NBER WORKING PAPER SERIES ENTRY AND ASYMMETRIC LOBBYING: WHY GOVERNMENTS PICK LOSERS. Richard E. Baldwin Frédéric Robert-Nicoud

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1 BER WORKIG PAPER SERIES ETRY AD ASYETRIC LOBBYIG: WHY GOVERETS PICK LOSERS Richard E. Baldwin Frédéric Robert-icoud Working Paper ATIOAL BUREAU OF ECOOIC RESEARCH 050 assachusetts Avenue Cabridge, A 0238 February 2002 Our thanks to Alan anning and Gene Grossan for feedback and the Swiss ational Science Foundation for financial support. The views expressed herein are those of the author and not necessarily those of the ational Bureau of Econoic Research by Richard E. Baldwin and Frédéric Robert-icoud. All rights reserved. Short sections of text, not to exceed two paragraphs, ay be quoted without explicit perission provided that full credit, including notice, is given to the source.

2 Entry and Asyetric Lobbying: Why Governents Pick Losers Richard E. Baldwin and Frédéric Robert-icoud BER Working Paper o February 2002 JEL o. F, L5 ABSTRACT Governents frequently intervene to support doestic industries, but a surprising aount of this support goes to ailing sectors. We explain this with a lobbying odel that allows for entry and sunk costs. Specifically, policy is influenced by pressure groups that incur lobbying expenses to create rents. In expanding industry, entry tends to erode such rents, but in declining industries, sunk costs rule out entry as long as the rents are not too high. This asyetric appropriablity of rents eans losers lobby harder. Thus it is not that governent policy picks losers, it is that losers pick governent policy. Richard E. Baldwin Graduate Institute of International Studies, Geneva a, ave de la Paix 2 Geneva Switzerland and BER baldwin@hei.unige.ch Frédéric Robert-icoud LSE, Econoics Departent Houghton Street London WC2A 2AE UK

3 Entry and asyetric lobbying: Why governents pick losers Richard E. Baldwin Graduate Institute of International Studies, Geneva Frédéric Robert-icoud London School of Econoics & Political Science 5 Deceber 2000: This version Deceber 200 ABSTRACT Governents frequently intervene to support doestic industries, but a surprising aount of this support goes to ailing sectors. We explain this with a lobbying odel that allows for entry and sunk costs. Specifically, policy is influenced by pressure groups that incur lobbying expenses to create rents. In expanding industry, entry tends to erode such rents, but in declining industries, sunk costs rule out entry as long as the rents are not too high. This asyetric appropriablity of rents eans losers lobby harder. Thus it is not that governent policy picks losers, it is that losers pick governent policy.. Introduction Governents that try to pick winners and losers usually choose the latter, according to an old adage. Soe of the clearest exaples coe fro trade policy. In the US and Europe, the ost protected sectors agriculture, textiles, clothing, footwear, steel and shipbuilding have all been in decline for decades. Counter exaples are rare. Even when a growing sector gets protection, such as the US seiconductor industry, the protection tends to focus on arket segents like eory chips in which the doestic industry is losing ground. A related phenoenon is the IBY syndroe (ot in y Back Yard) whereby special interest groups see to fight harder to avoid loses than they do to achieve gains. In searching for an accounting of this phenoenon the natural place to start is the political econoy literature. The key approach for our purposes is the so-called pressure group or lobbying approach that was launched by the classic papers of Stigler (97) and Peltzan (976) in the context of industrial regulation. The approach subsequently found a very natural hoe in the field of international trade after a series of papers showed that it provides iportant insights into why observed trade policy deviates so radically fro welfare axiising policies. The path-breaking papers here are Hillan (982), which took the political support function approach, and Findlay and Wellisz (982), which introduced the tariff-foration function approach. ore recently, the pressure-group approach been extended to include ore explicit odelling of how lobbying expenditures affect policyakers choices. agee, Brock and Young (989) work with a odel where political contributions influence the outcoe of elections, but the doinant odel in this literature is now the protection for sale odel of Grossan and Helpan (994). As Rodrik (995) Our thanks to Alan anning and Gene Grossan for feedback and the Swiss ational Science Foundation for financial support.

