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July/August 1994 Volume 79, Number 4 Federal Reserve Bank of Atlanta In This Issue: / n c o m e Inequality and Economic Growth: Evidence and Recent Theories information Ambiguity: Recognizing Its Role in Financial Markets FYI—Commercial Bank Profits /cpnpmìc j^eYiew July/August 1994, Volume 79, Number 4 bonomìe ^feview Federal Reserve Bank of Atlanta President R o b e r t P. Forrestal Senior Vice P r e s i d e n t a n d Director of R e s e a r c h Sheila L. T s c h i n k e l Research Department B. Frank King, Vice President and Associate Director of Research William Curt Hunter, Vice President, Basic Research and Financial Mary Susan Rosenbaum, Vice President, Macropolicy Thomas J. Cunningham, Research Officer, Regional William Roberds, Research Officer, Macropolicy Larry D. Wall, Research Officer, Financial Public A f f a i r s Bobbie H. McCrackin, Vice President Joycelyn T. Woolfolk, Editor Lynn H. Foley, Managing Editor Carole L. Starkey, Graphics Ellen Arth, Circulation The Economic Review of the Federal Reserve Bank of Atlanta presents analysis of economic and financial topics relevant to Federal Reserve policy. In a format accessible to the nonspecialist, the publication reflects the work of the Research Department. It is edited, designed, produced, and distributed through the Public Affairs Department. Views expressed in the Economic Review are not necessarily those of this Bank or of the Federal Reserve System. Material may be reprinted or abstracted if the Review and author are credited. Please provide the Bank's Public Affairs Department with a copy of any publication containing reprinted material. Free subscriptions and limited additional copies are available from the Public Affairs Department, Federal Reserve Bank of Atlanta, 104 Marietta Street, N.W., Atlanta, Georgia 30303-2713 (404/521-8020). Change-of-address notices and subscription cancellations should be sent directly to the Public Affairs Department. Please include the current mailing label as well as any new information. ISSN 0732-1813 (Contents Federal Reserve Bank of Atlanta Economic Review July/August 1994, Volume 79, Number 4 i n c o m e Inequality and Economic Growth: Evidence and Recent Theories Roberto Chang Economic inequality is often viewed as a social problem calling for government attention. However, whether income disparities should be, or can effectively be, ameliorated by government intervention is an unsettled question. Many policies aimed at reducing inequality provide negative incentives for economic efficiency, implying that there is a trade-off between equality and growth. The terms of such a trade-off are unknown, though, and the result is shaip disagreement in evaluating policy options. This article reviews selected recent research developments on the relation between income equality and economic growth. The author discusses the finding that countries that grow faster also exhibit a more egalitarian income distribution, which may suggest that redistributive policies have a positive effect on income growth. His analysis focuses on the two main classes of theories—politicoeconomic theories and financial imperfections theories—that have been advanced to explain the inequality-growth relationship. He concludes that at this point knowledge in the area has not developed enough to yield unambiguous lessons for public policy. /nformation Ambiguity: Recognizing Its Role in Financial Markets Jie Hu FYI— Commercial Bank Profits in 1993 W. Scott F r a m e a n d C h r i s t o p h e r L. H o l d e r Uncertainty plays a prominent role in the world of business and economics, yet traditional economic theory has had only limited success in providing models for dealing with uncertainty and individuals' behavior under this condition, and many economic issues remain unexplained. This article suggests that one promising area of research, essentially ignored until recently, may be the idea of information ambiguity. Using lotteries as an example, the author provides a brief and intuitive illustration of why information ambiguity, or Knightian uncertainty, is significant in rational decision making and shows how it may be modeled. He demonstrates the usefulness of its application in understanding several unexplained phenomena in the financial markets such as why asset prices are usually more volatile than asset fundamental values. The author concludes that while the mathematical representation of information ambiguity is in developmental stages, applying the concept to analysis promises to add new and useful insights. As the economy as a whole improved, U.S. commercial bank profitability reached postwar record highs in 1993. And, by some measures, southeastern banks fared even better than their peers nationwide. This article examines the reasons for this increased profitability—primarily a decline in loan-loss provisions that resulted in wider adjusted net interest margins. Extensive tables provide details about bank profitability from 1989 through 1993. income Inequality and Economic Growth: Evidence and Recent Theories Roberto Chang eople care about the behavior of gross national product. But people also care, perhaps with more intensity, about equality and the distribution of national income. Even in wealthy countries such as the United States, economic inequality is often associated with poverty, crime, and social unrest. 1 Extreme inequality is widely considered to be a m a j o r cause behind political instability and even civil wars. 2 The author is a senior economist in the macropolicy section of the Atlanta Fed's research department. He thanks Mary Rosenbaum, Ellis Tollman, Michael Devereux, and Robin Rosen Chang for comments. Federal Reserve Bank of Atlanta Because inequality is a social problem, a natural reaction is to demand that the government do something about it. But whether income disparities should be, or can effectively be, ameliorated by government intervention is an unsettled question. M u c h of the uncertainty arises from the imperfect knowledge of the relation between income equality and economic growth. Policies aimed at reducing inequality are c o m m o n l y believed to provide negative incentives for economic efficiency, implying that there is a tradeoff between equality and growth. However, the terms of such a trade-off are unknown, and this ignorance translates into sharp disagreements in evaluating policy options. Witness, for example, the recent debate about whether economic growth in the United States in the last decade benefited mostly the rich or the poor. Many economists argued that increased income inequality accompanied the long expansion of the 1980s—that is, the rich became relatively richer—and that public policy could have (and should have) prevented this outcome at little economic cost. Dissenting economists, while admitting that inequality increased, argued that policies toward preventing it would have provided strong incentives against growth. 3 The debate was not about the fact that inequality worsened but about the price that had to be paid, in terms of economic growth, for a more egalitarian outcome. Economic Review 1 Because of its importance for public policy, the relationship between income equality and economic g r o w t h h a s long b e e n a m a j o r topic in e c o n o m i c research. T h i s essay selectively reviews s o m e recent d e v e l o p m e n t s in this area, emphasizing their consequences for public policy. Keeping in mind the perc e i v e d t r a d e - o f f b e t w e e n e q u a l i t y and g r o w t h , the discussion in particular sifts recent findings for implications about the effects on e c o n o m i c growth of redistributive policies—that is, of policies whose main objective is to reduce inequality. A review of recent studies using cross-country data discloses an important empirical fact: countries that grow faster also exhibit a more egalitarian income distribution. 4 This feature of the data suggests that redistributive p o l i c e s m a y h a v e not a d e t r i m e n t a l but a positive effect on the growth rate of national income; there m a y in fact be no conflict between promoting growth and reducing inequality. Other interpretations are possible, however. For instance, the empirical association between growth and equality may imply that policies primarily aimed at stimulating g r o w t h also have a "trickle-down" effect, reducing inequality as a by-product. D i s c r i m i n a t i n g a m o n g the alternative interpretations of the evidence is important because deciding the emphasis of government policy depends on which interpretation is taken to be correct. But choosing wisely between the competing theories is a difficult matter. In particular, a crucial assumption concerns the direction of causality: Does growth affect income distribution? Or, is it that inequality affects growth? The discussion focuses on the two main classes of theories—politicoeconomic theories and financial imperfections theor i e s — t h a t h a v e b e e n a d v a n c e d to e x p l a i n t h e inequality-growth relationship. The conclusion reached is that, although much progress has been achieved on this subject, the state of current k n o w l e d g e does not yet warrant firm prescriptions for public policy. Tlie Kuznets Curve Although the link between inequality and growth has preoccupied economists for centuries, modern research on this connection originated in a seminal study by Simon Kuznets (1955). Kuznets advanced the surprising theoretical conjecture that as a country's national i n c o m e g r o w s , its i n c o m e d i s t r i b u t i o n m u s t initially become less, rather than more, egalitarian. He also conjectured that growth brings about more equal- Econom ic Review 2 ity only after the country's income has surpassed some threshold level. In other words, Kuznets argued that the evolution of income distribution follows a U-curve: e c o n o m i c e x p a n s i o n m a k e s p o o r p e o p l e relatively poorer in the initial stages of a country's development and relatively richer at more advanced stages. Kuznets's hypothesis was based on the theories of economic growth prevalent in the fifties, coupled with empirical observation. Those theories explained growth as a process by which the working population moved f r o m traditional activities such as agriculture to a m o r e productive industrial sector. 5 The empirical observation was that incomes in the traditional sector were typically lower and m o r e narrowly distributed than industrial incomes. Under these conditions, Kuznets argued, the development experience of a typical country was likely to be coupled with both higher per capita incomes and greater income inequality, as it meant that over time an increasingly larger fraction of the population would be located in the more productive but more unequal industrial sector. K u z n e t s ' s theory implies that redistributive policies (those that tax the rich to give to the poor) have negligible e f f e c t s on d e v e l o p m e n t . T h e behavior of i n c o m e distribution is viewed as e n d o g e n o u s — t h a t is, explained by the theory as an o u t c o m e of the development process. In contrast, growth is treated as exogenous, not explained by the theory and, in particular, not a f f e c t e d by i n c o m e d i s t r i b u t i o n . B e c a u s e growth affects income distribution but not vice versa, economists say that causality in Kuznets's theory runs one way, f r o m growth to income distribution. The implication is that, although one can justify redistributive policies on the basis of equity considerations, it cannot be argued that redistribution accelerates overall development. 6 The question of the effects of redistributive policies on g r o w t h r e s u r f a c e s in the m o r e recent literature, and again the answer depends crucially on assumptions about the direction of causality. In spite of the importance of the questions Kuznets raised, subsequent research in macroeconomics largely ignored distributional issues. 7 Three conditions probably account for this fact. First, empirical evidence supporting the existence of a "Kuznets curve" turned out to be inconclusive. 8 Also, while the Kuznets curve was considered to be a long-run phenomenon, most macroeconomists were focused on short-run fluctuations— that is, on the business cycle. 9 Finally, in the 1970s and 1980s macroeconomic research turned attention to rational expectations models. These models assumed that economic actors make decisions efficiently using all i n f o r m a t i o n a v a i l a b l e a b o u t t h e i r e n v i r o n m e n t . July/August 1994 that cross-country data yield a robust relation between inequality and not the level of income but the longrun growth rate of income. Properly m o d e l i n g these c h o i c e p r o b l e m s required mastering new tools from decision theory. So, in order to k e e p their m o d e l s m a n a g e a b l e , m a c r o e c o n o m i s t s i m p o s e d s o m e s t r o n g s i m p l i f y i n g a s s u m p t i o n s on them. In particular, it became conventional in macroec o n o m i c m o d e l s to a s s u m e t h a t t h e b e h a v i o r of households was well approximated by the behavior of an average or " r e p r e s e n t a t i v e " individual; likewise, the business sector was usually a p p r o x i m a t e d by a "representative" firm. These assumptions allowed m a c r o e c o n o m i c s to m a k e considerable progress, but they also prevented the study of distributional questions. Zong-Run Growth and Inequality In an important contribution, Torsten Persson and Guido Tabellini (1994) showed, using data f r o m many countries, that long-run growth rates of i n c o m e are positively associated with measures of income equality. Their crucial finding is worth examining in some detail. 1 0 T h i s situation has changed. T h e r e has been a recent r e s u r g e n c e of i n t e r e s t in the d e t e r m i n a n t s of long-run growth, following the influential papers of Paul M . R o m e r (1986) and Robert E. Lucas (1988). In a d d i t i o n , m o d e l s of d y n a m i c m a c r o e c o n o m i c s are much better understood today, and incorporating distributional issues into them has become feasible. Finally, and perhaps most importantly, it was discovered Chart 1 displays representative data for a sample of forty-eight countries. Each country is represented by a point m e a s u r i n g the long-run g r o w t h rate of its inc o m e and the equality of its income distribution. In the vertical axis, the 1960-85 average annual growth rate of its per capita gross domestic product (GR6085) is a proxy for a country's income growth rate." T h e Chart 1 I n c o m e Distribution and Long-Run G r o w t h GR6085 (Income Growth) Korea * • • ^Brazil • • • • •• • • • •• • • • • • — • .... •• •.—- • • t • • • •Venezuela •Chad —i 7.5 10.0 12.5 15.0 MID20 (Income Distribution) 17.5 20.0 The chart displays representative data for a sample of forty-eight countries. Each country is represented by a point measuring the long-run growth rate of its income and the equality of its income distribution. In the vertical axis, the 1960-85 average annual growth rate of its per capita GDP (CR6085) is a proxy for a country's income growth rate. The proxy for its income equality, in the horizontal axis, is the share of its national income earned by the middle 20 percent of its population (MID20). The positive slope of the regression line indicates that, on average, countries that grew faster between 1960 and 1985 also had a more egalitarian distribution of income. Federal Reserve B a n k of Atlanta Economic Review 3 proxy for its income equality, in the horizontal axis, is the share of its national income earned by the middle 20 p e r c e n t of its p o p u l a t i o n ( M / D 2 0 ) . 1 2 M / D 2 0 is supposed to be a measure of the income of the middle class: a higher value of MID20 is taken to express a more egalitarian income distribution. 