February 00 Noise Traer Risk an the Political Economy of Privatization Abstract The noise traer moel of De Long et al. provies a plausible account of the etermination of the equity premium. Extension of the moel to allow for privatization of publicly-owne assets yiels insights into the positive political economy of privatization an into the normative question of how policies shoul be evaluate in the presence of mistaken beliefs. JEL Classification: E6 Key wors: equity premium, noise traer risk, privatization. Simon Grant Department of Econometrics & Operations Research an CentER Fellow, Tilburg University an School of Economics Australian National University John Quiggin School of Economics Australian National University Financial support for this project has been provie by the Australian Research Council s Large Grant A79800678. Quiggin also gratefully acknowleges income support from an ARC senior research fellowship.
1 Introuction The well-known equity premium puzzle (Mehra an Prescott 1985) is closely relate to the less familiar, but equally surprising, observation that the procees from privatization are frequently lower than plausible estimates of the present value of future earnings, iscounte at the real bon rate (Vickers an Yarrow 1988, Quiggin 1995). De Long et al. (1990), formalizing the ieas of Shiller (1989), present a moel which explains the equity premium as a consequence of excess volatility in financial markets introuce by the istorte an stochastic, beliefs of misinforme investors referre to as noise traers. De Long et al. show that, although both noise traers an sophisticate investors aremaebetteroff in ex ante terms (given their beliefs) by the availability of trae, this apparent welfare improvement arises at the expense of those holing equity when trae is introuce, such as entrepreneurs making initial public offerings. In this paper, we examine the implications of volatility generate by noise traers for the appropriate risk premium for public investments, an for the welfare an istributional effects of privatization. We moify the De Long et al. moel to allow for the existence of an asset that is initially publicly owne, but is otherwise similar to the private asset consiere by De Long et al. We then examine the consequences of privatization for asset prices an emans, an for the welfare of ifferent groups. We show that if the equity premium arises from the mistaken beliefs of noise traers, privatization may reuce public sector net worth. Moreover, evaluate in terms of the correct beliefs of sophisticate investors, there is a reuction in social welfare associate with privatization. The Analysis Following De Long et al. (1990) we introuce a strippe-own overlapping generations moel with two-perio live agents an a single consumption goo. The only ecision an agent makes is her choice of portfolio when young to finance her consumption when ol. There is no funamental risk an all assets pay a fixe real ivien r. One asset, the safe asset, is in perfectly elastic supply. Any unit of the safe asset can be converte into one unit of the consumption goo, an vice versa. As De Long et al. note, the safe asset is formally equivalent to a storage technology that pays a real net return of r. Furthermore, if we take the consumption goo in each perio as the numeraire, the price of the safe asset is always one. A secon asset, that we shall interpret as the pre-privatization economy-wie portfolio of equity, is in fixe supply, normalize to one. The price of this equity asset in perio t is enote by p e t. Extening De Long et al., we introuce a thir asset that is also in fixe supply, x<1, an that generates a real ivien r. Initially, this asset is owne by the government an 1
finance entirely through short-term (one-perio) government ebt. Government ebt, the fourth asset in our moel, pays a guarantee fixe real interest r. As government ebt is a perfect substitute for the safe asset, its price in every perio is always one. Every generation is the same size an can be ivie into two classes: a proportion λ who are noise traers (enote N), an a proportion 1 λ who are sophisticate investors (enote I)..1 The Pre-Privatization Equilibrium For any perio t in which the thir asset remains in government ownership, the government issues x units of new ebt (of one-perio maturation) which is purchase by iniviuals who are young in perio t. Using the procees of this bon sale together with the real ivien generate by the government-owne asset, the government pays out the amount (1 + r) x to the holers of the x units of government ebt that was issue in perio t 1 an that has matureinperiot. In each perio, the representative sophisticate investor has rational expectations about the istribution of returns from holing a portfolio with risky assets, an so maximizes her expecte utility given the istribution of her wealth implie by her portfolio choice. In each perio t, the representative noise traer who is young in that perio misperceives the expecte price of the asset in perio t +1by a normally-istribute ranom variable e t N ³, σ. We assume that both sophisticate investors an noise traers are expecte utility maximizers characterize by a constant coefficient of absolute risk aversion equal to γ. Anagent who is young in perio t chooses her portfolio to maximize her certainty equivalent consumption in perio t +1. That is, she maximizes w γσ w/, where w is the expecte final wealth in perio t +1,anσ w is the variance of her perio t +1wealth. De Long et al. (1990) show that, in a stationary equilibrium, that is, where one imposes the requirement that the unconitional istribution of p e t+1 be ientical to the istribution of p e t, the pricing rule for equity takes the form p e t =1+ λ (e t ) 1+r + λ r γλ σ r (1 + r), (1) where λ σ / (1 + r) is the constant one-perio-ahea variance of p e t. 1 Since noise traers allocate more of their wealth to equity than o sophisticate investors, an earn negative capital gains on average, they can earn higher expecte returns than sophisticate investors only if the ivien on equity amounts to a higher rate of return on 1 See De Long et al. (1990) pp. 708 11 for the erivation.