4 2 notes, the great advantage of this odel is that it provides clear-cut icro foundations for lobbying and its effects in a tractable and fairly general setting. 2 The loser s paradox At the heart of the pressure-group approach is the presuption that special interest groups (SIGs) who spend the ost on lobbying or other political activities are, other things equal, the ones that get the ost governent support. In this light, the success of sunset industries in winning a disproportionate share of governent support is paradoxical. After all, lobbying dollars of expanding industries should be just as welcoed by politician as those of declining industries and an industry s ability to finance lobbying expenditures and its interest in obtaining governent support should be positively related to its size, eployent and/or profitability; one would expect the highest levels of governent support in the biggest and strongest sectors rather than in ailing sectors. In the sae light, the IBY syndroe observed in issues ranging fro health care refor to the location of landfill sites is curious since lobbying to reverse losses and lobbying to secure new gains ight be expected to be equally attractive to special interest groups. Our paper uses the pressure-group approach in particular that of Grossan and Helpan (994) to account for the surprising aount of support that goes to declining industries. Our basic story is siple. Governent policy is influenced by pressure groups and such lobbying is expensive. Special interest groups spend the oney in order to create rents that they can appropriate. 3 There is, however, a strong asyetry in the ability of expanding and contracting industries to appropriate the benefits of lobbying. In an expanding industry, policy-created rents attract new entry that erodes the rents. In the extree, free and instantaneous entry obviates all rents. This is not true in declining industries. Since sunk arket-entry costs (e.g., unrecoverable investents in product developent, training and brand nae advertising) create quasi-rents, profits in declining industries can be raised without attracting entry as long as the level of quasi-rents does not rise above a noral rate of return on the sunk capital. Plainly, asyetric appropriability iplies an asyetric incentive to lobby. The result is that losers lobby harder, so governent policy doesn t pick losers; losers pick governents policy. A corollary to this reasoning accounts for the curious tendency of special interest groups to fight harder to avoid losses than they do to win new gains. Literature Review any explanations of the loser s paradox have been suggested. One of the earliest and best known is the conservative social welfare function (CSWF) of Corden (974). As Corden introduces it, any significant absolute reduction in real incoes of any significant section of the counity should be avoided. In ters of welfare weights, increases in incoes are given relatively low weights and decreases very high weights. While this sort of governent-with-a-heart explanation ay have a good deal of explanatory power, it coes close to assuing the answer. oreover at least in developed nations, governents have any policies for redistributing incoe and cushioning shocks (incoe taxes, uneployent insurance, retraining schees, etc.), so even if caring were a ajor otive in governent policy, an optiising governent would separate industry support fro pure incoe distribution considerations. An even ore iportant critique is that the conservative social welfare function does not account for the fact that not all declining industries win assive 2 See Grossan and Helpan (200) for a synthesis. 3 Using US data, Gawande and Bandyopadhyay (2000) provide soe evidence that protection is indeed for sale. See footnote 5 below.

5 3 governent support. In the 980s for instance, the real wages of US unskilled workers fell substantially but only a sall subset of these attracted governent support. As the work of Goldberg and aggi (999) shows, well-organized sectors, for exaple US apparel workers, are the ones that induced the US governent to adopt distortionary policies that softened the fall in their real incoes. In sae spirit as the CSWF are the equity-concern odel of Baldwin (982) and the status-quo odel of Lavergne (983). One of the ost intuitive explanations for the loser s paradox turns on Anne Krueger s use of the identity bias to account for what she calls asyetries in the political arket. The bias, according to Krueger (990), is that people care ore about the welfare of specific, known individuals than they do about unidentified, face-less individuals. To see how it could explain asyetric governent support, contrast the ipact of a subsidy to a declining sector with one to an expanding industry. Both subsidies will alter the allocation of eployent, but in the ailing industry the jobs saved are identified ex ante with specific individuals, while the jobs created in the expanding sector cannot be identified with any specific individual, ex ante. In a way, this provides psycho-icro foundations, of the type associated with Schelling (984), for the CSWF approach. As such, Krueger s explanation relies on the shape of policyakers objective function and thus shares the shortcoings of the CSWF solution. A related paper, but one that relies on ore standard icroeconoic behaviour, is Fernandez and Rodrik (99). These authors use a echanis that is related to the identity bias notion to account for the reluctance of governents to adopt changes in policies, i.e. refors. To see this, consider a siple econoy with 45% of workers in one sector and 55% in another and a hypothetical refor that will help workers in the initially sall sector and hurt those in the initially big sector. oreover, the refor will shift eployent so that 60% of workers are eventually in the sector that is helped, i.e. the sector that was initially sall. If each worker knew what her fate would be ex ante, the refor would easily garner support fro a ajority of workers. However, workers in the initially large sector do not know, ex ante, in which sector they will end up ex post; the probability that they ove to the helped sector is quite sall, just 5/55, so each one of the ay oppose the refor ex ante. otice that while the identity bias operates via the psychology of policyakers in the Krueger odel, the Fernandez-Rodrik odel relies on nothing ore than individual rationality and the assuption of a rando selection device. Another solution with solid icro-foundations is proposed by Hillan (989), who views trade policy as social insurance against exogenous changes in coparative advantage; this odel could account for the asyetric protection of losers. Although it is difficult to discern the underlying forces in their odel, agee, Brock and Young (989) also clai to explain asyetric protection with their copensation effect. Another line of research that is tangentially related to the losers paradox is the study of the collapse of senescent industry. The seinal papers, Hillan (982) and Cassing and Hillan (986), applied the political support function approach to the question of why declining industries continue to decline despite the protection they receive with a special ephasis on their eventual collapse. Subsequent iportant contributions include atsuyaa (987), Van Long and Vousden (99), and Brainard and Verdier (997). While this branch of the literature is also concerned with sunset sectors, its focus is a quite different in that it

