the way firms operate.

12 For example, Johnson and Loveman (1995) writing on Poland deal with many of the sameissues as Groves et al. (1994, 1995) on China.

13 For a detailed analysis of the required changes see the Prochnik and Szczecin shipyard casesin Loveman et al. (1994).

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and substantial financial support from the central government. Since the endof the communist regime in 1989, its managers have attempted to maintainthe organizational structure of the 1970s in an international market wherethe emphasis is on efficiency, cost control, specialization, and, above all,profitability. Performance at the shipyard has been poor because socialistmanagement methods are not appropriate in a market system.

In contrast, at the Szczecin shipyard, the chief executive developed a com-petitive advantage by focusing on mid-size container ships and reducingproduction cycle times. A larger number of workers were concentrated on asmaller number of slipways and a performance-enhancing compensationscheme was implemented. The manager also decreased operating costs byshedding nonproductive assets and reducing the number of employees notdirectly involved in ship assembly. Finally, he eliminated most intermediarymanufacturing at the yard and focused workers’ efforts on building ships.

The Szczecin shipyard changes are a good example of the required reorgani-zation of work at the firm level.14 Almost everything about the way thatalmost every product in these economies is produced and distributed changesduring economic reform. The policy reform created the incentive to switchinto new activities, e.g., through starting export-oriented production or creat-ing new private firms. The new activities have higher expected profit but theactual relative return between new and old activities at any moment is un-known and it is costly to switch from the old to the new way of running afirm. Many firms naturally delay making the switch. The next section beginsto build a formal model of firms’ decisions and optimal reform intensity.

3. SINGLE FIRM MODEL

We begin by modelling the decision of a single manager who controls afirm (we use the terms manager and firm interchangeably).15 We derive theoptimal policy for the firm and show how it depends on various parameters.

The firm must engage in one of two mutually exclusive activities: old,represented by 0; and new, represented by 1. It is always possible to switchinto the new activity but we assume that initially, at time t0 , the firm isengaged in the old activity.16

14 For another case of restructuring that reveals the profound nature of the required change,see Dyck and Hopper Wruck (1995). Further supportive evidence is provided by Carlin et al.’s(1994) survey of case studies from all post-communist countries.

15 In this section, we implicitly assume that the firm was in operation both before and afterthe change of economic system. However, it would make no difference to our results if someof the firms we consider had zero returns, i.e., did not operate under communism.

16 For example, a policy reform may for the first time make it possible to start export-orientedproduction or to create a private firm. The new activity represents managers putting effort intoachieving new goals rather than achieving immediately those goals.

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We denote the return from activity i as p(i), where

p(0) Å I,

p(1) Å R.

Here I is assumed to be constant and R is a combined Ito process and jumpstochastic process, i.e., R fluctuates as an Ito process of standard Brownianmotion, but in each time interval dt there is a probability ldt that an event,e.g., a policy change, occurs and R increases by g(R),

dR Å a(R)dt / s(R)dz / g(R)dq, (1)

where a(R) is the drift of the process, s(R) is the variance, g(R) is themagnitude of a jump when a Poisson event occurs, dz is the increment of astandard Wiener process, and dq is the increment of a Poisson process withmean arrival rate l.17 As is standard, we assume that dq and dz are indepen-dent; i.e.,

E(dzdq) Å 0.

The Ito process represents the randomness in the relative return of the newactivity due to the inherent instability of a post-planning economy.18 Notethat while there is a trend change in the attractiveness of the new activity,which can be increasing or decreasing, the random increments to R can beboth up and down.

We are assuming that, if a policy event occurs, R increases by the magnitudeg(R) with probability 1. The Poisson process represents reforms that increasethe return from the new activity and represents the idea that, while the govern-ment does not completely control the change in relative returns faced byfirms, it can accelerate the changes or make them larger when they occur.19

We assume the jump is only up because policy changes are assumed to bein favor of the new activity. In this model, as in many reforming countries,

17 The continuous time stochastic process R(t) is an Ito process (defined by dR Å a(R)dt /s(R)dz, where dz is the increment of a Wiener process.)

18 These economies typically have a rapid changing competitive environment, particularly withthe development of imports. For details on how this affects firms, see Johnson and Loveman(1995).

