The political economy of declining industries: Senescent industry collapse revisited

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Journal of International Economics 42 (1997) 221-237

ELSEVIER

The political economy of declining industries: Senescent industry collapse revisited S. Lael Brainardasb,Thierry Verdierc3d‘” “MIT Sloan School, Cambridge, MA, USA ‘NBER, Cambridge, MA 02138, USA ‘CERAS, Paris, France ‘DELTA-ENS Paris, France ‘CEPR, 25-28 Old Burlington Street, London, WIX ILB, UK Received 12 December 1995; accepted 15 February 1996

Abstract Many observers have noted a strong tendency for protection, once it is instituted, to persist over time. This paper first shows that persistent protection arises whenever lobbying is an alternative to costly adjustment. With endogenous protection, the level of tariffs is an increasing function of past tariffs: the more an industry lobbies, the greater the current protection it receives and the less it adjusts, and the less the industry adjusts the more effective it is as a lobby in the future. When the costs of lobbying and adjustment are fully variable, declining industries contract more slowly over time and never fully adjust. However, the paper shows that adding a fixed cost of lobby formation or maintenance is sufficient to generate an endogenous collapse of protection, such as that predicted by Cassing and Hillman (1986, American Economic Review 76, 516-523), in which an industry abruptly terminates its lobbying and loses its protection. Finally, the paper examines the well-documented bias against growing industries in the lobbying process. Key words:

Lobbying; Adjustment; Trade policy

JEL classtjication:

D72; F13

0022-1996/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved PII SOO22-1996(96)01432-E

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1. Introduction

This paper shows how persistent protection emerges from an interaction between costly industry adjustment and lobbying. It then goes on to explore circumstancesunder which protection endogenously collapses. The tendency for protection to persist once it is instituted is one of the central stylized facts in trade. In studies of both the Kennedy and Tokyo Rounds of the GATT, Baldwin (1985) found that industries received more protection following each round the greater were their levels of protection going into each round, even after controlling for industry labor force characteristics, growth rates, and import penetration ratios. Marvel and Ray’s study of the Kennedy Round reached a similar conclusion, controlling for industry growth rates, industry concentration, comparative advantage, and buyer concentration. In empirical tests explaining corporations’ positions on six trade initiatives during the 1970s Pugel and Walter (1985) found that the demand for protection was strongly increasing in the industry’s initial tariff level, controlling for import penetration and variables measuring exporting strength. Such persistence can be derived in a setting with lobbying and costly adjustment. Supposeowners of industry-specific capital can respond to an adverse trade shock by either undertaking costly adjustment or lobbying politicians for protection. Their choice will depend on the relative returns to adjusting and lobbying, which in turn depend on the value politicians place on lobbying revenues relative to the welfare cost of protection. By introducing an explicit lobbying processsimilar to that of Grossmanand Helpman (1992) into a dynamic framework, it can be shown that the level of tariffs is increasing in past tariffs. The more an industry lobbies, the greater the current protection it receives and the less it adjusts, and the less the industry adjusts the greater its returns from lobbying next period. With fully variable costs of lobbying and adjustment, the lobbying feedback effect implies that declining industries contract more slowly over time, permanently cushioned by protection, and never fully adjust to their free-market output. This smooth dynamic adjustment path contrasts sharply with the central prediction of the Cassing and Hillman (1986) model in which protection is abruptly terminated and the industry collapses, following an initial period of gradual adjustment to an adverse trade shock.’ The discontinuous adjustment behavior is attributable to an ad hoc inflection point in a tariff responsefunction, which is otherwise increasing in the level of labor in an industry. Below we show that such an endogenous collapse can be derived in a model with explicit ‘Lawrence and Lawrence (1985) also develop a model in which labor adjustment in a declining industry is discontinuous. However, there is no political intervention in their model. The discontinuity is attributable to the combination of lumpy capacity reduction with monopoly behavior on the part of labor.