6 4 takes as a point of departure that declining industries will receive protection; our paper seeks to understand why this is so. 4 The ain idea in our odel is based on an unpublished anuscript by one of the authors, Baldwin (993), but our paper differs significantly in its odelling strategy and the rigour of the analysis. Baldwin (993) relied on unanticipated, but peranent changes in the degree of foreign copetition to generate differences between winners and losers and did not explicitly allow for the siultaneous existence of both types. This paper generalizes Baldwin (993) using a odel in which different industries face idiosyncratic, teporary deand shocks, agents are forward looking and policy setting is interteporal. We also note that Grossan and Helpan (996) extended the basic asyetric lobbying fraework of Baldwin (993) by considering free riding by new entrants in winning sectors. Their ain arguent is that it is free riding rather than entry, which causes the asyetry; we re-visit this issue below. We note that the sunk-cost based solution we propose in this paper is copleentary to all the aboveentioned solutions. Epirical studies of the losers paradox The lobbying success of losers the losers paradox has been extensively docuented epirically. In the US, Hufbauer and Rosen (986), Hufbauer, Berliner and Elliot (986), and Ray (99) have docuented that declining industries receive a disproportionate share of protection. Particularly successful are agriculture, textiles, footwear, clothing and steel, all of which have experienced secular declines in eployent and GDP shares in the US. For instance, in their introduction Hufbauer and Rosen (986) write: With bipartisan regularity, Aerican presidents since Franklin D. Roosevelt have proclaied the virtues of free trade. They have inaugurated bold international progras to reduce tariff and non-tariff barriers. But alost in the sae breath, ost presidents have advocated or accepted special easure to protect proble industries.... The United States is not the only country to have experienced copetition in ature industry fro foreign goods. ost industrial countries, in Europe, Japan and elsewhere, have encountered siilar difficulties. ore directly, any econoetric studies have found that being a loser in ters of eployent, output or iport copetition helps an industry get ore protection. Baldwin (985) and Baldwin and Steagall (994) find a strong correlation between positive serious injury findings of the US International Trade Coission and reduced industry profits and eployent. Glisann and Weiss (980) find that above-trend incoe increases are correlated in reductions in protection in Gerany between 880 and 978. arvel and Ray (983) find that an industry s growth rate has a negative ipact on its level of protection. This is confired by Baldwin (985) s finding that industries which were ost successful in resisting tariff cuts in the Tokyo Round were characterised by, inter alia, relatively slow or negative eployent growth as well as by high and rising iport penetration ratios. ore recently, econoetric evidence fro Ray (99) shows that declining industries tend to get ore protection, and Trefler (993) finds that an increase in iport penetration tends to 4 any of these papers conjecture as to why declining, as opposed to expanding, industries so frequently garner governent support, but this is not their ain focus. In particular, Brainard and Verdier (997) suppose that credit constraints prevent an expanding sector fro investing in the lobbying it needs to get protection. Also, Hillan (989) discusses the asyetrical effects of entry, but does not incorporate it into his foral odel.

7 5 increase the level of protection a sector is afforded. 5 Furtherore, a nuber of econoetric studies have found that average tariff levels tend to rise in recessions, for exaple Ray (987), Hansen (990), O Halloran (994); Gallarotti (985) finds the sae for 9 th and 20 th century tariffs in the US. In a siilar light, the tie-series approach of Bohara and Kaepfer (99) show that tariffs are Granger-caused (positively) by uneployent and real GP. We also note that the systeatic favouring of losers is actually inscribed in international and national trade laws. GATT generally prohibits countries fro pursuing policies that favour doestic firs over foreign firs. The ajor exceptions to this principal (safeguards, duping duties and countervailing duties) involve situations where iports cause or threaten to cause aterial injury to an established industry. In contrast, there are no general exceptions that allow a country to proote the interests of an expanding industry. These principles can also be found in national laws. For exaple, US trade laws ake decline, appropriately interpreted, an explicitly requireent for trade protection. If one accepts the view that political econoy forces shape national and international trade laws, the aboveentioned asyetry is puzzling. Lobbying dollars of expanding industries should be just as welcoed by politician as the dollars of declining industries. Therefore it is odd that politicians should have adopted laws that greatly restrict their ability to proote profits in expanding sectors, while at the sae tie creating loopholes that allow the to boost the profits of declining industries. Plan of the paper The paper is structured as follows. The next section develops the static econoic and political-econoic odel. Section 3 introduces the dynaic structure of the odel and solves the gae allowing for entry. Section 4 considers extensions and Section 5 concludes. 2. The basic odel Foralization of the asyetric lobbying effects discussed in the introduction requires a odel that first shows how industry support affects the fortunes of firs that ay lobby and then connects these changing fortunes to the political decision-aking process. To this end we present a very siple odel of the econoy whose special features siplify the algebra; we shall argue, however, that the basic results in the paper do not qualitatively depend upon these special features. In particular, we cobine a standard onopolistic copetition odel with the lobbying odel of Grossan and Helpan (994) Tastes and technology Consider an econoy with + sectors. The plus one sector, produces a hoogenous good, A, under constant returns and perfect copetition using labour L. By choice of units, one unit of L produces one unit of A. There is also a large nuber,, of syetric industrial sectors that are arked by increasing returns and onopolistic copetition. A typical industrial fir faces variable costs equal to βwx were x is fir output, β is the unit labour requireent, and w is the wage. In this section, we take the nuber of firs as given to fix ideas, delaying consideration of entry to section 3. 5 Interestingly, Gawande and Bandyopadhyay (2000), who explicitly test the Grossan-Helpan fraework using cross-industry data on US non-tariff barriers coverage rations and US lobbying spending, find a negative relationship between iport penetration and the level of protection when the sector is not organised; this relationship is positive otherwise. 6 Typically, the new political econoy literature works with a Ricardo-Viner odel.