19 This assumption is more appealing than assuming the government faces an optimal stoppingproblem in which the only issue is when to make a single policy change of precisely knownsize. Even in the Polish radical reform there were important policy changes, such as increasesin administered prices and the initiation of small-scale privatization that were made after theJanuary 1, 1990 ‘‘big bang’’ (Johnson and Kowalska, 1994). Some form of large-scale privatiza-tion has been promised by every Polish government since 1989 but has yet to be implemented.

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firms know that the government wants to reform but there is uncertainty aboutboth the size of reforms and when the reforms will occur.20

The manager can switch from the old to the new activity and also fromnew back to old but the switching cost depends on which switch is beingmade and, in general, on the intensity of the policy innovation. The cost ofswitching from mode i to mode j is Sij , and we define

S01 Å C0lF,

S10 Å C1lF,

where F measures the size of the Poisson jump as a percentage of the currentvalue of the relative return process, i.e., g(R) Å (1 / F)R.

This assumption formalizes the idea that a more radical policy processrequires a more costly type of change. Adjustment costs are linear in themagnitude of the policy change, so a larger policy change implies a largercost if the firm responds at all.21 Note that if one or both of these switchovercosts are fixed, i.e., do not depend on the policy process, the analytics of thissection are modified only slightly and the comparative statics effects are notaltered.22 A more intense reform means a higher expected rate of increase ofR but also a larger variance of the reform process and a higher cost ofswitching.

The optimal switching problem in activity modes can now be solved bydynamic programming. Without loss of generality, we assume that the firmis risk-neutral. The value of the firm’s optimal policy is F(R, t, m), wherethe current return is R, time is t, and the firm’s mode of operation is m. WhenR changes to R*, the firm chooses its mode to maximize

F(R, t, m)Åmaxm={p(m*)dt0 Smm= / (1/ rdt)01E[F(R*, t/ dt, m*ÉR, m)]},

(2)

where m and m* √ {0, 1} are the modes at times t and t / dt, respectively,the discount rate per unit time is denoted r, and E is the expectation operatorwith respect to R.

The Bellman equation is given by

rdtF(R, t, m) Å maxm={p(m*)dt(1 / rdt) 0 Smm=(1 / rdt) / E(dF)}. (3)

20 In this framework, a single policy jump of unknown arrival time is a special case in whichthe Poisson process has a very low arrival rate.

21 It would not change our results if the adjustment costs were convex in the size of the policychange.

22 In the next section, we show that the results are not affected by assuming a fixed switchingcost.

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Given that the time horizon is infinite and that a, s, and g are independentof time, the appropriate form of Ito’s lemma is

E(dF) Å [a(R)(dF/dR) / (1/2)s2(R)(d2F/dR2)

/ l{F(R / g(R), m) 0 F(R, m)}]dt. (4)

Substituting back into the Bellman equation (3), rearranging, dividing by dt,and letting dt go to 0 gives a differential equation that can be solved for F,

(1/2)s2(R)(d2F/dR2) / a(R)(dF/dR) 0 (r / l)F

/ lF(R / g(R), m) / p(m) Å 0. (5)

To obtain closed form solutions, we need to make more specific assump-tions about the process R. Here we assume that R fluctuates as a geometricBrownian motion, with a probability ldt that an event will occur in each timeinterval dt that will increase R by F percent of its value, and thus

dR/R Å adt / sdz / (1 / F)dq. (6)

Providing we assume that the expected increase in the new return on the newactivity does not exceed the discount rate, so a / lF 0 r õ 0, then thefollowing proposition holds, keeping in mind that R cannot be less than zero.

PROPOSITION 1. As long as a / lF 0 r õ 0, the optimal policy is asfollows. If the firm is in mode 0, it will continue in this mode until R reacheslevel R**, at which time it will change to mode 1. If the firm is in mode 1,it will continue in that mode until R reaches R*, when it will change to mode0. Naturally, R** ú R*.

Proof. In Appendix 1. j

With the firm in mode 0, in the range (0, R**) its value is given by

(1/2)s2R2F9(R, 0) / aRF*(R, 0) 0 (r / l)F(R, 0)

/ lF[(1 / F)R, 0] / I Å 0. (7)

Similarly, with the firm in mode 1, in the range (R*, `), the value is

(1/2)s2R2F9(R, 1) / aRF*(R, 1) 0 (r / l)F(R, 1)

/ lF[(1 / F)R, 1] / R Å 0. (8)

The solution of these differential equations (7) and (8) is

F(R, 0) Å ARh / I/r, (9)

F(R, 1) Å BRu / R/(r 0 a 0 lF), (10)

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where h ú 1 and u õ 0.23 In both (9) and (10), the first terms (ARh and BRu)represent the option value of being able to switch into the other mode atsome point in the future while the second terms are the value of the firm ifit remains in the current mode.