average than the same ivien on the safe asset (an the government bon). That is, equity must sell at an average price below its funamental value of one. Hence we shall assume that equities are unerprice, that is, E [p e t] < 1, orequivalently, γλσ (1 + r) > 0. () Provie the variance of the representative noise traer s misperception of the expecte price of the asset tomorrow is sufficiently large, this is consistent with the hypothesis that noise traers are bullish on average, that is, > 0.. The Post-Privatization Equilibrium We shall now consier the situation where the government announces at the beginning of perio 0 that it is privatizing the thir asset which it has hel in government ownership up to that ate. The amount (1 + r) x owing on the outstaning stock of government bons which are hel by the current ol generation, will be pai out of the ivien xr generate bytheassetantherevenuep ne 0 x generate by the sell-off of the x units of supply of this assetatthepricep ne 0. Any shortfall (respectively, winfall) will be met by a stream of higher (respectively, lower) taxes in each subsequent perio that has the same net present value as the shortfall (respectively, winfall). As a natural generalization of the De Long et al. moel, we assume that the misperceptions in perio t (for t 0) of the expecte price of equity an the expecte price of the privatize asset (the new equity ) in perio t +1 are inepenently an ientically istribute as bivariate normal e t N 1, 1 β σ. 1 β 1 ne t We assume that the government has to make its ecision to privatize the asset before e 0 an ne 0 are realize. To ai the exposition let us introuce the following notations: e t t =, p p e t t =, µ µ e t t = = p e t+1 Et, Σ t = Et ne t p ne t µ ne t h³ ³ i p i t+1 µ i t p j t+1 µj t i,j=e,ne 1 an 1 = 1 Consier a sophisticate investor with an amount c 0 to invest in perio t. Her objective is to choose a portfolio q T I =(qe I,qne I ), where qe I is her holing of equity an qne I is her holing 3 p ne t+1.
of the privatize asset, an the remainer of her wealth (c 0 p T t q I )isinvesteinthesafe asset an/or government bons. Her optimal portfolio choice maximizes: c 0 (1 + r)+[r1 + µ t (1 + r) p t ] T q I γ qt I Σ t q I. (3) Similarly, the representative noise traer with an amount c 0 to invest in perio t, choosesa portfolio q T N =(qe N,qne N ) that maximizes c 0 (1 + r)+[r1 + µ t (1 + r) p t ] T q N γ qt NΣ t q N + T t q N. (4) The only ifference between (3) an (4) is the last term of (4) which reflects the noise traers misperceptions of the expecte returns from holing equity an from holing the privatize asset. The corresponing first orer conitions erive from (3) an (4) yiel the asset emans q I = 1 γ Σ 1 t [r1 + µ t (1 + r) p t ] (5) q N = 1 γ Σ 1 t [r1 + µ t (1 + r) p t + t ]. (6) Solving for the market-clearing prices we obtain p t = 1 1+r [r1 + µ t + λ t ] γ 1+r Σ t 1 x. (7) To fin the stationary equilibrium we solve (7) recursively to obtain p t = 1+ λ 1+r ( t 1)+ λ r 1 γ r Σ 1 t. (8) x Inspection of (8) reveals a time-invariant variance covariance matrix for p t of Σ = λ σ 1 β (1 + r) β 1 That is, we have p e t = 1+ λ (e t ) 1+r t = 1+ λ (ne t ) 1+r p ne + λ r γλ σ (1 + βx), (9) r (1 + r) + λ r γλ σ (β + x). (10) r (1 + r) Notice that for small x, the correlation coefficient β is approximately equal to the beta coefficient that woul come out of the stanar CAPM. 4
.3 Welfare Effects of the Privatization The intertemporal prouction technology for the consumption goo implicitly emboies a real net return of r. Hence, welfare changes across generations in this economy can be characterize in terms of the net present value of the changes in consumption streams using a iscount rate of r. For t 0, let CE I t (respectively, CEN t )enotefortherepresentativesophisticate investor (respectively, noise-traer) who is young in perio t 1, the change that results from the privatization in his or her certainty equivalent consumption in perio t. Noticethatfor t 1, CE N t is calculate with respect to the misperceive estimate of