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interaction between a politician and specific factor owners, but it requires a nonconvexity in the lobbying process, such as a recurring fixed cost. Finally, the model is designedso that it can be applied symmetrically to the case of a growing industry. We examine this case to make the point that the disproportionate shareof protection afforded to mature industries in countries such as the United Statesis better explained by a bias in the political processthan by pure economic differences.We also discuss the implications for general equilibrium. This paper joins a growing literature on protection and lobbying in declining industries. Hillman (1982) usesthe regulatory capture framework of Stigler (197 1) and Peltzman (1976) to examine political-support protectionist responses to declining industries. He shows that endogenousprotection only partially compensatesspecific factors in an import-competing industty for an adverseterms-of-trade shock. Long and Vousden (1991) extend the analysis to a general equilibrium Ricardo-Viner framework, and discuss how this partial compensation result is affected by the degree of risk aversion of the specific factor owners and by the way tariff revenues are redistributed. In both papers,the analysis is static and the political support function is specified exogenously as a black box. A variety of papers have also investigated dynamic aspects of protectionist policies. Matsuyama (1990), Tornell (1991), and Brainard (1994) analyze circumstancesin which the adjustmentpath under protection is socially suboptimal in the absenceof lobbying due to a dynamic inconsistency problem. However, Cassing and Hillman’s analysis of senescent industry collapse is unique in explicitly considering the effect of lobbying on industry dynamics. The paper proceedsas follows. Section 2 develops an infinite horizon model of the interaction between a trade-impacted industry and a politician. Section 3 considers industry collapse. Section 4 considers growing industries and the implications for general equilibrium. Section 5 concludes. 2. Lobbying and adjustment We focus on an industry that experiencesan unanticipated price shock at time 0. The industry employs a specific factor, which is fixed, and a variable factor. The variable factor is supplied competitively, and any rents accrue to the owners of the specific factor. At the beginning of each period f, there is a capacity level in the industry, yr. Each period, the specific factor owners choose to adjust capacity by some amount x, (where x > 0 implies contraction). Production takes place after the adjustment has occurred. Given the fixed specific factor input, output is assumed equal to the net level of capacity, z, = yI -x,, which is also just equal to the capacity level at the beginning of the next period, y,+,. For clarity, we restrict consideration to linear demandand quadratic costs.There is a cost of adjustment, 4, which is a quadratic, increasing function of the amount

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of adjustment: 4(x,) = &f/2. The cost of production is also assumedquadratic and increasing in output: C(q,) = q:/2. The industry is a price taker on international markets. Domestic demand is a linear, decreasingfunction of the domestic price pt: D(p,) = u - pt. In the absence of intervention, the domestic price is just equal to the exogenously given world price, P,,,. The international price is assumed constant over time, with the exception of a discrete jump at time 0. Prior to that time, both the international price and the domestic price are constant at p,,, which is consistent with an equilibrium output level, y,,. The output level is chosensuch that the marginal cost of production equals the price: C’(y,) = pO, which implies y,, = pO. At time 0, a permanent shock in the international market causesa decline in the world price to p,
(1)

The policymaker values both social welfare, W, and lobbying contributions in different degrees.We assumethat the utility function in period t is linear in both elements: G(P,,Y,J~,)= PWP,,Y,JX,)+ (1 - /W’t(~,av)

(2)

where the weight on welfare, /3, lies between l/2 and 1. Welfare in period t is the sum of consumer surplus, industry profits and tariff revenue: m WP,,Y,J,)

= I W)du + P,(Y~J,) - C(Y, - xt) - 4(x,) p, + (P, -P,MY,#,J,)

(3)

where M(y,,p,) = D(p,) - (yt - xt) is the import demand function. This objective function is the partial equilibrium, dynamic analogue of that developed in Grossmanand Helpman ( 1992).3The most straightforward interpretation is that the *The analysis implicitly assumesthat holding idle capacity is more costly than adjusting. “The welfare weight parameter, a, in Grossmanand Helpman is just equal to /3/( 1 - p) here.

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politician values contributions for their consumption value. The objective function could alternatively be interpreted as maximizing the probability of re-election at the end of the adjustment period, where the probability is linearly increasing in contributions and welfareP In the interests of simplicity, it ignores a host of interesting features of political interaction, especially competition between political parties. But, as Grossman and Helpman point out, evidence that lobby groups disproportionately make contributions to incumbents and frequently contribute to candidates after they have won suggests this simplification has some empirical credence, as does evidence that lobbies often make contributions to both parties. 2.1. Adjustment precedes tariff choice In order to derive an explicit path of adjustment for output and domestic prices over an infinite horizon, we assume a simplified timing structure of the stage game. Each period, the industry is assumed to choose its adjustment level and its contribution schedule simultaneously, after which the politician chooses a tariff level to maximize utility. Both the industry and the politician are assumed to employ Markov strategies. The state variable is the capacity, whose evolution is described by the simple equation: (4)