The solutions also have to satisfy two sets of boundary conditions. Thevalue matching conditions require that the value of the firm at the boundaryin its original mode be equal to its value in the new mode, net of the adjustmentcost:

F(R**, 0) Å F(R**, 1) 0 S01 , (11)

F(R*, 1) Å F(R*, 0) 0 S10 . (12)

The high-order contact or smooth pasting conditions require that the marginalpayoff from increasing R be the same in both modes at the boundary,

F*(R**, 0) Å F*(R**, 1), (13)

F*(R*, 0) Å F*(R*, 1), (14)

where F* is the first derivative of F with respect to R.Substituting the solutions for F(R, 0) and F(R, 1) into the boundary condi-

tions and rearranging gives four equations which can be solved for R** andR*:

AR**h / I/r Å BR**u / R**/(r 0 a 0 lF) 0 S01 , (15)

BR*u / R*/(r 0 a 0 lF) Å AR*h / I/r 0 S10 , (16)

hAR**h01 Å uBR**u01 / 1/(r 0 a 0 lF), (17)

hAR*h01 Å uBR*u01 / 1/(r 0 a 0 lF). (18)

As is usual for this type of problem, we cannot obtain a closed formsolution to this system of equations and therefore, we use numerical simulationto study the results.

The hysteresis bands, i.e., the critical levels of R* and R** between whichthere is a zone of inaction so that the firm stays in its existing mode ofoperation, depend on the variance s as follows. The upper band rises and thelower band falls as the variance increases. Higher uncertainty means the newactivity must yield a larger relative return in order for the manager to switchout of the old activity. The interpretation is that when the manager is more

23 h ú 1 and u õ 0 are the roots of the nonlinear equation

(1/2)s2b(b 0 1) / ab 0 (r / l) / l(1 / F)b Å 0,

where (r 0 a 0 lF) must be greater than zero for h ú 1 and u õ 0.

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uncertain about whether the new opportunity will continue to have a higherreturn—for example, because he is uncertain about whether the governmentwill last and pursue consistent policies—he will be more reluctant to incurthe switching cost. However, if the firm is already in the new mode, higheruncertainty means a lower relative return is necessary before it switches backto the old mode as there is a higher value to waiting in anticipation of higherrelative returns from the new activity.

An increase in the size of the Poisson jump, F, also causes the hysteresisband to widen. A higher F means a larger switchover cost and requires ahigher R in order for the manager to be willing to switch.24 In addition, ahigher F increases the variance of the return process. As we show in Appendix2, ignoring terms in dt2 and higher, the variance is

V(dR) Å (s2 / lF2)R2dt. (19)

This formula shows the two components of the variance: the first, s2R2dt,comes from the Brownian motion part of the process and is conditionedon no jump occurring and the second, lF2R2dt, accounts for the possibilityof a jump.

Increasing the mean arrival rate of the Poisson process, l, has a similareffect to increasing F. Making the policy more intense actually raises thevariance of the stochastic process. Note that this effect would be unchangedeven if we modeled the switchover cost as a constant independent of lF.25

In our subsequent analysis therefore, we can consider the product lF to bethe parameter controlled by the government. A higher value of lF represents amore intense policy reform. More radical reform therefore means both largerjumps and a higher mean arrival rate, which will tend to increase the valueof R faster but also raise the adjustment cost for switching between modes.It is usual to consider the hysteresis band only up to the point where a /lF 0 r is just less than zero, this is the region within which the expectedgrowth in the return on the new activity is less than the rate at which futurereturns are discounted. Once this threshold is crossed, the firm’s value toswitching goes to infinity and, unless its switching cost increases at least asfast, the firm will switch right away. In other words, if the policy reform issufficiently intense, the option value of waiting represented by the hysteresisband is overcome. The following section explores this result in more detail.