8 6 Instantaneous utility is linear in the consuption of A and a two-tier index of industrial-goods consuption: / σ χ / σ / σ () U A + α ln D; D c( j) dj; σ > 0 Here D is the CES consuption index for typical industrial sector, c j is consuption of variety j in sector, is the nuber (ass) of such syetric varieties within a typical sector, σ is the constant elasticity of substitution aong varieties, and α is a deand-shift paraeter. is fixed. ote that inclusion of the paraeter χ akes the CES aggregate D ore general than the usual functional for. The paraeter χ easures the preference for diversity and in the standard love-for-variety preferences, χ is taken to be zero iplying that consuers could becoe unboundedly happy by consuing an infinitely sall aount of infinitely any varieties. To avoid this feature, and to siplify our algebraic expressions, we neutralise the love-of-variety aspect by taking χ. Iportantly, we assue rando preferences in the sense that α is either α H or α L where α H >α L, i.e. each sector faces either high or low deand. 7 The odel features a continuu of consuers endowed with a share equal to s(i) for consuer i of the econoy s labour and of all firs equity, so the individual budget constraint is: (2) A i τ j j j 0 s()( i wl+ Π T) p A + p c dj where Π is operating profit fro all sector- firs, L is the econoy-wide labour endowent, T is the total lup-su tax collected, τ is an ad valore tax or subsidy factor (i.e. the rate is τ-, with this being a tax if positive, or subsidy if negative). Producer prices are denoted as p so consuer prices are τp (τ is fully passed on to consuers under Dixit- Stiglitz onopolistic copetition). We noralise the econoy s total labour endowent to unity, 8 so optial aggregate deand for a typical variety j in a typical sector, and the aggregate deand for A are: (3) α ( τ p ) c A w T p c dj p σ j j ; ( + )/ Π τ j j A σ j 0 ( τ ) pj dj j 0 As usual, the producer price, p j, for typical industrial fir j is related to arginal costs according to p j (-/σ)βw. By choice of units (viz. β-/σ) and taking L as nueraire, we can without loss of generality set p j for all firs in all sectors. Consequently, a typical fir s flow of operating profit is 9 : 7 Our qualitative results would hold if we assued technology shocks rather than deand shock (ore on this in Section 4.2). 8 Accordingly, we assue that Σα is sall enough so that production of A is always positive at equilibriu. 9 Rearranging the fir s first order condition to (p i -βw)c i p i c i /σ and using the deand function and syetry of varieties yields the result.

9 7 α (4) π ; α { αl, αh}, Π π στ where within-sector syetry allows us to drop the fir subscript. Using the ex ante syetry of sectors, it proves convenient to index sectors by the state of deand faced, denoting the Π earned by those facing high and low deand as Π H and Π L, respectively; plainly Π H >Π L for any given level of τ Utilitarian benchark In the sequel, we introduce a political process governing the choice of τ, but intuition is served by first identifying the socially optial τ. Specifically, the governent chooses sector-specific taxes (τ>) or subsidies (τ<) to axiise aggregate welfare easured by a paraeter a ties the su of consuers utility. 0 The A-sector is untaxed and the lupsu tax T is adjusted to aintain a balanced budget. By syetry of firs, the lup-su tax revenue (which ay be negative) required to ipleent the vector τ is just the su over all of (-τ ) c. Using (4), together with the solutions for T, p and c, in () we find that the Benethaite objective is: α / σ (5) W a( + α ln( ) ) τ τ where we have chosen units of A to noralise p A to unity. axiising this with respect to τ (all ) requires the governent to offset the only distortion in the econoy, naely the onopolistic pricing distortion, and this iplies that the optial utilitarian policy is: (6) τ β ( / σ ). for all sectors. This clearly entails a subsidy (τ< is a subsidy while τ> is a tax) to all industrial sectors since σ>. ote also that since there is only one distortion and lup-su taxation is possible, the Benthaite governent can attain the first best. With this utilitarian benchark in hand, we turn to the lobbying gae, where the policyaker ay be influenced by political contributions Lobbying Hillan (989) and Baldwin (985) point out that under realistic assuptions, elected officials ay not be fully aware of the econoic interests of their constituents. And their constituents ay not be failiar with all the policies (and their econoic consequences) chapioned by their elected representatives. Consequently, Baldwin (985) notes, a group of voters ay have to engage in tie-consuing and costly lobbying activities to bring its viewpoint to the attention of legislators. Siilarly office-seekers need funds to infor the voters of how they have served the or will do so in the future. The so-called pressure group odel, or lobbying odel, developed by Olson (965) and others, focuses on the costs and benefits of lobbying and its ipact on policy. This class of odels abstracts fro electoral politics, assuing that the governent is entrenched or at least that every elected governent will react in the sae way to lobbying. See Grossan and Helpan (200) for foral odelling of these ideas. 0 We introduce, a without loss of generality to facilitate the algebra in the sequel. See the appendix for details of the calculation.