the prices of ol equity an the privatize asset for perio t that is mae by the noise traers in the perio in which they are young (that is, perio t 1). Let B 0 enote the change in the government s buget in perio 0 that arises as a result of the privatization. If we let W enote the sum of B 0 an the net present value of the changes in the certainty equivalent consumption of every generation, then the ex ante change is given by h i h i X (1 λ) E CE I t + λ E CE N t E [ W] =E [ B 0 ]+ (1 + r) t. (11) t=0 Let y enote the value the variable y woul have taken if the government ha not privatize the asset in perio 0. We consier the changes to each group in turn. Government E [ B 0 ] = E [p ne 0 ] x + xr x (1 + r) = λx Ã! γλσ r (β + x). (1) (1 + r) Assuming that conition () is satisfie, so that there is a positive equity premium, the government will be worse off whenever β + x is sufficiently close to or greater than 1. Consumers in perio 0. These consumers have alreay mae their portfolio choice in the previous perio. The only action they unertake in perio 0 is to sell their portfolio on the market to finance their consumption. Inspection of (1) an (9) reveals that p e 0 an p e 0 have the same variance. Hence it follows that: h i h i (1 λ) E CE I 0 + λ E CE N 0 = E [p e 0 p e 0]= γλ σ r (1 + r) βx, which means that consumers in perio 0 will lose (respectively, gain) if the noise traers misperceptionoftheexpectepriceofthenewlyprivatizeassetinthenextperioispositively (respectively, negatively) correlate with their misperception of the expecte price of the ol equity in the next perio. Consumers in perio t 1. 5
Utilizing (5), the sophisticate traer s asset eman function, an the expressions for the equilibrium prices (i.e. (9) an (10)) wehave CE I t = (1 + r) γσ β e t 1 ne à t 1 γλ ³1 β + x σ (1 + r) µ β + x! λ e t 1. Thus, ³ h i (1 + E CE I r) (1 β)( ) +(1+β) σ à γλσ µ t = γ (1 + β) σ + xλ (1 + r) β + x!. (13) Similarly, using the asset eman function for the noise traer (i.e. (6)) alongwith(9) an (10) yiels CE N t = An so, h E CE N t (1 λ) (1 + r) β e λ γσ t 1 ne à t 1 γλ ³1 β + x σ (1 + r) i = µ β + x! +(1 λ) e t 1. ³ (1 λ) (1 + r) (1 β)( ) +(1+β) σ à γλ σ µ λ γ (1 + β) σ +x (1 + r) β + x! +(1 λ). (14) Hence the per capita change in the ex ante certainty equivalent consumption for the generation who will be consumers in perio t ( 1) is h i h i (1 λ) E CE I t + λ E CE N ³ t (1 λ) (1 + r) (1 β)( ) +(1+β) σ à γλ σ µ = λ γ (1 + β) σ + x (1 + r) β + x!. (15) Collecting terms, this yiels in net present value terms E [ W ]= λx à µ γλσ r (1 + r) β + x! ³ (1 λ)(1+r) (1 β)( ) +(1+β) σ + rλγ (1 + β) σ. (16) Alternative measure expecte utility with respect to true istribution. An alternative measure of the welfare effects of the privatization is to evaluate the expecte utility of every agent with respect to the true istribution of consumption. The only agents this affects are the noise traers who will be consuming in perios 1,,...Let CE N t enote this value. CE ³ N t = CE N t T t 1q N e t 1q e N. 6
where T t 1q N e t 1q e N = x ne t 1 + (1 λ)(1+r) γλ σ ³1 β ³ β e t 1 β e t 1 ne t 1 + ne t 1. This gives us a correcte measure of the change in ex ante welfare of Ã! h E W c i = γλ σ r (1 + r) βx + x (1 λ)(1+r) ³ (1 β)( ) +(1+β) σ rλγ (1 + β) σ. (17) Notice that the ifference between (16) an (17) is ³ λx (1 λ)(1+r) (1 β)( ) +(1+β) σ r + rλγ (1 + β) σ. The first term reflects the extra consumption that noise traers misperceptions lea them to expect, on average, to receive by holing the privatize asset while the secon term reflects the certainty-equivalent consumption cost of the risk associate with taking bets base on misperceive expecte future prices of the privatize asset. 