1 3 It is apparent f r o m Chart 1 that the data show a n o i s y but p o s i t i v e r e l a t i o n b e t w e e n GR6085 and MID20—that is, b e t w e e n growth and equality. T h e chart also shows a "regression l i n e " that represents the best-fitting linear approximation to the data. The slope of the regression line is positive, indicating that, on average, countries that grew faster between 1960 and 1985 also had a more egalitarian distribution of inc o m e . A s in any empirical relation, there are many, sometimes large departures from the regression line. For example, Venezuela and Chad display a relatively egalitarian distribution of income, but they have grown very slowly; Brazil has grown very rapidly in spite of substantial income inequality. But these are exceptions to the generally positive association between equality and growth. To investigate the g r o w t h - e q u a l i t y relation m o r e carefully, one needs to take into account the effect that third variables may have on that relation. The growth rate of a country's income may be linked not only to its income distribution but also to its level of educational attainment or its initial level of income, for example. If these additional variables are systematically related to measures of equality and growth, Chart 1 does not isolate the true association between inequality and growth but instead reflects the simultaneous effects on growth and equality of the additional variables. Third variables can be controlled for with the help of multivariate regression analysis. Typically, doing so involves calculating least squares regressions of G N P growth on income distribution and a number of other control variables. 1 4 A representative result for this data set is GA6085 = - 2 . 5 9 - 0.00052 GDP60 + 0.041 PS60 + 0.187 MID20, w h e r e , as b e f o r e , GR6085 m e a s u r e s growth and MID20 m e a s u r e s income distribution while GDP60 (level of 1960 real, or i n f l a t i o n - a d j u s t e d , G D P per capita) and PS60 (1960 primary school enrollment ratio) are control variables. 1 5 T h e coefficients in the above regression are all statistically s i g n i f i c a n t , and their signs m a y be given plausible interpretations. GDP60 has a negative sign, m e a n i n g that countries that had a relatively low per Econom ic Review 4 capita G D P in 1960 grew, on average, relatively faster than other countries during the 1960-85 period. This result is consistent with the view that poorer countries tend to "catch u p " with richer ones or, equivalently, that the income levels of different countries tend to c o n v e r g e . T h e positive sign of PS60 indicates that c o u n t r i e s w h o s e e d u c a t i o n a l s y s t e m was m o r e advanced by 1960 grew faster, on average, during the 1960-85 period. This finding agrees with the conventional view that countries with better-educated populations have more favorable growth experiences. For the purposes of this study, the most important result is the sign and magnitude of the coefficient of MID20, which may be given the following interpretation: other things being equal, if the share of G N P accruing to the middle class of a country increases by 1 percent, its long-run growth rate increases by 0.187 percent. This effect m a y not seem significant, but differences in growth rates of this magnitude do make, after compounding, a large difference in income levels and welfare. For example, suppose that two countries A and B had a 1960 G N P per capita of US$ 1,000, and all their characteristics were identical and equal to those of the average country in the sample except that the middle-class G N P share in country A was 1 percent larger than that of the average. Then the per capita G N P predicted for the end of this decade would be US$2,337 for country A and only US$2,172 for country B, and the difference would keep growing. Chart 2 displays the results. As in Chart 1, the horizontal axis uses MID20 as a proxy for income distribution. But along the vertical axis is m e a s u r e d the c o m p o n e n t of growth that is not explained by PS60 and GDP60, called GRRES. In other words, GRRES measures long-run growth after controlling for the effect of initial income and education. Comparing Charts 1 and 2 shows that GRRES is m o r e strongly associated and is s o m e w h a t m o r e r e s p o n s i v e to M I D 2 0 than G/?6085. By implication, the inequality-growth relation becomes more significant after taking into account the effect of other variables. These results replicate Persson and Tabellini's initial f i n d i n g of a p o s i t i v e e q u a l i t y - g r o w t h relation. Other authors have checked the robustness of Persson and Tabellini's finding, with results generally supportive of their claim. 1 6 From these results, it is tempting to conclude that the data imply that income equality boosts growth. If that were the case, then the consequences for public policy would be e n o r m o u s : one could argue that reducing inequality does not imply sacrificing economic growth but, on the contrary, results in faster growth. July/August 1994 But is the existence of an empirical association between equality and growth in fact sufficient to conclude that more equality helps growth? Generally not. College statistics courses stress that an empirical correlation between two variables does not necessarily tell anything about how one of the variables actually affects the other. That lesson applies in this context: the empirical evidence is consistent with the view that redistributive policies help growth but also with the alternative view that faster growth creates greater equality. This is an e x a m p l e of w h a t e c o n o m i s t s call "observational equivalence": two different hypotheses—(1) equality helps growth, and (2) growth reduces inequality—may be consistent with the same e v i d e n c e (equality and growth are positively correlated). In this case, solving the observational equivalence problem amounts to taking a stand about the direction of causality between equality and growth—that is, deciding which variable will be taken as being affected by the other. The only way to determine the direction of causality and, more importantly, to understand the economic mechanisms that explain the above empirical findings is to f o r m u l a t e theoretical m o d e l s of the links be- tween growth and inequality. By analyzing theoretical m o d e l s one can isolate the a s s u m p t i o n s underlying alternative explanations of the data. Doing so is helpful because sometimes these assumptions turn out to be implausible and also because it allows one to derive f u r t h e r i m p l i c a t i o n s of these a s s u m p t i o n s that can be tested empirically. Two main classes of theories of the growth-equality link have emerged: theories that focus on the relation b e t w e e n e c o n o m i c s and politics, and t h e o r i e s that stress the role of imperfect financial markets. E a c h class shall be examined in turn. Politicoeconomic Theories In searching for e x p l a n a t i o n s of the i n e q u a l i t y growth relationship, it is natural to start by looking at the links b e t w e e n politics and e c o n o m i c s . A f t e r all, it is intuitively plausible that inequality is h a r m ful for a c o u n t r y ' s political situation, w h i c h in turn is likely to a f f e c t g r o w t h . M a n y r e c e n t m o d e l s of Chart 2 Partial Association, I n c o m e Distribution versus G r o w t h GRRES MID20 (Income Distribution) As in Chart I, the horizontal axis uses MID20 as a proxy for income distribution. Along the vertical axis, GRRES measures long-run growth after controlling for the effect of initial income and education. Comparing Charts 1 and 2 shows that CRRES is more strongly associated and is somewhat more responsive to MID20 than GR6085. By implication, the inequality-growth relation becomes more significant after taking into account the effect of other variables. Federal Reserve B a n k of Atlanta Economic Review 5 inequality and growth are attempts at formalizing this intuition. Persson and Tabellini's original (1994) contribution p r o v i d e s a g o o d e x a m p l e of p o l i t i c o e c o n o m i c models. Persson and Tabellini advanced a theory that emphasized how government policies are determined in d e m o c r a t i c societies. T h e y e x a m i n e d a m o d e l in w h i c h taxes and t r a n s f e r s are c h o s e n via m a j o r i t y rule. An i m p l i c a t i o n of this political m e c h a n i s m is that the poorer the majority of voters, the larger the amount of redistribution f r o m wealthy to poor people that will be approved. The problem is that some of the taxes that finance redistribution also discourage capital a c c u m u l a t i o n , w h i c h in P e r s s o n and T a b e l l i n i ' s setup is the engine of growth. Demonstrating why Persson and Tabellini's model implies a positive growth-equality relation, similar to the o n e f o u n d in c r o s s - c o u n t r y data, is straightforward. Suppose that there are t w o countries, A and B, identical in all respects except that A has a more egalitarian wealth distribution. Then A"s majority of voters is likely to be wealthier than B ' s . Since this fact implies, according to Persson and Tabellini, that A's majority will approve less redistribution than B's, taxes will be lower in A. Hence, there will be m o r e investment and faster growth in A than in B. Persson and Tabellini's m o d e l , and others in the s a m e spirit (for example, Alberto Alesina and Dani Rodrik 1994; Giuseppe Bertola 1993), make the crucial assumption that the distribution of wealth is exogenously given, and then derive the c o n s e q u e n c e s for growth. According to this assumption, the direction of c a u s a l i t y r u n s f r o m w e a l t h d i s t r i b u t i o n t o growth: wealth distribution affects growth, but growth does not affect wealth distribution. (Note that causality runs in the opposite direction relative to Kuznets's model.) The implication is that redistributing wealth f r o m rich to p o o r p e o p l e , which m a y b e d e s i r a b l e f r o m an equity perspective, will also raise the rate of growth by changing the outcomes of the political decision process. B y making the majority of voters relatively w e a l t h i e r , r e d i s t r i b u t i v e p o l i c i e s r e d u c e the taxes that the majority will approve, and lower taxes result in more investment and faster growth. N o t e that Persson and Tabellini's theory predicts a n e g a t i v e relation b e t w e e n wealth i n e q u a l i t y and growth. T h e empirical relation b e t w e e n income inequality and growth is seen as an a p p r o x i m a t i o n of that " t r u e " r e l a t i o n . For e x p l a i n i n g the e m p i r i c a l patterns, there m a y b e s o m e value in this position b e c a u s e i n c o m e distribution and wealth distribution are highly c o r r e l a t e d . But f o r policy a n a l y s i s , ne- 6 Econom ic Review glecting the fact that income distribution is an endogenous variable may be dangerous, even if one accepts that a politicoeconomic mechanism is generating the inequality-growth relationship. For example, it is possible that, in spite of the existence of a positive income equality-growth relation in the data, redistributing wealth has no effect on econ o m i c growth. This point was m a d e formally by Roberto C h a n g (1993). In that study's m o d e l , fiscal policy is determined not by majority rule but by the negotiations between two political parties that represent different social groups. The model implies that inc o m e equality and growth are both e n d o g e n o u s variables and m a y exhibit a positive relation across countries, just as in cross-country data. If these results were taken as a proxy for an underlying relation bet w e e n wealth equality and growth, one would c o n c l u d e that redistributing wealth w o u l d increase the growth rate. But this would be an inaccurate conclusion. In C h a n g ' s (1993) model, redistributing wealth f r o m the rich to the poor does not change the relative bargaining power of the two parties; hence, it has no effect on fiscal policy and growth. 1 7 To s u m m a r i z e the discussion to this point: it has been shown that politicoeconomic models are consistent with the inequality-growth relation observed in cross-country data. But m o d e l s of this kind are not identical to e a c h other, and in fact they m a y d i f f e r sharply in their implications for the effects of redistributive policies on growth. The fact that different m o d e l s are consistent with the i n e q u a l i t y - g r o w t h relation but yield c o n f l i c t i n g policy advice indicates that, in o r d e r to d e t e r m i n e which model is m o r e accurate, it is necessary to c o m pare models- on the basis of their empirical implications other than the inequality-growth relation. S o m e p r o g r e s s in this regard has been m a d e by R o b e r t o Perotti (1992). Perotti rightly argued that many polit i c o e c o n o m i c models, including that of Persson and Tabellini, rely on two distinct assumptions: that more inequality is associated with larger tax-transfer schemes, and that larger t a x - t r a n s f e r s c h e m e s are negatively associated with growth. These assumptions imply that the d a t a should exhibit a positive relation between income inequality and the share of government transfers in G D P and a negative association between the share of transfers and G D P growth. But in fact, as Perotti points out, the data show very weak support for both implications. Perotti concluded that m o d e l s of the Persson-Tabellini type m u s t be rejected: they imply a negative inequality-growth relation but for the wrong reasons. 1 8 July/August 1994 Perotti's contribution has placed a question mark on models in which inequality hurts growth through its effect on the majority's choice of taxes and transfers, although his conclusions can be challenged on a n u m b e r of p o i n t s . F i r s t , t h e s h a r e of g o v e r n m e n t transfers in G D P may be a very bad proxy for redistributive policy. In many countries redistribution takes the f o r m not of f o r m a l t r a n s f e r s but of " i n f o r m a l " ones: creation of unproductive bureaucratic j o b s for party m e m b e r s , allocation of valuable licenses and quotas to friends, and so forth. Second, the data seem to provide little information about the hypothesis that Perotti wants to test, partly because he works with a relatively small n u m b e r of observations. To address the questions raised by Perotti's findings, Alesina and Perotti (1993) have recently argued that the link between inequality and growth is not through fiscal policy but is more direct. In their view, income inequality causes "political instability," which in turn depresses investment and retards growth. This kind of mechanism sounds intuitively plausible, but economic analysis requires more concreteness. What exactly is political instability? How can it be measured? Alesina and Perotti avoid giving a definition, instead treating political instability as an unobservable variable that affects a number of other variables, such as the number of coups per year, number of political assassinations, frequency of changes in the executive power, and the like. In this way they construct, for each country, an " i n d e x " of political instability. Finally, they examine international data to see if greater income inequality is associated with a higher value of the instability index and if a higher index is related to lower investment and/or growth. The data show support for both links. Financial Imperfections Theories The intuition behind a second class of models of the inequality-growth relationship can be illustrated with a simple story. Consider an e c o n o m y peopled by m a n y families that, initially, have different levels of wealth. Each family has access to two different productive opportunities or projects. O n e of the projects is more attractive than the other; in particular, the output of the first project grows faster than the output of the second. U n d e r t a k i n g the m o r e p r o f i t a b l e , highgrowth project requires paying a set-up cost up front, however, while the less-productive project entails no such cost. In the absence of its set-up cost, all families would u n d e