10 8 Explicit consideration of such iperfections would require a odel that is very uch ore coplicated than we need to exaine the basic logic of asyetric lobbying. Thus, following standard practice (see, for exaple the political support function approach of Hillan, 989, and the foral lobbying approach of Findlay and Wellisz, 982) we skip the icro odelling of how lobbying funds influence policy choices. Rather we follow the approach in Grossan and Helpan s seinal 994 paper in which lobbying expenditures, in the for of contributions, are just assued to directly enter the objective function of the governent. Specifically, we odel lobbying as a enu auction (Bernhei and Whinston, 986), and we assue that all industrial sectors are perfectly organised in the Grossan-Helpan sense (i.e. all firs in a sector act as one when it coes to political contributions). 2 Contributions ade by sector- are denoted as C. Consuers and the untaxed A-sector are unorganised and thus do not lobby. Governent s objective, lobbies and contributions As in Grossan and Helpan (994), the governent s objective function Ω is a weighted su of lobby contributions and aggregate social welfare W: (7) Ω W + G I C ; G {0,}, I {0,} where the first ter WaU is the utilitarian social welfare function fro (5), and the second ter is total political contributions; the binary variable G reflects the fact that the governent always has the option of rejecting contributions fro any sector and the binary variable I reflects the lobbying choice of a sector (I 0 iplies no lobbying). By way of interpretation, note that a pure Benthaite governent would be characterised by a and a pure Leviathan by a0, so a captures the extent to which governents care about social welfare as opposed to political contributions. itra (999) adds a lobby-foration stage to the Grossan-Helpan setting. He assues an exogenous fixed cost of getting organised, assued to differ across sectors, and study how this affects the equilibriu outcoe. By contrast, we assue that the fixed cost of lobbying is zero for all, but instead endogenise the decision to lobby actively or not. This decision is taken according to an external factor that has nothing to do with an exogenous cost of lobbying per se. The vectors τ and G are the governent s choice variables. Lobbies contribute in order to induce the governent to deviate fro the utilitarian first best. As in the Grossan- Helpan odel, we restrict contributions to be globally truthful, so if an industrial sector decides to lobby (i.e. I ), its contribution is C (τ)π (τ)-b, where B is a scalar; if it decides not to contribute (i.e. I 0) then C (τ)0 for all τ. 3 B is the vector of which B is a typical eleent. The all-lobby outcoe An equilibriu in this world is defined by the governent s strategy (i.e. the vectors τ and G), and the -sectors strategies (i.e. the vectors I and B). The payoff function of a typical sector is Π -B. The governent s payoff function can be written as: 2 Given that the representative consuer owns soe of all firs, there is an issue about lobbying incentives. Grossan and Helpan (994) deal with these by assuing un-diversified portfolios. To keep our odel as strealined as possible, we just assue that firs are concerned only with their own profit when lobbying. 3 Locally truthful strategies are the only ones to survive the coalition proofness refineent introduced in Bernhei et al. (987).

11 9 α β α (8) Ω a( + α ln( ) ) + IG( B) τ τ τσ where we have used (5), (4) and the fact that contributions are truthful. We shall calculate the B s below, but taking the as given for the oent, we investigate what policy would be chosen if a typical sector chooses to ake contributions and the governent chooses to accept the (i.e. I G, all ). In this politically influenced case, the typical eleent of τ that axiises (8), can be shown to be: I (9) τ β. aσ Three rearks are in order. First, recalling that β -/σ is the first-best subsidy, the subsidy vector in the lobbying equilibriu equals the utilitarian benchark only when the governent is benevolent (a ), or when no group contributes (all I s0). Second, (9) shows that the acceptance of contributions induces the governent to subsidize a sector beyond the social-welfare axiising level. This allows the sector to sell ore even as it continues to price onopolistically. Third, due to our functional fors, each sector s τ depends only on the sector-specific organisation variable and paraeters, with the subsidy increasing in the profit argin /σ and decreasing in the paraeter a that easures the governent s concern for social welfare. 4 Characterisation of the equilibriu is facilitated by the fact that the governent s participation constraint is just binding in equilibriu (as usual in the Grossan-Helpan approach). Thus, the B s are chosen by lobbies to ake the governent just indifferent between allowing τ to be influenced by accepting contributions, and choosing its outside option, which is to refuse contributions fro a sector and set that sector s subsidy to the utilitarian optial described in (6). That is, assuing all other sectors are lobbying and contributing, sector- s contribution, which equals Π -B, ust be large enough to ake the governent indifferent between accepting its contribution, i.e. choosing G (and thus setting τ β-/aσ) and refusing its contribution, i.e. choosing G 0 (and thus setting τ β). In sybols, the equilibriu B ust satisfy: dev α β α (0) Ω * Ω aα (ln ) (ln ) + Π B 0 β / aσ β / aσ β where Π is evaluated at τ β-/aσ. Here Ω* is the governent s payoff in the all-lobby outcoe viz. (8) evaluated at τ i β-/aσ (all i) with all sectors contributing and Ω dev is the governent s payoff where τ i β-/aσ and G i (all i but ), G 0, and τ β. The ash equilibriu To show that the all-lobby outcoe is a ash equilibriu with (9) giving the equilibriu τ s, we show that a typical sector gains fro lobbying even when its contribution is large enough to induce the governent to accept its contributions. The inforal arguent is quite siple. A sector s contribution induces the governent to choose a policy that while sub-optial fro the utilitarian perspective transfers oney fro consuers to firs. To respect the participation constraint, a sector s net contribution need only copensate the governent for the reduction in social welfare (i.e. the reduction in the W part of Ω). Because the social welfare loss is second-order while the transfer is first-order, all sectors will indeed find it in their interests to contribute. Finally the governent is, by 4 This is due to the additively separable preferences; generally, all paraeters would be relevant.