Y,+, =Yt -5 Then the politician’s value function is: V,(Y,) = max,[PW(p,,Y,)

+ (1 - PF,(P,ypw) + sV,(y~+l)’

(5)

Given the relationship between the domestic price and the contribution level embodied in the politician’s first-order conditions, the industry maximizes its value function by its choice of contribution and adjustment levels: VAY,> = ma+,

[

PLY, - 4

-

(Y, - d2

2

4-e

- -Tj- - F,(P,,P,) + PVAY,+,)

1 (6)

With this timing structure and Markov strategies, the politician’s protection decision affects only the contemporaneous levels of the contribution and adjustment. Therefore, the politician’s problem can be simplified to a static maximization problem. The first-order condition yields an expression equalizing the marginal industry contribution to the marginal welfare cost of an increase in the domestic price level weighted by the relative valuation of welfare: 41f instead the politician were maximizing re-election probabilities each period, it would require linking future payoffs to current contributions via the probability of current period re-election. This would considerably complicate the analysis.

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- p,)D’(p,) = dFt(;pw) f

(7)

Faced with this tariff response function, the industry’s problem simplifies considerably, permitting the first-order condition to be expressedas a second-order difference equation. The industry chooses its contribution (or equivalently the domestic price) in period t so that the marginal cost of lobbying just equals the marginal benefit to the industry from increased protection:5

This is the condition that Grossmanand Helpman term “local truthfulness.” In equilibrium, the industry choosesa contribution schedulethat satisfiesEq. (7) and Eq. (8) and leavesthe politician just indifferent betweenfree trade and implementing the desired tariff and receiving the associated contribution. These three conditions together yield:

where a = (1 - p)I/3 is the politician’s relative valuation of contributions, and Yt -y,+1 is substituted for x,. The first-order condition with respect to the adjustment level is: Pt= -P~Y,+,+(l+~(l+P)lY,+,-~Y*

(10)

Eq. (9) and Eq. (lo), together with the initial condition that the capacity at time 0 is equal to the initial price level, p0 (and setting the coefficient on the larger root to 0) are sufficient to describe the industry’s optimal adjustment path: Proposition 1.

1. The industry s optimal adjustment path under lobbying is: Y, = p. - & (

>

b(a)’ + &

(11)

‘The equilibrium tariff can alternatively be derived by restricting consideration to differentiable contribution schedules and assuming that the industry provides no contribution if there is no protection: F,(p,,p,) = 0. This assumption can be justified here because there are no competing lobbies, whereas in the Grossman and Helpman framework, each industry’s contribution includes a constant that is equal to the difference between its return when it lobbies and when it does not, given the equilibrium contributions of competing lobbies.

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where the root is defined as b(a)

= 1-a+~(1+p)-~(l-a)2+2(1-a)~(l+p)-4pr$2+~2(1+p)2 249 (12) and 0 0. 2. The path of the associated equilibrium tariff is: 0, = b(a)‘?a + (1 - b(a)‘)& w

(13)

The proof is straightforward. The adjustmentpath under lobbying can be contrastedwith the adjustmentpath in the free-market equilibrium, which is obtained by setting the politician’s weight on welfare to 1 (a = 0) in Eq. (11): Y,

= (P,, - P,)b(O)’ + P,

(14)

Comparing Eq. (11) and Eq. (14) reveals that lobbying affects the adjustmentpath through three channels. The equilibrium capacity is higher each period because lobbying reduces both the cumulative amount of adjustment that takes place and the rate of adjustment,and these two effects more than offset the reduction in the coefficient, p0 - p, /( 1 - a), due to the reduction in the price shock. The rate of adjustment is slower and the long-run equilibrium level of capacity is higher, the greater is the politician’s preference for contributions relative to welfare. With lobbying, output is adjusted downward smoothly, at a decreasingpace, eventually converging to a level that is permanently above the efficient level. Free market adjustment is compared with two alternative (a= 0.5; a=0.85) protected paths of adjustment in Fig. 1. The level of protection, 6,, declines smoothly and gradually with output over time, reflecting the effect of past protection through the current capacity. Eq. (13) establishesthat the tariff is higher at each point of time, the larger is the initial adverseshock or shift of comparative advantage,pO/p,. This is analogousto “the compensationeffect” of Magee et al. (1989). The larger the initial shock, the more the industry must adjust in order to adapt to the new international environment, and the larger are the incentives to lobby for protection to mitigate the need for costly adjustment. The persistenceof protection can be seenmost clearly by expressingthe tariff in terms of the previous tariff: @=(l-b(a))l-a -!-

+ b(a)O,-,

(15)

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ADJUSTMENT TO NEGATm

110 .