r t a k e only the h i g h - g r o w t h p r o j e c t . T h e s a m e would be true if borrowing and lending markets were perfect b e c a u s e then an initially poor f a m i l y w o u l d be able to obtain a loan to pay for the set-up cost of the better project. Suppose, though, instead that f a m i lies cannot borrow; the project that any given family can undertake is limited by its initial wealth. S u c h families m a y b e unable to pay the set-up cost associated with the high-growth project, and this situation m a y persist over time if families that are too poor initially never accumulate enough f u n d s . Alesina and Perotti have pushed the theory in an interesting direction, and their initial examination of i n t e r n a t i o n a l data s e e m s to lend s o m e c r e d e n c e to their conjectures. More research is needed, however, to verify the robustness of their results as well as to further understand the notion of "political instability" that is central to their theory. Moreover, the policy implications of their theory are unclear. The initial distribution of wealth b e c o m e s crucial for determining the e c o n o m y ' s overall growth rate. If initial w e a l t h is c o n c e n t r a t e d in very f e w f a m i l i e s , o n l y t h e s e f e w u n d e r t a k e the h i g h - g r o w t h p r o j e c t while most others will be stuck in the relatively unp r o d u c t i v e p r o j e c t , m a k i n g the e c o n o m y ' s a v e r a g e g r o w t h rate low. A m o r e even w e a l t h d i s t r i b u t i o n m a y e n a b l e m o r e f a m i l i e s to start the h i g h - g r o w t h p r o j e c t , i n c r e a s i n g o v e r a l l g r o w t h . T h i s s t o r y is therefore consistent with the empirical positive association between growth and equality: countries with very u n e q u a l initial wealth distribution m u s t g r o w m o r e slowly and exhibit less income inequality than c o u n t r i e s in w h i c h initial w e a l t h was m o r e evenly distributed. T h i s s e c t i o n h a s s h o w n that p o l i t i c o e c o n o m i c models have had success at reproducing the empirical relation between equality and growth. S o m e prominent models imply that redistributiVe policies increase growth. But the fact that other models do not support that conclusion points to the need for discriminating a m o n g the competing models on the basis of empirical implications other than the equality-growth relation. Work along these lines has yet to yield clear-cut answers. T h e above story illustrates the basic m e c h a n i s m behind models that stress that financial imperfections m a y e x p l a i n the c r o s s - s e c t i o n a l results of c o n c e r n here. 1 9 Two assumptions are crucial in these models. The first is that a high-growth project requires some set-up cost that must be paid for up front although the p r o j e c t ' s output is obtained only in the f u t u r e . T h e second important assumption is that borrowing markets are imperfect, which implies that families without e n o u g h f u n d s to c o v e r the s e t - u p c o s t of the Federal Reserve Bank of Atlanta Economic Review 7 high-growth project cannot undertake the project for lack of financing. A good e x a m p l e of this a p p r o a c h is research by Oded Galor and Joseph Zeira (1993). Galor and Zeira examined a model in which parents leave bequests to their children, w h o in turn leave bequests to their own children, and so on. Acquiring education is costly (the set-up cost). Going to school is a good investment because an educated person can work as a skilled worker, and skilled workers are more productive and earn higher income than unskilled ones; also, the productivity and income of the former grow faster than those of the latter. A s a consequence, everybody would like to get an education. B u t — a n d this is the point at which f i n a n c i a l m a r k e t i m p e r f e c t i o n s p l a y an i m p o r t a n t role—only those with large enough bequests can afford to pay for their education. In the long run, the population is split b e t w e e n t w o groups of families: wealthy f a m i l i e s earning high and f a s t - g r o w i n g inc o m e , a n d p o o r f a m i l i e s w h o s e m e m b e r s are u n skilled, low-wage workers caught in a relative poverty trap. The number of families that become wealthy or poor, and hence the e c o n o m y ' s overall growth rate and income distribution, depends on the initial distribution of wealth, which determines which families can pay for education. Models of financial imperfections have noteworthy implications for public policy. O n e of them is that adequate redistributive policies may simultaneously reduce income inequality and enhance growth. This possibility is similar to that suggested in some politicoeconomic models, but the mechanism is different: in models of financial imperfections, redistributive policies may accelerate growth by helping poor families finance set-up costs and escape from relative poverty. A more novel and more interesting implication of these models is that policies aimed at reducing imperfections in borrowing markets may, in the long run, reduce income inequality and e n h a n c e growth. Recall that in these models poor families remain poor because they cannot borrow enough to finance the set-up costs of undertaking high-growth projects, even if such projects are the most profitable ones. It follows that poor families would escape relative poverty if public policy could help remove their borrowing constraints. It m u s t be a c k n o w l e d g e d , however, that w h e t h e r public policy can in fact alleviate the effects of borrowing market imperfections may depend on why such imperfections exist in the first place. For example, suppose that borrowing constraints are caused by an asymmetry of information between borrowers and lenders. 2 0 Then it is likely that government policy can Econom ic Review 8 eliminate the borrowing constraints if and only if the government has better information than do borrowers and lenders (an assumption that is often difficult to defend). If so, policy analysis m a y be sensitive to the exact specification of financial imperfections. More research is needed on this aspect of the theory. 21 In fact, more development of the theory is needed also because some prominent models in the literature have some counterfactual implications, the elimination of w h i c h will probably require nontrivial m o d i f i c a tions. For instance, Galor and Zeira's (1993) model implies that there is very limited social mobility: in the long run, rich families remain rich and poor families remain poor. This conclusion contradicts the fact that advanced economies exhibit a significant degree of social mobility. On the other hand, models that predict significant social mobility typically assume, because of technical difficulties, that there is no long-run growth (for instance, Banerjee and N e w m a n 1991). While such simplifying assumptions have been important to enabling development of the theory, one must recognize that actual economies exhibit both social mobility and long-run growth. Developing a satisfactory model that reproduces both features of the data remains an important theoretical challenge. Models of imperfect financial markets seem promising for explaining the equality-growth relation, and they have been useful for directing attention toward the link between credit markets, distribution, and growth. Before accepting their policy r e c o m m e n d a t i o n s , though, further development of the theory is needed. It must also be kept in mind that financial imperfections models are not the only ones that explain the correlation between income equality and growth; politicoeconomic theories are also consistent with that correlation. Demonstrating the superiority of financial imperfections explanations will probably require developing models with a more complete specification of the financial sector and testing their other implications in addition to the growth-equality correlation. Conclusion Empirical evidence discussed in this paper displays a positive association between i n c o m e equality and e c o n o m i c growth. D o e s this observation imply that appropriate g o v e r n m e n t intervention can simultaneously achieve m o r e equality and faster growth? T h e jury is still out, and the answer depends on delicate but interesting questions of economic theory. July/August 1994 T h e d i s c u s s i o n has shown that m a n y alternative models can generate a positive relation between growth and equality. But these models differ on important aspects, most f u n d a m e n t a l l y on which varia b l e s are t a k e n as e x o g e n o u s and w h i c h o n e s are determined e n d o g e n e o u s l y . It is clear that m o r e research is needed (and is currently taking place) in order to determine the relative relevance of the different theories. In particular, the alternatives need to be evaluated on the basis of their additional implications for the data, perhaps by applying econometric methods: Perotti's (1992) study is a good start in that direction. Less formal checks may also be useful. For instance, s o m e of the c o m p e t i n g m o d e l s have c o u n t e r f a c t u a l implications, such as limited social mobility in the Galor-Zeira model. These implications m a y turn out to be decisive reasons to reject such models. Discriminating among the alternative models is not merely an intellectual exercise but is fundamental for policy evaluation. Although all the models reviewed in this paper are consistent with the observed correlation between growth and equality, they have very different policy implications. Thus it is fair to say at this point that knowledge has not developed enough to yield unambiguous lessons for public policy. Nevertheless, it should be evident that there has been progress and that o n g o i n g research in this area will c o n t i n u e to c o n tribute toward that goal. Notes 1. See, for instance, chapter 4 of the 1992 Economic Report of the President, which discusses income distribution and poverty. 2. A good example is contemporary Peru, where the income received by the top f i f t h of the population is seventeen times as large as the income received by the bottom fifth. This degree of inequality is widely blamed for the Shining Path terrorist rebellion that has resulted in m o r e than 25,000 deaths since 1980. 3. See Baily, Burtless, and Litan (1993), Krugman (1994), and Haslag and Taylor (1993) for recent discussions of the U.S. case. 4. One reason to focus on cross-country studies is that time series s t u d i e s of the i n e q u a l i t y - g r o w t h correlation are rather scarce. Perhaps this is due to two facts: (1) income distribution time series are difficult to find except for a few advanced countries, and (2) constructing a series of the underlying "long-run" growth component from the per capita G N P series is a hard and unsettled question. 5. The classic statement of such views is Lewis (1954). 6. In recent models of the Kuznets curve, such as that of G r e e n w o o d and J o v a n o v i c (1990), causality runs both ways, and redistributive policies do affect development. 7. But the Kuznets hypothesis was a very active area of research in the field of economic development. For a survey, see Adelman and Robinson (1989). 8. For a recent examination, see Anand and Kanbur (1993). 9. It is not that long-run issues were ignored. In fact, research in the field of economic growth and development was very active, and many growth models developed between 1960 and 1985 were the forerunners of the current generation of growth models. But it is fair to say that macroeconomics was dominated by business cycle questions. 10. The calculations in this section were performed by the author, based on data described below. Federal Reserve Bank of Atlanta 11. G/?6085 is taken from the appendix to Barro (1991), which in turn is extracted from the Penn World Table described by Summers and Heston (1988). 12. MID20 is measured around 1960 and is taken from Persson and Tabellini (1993), who in turn took the series from Paukert (1973). 13. Using other measures of income inequality, such as Gini coefficients, does not affect the qualitative conclusions described here. See, for instance, Galor and Zang (1992), who report similar findings using Gini coefficients as their measure of income equality. 14. See Barro (1991) for a thorough analysis of growth in a cross-section sample. 15.M/D20 and PS60 arc also taken from the Barro data set. The t statistics associated with GDP60, MID20, and PS60 are - 2 . 9 7 , 2.29, and 4.38, respectively. They are all significant at the 5 percent confidence level. The R 2 of the regression is 0.363. 16. A m o n g others, see Alesina and Rodrik (1994), Perotti (1992), Galor and Zang (1992). 17. How is it, then, that the data exhibit a positive income equality-growth correlation? The author's suggested explanation is that there are underlying differences in productive technologies across countries. The model implies that a m o r e productive technology may tilt bargaining power toward the political party that represents the poor, thus implying that more redistribution will be agreed upon. But a more productive technology also allows for faster growth, even after taking into account the higher taxes needed to finance redistribution. Hence, if the main source of the variation in cross-country data is some unobserved determinant of technology, the data will exhibit a positive relation between income equality and growth. Such a relation cannot be exploited by public policy, however. For a related argument, see Wright (1993). Economic Review 9 18. In contrast, Perotti's results are consistent with the model in Chang (1993). 19. Examples of this line of research are Aghion and Bolton (1991), B a n e r j e e and N e w m a n (1991), Galor and Zeira (1993), Galor and Zang (1992). 20. An example is a situation in which each borrower has access to either a "good" or a "bad" project, and lenders can- not observe the quality of the borrowers' projects. In this case, it may happen that a borrower with a good projcct cannot get a loan because he cannot convince lenders that his project is in fact a " g o o d " one. 21. For more detailed analyses of the effects of government intervention in economies with imperfect capital markets, see Lacker (1994) and Srinivasan (1994). References Adelman, Irma, and Sherman Robinson. "Income Distribution and D e v e l o p m e n t . " In Handbook of Development Economics, edited by Hollis Chenery and T.N. Srinivasan, 9491003. Amsterdam: North Holland, 1989. Haslag, Joseph, and Lori Taylor. "A Look at Long-Term Developments in the Distribution of Income." Federal Reserve Bank of Dallas Economic Review (First Quarter 1993): 1930. Aghion, Phillipe, and Patrick Bolton. "A Trickle-Down Theory of Growth and Development with Debt-Overhang." Delta (Paris). Photocopy. 1991. Alesina, Alberto, and Roberto Perotti. "Income Distribution, Political Instability, and Investment." National Bureau of Economic Research Working Paper 4486, 1993. Alesina, Alberto, and Dani Rodrik. "Distributive Politics and Economic Growth." Quarterly Journal of Economics 109 (1994): 465-90. Lacker, Jeffrey M. "Does Adverse Selection Justify Government Intervention in Loan Markets?" Federal Reserve Bank of Richmond Economic Quarterly 80 (Winter 1994): 61-95. Lewis, W. Arthur. "Economic Development with Unlimited Supplies of Labor." Manchester School Economic and Social'Studies 22 (1954): 139-91. Anand, Sudhir, and S.M.R. Kanbur. "The Kuznets Process and the Inequality-Development Relationship." Journal of Development Economics 40 (1993): 25-52. Baily, Martin, Gary Burtless, and Robert Litan. "Growth with Equity: E c o n o m i c Policymaking for the Next C e n t u r y . " Washington: Brookings Institution, 1993. Banerjee, Abhijit, and Andrew Newman. "Risk Bearing and the Theory of Income Distribution." Review of Economic Studies 58 (1991): 211-35. Barro, Robert J. " E c o n o m i c G r o w t h in a Cross-Section of Countries." Quarterly Journal of Economics 106 (1991): 407-43. Bertola, Giuseppe. "Factor Shares, Saving Propensities, and E n d o g e n o u s G r o w t h . " American Economic Review 83 (1993): 1184-98. Chang, Roberto. "Political Party Negotiations, Income Distribution, and Endogenous Growth." New York University Working Paper, 1993. Galor, O d e d , and H y o u n g s o o Zang. " F a m i l y Size, Income Distribution, and Economic Growth: Theory and Crossc o u n t r y Evidence." Brown University Working Paper 9219, 1992. G a l o r , O d e d , and Joseph Z e i r a . " I n c o m e Distribution and Macroeconomics." Review of Economic Studies 60 (1993): 35-52. Greenwood, Jeremy, and Boyan Jovanovic. "Financial Development, Growth, and the Distribution of Income." Journal of Political Economy 98 (1990): 1076-1107. 