12 0 construction, just indifferent to deviating fro the equilibriu, so its strategy of accepting contributions is ash. ote that since the inequality is independent of the state of deand, we see that both high and low deand sectors would lobby. To suarise this interediate result, we write: Result : When entry is ipossible, the outcoe where all sectors lobby regardless of the state of deand is a ash equilibriu. In this all-lobby outcoe, the levels of subsidies are given by (9). oreover, the outcoe where lobbying is done only by sectors facing low deand is not a ash equilibriu. The proof of this result boils down to the proof of a siple proposition. By construction, the equilibriu B s are set to induce the governent to accept all contributions, so all we need to show is that a typical sector will want to lobby. To this end, two facts are useful: τ equals β-/aσ if sector lobbies and β otherwise, and operating profit is decreasing in τ (i.e. increasing in the subsidy rate -τ ). Given these facts, a sector can gain fro lobbying provided only that the contribution it ust pay to the governent is sufficiently low. Specifically, denoting the sector- operating profit function as Π [ ], the net profit fro lobbying ust exceed the net profit fro not lobbying, i.e. Π [β-/aσ]-c > Π [β]. Given that contributions are truthful, the task is to show that B > Π [β]. The ash-equilibriu B is deterined by (0), which using (4) and (9) can be written as: α β α α/ σ () B aα ( (ln( ) ) (ln( ) ) ) + ; τ* β / aσ τ * τ * β τ * Since (4) iplies that Π [β]α /σβ, lobbying is worthwhile to sectors, if the following inequality holds: (2) α a(ln ln ) aβ ( ) + ( ) > 0 τ* β τ* β σ τ* β Observe that the equality either holds for sectors facing both low and high states of deand, or it holds for neither. By concavity of the log function, ln(/τ*)- ln(/β) exceeds τ*(/τ*- /β). Substituting this in (2) and rearranging, we see that the inequality is greater than soething that equals zero, i.e.: > ( a τ* aβ + )( ) 0 σ τ* β The right-hand side equals zero since a(τ*-β)-/σ, given (9). Finally, note that this reasoning shows that any equilibriu in which soe sector was not lobbying would not be a ash equilibriu since each sector would unilaterally gain fro lobbying. QED. 3. Entry and the incentive to lobby We now extend the odel to continuous tie and allow the nuber of firs in a typical sector to be deterined via free entry.

13 3.. Additional assuptions The representative agent axiises her lifetie utility, assued to be additively rt separable and equal to e Udt, where U is as in () and r>0 is the discount rate. The t 0 representative agent can chose to consue her incoe or to invest it in shares of new firs. Preferences are rando with the switching between α L and α H being governed a arkov process. Creation of a new industrial fir in any of the sectors entails a fixed cost consisting of one unit of capital. One unit of capital is produced fro F units of labour under conditions of perfect copetition, so the entry cost equals F. Iportantly, this capital is sunk in the sense that once a unit of capital is built it ust be eployed by an industrial sector or abandoned (since all consuers are identical, no firs will be sold in equilibriu), also it does not depreciate. 5 This cost is eant to reflect arket-entry costs as in the odel of Baldwin (988). Any industry in state α {α L,α H } at date t reains in the sae state α at date t+dt with probability -λdt. That is, shocks arrive at a Poisson rate of λ. We therefore have the arkov transition atrix depicted in Table. Table : The arkov transition atrix Transition probabilities α L -λdt λdt α H λdt -λdt The next task is to characterise the entry decision Entry Entry, as usual, is assued to occur instantaneously and up to the point where the equilibriu value of firs is no greater than the entry cost, F. Due to the stochastic deand, a single fir will have different values when it is facing high versus low deand. Value of the firs at steady-state The value of a typical fir in a typical sector, denoted as V, is the discounted valued of operating profits less any lobbying contribution. 6 By syetry, there are only two levels of V at steady state, one for firs in low-deand sectors, V L, and one for firs in highdeand sectors, V H. Specifically: (3) α L α H [ λ λ ] [ λ λ ] rdt VL bldt + e dtvh + ( dt) VL ; bl ( ΠL I LCL) / rdt V b dt + e dtv + ( dt) V ; b ( Π I C ) / H H L H H H H H where we oit the tie and sector subscripts since these values are constant at steady state and sectors face either high or low deand; note that the b s (a neonic for benefit) are the per-fir operating profit net of any contributions, so b i B i / (ih,l). These equations are easy to interpret. The value of a fir in state L at tie t is equal to the current flow of net profit plus the discounted expected value it will have at tie t+dt. With soe probability λdt it will transit to state H; with probability -λdt it will reain in 5 Adding depreciation is uncoplicated (see section 4.3) but is not necessary here. 6 As a special feature of our functional fors, total operating profit per sector is independent of the nuber of firs per sector, but the key point is that V is diinishing in.

14 2 state L. V H is defined analogously. In the liit of continuous tie, dt 0, by syetry aong industries and firs within industries, and rearranging, we get: rvl bl + λ( VH VL), rvh bh λ( VH VL) (4) ( r+ λ) bl + λbh ( r+ λ) bh + λbl VL, VH rr ( + 2 λ) rr ( + 2 λ) The top two expressions are standard asset-pricing equations, i.e. r ties the expected value of the fir ust equal the su of the current flow of net profit and the expected capital gain. The botto two expressions are the solution for the V s in ters of the b s. As the cost of entry is F, free-entry requires that the steady state nuber of firs per sector rises until the axiu value of a typical fir equals F. A fir s value ay differ between high and low deand states, so the entry condition is: (5) s. t. ax{ VH, VL} F ote that U in () is quasi-linear, so the transition dynaics are degenerate, i.e. iediately jups to its steady-state value * as soon as α α H. (It jups to soe 0 < if α α L initially. See below.) 3.3. The only-losers-lobby equilibriu We assert that the outcoe in which only sectors facing low deand lobby is a arkov perfect equilibriu (PE), and refer to it as the only losers lobby outcoe. In this dynaic version of the odel, the state variables are the nuber of firs in a typical sector,, which is influenced by players actions via free entry, and the vector of the states of deand facing each sector. Given our siple set up, a sector s strategy can be suarised by its decision to lobby or not, with this action possibility depending upon the state of deand. Forally, the only-losers-lobby equilibriu can be expressed as the set of sector strategies such that: 0, if α αh (6) I, if α αl where I and I 0 indicate, respectively, that sector is, or is not lobbying. ote that due to irreversible entry and the fact that Dixit-Stiglitz onopolistic copetition never produces negative operating profit, the nuber of firs active in each sector is constant in steady state. This and syetry of firs allows us to drop the sector subscript fro the s. In this outcoe, the values of a typical fir are: ll bl( r+ λ) + λbh ll bh( r+ λ) + λbl αh αl (7) VL, VH ; bh, bl ( B) rr ( + 2 λ) rr ( + 2 λ) σβ σ( β / aσ) where the superscripts ll signify the value of firs ipleenting (only) losers lobby strategies. To deonstrate that the only-losers-lobby outcoe is an PE, it is useful to establish that for any given, the value of a fir when it faces low deand is no greater than its value when it faces high deand, i.e. V V F. This feature is intuitively obvious and easy to ll L ll H