4. GOVERNMENT POLICY

To evaluate government policy we need to make an assumption about thedistribution of firms in the economy. Each firm has its own return function,

24 If there are fixed switchover costs, the band will have a similar shape.25 This is evident from the variance of the return process. Even if the switching cost were

constant, increasing l or F would increase the variance of the return process, thereby wideningthe hysteresis band.

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with the return of firm i in mode j denoted pi(j). All firms have the samereturn (I) in mode 0, but receive kiR in mode 1. There is a uniform distributionof returns to the new activity between 0 and aR. We assume all firms beginin mode 0 and have the same switching cost. To make the problem analyticallytractable, we assume that it is possible to switch from mode 0 to mode 1 butnot the reverse.

Assuming that the upper bound on the parameter distribution (a) is suffi-ciently large, at any given R0 there is a critical k* such that all firms with ki

¢ k* will switch to the new activity and all firms with ki õ k* will remainwith the old activity.

Given R0 and lF, the firm with ki Å k*, let us call it i*, must satisfy thevalue matching and smooth pasting conditions. Respectively, these are:

Fi*(k*R0 , 0) Å k*R0 0 I 0 C0lF, (20)

F*(k*R0 , 0) Å k*. (21)

Substitution gives

A(k*)Rb0 / I/r Å k**R0 0 I 0 C0lF, (22)

bA(k*)Rb010 Å k*, (23)

which can be solved to find

k* Å (b/(b 0 1)R0){I(1 / r)/r / C0lF}, (24)

A(k*) Å (1/R(b 0 1)){I(1 / r)/r / C0lF}. (25)

A higher value of lF reduces b, so b/(b 0 1) increases and k* rises. For agiven R0 , fewer firms will switch to the new mode because the higher lFmeans a larger adjustment cost and a wider hysteresis band which fewer firmsare able to cross.

The government’s payoff is proportional to the net present values offirms which have switched to the new activity.26 The government there-fore wishes to push all the firms into the new activity. However, as before,its only means of doing so is through altering lF. In this part of themodel, we assume that firms cannot switch back from the new mode tothe old mode.27

Firms are indexed by the restructuring factor k, which represents their

26 If the government incurs the cost of adjustment directly, this would reduce the intensity ofthe optimal policy only when gradual reform was optimal. The breakthrough level of radicalreform is generally not affected. Note also that, if the government incurs losses from each firmthat remains in the old mode, this will increase the intensity of optimal reform.

27 Note that including an option to switch back to mode 0 would make it impossible to solvethe problem because we would lack sufficient boundary conditions.

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return in the new activity relative to the stochastic process R.28 For notationalconvenience we drop the index i in our further discussion. The expectedpresent value of a firm at time 0 when the initial return is kR0 and the firmis in mode 1 is now given by

F0(kR0 , 1) Å E * pt(1)e0rtdt, (26)

where pt(1) Å kRt is the operating profit of a firm in mode 1 in period t. Theexpected value of the flow profit for this firm at any point in time is givenby

Ept(1) Å kR0e(a/lF)t. (27)

Substituting back into the expected value function gives29

F0(kR0 , 1) Å kR0/(r 0 a 0 lF). (28)

At time 0, firms with k* ° k ° a will switch to the new activity. At timet, the return from the new activity is expected to evolve to R0e

0(a/lF)t. Thiswould lower k*, causing firms with k* ° k ° k* to be able to switch, if theyhave not already done so, to the new activity. That k* ° k* can be seen bysubstituting for R0 into the equation for k*.

To make the analysis tractable, we assume the government evaluates itsutility at fixed intervals of time, denoted 0, t, 2t, and so on. Its benefit functionis therefore approximated by

G(lF) Å *a

k*0

w(k)F0(kR0 , 1)dk / g *k*

0

k*t

w(k)Ft(kRt , 1)dk

/ g2 *k*

t

k*2t

w(k)F2t(kR2t , 1)dk, (29)

where Ft(kRt , 1) is the expected present value of a firm that has just switchedto mode 1 at time t, k* is the critical ‘‘efficiency’’ level above which firmsswitch to the new activity at time t, g is the government’s discount factor,and w(k) are the weights given to firms according to their efficiency level.The true value of G(lF) depends on values over the entire time horizon ofthe problem, but we can obtain the same qualitative results by solving forjust three time periods. The value of a firm that switches in each period isas follows:

28 Terms in kR below can be interpreted as being net of ongoing adjustment costs. Thus thegovernment’s objective function includes recurring adjustment costs from the drawn-out processof firm-level restructuring. Higher adjustment costs of this kind mean a smaller flow of kR.