10 Econom ic Review Lucas, Robert E. "On the Mechanics of Economic Development." Journal of Monetary Economics (1988): 3-42. Krugman, Paul R. Peddling Prosperity. New York: Norton, 1994. Kuznets, Simon. "Economic Growth and Income Equality." American Economic Review 45 (1955): 1-28. Paukert, Felix. "Income Distribution at Different Levels of Development: A Survey of Evidence." International Labor Review 108 (1973): 97-125. Perotti, R o b e r t o . "Fiscal Policy, Income Distribution, and Growth." Columbia University Working Paper, 1992. Persson, Torsten, and Guido Tabellini. "Growth, Distribution, and Politics." In Political Economy, Growth, and Business Cycles, edited by Alex C u k i e r m a n , Zvi H e r c o w i t z , and Leonardo Leiderman, 3-22. Cambridge: MIT Press, 1993. . "Is Inequality Harmful for G r o w t h ? " American Economic Review 84 (1994): 600-622. Romer, Paul M. "Increasing Returns and Long Run Growth." Journal of Political Economy 94 (1986): 1002-37. Srinivasan, Aruna. "Intervention in Credit Markets and Development Lending." Federal Reserve Bank of Atlanta Economic Review 79 (May/June 1994): 13-27. Summers, Robert, and Alan Heston. "A New Set of International Comparisons of Real Product and Price Levels: Estimates for 130 Countries." Review of Income and Wealth 34 (1988): 1-25. Wright, Randall. "Growth, Taxation, and Redistribution." University of Pennsylvania and Federal Reserve Bank of Minneapolis Working Paper, 1993. July/August 1994 information Ambiguity: Recognizing Its Role in Financial Markets Jie Hu s uncertainty plays a salient role in economic life, proper models for capturing uncertainty and individuals' behavior under uncertainty are crucial for a sound u n d e r s t a n d i n g of the e c o n o m i c world. While traditional economic theory has had its successes in providing such models, many economic issues cannot be satisfactorily explained within its f r a m e w o r k . For example, in financial markets several phenomena remain unexplained: Why are asset prices usually more volatile than asset fundamental values? Why is it that asset prices m a y fall discontinuously or crash? Why are assets for initial public offering often underpriced? Why do public announcements cause increased trading volume of assets? These and other open questions have prompted economists to search outside existing theoretical models for answers. O n e of the missing ingredients, according to recent economic research, may be the concept of information ambiguity. The author is a senior economist in the financial section of the Atlanta Fed's research department. He thanks his colleagues in the financial section of the research department and Morton Kamien, Joseph and Carole Levy Distinguished Professor of Entrepreneur ship at Northwestern University, for helpful comments. Federal Reserve Bank of Atlanta Uncertainty that an economic agent faces usually arises f r o m the inaccuracy of available information. Different degrees of accuracy may serve to classify information into three categories. Consider drawing a ball f r o m an urn that contains a number of balls, each with one of three possible colors: red, black, and yellow. If one is allowed to see the ball, information about its color is deterministic; if one is not allowed to see the ball but is given the ratios of the three colors, then the chance that each color will be chosen is known and information about the color of the drawn ball is probabilistic; if one is neither allowed to see the ball nor given the exact ratios of the three colors, the exact chance for each possible color cannot be pinned down, and information about the color of the ball to be selected is ambiguous. Economic Review 11 Economic information available to an agent can be classified into the same categories. Accordingly, the indeterminateness featured by probabilistic information is called risk, and the indeterminateness caused by ambiguous information is called Knightian uncertainty, after Frank Knight (1921), the first economist to distinguish between the t w o types of indeterminateness. Subsequent to K n i g h t ' s contribution, however, the formal mathematical framework for analyzing information and uncertainty has essentially ignored the class of information that is ambiguous, and the practice of theory has been to reduce both risk and Knightian uncertainty to the single concept of risk. W h i l e Pricing a stock is like evaluating a lottery, with its payoff contingent upon the future performance of the firm. such an approach offers the virtue of simplifying economic models, it may ignore many important insights. Recent developments in decision science—the branch of economic theory that studies people's rational behavior—have provided some tools for modeling inform a t i o n a m b i g u i t y , and e c o n o m i s t s h a v e b e g u n to apply t h e m successfully to solving puzzles in traditional economic theory.' This article provides a brief and intuitive illustration of w h y information ambiguity—referred to syno n y m o u s l y as Knightian u n c e r t a i n t y — i s significant in rational decision m a k i n g . The discussion d e m o n strates one way in which information ambiguity m a y be m o d e l e d . W h i l e there are a n u m b e r of decision theories that model rational choices under Knightian uncertainty, they are logically related, and focusing on only o n e — d e v e l o p e d by Itzhak Gilboa and David Schmeidler (1989)—will serve the purpose of illustrating the basic intuition. 2 The article also shows applications of the concept of Knightian uncertainty in the study of financial markets, confining itself to the issues raised earlier. 12 Econom ic Review Tlie Significance of Information Ambiguity Using lotteries as an example will facilitate the discussion of information ambiguity since lotteries are useful for modeling many economic issues. For example, a contingency embedded in a financial asset is a kind of lottery, which entitles its owner to one of several possible p a y o f f s d e p e n d i n g on the o u t c o m e of some future events. Therefore, pricing a stock is like evaluating a lottery, with its payoff contingent upon the future performance of the firm. As another example, the e f f e c t s of an e c o n o m i c policy m a y also be viewed in terms of a lottery whose payoff depends on other unknown factors. The following analysis of lottery choices will be used to explain the so-called Ellsberg paradox and demonstrate the role of information ambiguity in people's behavior. To illustrate, imagine yourself in the following scenario, w h i c h tests y o u r choices. S u p p o s e you h a v e won a game in a carnival. Your award is a strange one: you are given the opportunity to get two lotteries. An opaque urn contains nine balls of identical size. A m o n g them, three are red, and the other six are either all black, or all yellow, or some black and some yellow. As listed in Table 1, four lotteries—A, B, A ' , and B ' — a r e based on drawing a ball from the urn. For example, lottery A entitles its owner to a payoff of $1 if a red ball is drawn f r o m the urn and to a payoff of $0 if a black or yellow ball is drawn. Similar interpretations are for the lotteries B, A ' , and B'. The game host leads you to the urn and tells you exactly the above information. He also points to a certificate signed by an independent agent, which confirms the contents of the urn. After you are convinced that the information given to you is true, the game host explains, "You will make two decisions: the first is to choose between lotteries A and B, and the second is to choose between lotteries A ' and B'. Then, you will draw a ball from the urn, and the color of the ball will detennine your cash award according to the lottery you have chosen from A and B. After that, you will put the ball back in the urn and draw again. The color of the ball drawn next determines your additional cash award according to the other lottery you have chosen f r o m A ' and B'. Now, please choose lotteries and draw the balls." A l t h o u g h the c h o i c e b e t w e e n A and B and the choice between A ' and B' may vary from one person to another, most people have the same choice pattern: A is preferred to B, and B' is preferred to A ' . In this discussion these will be referred to as the typical choic- July/August 1994 es. The underlying intuition may be as follows. While lotteries A and B both have the same possible payoffs of $1 and $0, the chance for each payoff in lottery A is unambiguous but in lottery B is ambiguous. Choosing A over B "feels safer." A similar line of thinking would apply to the choice of B ' over A'. The Ellsberg Paradox. Daniel Ellsberg (1961) was the economist who first proposed a setup similar to that in the carnival for considering economic choice patterns. He reported casual tests on the c h o i c e s of s o m e decision scientists and e c o n o m i s t s , including some f o u n d e r s of orthodox decision theory. Other researchers followed up with variants of his experiment in controlled environments, and it has n o w been established that the above preferences are indeed a systematic pattern (Colin F. C a m e r e r and Martin Weber 1992). However,- there is a paradox in the above typical choices. Orthodox decision theory (Leonard J. Savage 1954) "converts" ambiguous information into unambiguous information by assuming that a rational person has a unique guess about how many black or yellow balls are among the remaining six balls and makes decisions based on the guess—more balls of a certain color mean a greater chance for its corresponding payoff. If an agent follows this rule, preferring A to B should indicate that the ball combination is guessed to be less than three black balls or, equivalently, more than three yellow balls. However, preferring B ' to A ' indicates a guess that there are fewer than three yellow balls. The typical choices therefore imply more than one unique guess about the ball combination, which is inconsistent with orthodox decision theory (see Table 2). Table 1 Choosing among the Lotteries Six balls T h r e e balls Red Black Yellow ( U n a m b i g u o u s ) Lottery A $1 $0 $0 ( A m b i g u o u s ) Lottery B $0 $1 $0 ( A m b i g u o u s ) Lottery A' $1 $0 $1 ( U n a m b i g u o u s ) Lottery B' $0 $1 $1 Table 2 The Ellsberg Paradox There is a p a r a d o x in the t y p i c a l c h o i c e s because . . . Six balls T h r e e balls Red Black Yellow " A is preferred to B" implies a guess such t h a t . . . 3 balls < 3 balls > 3 balls "B' is preferred to A ' " implies a guess such t h a t . . . 3 balls > 3 balls < 3 balls . . . b u t o n l y o n e guess is a l l o w e d for the same setting in the o r t h o d o x d e c i s i o n m o d e l . The essence of the Ellsberg paradox is that traditional decision theory has failed to capture the special characteristic of ambiguous lotteries relative to unambiguous lotteries. An unambiguous lottery is one whose chance for each possible payoff is known, like lottery A, with its one-third chance for a payoff of $1 and two-thirds chance for a payoff of $0, or lottery B', which has a onethird chance for a payoff of $0 and two-thirds chance for a payoff of $1. In contrast, an ambiguous lottery is one whose exact chance for every possible payoff is not known, like lottery B or lottery A'. The reason for the ambiguity in this case is that the number of black or yellow balls is not known. In general, any information that is less accurate than can be represented by a unique probability distribution is ambiguous. 3 about the underlying chances for the payoffs of an ambiguous lottery. For example, an agent m a y have the unique guess that there are four black balls and two yellow balls and may m a k e all choices according to this guess. In other words, the traditional techniques have denied that a m b i g u o u s lotteries have any economic implications different f r o m those of unambiguous lotteries. It turns out that although such techniques are very successful in capturing people's choices when only unambiguous lotteries are involved, they fail to capture people's evaluation of ambiguous lotteries. O r t h o d o x d e c i s i o n t h e o r y d o e s not d i s t i n g u i s h evaluation techniques for the two types of lotteries but approaches them in practically identical ways by assuming that an agent can always have a unique guess Significance of the Paradox. The resolution of the E l l s b e r g p a r a d o x is i m p o r t a n t b e c a u s e in t h e o r e t i cal models people's economic decisions are often reduced to evaluating and choosing lotteries. Viewing Federal Reserve Bank of Atlanta Economic Review 13 the economic world as a system of correlated uncertain economic variables, assume that behind the system there is an u m that contains colored balls. The outcome of the economic world is determined by the color of the ball randomly drawn out. For example, to feature a system of e c o n o m i c v a r i a b l e s that h a s f o u r p o s s i b l e o u t c o m e s — X , Y, Z, and W—with r e l a t i v e c h a n c e s of 1/10:2/10:3/10:4/10, the urn may contain ten balls, with one ball (white) corresponding to the outcome X, two balls (green) corresponding to Y, three balls (gray) corresponding to Z, and the other four balls (orange) corresponding to W. Given that the economic world can be visualized as an urn containing colored balls, any economic action—a portfolio choice, a production plan, a policy decision, and so forth—whose effect is contingent on the outcome of the economic world is then a lottery determined by the color of the ball randomly drawn. In many cases ambiguous lotteries are more appropriate than unambiguous lotteries for capturing essential economic realities. More and more evidence suggests that it is inappropriate to blur the difference between unambiguous lotteries and ambiguous lotteries as orthodox decision theory does. Knight (1921) e m p h a sized the economic significance of this difference and pointed out that people's economic behavior when facing uncertainty differs significantly f r o m that w h e n facing risk. This is the case because the uncertainty of an ambiguous lottery is more "uncertain" than the risk of an unambiguous lottery. T h e f o r m e r involves one more fold of indeterminateness—not even the chance of each payoff is yet identified. This "one more fold of i n d e t e r m i n a t e n e s s " in a m b i g u o u s lotteries and p e o ple's additional cautiousness in evaluating them are missing in the traditional models. Box 1 Expected Value and Variance of an Unambiguous Lottery A lottery is represented by its r a n d o m p a y o f f — s a y , X. Denote the possible values of X by . . . , xn) and their corresponding probabilities by (pv . . . , pn). Its expected value, denoted by E[X], is then E[X]=xlP]+...+xnPn. Its variance, which measures the average deviation of the payoff f r o m its expected value, is VAR[X] = (xx - E[X\fpx 14 + . . . + (xn - Econom ic Review E[X})2pn. Recent developments in decision theory have laid a foundation for more appropriate techniques for evaluating ambiguous lotteries. One example is the theory by Gilboa and Schmeidler (1989). Evaluation techniques based on such theories have provided a tool for modeling economic situations that involve ambiguous inform a t i o n . 