15 3 establish forally. 7 Figure helps interpret the equilibriu by plotting values of a typical fir against the nuber of firs per sector. Since copetition lowers per-fir value, all lines slope downwards. The second and third lines indicate the only-losers-lobby outcoe for ll ll ll sectors facing high and low deand. These are arked V H and VL respectively; the V H line ll is above the V L line. Due to free entry, the value of a fir can never rise above F, so all the value lines are cut off at the horizontal line, F. Plainly, the steady state nuber of firs is * in the only-losers-lobby outcoe. The value of firs facing high deand will be F; point 2 gives the value of firs facing low deand. Figure : The free-entry equilibriu F V H al 3 6 ll V H ll V L V L al V L ll,dev 0 * ** Establishing the arkov perfect equilibriu Using the diagra, we can show that the only-losers-lobby outcoe is a arkov perfect equilibriu (PE). We start with the governent. At every tie t, the governent cannot, by construction of the B s, gain fro deviating fro the only-losers-lobby outcoe. Thus, accepting contributions and providing the politically influenced τ is ash in every subgae and state of the world. The arguent for high-deand sectors is siilar. o highdeand sector could gain fro deviating; after all, free entry ensures that the value of a typical fir cannot rise above F, so any lobbying effort would be useless. Thus, the strategy of no lobbying in high deand-states is ash in every subgae. Finally, low-deand sectors cannot gain fro deviation since ceasing to lobby would lower their value fro point 2 to point 3 in the diagra. ore specifically, under this deviation, the value of a typical fir facing low-deand sector would be dev dev (λb H +(r+λ)b L )/r(r+2λ), where b L is the per-fir operating profit in the low-deand state when the subsidy is the socially optial β, naely b dev L α L /σβ. Fro the proof of Result, 7 The proof is by contradiction. If V ll L>V ll H, then the free entry condition iplies F V ll L, so F> V ll H. This in turn iplies that the high-deand sector could lobby without attracting entry and so by Result it would. Since this contradicts the definition of the only-losers-lobby outcoe, we know V ll L V ll H F.

16 4 we saw that one-period lobbying is always worthwhile when it does not change, so we dev know that b L [-B+α L /σ(β-/aσ)]/ exceeds b L. Fro (4) this tells us that not lobbying in the low-deand state would lower the typical fir s value. We suarise these findings in: Result 2: Since free entry akes lobbying useless for sectors facing their entry argin (i.e. high-deand sectors), the only-losers-lobby outcoe is a arkov perfect equilibriu. By contrast, sectors facing low deand find their values below entry costs, so lobbying can raise their value. As it turns out, the only-losers-lobby outcoe is not the only PE, as Grossan and Helpan (996) have pointed out Other equilibria ote that starting fro *, lobbying in the high state does no good but neither does it do any har to firs facing high deand. If for whatever reason incubents in a sector with high deand actually did lobby, the results would be an increase in the nuber of firs to ** in the diagra. Iportantly, once the new entrants are irreversibly in the arket, a deviation by cessation of lobbying in the high-deand state would lower the value of the fir fro point 4 to 5 in the diagra, so no deviation would occur in the high-deand state. Likewise, no deviation would occur in the low-deand state, so this outcoe what we call the all lobby outcoe, denoted as al in the diagra is also an PE. We suarise this in: Result 3: When entry is free, the all-lobby outcoe is a arkov perfect equilibriu since once high-deand lobbying has increased the nuber of active firs, cessation of lobbying would lower the value of such firs. As before, sectors facing low deand can raise their value by lobbying, so lobbying in both states is also a PE. It is possible to arrive at the ** state since lobbying in the high-deand state starting fro * is both useless and costless in ters of incubents value in the highdeand state. Doinance of only-losers-lobby PE Although this second PE does exist, there are good reasons for believing that it would never occur. The basic arguent is that although the increase in the nuber of firs fro * to ** does not affect V H, it will lower the value of the fir once low-deand returns. ote that the value of a typical fir facing high deand is identical in the two PEs (naely F), but the value of a typical fir facing low-deand is lower in the all-lobby outcoe. To see this, observe that fro (4) with V H F, we have that V L i equals (b L i +λf)/(r+λ), where i equals ll (in the only-losers-lobby equilibriu) or al (in the alllobby equilibriu). Because b L is given by (6) with α α L and **>*, it is clear that V L al is less than V L ll (these values correspond to points 2 and 6 in the diagra). In short, although the lobbying-induced entry has no effect on the value of firs facing high-deand, the presence of ore firs lowers the value of the sae firs in the low-deand state. To suarise this we write: Result 4: While both the only-losers-lobby and all-lobby outcoes are PEs, the only-losers-lobby PE doinates the all-lobby PE in the sense that firs are indifferent between the two when facing high-deand, but strictly prefer the only-