29 Again, this holds only as long as (r 0 a 0 lF) ú 0.

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FIG. 1. Government function (G(lf)) plotted against reform intensity (lf). y-axis: governmentfunction (G(lf)); x-axis: reform intensity (lf). Top line has sigma equal to 0.1; middle line hassigma equal to 0.2; bottom line has sigma equal to 0.3. Parameter values: I Å 1, C0 Å 1, r Å0.9, R0 Å 1.5, a Å 8, a Å 0.1, s Å 0.1.

F0(kR0 , 1) Å * kR0e0(r0a0lF)tdt Å kR0/(r 0 a 0 lF), (30)

Ft(kRt , 1) Å * kR0e0(r0a0lF)te(a/lF)dt Å kR0/(r 0 2(a 0 lF)), (31)

F2t(kR2t , 1) Å *t

kR0e0rte(a/lF)2te(a/lF)dt Å kR0/(r 0 3(a 0 lF)). (32)

The switching thresholds are given by

k Å b(I(1 / r)/r / C0)/(b 0 1)R0 (33)

k Å b(I(1 / r)/r / C0)/(b 0 1)R0e0(r0a0lF)t (34)

kt Å b(I(1 / r)/r / C0)/(b 0 1)R0e0(r0a0lF)2. (35)

Now the overall government benefit function G(lF) evaluated for w(k) Å kis

G(lF)Å (a30 k*3)R0/3(r0 a0 lF)/ g(k*30 k*3)

1 R0/3(r0 2a0 2lF)/ g2(k*30 k*)R0/3(r0 3a0 3lF). (36)

Figure 1 shows that the benefit function achieves a local optimum for somevalue of lF. As long as a / lF 0 r is less than zero, there is a limit to

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FIG. 2. Simulation results for government function (G(lf)) plotted against reform intensity(lf). y-axis: government function (G(lf)); x-axis: reform intensity (lf). Top line has varianceequal to 0.1; middle line has variance equal to 0.5; bottom line has variance equal to 0.8.Parameter values: I Å 1, R0 Å 2, l Å 1, a Å 0.1, r Å 0.95, K10 Å 3, K01 Å 2, Firm 1 Å 0.5,Firm 2 Å 1, Firm 3 Å 1.5.

how fast the government wants to reform. As a first effect, a more intensereform raises the relative returns process and this creates a favorable environ-ment for the new activities and a positive inducement for firms to switch intothem, which will consequently raise the benefits to the government. However,a more intense reform policy increases the variance of the return process,which widens the hysteresis band of individual firms, which implies that firmswill wait longer before switching into new activities, thus delaying, and insome cases indefinitely postponing, the benefits to the government. The inten-sity of the reform should balance completely these counteracting forces inorder to maximize the government’s payoff function.

Note that these results hold even if firms can switch back to the old activity.In this case the problem can no longer be solved analytically, but we can runthe model numerically. The results for different parameter values are presentedin Figs. 2 and 3.30 These simulation results show the same structure as earlierresults. These figures also make clear that as the underlying variance increases,the optimal policy intensity (at the local optimum) declines. If initial conditions

30 The simulation shown here has three firms with the return function kR, where k Å 0.5, 1,and 1.5. R is calculated for three values of the variance (0.1, 0.5, and 0.8) using random samplesfrom the normal and Poisson distributions, assuming a starting value of R0 Å 2. Firms start inthe old activity and switch into the new activity if the conditions are right. They switch back tothe old activity if the return on the new activity falls sufficiently low.

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FIG. 3. Simulation results for government function (G(lf)) plotted against reform intensity(lf). y-axis: government function (G(lf)); x-axis: reform intensity (lf). Top line has varianceequal to 0.1; middle line has variance equal to 0.5; bottom line has variance equal to 0.8.Parameter values: I Å 2, R0 Å 2, l Å 1, a Å 0.1, r Å 0.95, K10 Å 3*f, K01 Å 2*f, Firm 1 Å0.5, Firm 2 Å 1, Firm 3 Å 1.5.

are worse, i.e., I is lower, then optimal reform intensity increases. There is alsono change in the qualitative results if we once again allow the switchover costto depend on the policy intensity, i.e., adjustment costs become convex.