0

1

2

3

4

5

Time

6

7

SHOCK

8

9

10

Fig. 1. Adjustment to negative shock.

The current tariff is linearly increasing in the tariff of the previous period, by an amount that is increasing in the politician’s relative valuation of contributions. Indeed, Eq. (15) provides a direct theoretical justification for the empirical results we cited earlier.

2.2. Adjustmentfollows tar@ choice It may seem that these results are driven by the timing structure of the stage game. However, Brainard and Verdier (1994) show in a two-period framework that the basic result remains robust with a more realistic timing structure, where in each of the two periods, the industry chooses its contribution function preceding and its adjustment level following the politician’s choice of protection. Although this three-move timing assumption assigns less commitment power to the industry’s adjustment choice each period compared with the two-move structure above, this is offset by the alternating sequence of moves in the infinite horizon context. Even with the tariff choice preceding adjustment, the level of protection in the second period is a decreasing function of the adjustment undertaken in the previous period, which in mm is a decreasing function of the first-period protection. Stated differently, higher current protection reduces current adjustment, which in turn increases the marginal gain from future lobbying and raises future protection. Moreover, the level of protection in both periods is increasing in the initial capacity and in the initial price shock. These results are stronger, the greater is the politician’s relative valuation of contributions.

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3. Senescent industry collapse Our result differs markedly from that of Cassing and Hillman (1986) who find that the industry declines smoothly up to some point, after which it suddenly loses protection and collapses. This result is attributable to the shape of their tariff response function, which switches from convex to concave at some threshold level of capacity. By making the tariff formation process explicit, the framework above makes clear that some kind of discontinuity would be required in the industry’s lobbying activities to yield a point of collapse. In particular, if participation in the lobbying process each period required the payment of a fixed cost in addition to the variable contribution, then the industry would lobby only as long as the intertemporal return to lobbying offsets the fixed cost. Such a recurring fixed cost might be associated with organizational costs such as maintaining an informational network, maintaining political connections, or hiring outside lobbyists. Assume that in order to offer a contribution schedule F(p,,p,) to the politician, the industry must pay a fixed cost, C, in each period. Assume also that if the industry does not pay the fixed cost at any time t, then it cannot lobby in any period after t. We start by defining the value functions for no lobbying, for permanent lobbying, and for a single period of lobbying followed by no lobbying. We then solve forward recursively to determine the optimal number of periods of lobbying before a switch to no lobbying. We also show how the level of the fixed costs affects the ranking of the value functions associated with permanent lobbying, no lobbying, and lobbying for a finite number of periods. The proofs are given in the Appendix of the working paper (Brainard and Verdier, 1993). We start by defining the value function of the industry without lobbying, V,(y):

1

V,(Y)= ma oszsy[ p,z -;

- +ry; z’2 + Pv,(Z)

(16)

with z = y - X. Next, define V,(y) as the value function of the industry when it lobbies permanently on the interval [O,y,,]: V,(y) = max 05z5.y P,Z [

(1 - a)z2 _ 4[Y - z12 2 - c + Pv,k) 2

1

(17)

Moreover, define V”,(y) as the value function of permanent lobbying with fixed costs of zero: V,(y) = Vi(y) - C/(1 - p). Results from Lucas and Stokey (1989) establish that these value functions are well defined, differentiable, continuous, and strictly concave. We next define an operator, T,, that associates to any continuous function V(.) on [O,y,] the new function (T,V) defined by: (T,V(Y)

= m=o,z5,

SP,Z

-

(1- a>z* _ 44Y -z>* 2

2

- c + pV(z)

1 (18)

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T,V(.) is the value of lobbying in the current period followed by the value function V(.) in the following period. Then, by iterating over T,, we can define ([Z’JkV)(y) as the value of lobbying for k periods followed by the value function V(.) on KtY,l.