4 T h e f o l l o w i n g section r e v i e w s traditional decision theory and then investigates ways in which the new developments in decision science capture information ambiguity and Knightian uncertainty, along with their potential applications in financial markets. Evaluating a Lottery in the Orthodox Theory As stated above, orthodox decision theory approaches both lottery types in similar ways based on the assumption that an agent can always have a unique guess about the chances for payoffs of an ambiguous lottery. The following discussion illustrates the evaluation techniques for both types of lotteries. An U n a m b i g u o u s Lottery. Consider lottery A in Table 1 as an example. Its evaluation rule is the answer to the following question: How much money (at most) is one willing to pay f o r this lottery? The (highest) price one is willing to pay for a lottery is called its certainty equivalent. (It may also be defined as the lowest price for which one is willing to sell it. The two definitions are the same.) O n e question is whether the certainty equivalent of this lottery is equal to the expected value, which is the sum of the possible p a y o f f s of the lottery, each weighted by its chance of occurring (its probability) (see Box 1). For this lottery, it is $1(1/3) + $0(2/3) = $1/3. This is an intuitively sensible conjecture because the expected value is s o m e h o w related to the " a v e r a g e value." If one could play the lottery repeatedly, then the average p a y o f f — t h e sum of all the payoffs divided by the number of repetitions—would indeed approach the expected value $1/3, with a very small error. The more one plays, the more likely one is to get a small error. Therefore, a price of $1/3 would let one "break even on average" in the long run. However, this argum e n t is b a s e d on the a s s u m p t i o n that lottery A is played repeatedly. What if there is not the chance to r e p e a t ? A m o d i f i e d j u s t i f i c a t i o n is as f o l l o w s : A l though one m a y not play the same lottery repeatedly, July/August 1994 playing many different and independent lotteries may also allow one to "break even on average" if the price for each lottery is set at its expected value (see Box 2). While this evaluation rule seems sensible, two important points are missing. First, the fluctuation of a lottery's payoff should discount its value because of one's limited ability to incur losses. For example, if not for a limited ability to incur losses, one could get rich by hanging around in Las Vegas with a simple strategy: Start betting an arbitrary amount—say, $100; for the next bet, wager twice (or a million times if one is greedy) as much as was lost previously; and stop as soon as one wins. (Restart the cycle to win even more money.) However, gamblers often go broke because they do not have an unlimited ability to incur losses before they get rich. This premise underlies the " G a m bler's R u i n " (Morris H. DeGroot 1987, 82). Second, and m o r e important to this discussion, is that people dislike uncertain situations because of not only their limited ability to incur losses but also their tendency to prefer sure gains—as the saying goes, " a bird in the hand is worth two in the bush." Suppose you are given the choice b e t w e e n t w o alternatives: Take $10 million and walk away, or play a lottery similar to lottery A in Table 1—call it A ' — f o r which you could win $30 million for drawing a red ball and $0 f o r d r a w i n g a black or y e l l o w ball. W h i c h o p t i o n would you prefer? If you are like the majority of peo- pie, you prefer the first option, even though the expected value of lottery A* is also $ 1 0 million. T h e price you are willing to pay for lottery A* must therefore be less than $10 million. In general, the tendency for people to discount a lottery f r o m its expected value is called risk aversion. The problem is how to redefine the certainty equivalent to reflect risk aversion. The potential fluctuation of the payoff of a lottery needs to be incorporated. A natural measure of the fluctuation is the variance of the lottery payoff, which is the average deviation of the payoff f r o m its expected value. For lottery A, the variance is introduced as follows. If the ball drawn is red (with one-third chance that it will be), the actual payoff is $1, and the difference of this payoff from the expected value $1/3 is $1 - $1/3; if black or yellow (with two-thirds chance), the actual payoff is $0 and the difference is $0 - $1/3. When the differences are summed, each term being weighted by its chance, the result is ($1 - $ l / 3 ) ( l / 3 ) + ($0 - $ l/3)(2/3) = $0, which is not a good measure of the fluctuation because the positive deviation cancels the negative deviation. To correct this cancellation, sum up the squared differences, each term being weighted by its chance, to get ($1 - $ l / 3 ) 2 ( l / 3 ) + ($0 - $l/3) 2 (2/3) = $2/9, Box 2 Break Even on Average C o n s i d e r u n a m b i g u o u s lotteries that are i n d e p e n - which is called the variance of lottery A. The bigger the variance, the riskier the lottery is. 5 Given this intuition, one way to model the certainty equivalent of a lottery may be dent of each other. S u p p o s e the r a n d o m payoff for lottery 1 is X,, for lottery 2 is X 2 , . . . , and for lottery n is Certainty Equivalent = Expected Value - C x Variance, Xn. T h e average of the random payoffs, (X 1 + X2+...+X>, is distributed around the average of their expected values, (£[X1]+£[X2l + . . . + £[XJ)/;i, with a small variance, (VAR\X] 1 + VAR\X2\ + ... + VAR[Xn])/n\ that is of m a g n i t u d e l/n and approaching zero as n bec o m e s big. T h e a v e r a g e p a y o f f for playing the s a m e lottery n times exhibits the s a m e properties. Federal Reserve B a n k of Atlanta where C is a positive coefficient. The bigger the coefficient C, the more risk averse the agent is. For example, if the coefficient C is equal to 3/4, the agent will assign a certainty equivalent of $1/6 to lottery A because $1/3 - (3/4)($2/9) = $ 1 / 6 — t h a t is, he or she thinks lottery A is worth $1/6. One step remains in completing the evaluation rule. What is the remaining problem? Recall the two lotteries A and A*, both contingent on the result of drawing a ball f r o m the s a m e urn, the only d i f f e r e n c e being that one has possible payoffs of $1 and $0 and the other has possible p a y o f f s of $30 million and $0. Intuitively, an agent is more risk averse in regard to lottery A* b e c a u s e the p a y o f f is m u c h b i g g e r . G e n e r a l l y speaking, attitudes toward risk change with the wealth Economic Review 15 Box 3 Evaluating an Unambiguous Lottery with a Utility Function It is a s s u m e d that a payoff gives an agent a certain level of satisfaction, called utility. Mathematically, utility is represented as a function of p a y o f f , called the utility function. S u p p o s e a lottery X has possible p a y o f f s (A,, . . . , xn) with probabilities (pv . . . , pn) and U(x) is the utility level of an agent w h e n payoff x is received. T h e n the certainty equivalent of lottery X is a price P such that U(P)=piU(xl) + ...+pnU(xn.) = E[U(X)l w h e r e E[U(X)] is called the expected utility of lottery X. On the basis of its expected utility, a lottery is ranked. In other w o r d s , w h e n an a g e n t ' s action d e t e r m i n e s w h i c h lottery she will have, she chooses an action such that the ensuing lottery yields the highest expected utility. T w o properties are usually attributed to a utility f u n c tion. O n e is that it is increasing in p a y o f f — t h a t is to say, involved. The above evaluation rule is cumbersome in representing such changes b e c a u s e its only f r e e parameter is the coefficient C—that is, because higher risk aversion is represented by a higher value of C, the v a l u e of C m u s t be a d j u s t e d as an a g e n t ' s attitude changes with wealth level. If this is the case, C is no longer a constant, which is not a very convenient factor for analysis. This scenario motivates the expected utility theory, which is a natural generalization of the above evaluation rule. Interested readers are referred to Box 3 for a brief illustration of the theory. An Ambiguous Lottery. Lottery B in Table 1 is an e x a m p l e of an a m b i g u o u s lottery. B e c a u s e all the chances for the payoffs are not known, the techniques developed for unambiguous lotteries are not directly applicable. However, a simple trick bridges the gap: A s s u m e that an agent has a unique guess about the number of black or yellow balls in the u r n — o n e black ball and five yellow balls, for example. Using the techniques for unambiguous lotteries, the agent computes the certainty equivalent on the basis of the ball combination as guessed. With this approach, lottery B is the same as an unambiguous lottery. There is, of course, one question that must be answered in order to complete such an evaluation rule: What is the relationship between the ball combination as guessed by the agent and the true ball combination in the urn? Current economic theory assumes a blunt answer: They are identical. What, then is the justification for such an assumption? 16 Econom ic Review a higher payoff gives higher satisfaction, w h i c h is a reasonable statement. T h e other is that a utility function inc r e a s e s at a d e c r e a s i n g rate: f o r e x a m p l e , $ 2 0 m i l l i o n gives m o r e satisfaction than $ 1 0 million but not twice as much. T h i s latter property ensures that an agent discounts a lottery f r o m its expected value, which is a generalized representation of risk aversion. A m o n g its many niceties, this representation allows for risk aversion to c h a n g e with wealth. In the context of this article, the f o r m u l a for c o m puting the certainty equivalent P of lottery X: P = E[X] - C Var[X], is an a p p r o x i m a t i o n of the e x p e c t e d utility theory in a special c a s e ( C h i - f u H u a n g and R o b e r t H . Litzenberger 1988, 59-62). Answer A: The agent learns through time. As the balls are drawn from the urn again and again, the agent modifies her guess, which gradually approaches the true ball combination. This answer essentially ignores the fact that there are cases in which balls m a y not have been drawn repetitively before. Consider a new firm, for example, that issues stock to raise capital. O n e m a y not have enough information to figure out the chance for each of its possible dividend levels. To determine the price of the stock, one is essentially dealing with an ambiguous lottery. The above argument simply ignores that such cases exist. Answer B: People who have a "wrong" guessed ball combination in mind will be weeded out by competition from those who happen to have the "correct" guess. Therefore, models with all agents having the "correct" guess in mind represent the essence of the economic world. I n r e a l i t y , t h e m i s m a t c h of t h e guessed ball combination and the true ball combination will not necessarily lead one to ruin. O n e possible scenario is that agents with " w r o n g " guesses m a y distort market prices to such an extent that agents with "correct" guesses may be intimidated, constrained by financial ability to rectify the distortion or by time limitations on outwaiting the distortion, and the incorrect guessers remain alive and well in the markets. Moreover, the " w r o n g " guessers m a y earn higher average return by bearing the additional risk of the price distortion they have created (J. B r a d f o r d D e L o n g and others 1990). In other words, the agents with " w r o n g " July/August 1994 guesses—in traditional theory called "irrational" market participants—will not necessarily be weeded out. In summary, the evaluation rule for an ambiguous lottery in the traditional decision theory consists of two points: (1) A rational agent forms a unique guess of how many balls of each color are in the urn and computes the certainty equivalent of the lottery based on the guess (Savage 1954). (2) The guess is always correct. Practically speaking, this evaluation rule has denied the need to distinguish an ambiguous lottery from an unambiguous lottery since "the guess is always correct." However, as the Ellsberg paradox demonstrates, the above techniques for evaluating an ambiguous lottery are not consistent with m o s t p e o p l e ' s c h o i c e s . This inconsistency motivates revising the orthodox decision theory. 6 A New Approach to Evaluating an Ambiguous Lottery O n e such revision features Knightian uncertainty and resolves the Ellsberg paradox. F r o m the discussion in the first section, it is clear that any model with a single g u e s s e d ball c o m b i n a t i o n will not achieve this goal. Furthermore, it is observed that the ambiguous lotteries, B and A ' , are inferior w h e n the other conditions are "comparable" to their respective unamb i g u o u s counterparts, A and B ' . With this intuition gained from the example of the nine-ball urn, it may be conjectured that an agent has several guessed ball combinations in mind instead of a unique one and uses one of the guessed ball combinations to compute the certainty equivalent of e a c h a m b i g u o u s lottery. T h e choice of the guessed ball combination m a y vary for different lotteries and reflect the c o m m o n sense of "playing it s a f e " — t h a t is, the agent picks a guessed ball combination that provides a conservative evaluation of each lottery. Gilboa and Schmeidler (1989) have formalized the theory of such a modification (see Box 4). They have proposed a set of rules that a rational agent may have f o l l o w e d in e v a l u a t i n g l o t t e r i e s , and the r u l e s are e q u i v a l e n t t o c l a i m i n g that an a g e n t h a s m u l t i p l e guessed ball combinations in mind and evaluates an ambiguous lottery conservatively: The agent evaluates it according to the " w o r s t " guessed ball combination to get the "lowest certainty equivalent." A s risk aversion is the tendency to discount the certainty equivalent of an unambiguous lottery f r o m its expected value because of the indeterminateness of its payoff, the ad- Federal Reserve Bank of Atlanta ditional discount for an ambiguous lottery in the above evaluation rule is called uncertainty aversion. Without detailed mathematical derivations, the example of the Ellsberg paradox can help provide an intuitive illustration of the theory. It is plausible to suggest that an agent has seven guessed ball combinations in mind: the first one with no black balls and six yellow balls, the second one with one black ball and five yellow balls, and so on. When making choices, the agent will pick one f r o m among the seven guessed ball combinations and treat it as if it were the true ball combination. Which ball combination is picked for evaluating each of the lotteries A, B, A ' , and B'? To be consistent with the behavior of most people, the rule supposes that the agent "plays it safe." That is to say, the agent thinks about the worst scenario and acts as if that were the case (Table 3). The worst case for lottery B is to be evaluated with the guessed ball combination that has no black balls and six yellow balls. The agent therefore should calculate the certainty equivalent of lottery B with this guessed ball combination. For lottery A, the seven guessed ball combinations give the same certainty equivalent, which is higher than the worst case for B. For this reason, the agent prefers A to B. The worst scenario for lottery A ' is to be evaluated with the guessed ball combination that has no yellow Box 4 Expected Utility Theory with Multiple Priors and the Maxmin Rule Gilboa and Schmeidler (1989) propose a set of rules that a rational agent may have followed in evaluating ambiguous lotteries. Their rules are equivalent to the following claim: The agent has a utility function U(x), where x is the payoff, and multiple subjective probabilities, denoted by jc,, . . . , %n, which form a set II. The certainty equivalent of lottery X is a price P such that U(P)=MINnenE[U(X)\n]. The essence of this evaluation rule is that an agent is conservative when information is ambiguous, which is to say that he or she reacts with uncertainty aversion. When choosing among different lotteries, an agent will pick the one with the maximum certainty equivalent. The choice is determined by the solution of MAX MINnenE[U(X)\n], which is the so-called maxmin rule. Economic Review 17 balls and six black balls. This guessed ball combination should be used to compute the certainty equivalent for lottery A ' . For lottery B ' , the seven possible g u e s s e d ball c o m b i n a t i o n s give the s a m e certainty equivalent, which is higher than the worst case for A'. The agent's preference, therefore, is for lottery B'. This illustration demonstrates how a theory of multiple guessed ball c o m b i n a t i o n s plus the "playing it safe" rule explains the typical choice pattern. As a result, the Ellsberg paradox is resolved. The next point to b e addressed is the relationship between the guessed ball c o m b i n a t i o n s and the true ball combination. It is assumed that, in most economic applications, the guessed ball combinations of a rational agent " m a t c h " the true ball combination in the following way: A m o n g the guessed ball combinations, there is one that is identical to the true ball combination. This assumption reflects the idea that a rational agent m a y not be able to weed out all the incorrect guessed ball c o m b i n a t i o n s w h e n information is a m biguous, but she does not want to miss the true ball combination that serves as the grain of truth buried among the guessed ball combinations. A s an example, in the nine-ball urn game, the agent's seven guessed ball combinations include the true ball combination. T h e assumption does not require that agents always i n c l u d e all the p o s s i b l e ball c o m b i n a t i o n s in their Table 3 Resolving the Ellsberg Paradox Evaluating Lotteries w i t h M u l t i p l e Guesses Red Yellow Black 3 balls 6 balls $1 $0 ( U n a m b i g u o u s ) Lottery A 3 balls 0 balls 6 balls $0 $1 $0 3 balls 6 balls 0 balls $1 $0 $1 ( A m b i g u o u s ) Lottery B ( A m b i g u o u s ) Lottery A ' 3 balls 6 balls $0 $1 ( U n a m b i g u o u s ) Lottery B' W i t h a "safe" guess for e a c h lottery, it f o l l o w s that A is preferred to B a n d B' is preferred t o A ' . 