Our general finding for all these cases is that once a / lF 0 r is equalto or greater than zero, the hysteresis band collapses and the government’svalue function jumps upwards. As long as the switchover cost is lower thanthe payoff in this condition, this is a global optimum. The only conditionunder which this optimum does not exist is when the switchover cost increasesfaster than the payoff, which is tending to infinity in our formulation. For amore detailed consideration of switchover costs and payoffs from reform, weturn now to the empirical evidence.

5. REFORM EXPERIENCES

The primary application of our theory is to interpret the reform of commu-nist countries. We cannot determine the precise values of our model’s parame-ters in different countries but we can use the model to provide a qualitativeassessment of experiences. In particular, we can address the question ofwhether reform has been sufficiently rapid in various contexts, beginningwith the important reference case of Poland.

When the Solidarity-backed government came to power in late 1989, Poland

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was in a deep economic crisis characterized by high inflation and shortagesof basic goods. The new reformers’ explicit goal was to change the economicenvironment so much that firms would be forced to change their behavior at once(Balcerowicz, 1994). Despite the high level of uncertainty about relative returns,the reform package introduced at the beginning of 1990 was sufficiently radicalto force most firms to begin restructuring right away (Frydman and Wellisz, 1991;Pinto et al., 1993). It also led to the rapid development of new private firms thathad operated only informally and on a very small scale under the old system(Johnson and Loveman, 1995). In both state and private sectors there was adistinct switching of activities and internal structure (Carlin et al., 1994).

Furthermore, the weakening of the reforms after mid-1991 and even the returnto power of the former communists have not caused firms to switch back to oldactivities (Slay, 1995). The increased uncertainty has presumably widened thehysteresis band, but this now makes firms more likely to stay with new activities.The Polish case shows that once radical reforms have caused switching to newactivities, it would require a very radical anti-reform to induce a reversal.

In contrast, in slowly reforming countries of Eastern Europe and the formerSoviet Union, such as Romania or Ukraine, the reforms have never beenstrong enough to force state enterprises into serious restructuring. As a result,the intensification of gradual reform, such as occurred in Ukraine at the endof 1994, has relatively little positive effect and firms have tended to remainwith their old activities. State sector enterprises have probably adjusted lessthan in Poland and there has certainly been less private sector development(Tedstrom, 1995).

The Chinese reform experience has also been gradual. The government hasslowly changed the incentives for producers to engage in new activities (Chenet al., 1992). Relative prices were altered steadily over time (McKinnon, 1993),new nonstate enterprises were permitted to spread (McMillan and Naughton,1992), and managerial incentives were strengthened over time (Groves et al.,1994). Does this mean the Chinese reforms have not been optimal?

In our model, radical policy is optimal unless the benefits of immediateswitching are outweighed by adjustment costs. In China it has been arguedthat policymakers perceived adjustment costs to be relatively large and consid-ered the benefits of rapid change in firm behavior to be low (Perkins, 1994).The government also retained effective control over the economy. The lowlevel of uncertainty about relative returns presumably induced firms to switcheven though the reforms were far from intense. The optimal policy may stillhave been radical, but the difference between the local (gradual) optimumand the global (radical) optimum need not have been large.31

31 This is one way to formalize the argument of Sachs and Woo (1994) that China had quitedifferent initial conditions, so reform could be slower.

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China had the advantage of being relatively stable. In the former SovietUnion, for example in Russia, there has been high inflation and associatedhigh uncertainty; gradual policy change has had only a slight positive impacton firms’ choice of activities. In countries such as Ukraine and Belarus,gradual reform has meant that, when actually incurred switchover costs aresmall, relatively few firms switch into new activities. In these cases, someeconomic reform has occurred but the policy intensity has almost certainlybeen less than optimal.32

6. CONCLUSION

Our model provides support for existing informal arguments about theoptimal intensity of policy reform in post-communist countries. Under generalconditions, and in contrast to most existing formal models, we find that radicalreform is optimal. This ceases to be the case only if the adjustment costs ofan immediate switch are very large.