Next by solving the first-order conditions, we derive the optimal level of output with capacity y when adjustment is nonzero as z(O,y) for no lobbying, z&y) for permanent lobbying, and z:(y) for one period of temporary lobbying. Forward recursion similarly permits the derivation of the optimal level of output with nonzero adjustment when t periods of temporary lobbying are anticipated, z:(y). Using these definitions, the properties of the value functions, and forward recursion on the temporary lobbying value function, we establish: Proposition 2. For all y E[O,y,], for all t 2 1,

1. the value function (flJ’V,)(y) is dffi erentiable and strictly concave; 2. (fla J’V,)(y) - (pJ’-‘V,)(y) is increasing in y; 3. z’-‘“(y) 0.

Proposition 2 (2) establishes that the value of lobbying an additional period before switching to no lobbying is increasing in y, while (3) establishesthat the optimal level of output for a given initial capacity level between0 and y, is greater under permanentlobbying than lobbying temporarily for t periods, and greater for an additional period of temporary lobbying. In any period when the industry has lobbied in the previous period, the industry chooses between lobbying and not lobbying. The value to an industry with an initial size y,, of t periods of lobbying followed by no lobbying is simply ([T,]‘V,))(y,). The basic problem then is: (19)

If the argmax of this problem is QJ, then permanent lobbying will prevail. Otherwise, the industry stops lobbying after a finite number of periods and loses protection. Before solving for the optimal number of periods of lobbying, it is useful to compare the value functions for temporary lobbying for different lengths of time and for permanent lobbying: Lemma 1. For all y,, >p,ll

-a,

1. if for some t 2 1, we have ([T,]‘)V,(y,) I ([T,]‘-‘)V,(y,), we also have ([T,l’+k~Vo(yo) ~([T,It+k-‘)Vo(y,);

then for all k > 0,

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2. if for some t 11,

we have V,(y,)

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5 ([T,]‘V,)(y,),

131

then for all k > 0, we also

have V,(Y,) <(FJ’+k)Vo(~o). Lemma 1 (1) implies that there is at most one finite solution r(yO) to Eq. (19), unless y, belongs to a set of isolated points y (such that ([T,]‘V,)(y) = Note that this holds for all C > 0. ([T,]“‘)V,(y)). Lemma 1 (2) establishes that if for some number of periods of temporary lobbying, t, the value of temporary lobbying exceeds the value of permanent lobbying, then this will also be true for any number of periods greater than t. Temporary lobbying will be chosen if and only if the value exceeds that of permanent lobbying: 3 t < 00such that ([T,]‘V,)(

yO) > VU
Defining 7’,’ as the operator T, associated with zero fixed costs, and recalling that V,” is the value of permanent lobbying with zero fixed costs, we rewrite this expression as: 3 t < 00such that C/ [ 1 - p] > [Vl)( yo) - ([Tz]‘V,)(

y,)] lp’.

Proposition 1 established that the value of lobbying permanently with zero fixed costs exceeds that of never lobbying: V,(y) < Vi(y) for all y > 0. By recursion it follows that with zero fixed costs, the value of lobbying permanently exceeds the value of temporary lobbying for any number of periods t: ([Ti]‘V,(y)) 0. It is also clear that with zero fixed costs the value of lobbying temporarily exceeds that of never lobbying, V,(y) < ([Tz]V,)( y) for all y > 0, since V,(O) = (TzV,)(O) = 0 and one can show that ([Ti]V,)( y) - V,(y) is increasing in y. Again, by recursion it follows that the value of lobbying for an additional period is < ([T~]‘+‘V,)(y) for all y > 0. always positive with zero fixed costs: ([Tz]‘V,)(y) Thus, we can conclude that the sequence of points ([Tz]‘V,)(y,) is monotonically converging to Vf(yo) from below. Define U, as the difference between lobbying permanently and temporarily for t periods with zero fixed costs: u, = [V~(yo) - ([T~]‘V,)(y,)]lp’. The condition for temporary lobbying above is equivalent to the condition: 3 t < w such that C/( 1 - p) > u,. Then the problem of deciding whether to lobby temporarily or permanently is reduced to an examination of the limit of the sequence of points, u,, relative to the discounted value of the fixed cost, C/( 1 - p). In particular, it can be shown by contradiction that: Lemma 2. The sequence of points (u,), is a decreasing all t L 0).

sequence (i.e. u, 2 u,,, for

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Since it is a decreasing, positive sequence, (u,),, converges towards a limit u 10. Lemmas 1 and 2 and Proposition 2 together are sufficient to establish the main result: Proposition 3:

1. There exists a limit, u = lim u, such that u L api/2[ 1 - p] > 0. 2. If the fixed cost C is such that C/( 1 - p) 5 u, then there is permanent lobbying and permanent protection. In this case, the adjustment path is given by Y1+1= z(u,y,) with the initial condition ye. 3. If the fixed cost C is such that C/( 1 - p) > u, then there exists a unique time r( yO) 2 0, such that the industry enjoys temporary protection for r(ye) periods, after which it stops lobbying and protection collapses. 4. When protection is temporary, the adjustment path during the lobbying periods always lies between the free trade and permanent lobbying adjustment paths. and a direct corollary: Corollary 1. If ([T,]V,)(y,)
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4. Growing industries A second important stylized fact in the political economy of trade, particularly in the US, is that declining industries receive a disproportionate share of protection. Empirical studies such as Marvel and Ray (1983) and Ray (1991) have documented this bias. We next investigate this bias by extending the framework of Section 2 to consider lobbying and adjustment in a growing industry. We start by again assuming there is no fixed cost. Again, there is an unanticipated permanent price shock at time 0, but now we assume p0 rises to the new world price level, pw. In the absence of protection, the industry will raise capacity each period, to adjust to the steady state level y, =p, > yO, so that adjustment is positive in equilibrium. The analysis of lobbying in a growing industry is symmetric to the case of decline, as are the maximizing levels of contributions and adjustment each period. Proceeding through the same steps as for the declining industry in Section 2 yields an expression for the equilibrium capacity in period t: y,=&-

(

&

--PO w >

where the characteristic root is defined in Eq. (12). A growing industry grows more rapidly when it lobbies than it would in the free market, at a rate increasing in the size of the price shock, and the steady state output exceeds that in the free market by an amount that increases with the politician’s preference for contributions. This finding suggests that the empirical evidence that declining industries receive a disproportionate share of protection is better explained by a bias in the political process than by pure economic differences. There are a variety of reasons why the political process may be biased against growing industries. First, in the presence of imperfect capital markets,’ liquidity constraints on lobbying activities may be more binding in a growing industry than in a declining industry. This would be the case if incumbent domestic firms in mature industries have more accumulated cash reserves from past retained profits relative to investment opportunities than do firms in emerging industries. To illustrate the effect of a liquidity constraint, assume that firms must finance both investment and contributions from current profits. The industry’s maximization program is modified to take into account the liquidity constraint as follows:

“Imperfect capital markets may exist because either it is not possible to borrow to finance lobbying, or investors are less optimistic about an industry’s future growth path than are industry participants due to asymmetric information.

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(

of International Economics 42 (1997) 221-237 r:+1

V~Y,J,) = m=p,,y,+, m+l - 2

+ 4) + Vf(Yt+1A+J

-

&Yt+* -Ytj2 _ 0-T -RJ2 2 2a

(1 > (21)

where A, is the multiplier on the liquidity constraint. Since the unconstrained equilibrium profit level rises monotonically over time, the constraint must bind initially and over a continuous interval, if it binds at all. When the constraint binds, it affects the equilibrium capacity only through the characteristic root:

(1 + A,,,) = (l+h,)

(22)

Thus, a binding constraint lowers the industry growth rate relative to the unconstrained lobbying path.’ However, the growth rate remains above the freemarket rate, and the long-run equilibrium value is the same as that for unconstrained lobbying. The equilibrium adjustment paths for the unconstrained lobbying equilibrium (al = OS), constrained lobbying equilibrium, and unconstrained free-market equilibrium are compared in Fig. 2. Second,a fixed cost in the lobbying processmight create a bias against growing industries. Suppose,as in Section 3, that the fixed cost does not dependon the size of the industry. If an industry ever starts to lobby, it will not subsequently stop lobbying, since the return to lobbying never decreasesin a growing industry. Thus, an industry chooseshow many periods to wait before it starts lobbying. If the per period return to lobbying exceeds the fixed cost in the first period, it lobbies permanently, and conversely if the fixed cost exceedsthe return to lobbying at the steady-statelevel of output under lobbying, then the industry never startslobbying. If the fixed costs lies in some intermediate range, then the industry waits for some optimal number of periods until it is large enough that the intertemporal return to lobbying exceedsthe fixed cost, and begins lobbying. Perhaps most importantly, mature industries may have an advantage over fledgling industries in their capacity to pay the cost of lobby formation. In the model above, we simply assume that an industry lobbies whenever the intertemporal return is positive, thereby ignoring the critical issue of lobby formation. However, researchin political science suggeststhat industries are more likely to overcome the free-rider problems of lobby formation when they have large ‘We were not able to solve for L, explicitly. However, by combining Eq. (22) with the liquidity constraint it can be shown that under sensible conditions b is declining in L and L is rising over time, so that b is decreasing over time.