18 Econom ic Review guesses, as in the above example, nor does it m e a n that there is no chance that agents miss the true ball combination. Instead, the idea is that in most economic situations, most agents will have a reasonably wide band of guesses that contains the true ball combination, leaving only an insignificant n u m b e r of agents having too narrow a band of guesses and missing the true ball combination (see Box 5). The new rule for evaluating an ambiguous lottery is s u m m a r i z e d as f o l l o w s : (1) A rational a g e n t f o r m s multiple guesses about the ball combination, picking the "worst" one to compute the certainty equivalent of the lottery. (2) T h e set of guessed ball combinations contains the true ball combination. Some Applications of Information Ambiguity Economists keep modifying their theories in attempts to better match empirical observations and predict future outcomes. Introducing the idea of information ambiguity is such an example. It will be useful to review some applications of the concept and consider how it aids in the understanding of financial markets. A financial asset, say, a bond or a stock, is a legal contract that entitles its owner to one of a set of possible payoffs or payoff streams contingent upon the future outcomes of some uncertain factors, such as the state of the economy, the performance of the firm, the overall demands in the financial markets, and so on. As economists compare uncertainties in the economic world to uncertainties in gambling games, a financial asset is likened to a lottery. The models for pricing a financial asset therefore are based on techniques for evaluating a lottery, as discussed above. An u n a m b i g u o u s lottery m o d e l s a financial asset whose fundamental value has a known chance for each possible level—that is, each uncertain economic variable contributing to the f u n d a m e n t a l value has been repeatedly observed before and its outcomes have exh i b i t e d c e r t a i n f r e q u e n c i e s . An a m b i g u o u s lottery models a financial asset whose fundamental value is determined by uncertain economic variables that have not been repeatedly observed before. Such economic variables c o m m o n l y exist given that repetitive observations of an economic variable are feasible only if the variable persists in the economy, and many uncertain variables like political shocks are unique, by nature denying repetitive observations. O n e example is the opening of the East European market after the Berlin July/August 1994 Box 5 Too Conservative or Not? O n e may suspect that an agent is being perhaps overly conservative in choosing the worst a m o n g the seven possible ball combinations to evaluate the lotteries. In other words, does the theory proposed by Gilboa and Schmeidler (1989) allow d i f f e r e n t i a t i n g d e g r e e s of uncertainty aversion? T h e answer is yes. T h e theory a c c o m m o d a t e s differential c o n s e r v a t i v e ness by varying the n u m b e r of guessed ball combinations. For example, if another agent is less uncertainty averse, h e may shrink his guesses to three ball combinations: the f i r s t is that t h e r e are t w o b l a c k balls a n d f o u r y e l l o w balls; the second, three black balls and three yellow balls; and the third, f o u r black balls and t w o yellow balls. This Wall crumbled. Other uncertain factors that appear to persist may in fact have to be viewed differently because of the evolution of environments. For example, as the structure of the financial markets has changed, the monetary policy of the Federal Reserve today may not be treated as the same variable it was fifteen years ago. Two caveats should be stated. First, as observed earlier, there are several decision theories that differ slightly in their mathematical formulations, but all essentially aim to capture the notion of information ambiguity. For the purposes of this discussion, the application examples presented here are demonstrated using the decision theory of Gilboa and Schmeidler (1989). Any of the others might have served as well. Second, each of the problems discussed below is a research area in and of itself. There may be other theories that provide alternative or complementary answers to the issues raised. It is not the intent of this paper to survey those areas, however, so the discussion will be limited to an intuitive illustration of plausible explanations based on information ambiguity. U n d e r p r i c i n g of Initial P u b l i c O f f e r i n g s . It is an empirical fact that most assets exhibit higher-thanaverage return after their initial public offerings. In other words, they are usually underpriced when initially offered (see Roger Ibbotson 1975). This pricing is inconsistent with efficient markets theory, which predicts that any such abnormally low prices would be arbitraged away. Keuk-Ryoul Yoo (1990) explains this puzzle by o b s e r v i n g that o u t s i d e investors u s u a l l y view a new asset as an ambiguous lottery because they lack knowledge about its historical returns. When they Federal Reserve B a n k of Atlanta a g e n t ' s evaluations of the a m b i g u o u s lotteries B and A ' will be higher than those of the previous agent. H o w e v e r , the choice pattern of " A is preferred to B and B ' is preferred to A " ' is still explained. O n e m a y question whether the a g e n t ' s three guessed ball combinations include the true ball combination. The a n s w e r is, n o t necessarily. H o w e v e r , t h e a s s u m p t i o n is that the g u e s s e d ball c o m b i n a t i o n s d o i n c l u d e the true ball combination because in most cases it is reasonable to believe that most people are uncertainty averse to such an extent that their set of guesses is w i d e e n o u g h to cover the true ball combination. T h a t is to say, this assumption represents the essence of most e c o n o m i c situations. evaluate it, they tend to follow a conservative approach by underpricing it. After the asset is issued, people acquire more information, ambiguity declines, and the price rebounds. Price Crashes. Any standard finance textbook is likely to include the statement that the price of a financial asset is determined by information about its fundamental value in such a fashion that no price drop is possible without commensurate adverse news (see, for e x a m p l e , Huang and L i t z e n b e r g e r 1988). T h e price crash of 1987, a m o n g other less d r a m a t i c ones, has challenged this theory. Jie Hu (forthcoming) demonstrates the plausibility of price crashes in terms of information ambiguity. Being an ambiguous lottery, an asset can be overvalued when a marketmaker is dealing with more buy orders than sell orders in a bull market, and in turn it can be undervalued when the marketmaker deals with m o r e sell orders than buy orders in a bear market. 7 Deep in a bull market, if trade orders due to liquidity d e m a n d s fluctuate such that the overall orders switch f r o m net demand to net supply at a point in time, then the asset price will fall from its overvalued level to its undervalued level. Such discontinuous price drops do not necessarily require any bad news as a catalyst and therefore can provide a plausible cause for price crashes. Volatility of Asset Prices. According to the standard representation of e f f i c i e n t m a r k e t s theory, the price volatility of a financial asset cannot exceed the volatility of its fundamental value. This observation is not consistent with empirical findings, however (see S t e p h e n F. L e R o y 1989, f o r e x a m p l e ) . J a m e s D o w and Sergio Ribeiro da Costa Werlang (1992), Larry Economic Review 19 Epstein and Tan Wang (1994), and Hu (1993) demonstrate that information ambiguity can cause the excess price volatility. Consider a marketmaker who executes trade orders with a price schedule with "positive slope." (A bigger buy order is executed at a higher unit price, or, equivalently, a bigger sell order is executed at a lower unit price). The steeper the price schedule, the more sensitive the price is to demand fluctuations, and the more volatile the price is. Information ambiguity increases the slope of the price schedule. The reason the price schedule is positively sloped is that higher asset value leads to higher demand f r o m better-informed traders and therefore higher overall demand, which warrants a higher price. Because it is fluctuation in the f u n d a m e n t a l value that drives the fluctuation of i n f o r m e d t r a d e r s ' d e m a n d , it follows that the price volatility should be proportional to the fundamental value volatility. However, when the f u n damental value of a financial asset is ambiguous, the m a r k e t m a k e r will "play it s a f e " by exaggerating his own information disadvantage. The result is a steeper price schedule than might be expected—and a m o r e volatile price. Trading Caused by Information Release. Traditional theory claims that neither public nor private information causes trading among rational people if they agree on the interpretation of information and the portfolios are balanced before the information has arrived 1. The British economist G.L.S. Shakle (1955) developed a theory of choice based on nonprobablistic descriptions of uncertainty. While similar in spirit to Knightian uncertainty, this theory has yet to gain wide acceptance. 2. Others include Bewley (1986), Gilboa (1987), and Schmeidler (1989). No judgment is implied about the relative virtues of the various decision theories. For a survey, see Camerer and Weber (1992). 3. A probability distribution is simply a listing of all possible outcomes of a lottery with their probabilities of occurring. 4. Hart (1974) establishes the conditions necessary for choice theories, such as the ones discussed here, to be consistent with financial market equilibrium. 20 Econom ic Review (see Paul Milgrom and Nancy Stokey 1982, for example). However, high trading volume observed around corporate announcement dates contradicts that statement (see William Beaver 1968, 91). Dow, Vicente Madrigal, and Werlang (1990) resolve the problem by considering information ambiguity. They reason that the return on a financial asset may be ambiguous and featured by multiple probabilities. New information may resolve the ambiguity, and when it does so there is portfolio rebalancing among investors. Conclusion W h i l e risk is the i n d e t e r m i n a t e n e s s f e a t u r e d by probabilistic information, Knightian uncertainty is the i n d e t e r m i n a t e n e s s f e a t u r e d by a m b i g u o u s i n f o r m a tion. Information ambiguity exists widely in the economic world, and Knightian uncertainty has profound e f f e c t s o n e c o n o m i c b e h a v i o r . H o w e v e r , the e c o nomics profession has ignored the significance of inf o r m a t i o n a m b i g u i t y until very recently. T h e m a t h ematical representation of information -ambiguity is only in its developmental stage, but applying the concept of information ambiguity to analysis has already yielded new and useful insights into many economic phenomena. 5. Variance measures the tightness of spread of a probability distribution around its expected value and is used extensively in finance as a measure of risks. 6. For an application of the orthodox theory to the forecasts of corporate earnings made by security analysts, see Ackert and Hunter (forthcoming). For a theoretical explanation of how "irrational" security analysts are able to remain gainfully employed while making inaccurate forecasts of corporate earnings, see Ackert and Hunter (1994). 7. When a marketmaker expects to end up with net sales of an ambiguous asset, she will set the price at the high end for protection. The opposite happens in a bear market. J u l y / A u g u s t 1994 References Ackert, Lucy F., and William C. Hunter. "Rational Expectations and Security Analysts' Earnings Forecasts." Financial Review (forthcoming). . "Rational Expectations and the Dynamic Adjustment of Security Analysts' Forecasts to New Information." Journal of Financial Research 17 (Fall 1994): 387-401. Beaver, William. "The Information Content of Annual Earnings Announcements." Empirical Research in Accounting, supplement to Journal of Accounting Research 6 (1968): 67-92. Bewley, Truman. "Knightian Decision Theory: Part I." Cowles Foundation Discussion Paper No. 807, 1986. Camerer, Colin F., and Martin Weber. "Recent Developments in M o d e l i n g P r e f e r e n c e s : Uncertainty and A m b i g u i t y . " Journal of Risk and Uncertainty 5 (1992): 325-70. DeGroot, Morris H. Probability and Statistics. Reading, Mass.: Addison-Wesley, 1987. De Long, J. Bradford, Andrei Shleifer, Lawrence H. Summers, and Robert J. -Waldmann. "Noise Trader Risk in Financial Markets." Journal of Political Economy 98, no. 4 (1990): 703-37. Dow, James, Vicente Madrigal, and Sergio Ribeiro da Costa Werlang. "Preferences, Common Knowledge, and Speculative Trade." Fundacao Getulio Vargas Working Paper No. 149, 1990. Dow, James, and Sergio Ribeiro da Costa Werlang. "Excess Volatility of Stock Prices and Knightian Uncertainty." European Economic Review 36 (1992): 631-38. Ellsberg, Daniel. "Risk, Ambiguity, and the Savage Axioms." Quarterly Journal of Economics 75 (1961): 647-69. Epstein, Larry, and Tan Wang. "Intertemporal Asset Pricing under Knightian Uncertainty." Economeirica 62 (March 1994): 283-322. Gilboa, Itzhak. "Expected Utility Theory with Purely Subjective Non-Additive Probabilities." Journal of Mathematical Economics 16 (1987): 65-88. Federal Reserve B a n k of Atlanta Gilboa, Itzhak, and David Schmeidler. "Maxmin Expected Utility with Non-Unique Prior." Journal of Mathematical Economics 18 (1989): 141-53. Hart, Oliver D. "On the Existence of Equilibrium in a Securities Model." Journal of Economic Theory 9 (1974): 293311. Hu, Jie. "Excess Return, Excess Volatility, and Negative Autocorrelation Caused by Uncertainty Aversion and Risk Aversion." Federal Reserve Bank of Atlanta W o r k i n g Paper 93-16, December 1993. . "Market Breakdowns and Price Crashes Explained by Information Ambiguity." Federal Reserve Bank of Atlanta working paper, forthcoming. Huang, Chi-fu, and Robert H. Litzenberger. Foundation for Financial Economics. New York: Elsevier Science Publishing, 1988. Ibbotson, Roger. "Price Performance of Common Stock New Issues." Journal of Financial Economics (1975): 235-72. Knight, Frank. Risk, Uncertainty, and Profit. Boston: Houghton Mifflin, 1921. LeRoy, Stephen F. "Efficient Capital Markets and Martingales." Journal of Economic Literature 27 (1989): 1583-1621. Milgrom, Paul, and Nancy Stokey. "Information, Trade, and C o m m o n K n o w l e d g e . " Journal of Economic Theory 26 (1982): 17-27. Savage, Leonard J. Foundation of Statistics. New York: John Wiley and Sons, 1954. Schmeidler, David. "Subjective Probability and Expected Utility without Additivity." Econometrica 57 (May 1989): 571-87. Shakle, G.L.S. Uncertainty in Economics. Cambridge: Cambridge University Press, 1955. Yoo, Keuk-Ryoul. "A Theory of the Underpricing of Initial Public O f f e r i n g s . " Northwestern University. Photocopy. 