This paper has focused on issues related to post-communist reform, butthe same mathematical approach could be used much more broadly. Issuesof organizational change, in particular, how managers can best alter the opera-tions of an individual firm, can be treated in the same way. Strong argumentshave been made in support of both re-engineering, a form of shock therapy,and total quality management, i.e., gradualism, but so far there has been littleattempt to determine the conditions determining the optimal pace of change.With some minor modifications, our model can be used to address this prob-lem. Further extensions could combine the analysis of stochastic and nonsto-chastic control methods.

APPENDIX 1

Proof of Proposition 1

In the absence of a switchover cost, a firm in old activity 0 will switch tothe new activity 1 when R Å I. It will also switch back to the old activity atthe same level of R, which we call the Marshallian threshold, denoted RM,i.e., RM Å I. Now for a firm operating in mode 0 and for values for which itis optimal to continue operating in mode 0, it holds that

(1/2)s2R2F9(R, 0) / aRF*(R, 0) 0 (r / l)

1 F(R, 0) / lF[(1 / F)R, 0] / I Å 0, (A-1)

32 In this regard, our model provides formal support for the arguments of Aslund (1995) andLeitzel (1995) about Russian reform.

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and for a firm operating in mode 1 and for values of R for which it is optimalto continue in mode 1, it holds that

(1/2)s2R2F9(R, 1) / aRF*(R, 1) 0 (r / l)

1 F(R, 1) / lF[(1 / F)R, 0] / R Å 0. (A-2)

The solutions for the above equations are

F(R, 0) Å ARh / I/r,

F(R, 1) Å BRu / R/(r 0 a 0 lF),

where h ú 1 and u õ 0 are the roots of

(1/2)s2b(b 0 1) / ab 0 (r / l) / l(1 / F)b Å 0.

Define

G(R) Å F(R, 1) 0 F(R, 0) Å BRu 0 ARh / R/(r 0 a 0 lF) 0 I/r.

For small values of R, the dominant term in G(R) is BRu, which is decreasingand convex. For large values of R, the dominant term is 0ARh, which isnegative, decreasing, and concave. Applying the value matching and smoothpasting conditions at the critical values R* and R**, we get

G(R**) Å C0lF,

G(R*) Å 0C1lF,

G*(R**) Å 0,

G*(R*) Å 0.

This implies the graph of G(R) against R has a S-shape over the range R* toR**. It is tangential to the horizontal axis at height C0lF at R** and at height0C1lF at R*. Also, G(R) is concave at R** and convex at R* (see Fig. A1).At the upper threshold, subtract (A-1) from (A-2). Then

(1/2)s2R**2G9(R**) / aR**G*(R**) 0 (r / l)

1 G(R**) / lG[(1 / F)R**] / R** 0 I Å 0.

Substituting from the boundary conditions and rearranging gives

R** Å I / (r / l)G(R**) 0 lG[(1 / F)R**] 0 (1/2)s2R**2G9(R**).

Now G(R**) is greater than G((1 / F)R**), from Fig. A1 and G9(R**) õ0. Then

(r / l)G(R**) 0 lG[(1 / F)R**] ú 0

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FIG. A1. Government return function plotted for various values of the return on new activity,R Å (y-axis) government function (G(R)); (x-axis) reform function.

and

R** ú I Å RM.

Similarly, at R*, it can be shown that

R* õ I Å RM.

APPENDIX 2

Derivation of V[dR]

Using the random walk approximation of the return process, we have:

dR Å Radt / sR(dt)0.5 with probability 0.5(1 0 ldt)

Radt 0 sR(dt)0.5 with probability 0.5(1 0 ldt)

Radt / FR with probability ldt

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Ignoring terms with the following in dt2 and higher, we can derive thevariance as follows:

E[dR] Å 0.5(1 0 ldt)(Radt / sR(dt)0.5) / 0.5(1 0 ldt)(Radt 0 sR(dt)0.5)

/ (Radt / FR)ldt Å Radt / FlRdt.

E[dR2] Å 0.5(1 0 ldt)(Radt / sR(dt)0.5)2

/ 0.5(1 0 ldt)(Radt 0 sR(dt)0.5)2 / (Radt / FR)2ldt

Å (1 0 ldt)(R2a2dt2 / s2R2dt) / ldt(R2a2dt2 / F2R2 / 2aFR2dt).

V[dR] Å E[dR2] 0 E[dR]2 Å (s2 / lF2)R2dt.

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