3 The political economy of privatization The analysis above yiels a range of insights into the political economy of privatization. First, consier the impact on government. From (1), privatization will, for plausible parameter values, reuce the net worth of government. However, this reuction is obscure by the stanar system of government financial statistics (GFS) in which the returns from asset sales are treate as revenue (or sometimes negative expeniture) in the year in which sales take place. Thus, from the viewpoint of ministers an officials relying on the GFS statistics, privatization always yiels an improvement in the government s financial position (provie the sale price excees one year s earnings, that is, p ne 0 >rin our moel). This was an important element of the case for privatization in the Unite Kingom (Zahariais 1995) an Australia (Quiggin 1995). The effect on the government may also be consiere as the effect on a taxpayer voter who satisfies Ricarian equivalence but oes not participate in the equity market. In general, non-shareholers have been hostile to privatization, suggesting that they may be closer to Ricarian equivalence than experts using the Government Financial Statistics system. The effect on perio-zero consumers may be taken as a proxy for the effect on holers of private equity at the time of privatization, an particularly on those who wish to sell equity, for example, through initial public offerings. Large-scale privatizations have frequently raise concerns that the creation of large quantities of new equity will excee the willingness of markets to buy equity at existing prices (which will be the case in our moel when β > 0). This is one reason for the popularity of partial privatization (in our moel, small values of x). 7
The most interesting welfare issues arise with respect to consumers in perios greater than t 1. We may consier three possible policy frameworks, referre to as paternalist, preference-maximizing an libertarian. A paternalist government woul seek to maximize an objective welfare measure base on the true probability istribution. Uner the assumptions of the moel presente above, such a government woul always retain full public ownership. A preference-maximizing government woul unertake privatization if an only if the expecte aggregate benefit (17) was positive. Finally, a libertarian government woul always unertake privatization. It is of interest to consier the circumstances uner which these approaches woul obtain the political support of voters. For the paternalist case, suppose that voters know that market fluctuations are generate by noise traers with mistaken beliefs an o not know whether their own beliefs are mistaken. If iniviuals acte on this knowlege as traers, common priors an common knowlege of rationality woul imply a no-trae equilibrium (Milgrom an Stokey 198). To erive a self-paternalist outcome we assume instea, following Elster (1979), that iniviuals know that, as traers, they will act on their beliefs. As voters they are therefore willing to bin themselves in avance not to trae. Uner the conitions of the moel presente above, all self-paternalist voters will prefer the pre-privatization outcome to the post-privatization outcome. A libertarian policy may be justifie on grouns of process alone, without reference to welfare outcomes (Nozick 1974). Alternatively, given a methoological commitment to core hypotheses of market efficiency an iniviual rationality, moels such as that of De Long et al. (1990) must be rejecte in favor of moels in which the market price of equity reflects the true social cost of risk. If a moel of the latter class is correct, government ownership conceals risks that are, in reality, borne inirectly by taxpayers (Domberger 1995). If this view is accepte, then all voters will prefer privatization. An intermeiate case arises if all voters believe their own estimates of risks an returns are unbiase. In this case, privatization will generally be viewe as beneficial by both sophisticate traers an noise traers (assuming they ignore any losses incurre by governments), but will, uner the conitions note above, reuce the net worth of government an the welfare of perio 0 consumers. In the absence of compensation, the political outcome will be etermine by the relative strength of gainers an losers. Suppose the effects of reuctions in