1990. Economic Review 21 FYI Commercial Bank Profits in 1993 W. Scott Frame and Christopher L. Holder M ^ m M m — ^ ^ m • The authors are economic analysts in the financial section of the Atlanta Fed's research department. They gratefully acknowledge comments from Sheila Tschinkel, Frank King, Bobbie McCrackin, Larry Wall, Aruna Srinivasan, and Hugh Cohen. They thank S her ley Wilson for research assistance. 22 Econom ic Review rofitability of c o m m e r c i a l b a n k s in the United States reached postwar records in 1993, building on the earnings improvements achieved in 1992. Banks in the Southeast enjoyed a similar performance. These unusually high profits allowed banks to continue to add significantly to their capital positions. The growth in earnings resulted primarily f r o m a decline in loan-loss provisions, which f u r t h e r widened adjusted net interest margins. 1 (Tables 1 and 2 provide interest margin and loan-loss data on the nation's banks for the years 1989 through 1993). This decline was a result of banks' portfolios improving in concert with the U.S. economy as a whole, the disappearance of many problem institutions, and years of charge-offs. 2 Increases in loan growth, net noninterest revenue, and gains from securities sales also boosted the industry's 1993 record net income (see Tables 3-7). The uncommonly high earnings achieved by U.S. commercial banks during the past two years have been a direct result of a favorable banking climate. Macroeconomic factors and a relatively steep yield curve have provided the best conditions for high profitability in more than a decade. Falling interest rates in 1993, coupled with declining provisions for loan losses, widened banks' interest margins. However, future interest rate increases could reduce earnings. July/August 1994 2?ank Profitability Measures The two primary profitability ratios, return on assets (ROA) and return o n equity ( R O E ) , reflect the large increase in net income (5.75 percent) enjoyed by banks in 1993. (See Tables 8 and 9. A detailed discussion of the various profitability measures and their significance can be found in Box 1.) B a n k s ' ROA increased to 1.23 percent in 1993 from 0.95 percent in 1992, and R O E rose to 15.78 percent f r o m 13.24 percent. The improvement in ROE lagged slightly behind g r o w t h in R O A b e c a u s e b a n k s used s o m e of their profits to improve their capital ratios. 3 While banks of all sizes a c h i e v e d h e a l t h y g a i n s , the largest b a n k s ( t h o s e with assets e x c e e d i n g $1 b i l l i o n ) m a d e the greatest advances in profitability. T h e i m p r o v e m e n t in b a n k s ' a d j u s t e d net interest margin from 1992 to 1993 can be attributed primarily to declining loan-loss expenses. Three additional factors led to improvements in net income in 1993: interest e x p e n s e s fell m o r e than interest revenues; gains f r o m securities sales r e m a i n e d close to historically high levels (although down from 1992); and noninterest revenues continued to grow. (While noninterest expenses remained higher than noninterest revenue, the gap narrowed in 1993.) - Provision for Loan and Lease Losses. Bank credit quality continued to improve rapidly in 1993 as a result of three factors. The first was the sustained U.S. economic expansion. A second factor was the disappearance of many weak institutions through mergers and failures. The n u m b e r of U.S. commercial banks fell from 12,493 at the end of 1989 to 10,892 as of December 31, 1993, a net loss of 1,601 institutions. The Federal Deposit Insurance Corporation (FDIC) was involved in 6 6 0 bank closings and assistance transactions during this four-year period. A third factor that led to improved credit quality in 1993 was that many problem loans had been purged f r o m banks' balance sheets during the previous few years. A s the condition of the b a n k i n g i n d u s t r y h a s i m p r o v e d , b a n k s h a v e needed to put aside less for future bad loans, leading to increased profits. In 1993 total provisions for loan and lease losses declined 36.38 percent f r o m the 1992 level. Table 2 shows that commercial b a n k s ' loan-loss provisions as a percentage of interest-earning assets fell to 0.53 percent ( f r o m 0.88 percent in 1992 and 1.17 percent in 1991). While the nation's largest banks still set aside the greatest percentage of their assets for loan losses (0.61 percent), they posted the most impressive de- Federal Reserve Bank of Atlanta cline in loan-loss provisions and a c c o u n t e d for the bulk of the 1993 reduction (in dollar terms) of loanloss expenses. Preliminary figures for the first quarter indicate a continued decrease in loan-loss provisions during early 1994. Intermediation. Yields for U.S. Treasury securities fell across the board in 1993, resulting in a slightly less steep yield curve (see Chart 1). The effect of this r e d u c t i o n in m a r k e t i n t e r e s t r a t e s w a s s m a l l e r f o r b a n k s ' interest r e v e n u e s , w h i c h d e c r e a s e d by 3.97 percent, than for interest expenses, which fell 13.17 percent. However, with the rapid g r o w t h in interest earning assets (up 5.72 percent in 1993), the interest margin (excluding loan-loss provisions) actually narrowed. In other words, while the margin on interest earning assets fell, the v o l u m e increased, adding to Profitability of commercial banks in the United States reached postwar records in 1993. 1993 net income (see Tables 1 , 3 , and 4). The 5.72 percent increase in interest earning assets was the largest in seven years, reflecting the first increase in net loans since 1990. (Commercial bank balance-sheet developments for U.S. and southeastern banks during 1993 are shown in Box 2.) I n t e r e s t e a r n i n g s o n c o m m e r c i a l and i n d u s t r i a l loans and interest and dividend income on U.S. Treasury securities and U.S. government agency and corp o r a t i o n o b l i g a t i o n s d e c l i n e d m o s t in p e r c e n t a g e terms. 4 The largest factor in b a n k s ' 1993 decline in interest expenses was a reduction of interest paid on deposits (which fell by 23.04 percent from 1992 levels), due to both declining interest rates and a shift by banks toward the use of less costly deposit accounts, such as transaction accounts and m o n e y market deposit accounts ( M M D A s ) (see Table 10). Lower interest rates have reduced the opportunity costs associated with holding cash balances in these types of accounts. Economic Review 23 Chart 1 Yield Curve for U.S. Treasuries Source: Federal Reserve Bulletin, Table 1.35; three-month bill adjusted to bond equivalent. In addition, n o n e a r n i n g c o m p e n s a t i n g b a l a n c e s increased during 1993. Banks responded to a steepening and falling yield curve in 1992 by cutting interest expense (per dollar of assets). Table 4 shows that this trend continued in 1993. S e c u r i t i e s G a i n s . B a n k s h a v e d r a m a t i c a l l y increased their securities holdings in recent years, particularly of U.S. Treasury securities and U.S. government agency and corporate obligations. 5 In 1993 banks continued to take advantage of declining interest rates by selling securities previously acquired at higher rates. 6 However, as Table 5 shows, pretax gains from the sale of securities (per dollar of assets) decreased by onethird from record 1992 levels. Still, gains from securities sales r e m a i n n e a r h i s t o r i c a l l y h i g h levels and contributed to high earnings in 1993. In addition, banks held large amounts of unrealized capital gains at the end of 1993, which could be used to help profitability in the f u t u r e . 7 Interest rate increases in early 1994, however, have reduced these unrealized gains, as well as those expected from securities sales this year. Noninterest Income. Increases in activities generating fee income have been a long-term trend in the banking industry. 8 A more competitive lending environment and information and technology changes have 24 Econom ic Review prompted banks to use fee income to replace lower interest revenues. While noninterest expenses continued to be larger in dollar terms than noninterest revenues, b a n k s of all sizes continued to reduce this g a p last year. In 1993 b a n k s increased their noninterest revenue an average of 14.28 percent f r o m 1992 levels (see Table 6); gains and fees from assets held in trading accounts (up 107.39 percent), other fee income (up 9.43 percent), and other noninterest income (up 20.42 percent) accounted for most of the gain. The nation's largest banks continue to record the highest levels of noninterest income (2.34 percent of assets in 1993), reflecting the greater array of fee-based products and s e r v i c e s they o f f e r . Total n o n i n t e r e s t e x p e n s e rose modestly in 1993, up 6.59 percent over 1992 levels, with the increase evenly divided among several categories (see Table 7). Capital Improvements Banks have been adding significant capital to their balance sheets since the late 1980s. Total equity capital at banks rose f r o m $203.7 billion on D e c e m b e r 31, July/August 1994 Box 1 Profitability Measures The three primary measures presented in this article to gauge bank performance are adjusted net interest margin, return on assets, and return on equity. Adjusted net interest margin is simply the difference between a bank's interest income (adjusted for tax-exempt securities earnings and loan-loss provisions) and interest expenses, divided by average interest-earning assets. This measure is similar to a business's gross profit margin except that sales of fee-based services by banks are not included.1 Return on assets, or the ratio of net income to average assets, demonstrates how profitably a bank's management is using the firm's assets. In contrast, return on equity, or the ratio of net income to average equity, tells a bank's shareholders how much the institution is earning on the book value of their investments. Analysts looking to compare profitability (while ignoring differences in equity capital ratios) generally focus on ROA, while those wishing to focus on returns to shareholders look at ROE. The three measures are defined as follows: Adjusted Net Interest Margin = Adjusted Interest Revenues - Interest Expense Return on Equity = Net Income Average Equity Capital Average interest-earning assets, consolidated assets, and equity capital are derived by averaging beginning-, middle-, and end-of-year balance-sheet figures. The bank data used in this article were taken from the federal bank regulators' quarterly Report of Condition and Income (Call Report) for insured domestic commercial banks. The sample consists of all banks that had the same identification number at the beginning and the end of the year. The number of banks in the 1993 sample is 10,892, a 4.20 percent decline from 1992. The number of banks in the six-state region defined as the Southeast was 1,565, a 2.43 percent decline from 1992. Note 1. Fee-based (noninterest) income is derived from deposit service charges, charges for letters of credit, and other bank-related activities. Average Interest-Earning Assets Return on Assets = Net Income Average Consolidated Assets 1989, to $295.1 billion at the end of 1993, an increase of 44.8 percent over the four-year period. Following the poor performance of U.S. commercial banks in the late 1980s, r e g u l a t i o n s initiated in the early 1990s have given banks particular incentive to increase their capital positions. New risk-based capital requirements divide assets into risk categories and require holding additional capital against the riskiest assets. In addition, the Federal Deposit Insurance Corporation Improvement Act (FDICIA) gave advantages to highly capitalized b a n k s and specified penalties, including closure, for banks with low capital levels. Creditors and stockholders also have required increased capital as a greater cushion against failure, in light of deposit insurance reform, which has shifted some risk f r o m the government to market participants. Federal Reserve Bank of Atlanta Distribution by Size and Condition Banks of all sizes and conditions again grew m o r e profitable in 1993, signaling broad strength within the industry. In analyzing 1993 bank profitability, a distribution ranking e a c h b a n k by R O A ( f r o m lowest to highest) was constructed, and banks representing the twenty-fifth, fiftieth, and seventy-fifth percentile were singled out. C o m p a r i n g these b a n k s ' 1993 r e t u r n s with those achieved in previous years d e m o n s t r a t e s the vast improvement by banks of all sizes and conditions (see Tables 11-13). T h e least p r o f i t a b l e b a n k s , in p a r t i c u l a r , m a d e tremendous strides, posting a 12.8 percent increase in ROA f r o m 1992 levels. T h e significant progress by Economic Review 25 banks in the twenty-fifth percentile indicates the viability of the least profitable institutions and may be p r i m a r i l y attributed to the d i s a p p e a r a n c e of m a n y problem institutions and an improvement in loan portfolios, as reflected by the significant across-the-board declines in loan-loss provisions. Banks in the Southeast Bank performance in the Southeast generally mirrored or exceeded that of banks nationwide (see Tables 14-28 for data on bank profitability in the Southeast). 9 In 1993 average ROA for all banks in the region rose to 1.26 percent, and average R O E climbed to 15.56 percent. Only Georgia banks posted declines in ROA Some profitability measures indicate that southeastern banks fared better in 1993, on average, than their peers across the United States. and R O E in 1993 after leading the region in ROA during 1992. G e o r g i a b a n k s ' profitability slid in 1993 p r i m a r i l y b e c a u s e t h e y c o n t i n u e d to e x p e n s e the greatest amount for loan losses. In contrast, Louisiana b a n k s realized large p r o f i t a b i l i t y g a i n s in 1993 as R O A and R O E led the r e g i o n at 1.73 p e r c e n t and 20.88 percent, respectively. L o u i s i a n a ' s r e m a r k a b l e improvement can be directly attributed to the state's negative loan-loss expense ratio of - 0 . 1 9 percent, an improving local economy, and the resolution of most p r o b l e m institutions. (Banks usually reduce current income to add to loan-loss reserves. However, L o u i s i a n a b a n k s , o n a v e r a g e , e n t e r e d 1993 with h i g h loan-loss reserves, and many took the unusual step of using e x c e s s l o a n - l o s s r e s e r v e s to i n c r e a s e net income.) S o m e profitability m e a s u r e s indicate that southeastern banks fared comparatively better in 1993, on average, than their peers across the United States. The 26 Econom ic Review adjusted net interest margin (as a percentage of interest-earning assets) was higher for banks in the Southeast, at 4.53 percent, than the national average of 4.02 percent. In addition, loan-loss expenses as a percent of a s s e t s d e c r e a s e d s u b s t a n t i a l l y in the S o u t h e a s t and remain well below the national average. T h e s e figures reflect the continued overall health of the region's banks. Noninterest revenues and expenses for the smallest and largest southeastern banks differed markedly f r o m comparable 1993 national averages. The Southeast's smallest banks were able to earn considerably more noninterest revenue (as a percent of assets) than their national counterparts primarily because of service charges on deposit accounts and other fee and noninterest income. 