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ALVZW’MENT TO POSITIVE SHOCK

4

2

0 1

3

10

8

6 5

7

9

‘l?me Fig. 2. Adjustment to positive shock.

committed resourcesand establishedunions. Growing industries are characterized by rapidly changing market structures and a high likelihood of future entry, while declining industries are more likely to have stable market structureswith a reduced threat of domestic entry. If lobby formation requires the payment of some sunk cost, the greaterrisk that future rents will be dissipatedwith entry may make lobby formation more difficult in growing industries than in declining industries with clearly identified players and more predictable rents. 4.1. Implications for general equilibrium

These results ignore potential spillover effects of lobbying acrosssectors,which is a central consideration in understanding the effect of lobbying on dynamic resource allocation. In a general competition for protection, there are a variety of channels whereby the equilibrium pattern of protection might result in a diversion of resources away from infant industries toward industries with declining competitiveness.However, even in general equilibrium, it appearsthat a bias in the political processwould be required to explain the disproportionateprotection given to declining industries. The results derived by Grossmanand Helpman (1992) in a static general equilibrium framework, where protection spills over between interest groups through consumption, suggestthat mature sectorswould gain protection at the expenseof infant industries in a competition for protection if the infants were less well organized than mature industries for any of the reasons cited above. Similarly, in a model where there is a limited supply of a common factor of production, or the import-competing sector produces an input used by the

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exporting sector, the equilibrium pattern of protection might result in resources being diverted away from growing industries to mature industries, distorting adjustment in both directions.

5. Conclusion Motivated by the strong empirical regularity that the best predictor of future protection is past protection, this paper has analyzed the adjustment path in declining industries under endogenous protection. By introducing an explicit political objective function similar to that developed in a static framework by Grossman and Helpman (1992) into a dynamic model with convex adjustment costs, the paper shows that the level of tariffs is an increasing function of past tariffs. In this model, industry adjustment and lobbying are substitutes: the more an industry lobbies, the greater the protection it receives and the less it adjusts, and the less the industry adjusts the more effective it is in lobbying next period. Lobbying is an increasing function of the initial price shock, or equivalently of the gap between the initial level of capacity and the long-run equilibrium level. The paper finds that in the absence of nonconvexities in the lobbying process, the paths of lobbying and adjustment are smooth. The industry contracts output gradually over time to a level that is permanently above the free-market level by an amount that increases in the value the politician places on lobbying contributions relative to welfare. This result contrasts sharply with the Cassing and Hillman (1986) finding that there is a point of collapse, which corresponds to an inflection point in an ad hoc tariff response function. Here, we derive a similar endogenous collapse in the path of protection by introducing a recurring fixed cost associated with the organizational costs of lobbying. When the fixed cost lies in a range defined by the difference in returns between lobbying and not lobbying at the initial level of capacity and at the steady-state level under protection, the industry lobbies and receives protection for some finite number of periods and then abruptly stops lobbying, resulting in a collapse in protection and accelerated adjustment. The rate of adjustment under temporary lobbying lies between the adjustment rates under permanent lobbying and no lobbying, and the associated long-run output level is just the free-market equilibrium. Ultimately, the question of whether adjustment and protection are smooth or discontinuous is empirical. To the best of our knowledge, there have been no systematic investigations comparing adjustment paths across industries. Several articles that investigate a small number of industries do not address this issue directly. However, our purpose was to investigate the conditions that determine the adjustment path rather than to establish the validity of a particular path. In addition, the paper shows quite clearly that in a partial equilibrium framework, growing industries grow faster under endogenous protection unless there is some bias against growing industries in the political process that makes

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lobby formation costly. These results are suggestive for general equilibrium, where such a bias in combination with a resource constraint or a vertical relationship between infant and mature industries would result in a dynamic misallocation of resources between sectors.

Acknowledgments We are grateful to Gene Grossman, Elhanan Helpman, and two anonymous referees for helpful suggestions.

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