government net worth are borne primarily by net recipients of government expeniture an by taxpayers who o not hol, or wish to hol, equity. We will refer to this group simply as government supporters. Similarly, the effects on perio 0 consumers is a proxy for the effects on those who hol substantial equity an expect to be net sellers. We will refer to this group as ol money voters. Then, in the absence of compensation, the political feasibility of privatization epens on the formation of a coalition of sophisticate an noisy traers which can overcome the resistance of government supporters an ol money voters. This seems to be an accurate e- 8
scription of the support base of the Thatcher government in the Unite Kingom (Zahariais 1995). If lump-sum compensation is feasible an is always pai to losers, voters will prefer privatization as long as (16) is positive. The sign of (16) will epen on the magnitue of the aggregate bias λx r, the riskiness of equity markets, an on the risk-aversion of the representative voter/consumer. Thus we might expect the political popularity of privatization to vary in line with social changes that affect risk-aversion an with changes in estimates of the riskiness of equities. It is interesting to observe that the rise of privatization in the 1980s coincie with a rapi ecline in the proportion of voters an politicians ol enough to recall the Great Depression. The analysis above must be moifie to take account of other factors that will affect the esirability of privatization. Where privatization is accompanie by an increase in operating efficiency the benefit from this increase shoul be taken into account. One possibility is to assumethatthetruereturninperio1isgreaterthanr. On the other han, the fiscal an social returns to privatization may be reuce if governments are unable to commit themselves regaring the possibility of renationalization or averse regulation (Zeckhauser an Horn 1989) or if the privatize firm is characterize by monopoly power an/or externalities requiring close regulation (King & Pitchfor 1999). In the analysis presente above, governments are assume to respon irectly to the ex ante preferences of voters. The moel coul be enhance by consieration of strategic behavior such as that consiere by Perotti an Biais (001). In their moel, governments seek to reuce support for reistribution by using privatization to ensure that the meian voter hols shares an is therefore more likely to oppose policies of reistributing income from capital to labor. References De Long, J.B., A. Shleifer, L. Summers, an R.J. Walmann, 1991, Noise Traer Risk in Financial Markets, Journal of Political Economy, 98, 703-738. Domberger, S., 1995, What Does Privatization Achieve? - A comment on Quiggin, Australian Economic Review, 95, 43 47. Elster, J., 1979, Ulysses an the Sirens (Cambrige University Press, Cambrige). King, S.P. an R. Pitchfor, 1999, A Taxonomy of Optimal Ownership an Management Regimes. The University of Melbourne, Department of Economics, Research Paper No. 65. Mehra, R. an E.C. Prescott, 1985, The Equity Premium: a Puzzle, Journal of Monetary Economics, 15, 145 161. Milgrom, P. an N. Stokey, 188, Information, Trae an Common Knowlege,.Journal of Economic Theory, 6, 17 7. 9
Nozick, R., 1974, Anarchy, State an Utopia (B. Blackwell, Oxfor). Perotti, E.C. an B. Biais, 001, Machiavellian Privatization, American Economic Review (forthcoming). Quiggin, J., 1995, Does Privatization Pay?, Australian Economic Review, 95, 3 4. Shiller, R.J., 1989, Market Volatility (The MIT Press, Cambrige, MA). Vickers, J., an G. Yarrow, 1988, Privatization: An economic analysis (The MIT Press, Cambrige, MA). Zahariais, N., 1995, Markets, States an Public policy: Privatization in Britain an France (University of Michigan Press, Ann Arbor, Michigan) Zeckhauser, R. an M. Horn, 1989, The Control an Performance of State-owne Enterprises, in: P. Macavoy, W. Stanbury, G. Yarrow an R. Zeckhauser, es., Privatization an State-Owne Enterprises (Kluwer Acaemic Publishers, Boston). 10