17 5 losers-lobby equilibriu when facing the low-deand state. This akes the onlylosers-lobby PE focal. 4. Extensions We consider three extensions of our analysis in this section. We first allow for the possibility that new entrants free ride on the lobbying contributions by forer incubents for soe tie. We also show that assuing technological shocks yields the sae qualitative results as in the case of deand shocks described thus far. Finally, we apply our odel to sunset industries naely, for the case of peranent adverse shocks. 4.. Free riding In the spirit of the Grossan-Helpan lobbying approach, our basic odel assues that all firs in a sector are perfectly organised politically in the sense that they act as one when it coes to presenting and financing a contribution enu to the governent. To deal with entry, the basic odel extended this assuption to allow for entry in the siplest possible way, naely by supposing that all entrants iediately act as incubents. This of course this is not the only reasonable assuption (see Grossan and Helpan 996 for discussion of the issue) and, as we shall see, relaxing it has iportant iplications for Result 3. We shall show, however, that it does not alter (and even reinforces) our ain result, i.e. that free entry reoves the incentive for lobbying in sectors facing their entry argin since above noral profits are iediately and successfully grabbed by entrants. odelling free riding To odel free riding by entrants, we assue that new firs do not share the financing of contributions initially, but they do becoe perfectly organised (i.e. act identically to incubents) eventually. Specifically, all newly entered firs start as free riders but switch to non-free riders (i.e. becoe join the perfectly organised firs) according to a Poisson process arked by a hazard rate of φ. This switch is synchronised across all entrants in the sense that at any given oent all new entrants will either all be free riders, or will all be non-free riders. Furtherore, we assue that the switch to non-free rider status is peranent, so that eventually all firs are perfectly organised. ote that φ provides a natural paraeter for the extent of the free-riding proble since newcoers are expected to reain free riders for a period equal to /φ. Our basic odel iplicitly assues that φ is infinite. We begin by studying the all-lobby outcoe, i.e. where both high- and low-deand sectors lobby. Free riding coplicates calculation of the expected value of entering since we ust take account of the probability that: (i) the sector sees its deand change, and that (ii) the entrant experiences a shift in its free-riding status. Incubent firs in this case will have one of four possible values, naelyv H, u, V L, u, V H or V L ; these are, respectively, the value of an incubent facing high or low deand when entrants are unorganised (as shown by the subscript u ), and when the entrants have joined the lobby (as shown by a lack of a subscript). Three instantaneous probabilities are relevant to an incubent s value. These are: (i) the probability that the sector experiences a shift in deand but entrants reain free riders, viz. λ(-φ), (ii) the probability that the sector experiences a deand shift and entrants becoe non-free riders, viz. λφ, and (iii) the probability that the sector experiences no change in deand but entrants becoe non-free riders, viz. (-λ)φ. Taking account of these, the expected values of an incubent in the various states are:

18 6 (8) rv rv rv H, u L, u H b b b H, u L, u H λ[( φ)( V λ[( φ)( V λ( V H V L ) H, u L, u V V H, u ) + φ( V ) + φ( V )] ( λ) φ( V rvl bl λ( VL VH ) where the b s are the flow rewards to incubents in the various states. The related value equations for entrants are: (9) L, u H, u L, u V )] ( λ) φ( V V ( ) ( ) H L H, u rjh πh λ ( φ)( JH JL) + φ( JH VL) ( λ) φ( JH VH) rj π λ ( φ)( J J ) + φ( J V ) ( λ) φ( J V ) L L L H L H L L where J H and J L are the values of free-riding firs when the sector is facing high and low deand respectively. Since free riders do not contribute to lobbying expenses, the flow benefit of being a free rider in both the high and low states of deand exceeds the flow benefit of being an incubent, i.e.: (20) π b γ, π b γ 0 H H, u H 0 L L, u L where the γ s are constants. The free entry condition in this extension is J H F. Would high-deand incubents lobby? In the basic odel, when * incubents in the high-deand sector were indifferent to lobbying since although lobbying won the no benefits, neither did it har their value. ow we turn to evaluating whether high-deand sectors would still be indifferent to lobbying. Section 3 established that the value of high-deand incubents in the only-loserslobby outcoe was equal to F. To see whether high-deand sectors would be indifferent to lobbying we check whether the value of incubents at the oent they lobby i.e. at the instant of entry when entrants are still free riders, naely V H,u fro (8) is less than F. To this end we solve (8) and (9) for the values of incubents in the four possible states of the world (high or low deand and entrants free riding or not). The solutions are soewhat involved but we need consider only the difference J H -V H,u, which can be written as 8 : ( λ( φ) + r + φ) γ H + λ( φγ ) L (2) JH VH, u ( r+ φ)(2 λ( φ) + r+ φ) Given (20), we know this is positive for any finite φ. oreover, this difference liits to zero as φ approaches infinity. What this reasoning shows is that starting fro *, incubents facing high deand in the only-losers-lobby outcoe would never agree to lobby if there were any chance that free entrants would free ride, even for an infinitely short tie. This result reinforces our assertion that the only-losers-lobby outcoe is focal. 9 L, u V V L H ) ) 8 See the appendix below. 9 The idea here is akin to the trebling hand refineent. If incubents did ake a istake and lobby in the high state, thus raising the nuber of firs up to the point where J H F, they would continue to lobby since doing otherwise would lower their value even further. This result, however, relies on the lack of exit. If firs did exit, a one-tie istake would be corrected eventually. We thank Thierry Verdier for this point.