1 0 In contrast, the region's largest institutions generated noninterest revenues well below the national average because they relied less on off-balance-sheet activities (such as foreign exchange transactions and fiduciary activities) and other f e e inc o m e . All noninterest expense categories were above the n a t i o n a l a v e r a g e f o r the s m a l l e s t s o u t h e a s t e r n banks and below the national average for the largest institutions. 1 1 T h e viability of the S o u t h e a s t ' s smallest institutions h a s been q u e s t i o n e d in r e c e n t years b e c a u s e they had consistently u n d e r p e r f o r m e d (as m e a s u r e d by ROA and ROE) banks of similar size in the rest of the nation and larger banks in the region. 1 2 In 1993, however, R O A for the region's smallest banks rose sharply to 1.06 p e r c e n t , and R O E c l i m b e d to 9 . 2 3 p e r c e n t . 1 3 T h e w e a k e r p e r f o r m a n c e of the r e g i o n ' s smallest banks has been attributed to the large n u m ber of de novo institutions established in recent years (especially in Florida and Georgia) and higher loan losses. M a n y of the smaller institutions chartered in the past decade have disappeared. Growth, mergers, and failures explain the 44.66 percent decline in the n u m b e r of s m a l l b a n k s in the r e g i o n since 1989. Florida, which previously had the greatest n u m b e r of underperforming small banks, saw the largest drop in the n u m b e r of banks with less than $25 million in assets (63.75 percent since 1989). Of the eighty banks classified as small in 1989, approximately half grew out of the category, eleven were purchased by another institution, and five failed. 1 4 Also, loan-loss expense (as a percent of assets) for the region's smallest institutions continued to fall, to 0.34 percent. However, this figure remains 4 7 . 0 6 percent above the national average for banks of c o m p a r a b l e size. The increased profitability of the region's smaller banks is encouraging, but their p e r f o r m a n c e as the b u s i n e s s c y c l e July/August 1994 progresses will indicate h o w successful the remaining small b a n k s h a v e b e e n in c a r v i n g out m a r k e t niches. Conclusion Banks of all sizes and conditions had record profitability in 1993's environment of declining interest rates and an improving economy. The favorable conditions that have enabled banks to achieve unusually high profits in 1992 and 1993 contrast sharply with those that prevailed in the past decade. A m a j o r decline in loan-loss provisions was the catalyst for an increase in adjusted net interest margins, which led to higher 1993 earnings. Net income in 1993 was also h i g h e r b e c a u s e of an increased v o l u m e of interestearning assets, .gains f r o m securities sales, and continued growth in noninterest income. Preliminary f i g u r e s for the first q u a r t e r of 1994 indicate a continued decline in loan-loss provisions (as a percent of assets), leading to even wider adjusted net interest margins. B a n k s also appear to have maintained profitable spreads on interest earning assets despite the recent rise in interest rates, probably because loan rates have risen faster than rates paid o n d e p o s i t s . H o w e v e r , i n c r e a s e d loan d e m a n d in 1994 (particularly in the c o n s u m e r and c o m m e r c i a l s e g m e n t s ) m a y soon lead to increased c o m p e t i t i o n by banks for time and savings deposits, putting upward pressure on deposit rates and squeezing m a r gins. Also, 1 9 9 4 ' s rising interest rate e n v i r o n m e n t may have evaporated a portion of b a n k s ' unrealized securities profits. These conditions will m a k e further advancements in commercial bank profitability difficult to achieve in 1994. Box 2 Balance-Sheet Developments in 1993 1 During 1993 c o m m e r c i a l b a n k s increased their total assets by 5.70 percent (see T a b l e s A and B). T h e three asset categories that grew most w e r e assets held in trading accounts (up 51.95 percent), securities holdings (up 8.10 percent), and net loans (up 6.07 percent). T h e inc r e a s e in net loans is n o t e w o r t h y b e c a u s e loan g r o w t h has b e e n slow recently, a v e r a g i n g only 2.3 percent p e r year during the previous three years. On the right-hand side of the balance sheet, b a n k s ' liabilities rose 5.14 percent and total equity capital climbed 12.68 percent. A m o n g liabilities, d o m e s t i c b a n k deposits—the largest traditional source of bank f u n d s — r o s e a m e a g e r 0.52 percent, with all of the gain c o m i n g f r o m growth in non-interest-bearing accounts (interest-bearing accounts fell slightly). Total transaction accounts were u p 5.47 percent because of a 5.69 percent j u m p in d e m a n d d e p o s i t s , a n d n o n t r a n s a c t i o n a c c o u n t s w e r e d o w n 1.99 percent. (For a breakdown of deposit classes, see T a b l e 10.) However, other types of liabilities increased, with the categories of borrowed m o n e y and other liabilities significantly higher (up 42.80 and 22.65 percent, respectively). 2 Federal Reserve B a n k of Atlanta The equity position of commercial banks improved significantly in 1993 as undivided profits and capital reserves shot up 18.35 percent. This increase indicated banks were using their record profits to further enhance capital positions. In addition, net unrealized losses on marketable equity securities fell f r o m $62.3 million on D e c e m b e r 31, 1992, to - $ 2 . 9 billion at year-end 1993, r e p r e s e n t i n g a large unrealized gain. Notes 1.The discussion on balance-sheet items measures statement changes over the year from December 31, 1992, to December 31, 1993. For a comprehensive discussion of recent balance-sheet developments at commercial banks, see English and Reid (1994). 2. Other borrowed money is made up of the total amount borrowed on a bank's promissory notes, rediscounted notes and bills, loans sold that carry the bank's guarantee, and so forth. Continued on page 28 Economic Review 27 Continued from page 27 Table A B a l a n c e S h e e t for U.S. C o m m e r c i a l Banks (Millions of dollars) Dec. 31, 1993 Dec. 31, 1992 Percentage Change Assets Cash and balances due from depository institutions Non-interest-bearing balances and currency and coin Interest-bearing balances 188,135.2 83,755.3 198,981.8 97,883.6 (5.45) (14.43) Securities 827,937.8 765,911.0 8.10 Federal funds sold (6.06) 122,794.0 130,714.8 Securities purchased under agreements to resell 27,012.2 26,896.8 Loans and lease financing receivables Loans and leases net of unearned income Less allowance for loan and lease losses Less allocated transfer risk reserve Loans and leases, net of above items 2,139,682.2 52,380.3 172.2 2,087,129.7 2,022,088.9 53,968.5 343.0 1,967,777.3 0.43 5.82 (2.94) (49.81) 6.07 122,389.8 80,546.0 51.95 Premises and fixed assets 55,094.2 52,713.0 4.52 Other real estate owned 16,768.4 26,341.8 (36.34) 3,565.3 3,172.1 12.40 Customers' liability to this bank on acceptances outstanding 13,307.9 16,018.6 (16.92) Intangible assets 17,892.5 15,413.8 16.08 Assets held in trading accounts Investments in unconsolidated subsidiaries and associated companies Other assets Total assets 119,107.6 103,700.3 14.86 3,684,890.0 3,486,070.8 5.70 2,407,838.6 553,054.1 1,854,784.5 329,906.4 15,641.1 314,265.3 2,395,388.4 524,412.6 1,870,975.7 286,736.8 13,369.4 273,367.4 0.52 5.46 (0.87) 15.06 16.99 14.96 177,037.6 164,071.6 7.90 95,231.0 86,908.4 9.58 Liabilities Deposits In domestic offices Non-interest-bearing Interest-bearing In foreign offices, Edge and Agreement subsidiaries, and IBFs Non-interest-bearing Interest-bearing Federal funds purchased Securities sold under agreements to repurchase Demand notes issued to the U.S. Treasury Other borrowed money Mortgage indebtedness and obligations under capitalized leases 34,951.8 22,413.0 55.94 186,029.7 130,277.0 42.80 1,803.4 1,901.2 (5.15) (17.15) Bank's liability on acceptances executed and outstanding 13,402.4 16,176.6 Subordinated notes and debentures 37,147.8 33,521.0 10.82 106,431.0 86,773.8 22.65 3,389,779.9 3,224,167.8 5.14 3.7 3.0 21.99 Other liabilities Total liabilities Limited-life preferred stock and related surplus 28 Economic Review July/August 1994 Dec. 31, 1993 Percentage Change Dec. 31, 1992 Equity Capital 1,491.2 Perpetual preferred stock and related surplus Common stock Surplus Undivided profits and capital reserves Less net unrealized loss on marketable equity securities 32,479.1 31,780.4 126,130.9 133,244.0 (2,890.1) 116,961.6 112,584.2 62.3 (1,128.8) Cumulative foreign currency translation adjustments (5.30) 2.20 7.84 18.35 (4,737.84) 20.26 (938.6) 295,106.6 261,890.0 12.68 3,684,890.0 3,486,070.8 5.70 Total equity capital Total liabilities, limited-life preferred stock, and equity capital 1,574.7 Table B Balance S h e e t for C o m m e r c i a l Banks in the Southeast (Millions of dollars) Assets Cash and balances due from depository institutions Non-interest-bearing balances and currency and coin Interest-bearing balances Securities Federal funds sold 22,306.7 23,410.0 (4.71) 4.600.5 5,895.3 (21.96) 107.669.8 101,830.8 5.73 13,978.5 17,056.9 Securities purchased under agreements to resell 2,326.7 2,219.7 (18.05) Loans and lease financing receivables Loans and leases net of unearned income Less allowance for loan and lease losses Less allocated transfer risk reserve Loans and leases, net of above items 242,699.5 4,770.2 14.4 218,047.6 4,535.9 20.1 11.31 5.17 (28.36) 11.44 4.82 237.914.9 213,491.6 Assets held in trading accounts 1,091.0 1,112.4 (1.92) Premises and fixed assets 6,999.2 6,673.5 4.88 Other real estate owned 1.568.6 2,573.1 (39.04) 139.3 133.2 4.58 1.177.4 922.8 27.59 Investments in unconsolidated subsidiaries and associated companies Customers' liability to this bank on acceptances outstanding Intangible assets Other assets Total assets 1.776.7 1,516.3 17.17 7.156.5 7,266.9 (1.52) 408,705.8 384,102.8 6.41 323,256.6 63,649.8 259,606.8 1,945.1 19.9 1,925.1 313,692.0 60,546.8 253,145.2 1,114.1 98.4 1,015.7 3.05 5.12 2.55 74.59 (79.78) 89.53 Liabilities Deposits In domestic offices Non-interest-bearing Interest-bearing In foreign offices, Edge and Agreement subsidiaries, and IBFs Non-interest-bearing Interest-bearing Federal Reserve Bank of Atlanta Continued Economic on page 30 Review 29 Continued from page 27 Dec. 31, 1993 Dec. 31, 1992 Percentage Change Liabilities (continued) Federal funds purchased 19,343.4 15,133.9 27.82 Securities sold under agreements to repurchase 13,547.5 12,146.4 11.54 Demand notes issued to the U.S. Treasury 2,277.6 2,104.0 8.25 Other borrowed money 6,612.5 3,747.9 76.43 112.2 132.4 (15.26) 1,177.4 922.8 27.59 846.5 627.1 34.99 5,435.1 4,557.3 19.26 374,553.9 354,178.0 5.75 1.8 0.1 1,740.00 Mortgage indebtedness and obligations under capitalized leases Bank's liability on acceptances executed and outstanding Subordinated notes and debentures Other liabilities Total liabilities Limited-life preferred stock and related surplus Equity Capital Perpetual preferred stock and related surplus Common stock Surplus Undivided profits and capital reserves Less net unrealized loss on marketable equity securities Cumulative foreign currency translation adjustments 199.1 210.4 2,441.9 2,503.5 (2.46) 15,043.7 15,880.7 (584.6) 13,591.0 13,640.8 21.0 10.69 16.42 (2,883.81) 0 Total equity capital Total liabilities, limited-life preferred stock, and equity capital 0 (5.37) 0 34,150.0 29,924.7 14.12 408,705.8 384,102.8 6.41 Source: Data for Tables A and B from "Consolidated Reports of Condition for Insured Commercial Banks," 1992-93, filed with each bank's respective regulator. Table 1 Adjusted Net Interest Margin as a Percentage of Interest-Earning Assets (Insured commercial banks by consolidated assets) Year All Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$500 million $500 million$1 b i l l i o n $1 b i l l i o n + 1989 3.13 4.22 4.29 4.35 4.37 4.15 2.61 1990 3.06 4.26 4.23 4.23 4.11 3.95 2.59 1991 3.14 4.31 4.29 4.25 4.14 3.65 2.72 1992 3.80 4.64 4.69 4.64 4.50 4.31 3.48 1993 4.02 4.64 4.69 4.61 4.55 4.47 3.80 Source: Figures in all tables have been computed by the Federal Reserve Bank of Atlanta from data in "Consolidated Reports of Condition for Insured Commercial Banks" and "Consolidated Reports of Income for Insured Commercial Banks," 1989-93, filed with each bank's respective regulator. 30 Economic Review July/August 1994 Table 2 Loan-Loss Expense as a P e r c e n t a g e o f I n t e r e s t - E a r n i n g Assets (Insured commercial banks by consolidated assets) Year All Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$ 5 0 0 million $500 million$1 b i l l i o n $1 bill i o n + 1989 1.10 0.59 0.56 0.50 0.58 0.69 1.33 1990 1.11 0.50 0.53 0.53 0.67 1.00 1.30 1991 1.17 0.42 0.47 0.50 0.65 1.09 1.40 1992 0.88 0.39 0.35 0.40 0.54 0.78 1.04 1993 0.53 0.18 0.22 0.26 0.34 0.50 0.61 Table 3 T a x - E q u i v a l e n t I n t e r e s t R e v e n u e as a P e r c e n t a g e o f I n t e r e s t - E a r n i n g Assets (Insured commercial $25-$50 million banks by consolidated $50-$ 100 million assets) $100-$500 million $500 millionSi billion Year All Banks $0-$25 million 1989 11.62 10.71 10.86 10.89 11.14 11.32 11.87 1990 11.26 10.60 10.72 10.71 10.82 11.18 11.44 1991 10.03 9.97 10.06 10.05 10.07 9.94 10.03 1992 8.81 8.94 8.85 8.85 8.76 8.62 8.82 1993 7.94 7.82 7.91 7.84 7.79 7.76 8.00 $1 b i l l i o n + Table 4 I n t e r e s t Expense as a P e r c e n t a g e o f I n t e r e s t - E a r n i n g Assets (Insured commercial banks by consolidated assets) Year All Banks $0-$25 million $25-$50 million $50-$100 million $100-$500 million $500 millionSi billion $1 bill i o n + 1989 7.39 5.91 6.01 6.04 6.19 6.48 7.93 1990 7.09 5.85 5.96 5.96 6.03 6.23 7.55 1991 5.72 5.23 5.30 5.30 5.28 5.18 5.92 1992 4.13 3.90 3.81 3.81 3.73 3.53 4.30 1993 3.39 3.00 2.99 2.97 2.90 2.80 3.58 Federal Reserve B a n k of Atlanta Economic Review 31 Table 5 Securities G a i n s (Losses) b e f o r e T a x e s as a P e r c e n t a g e o f T o t a l Assets* (Insured commercial banks by consolidated assets) Year All Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$ 5 0 0 million $500 millionSi billion $1 b i l l i o n + 1989 0.02 0.00 0.01 0.01 0.01 0.00 0.03 1990 0.01 0.00 0.00 0.00 0.00 0.01 0.02 1991 0.09 0.05 0.05 0.06 0.07 0.07 0.10 1992 0.12 0.11 0.08 0.09 0.09 0.08 0.13 1993 0.08 0.07 0.06 0.06 0.06 0.07 0.09 0.00 indicates securities gains (losses) that are less than 0.01 percent of total assets. Table 6 N o n i n t e r e s t I n c o m e as a P e r c e n t a g e o f T o t a l Assets (Insured commercial banks by consolidated assets) Year All Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$ 5 0 0 million $500 millionSi billion $1 b i l l i o n + 1989 1.52 1.08 0.78 0.86 0.97 1.15 1.76 1990 1.63 1.08 0.82 0.83 0.93 1.30 1.91 1991 1.73 1.03 0.84 0.88 1.05 1.29 2.02 1992 1.88 1.23 0.86 0.90 1.14 1.31 2.20 1993 2.02 1.21 1.02 0.93 1.24 1.39 2.34 Table 7 T o t a l N o n i n t e r e s t Expense as a P e r c e n t a g e of T o t a l Assets (Insured commercial 32 banks by consolidated assets) Year All Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$500 million $500 millionSi billion $1 b i l l i o n + 1989 3.39 3.87 3.41 3.31 3.40 3.36 3.39 1990 3.50 3.93 3.46 3.32 3.34 3.56 3.53 1991 3.73 3.95 3.56 3.40 3.49 3.63 3.82 1992 3.91 4.06 3.57 3.44 3.61 3.73 4.03 1993 3.95 3.94 3.64 3.45 3.68 3.80 4.06 Econom ic Review J u l y / A u g u s t 1994 Table 8 P e r c e n t a g e R e t u r n o n Assets (Insured commercial banks by consolidated assets) Year All Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$500 million $500 million$1 b i l l i o n $1 b i l l i o n + 1989 0.50 0.59 0.73 0.88 0.92 0.89 0.35 1990 0.49 0.58 0.67 0.79 0.78 0.76 0.38 1991 0.54 0.62 0.72 0.83 0.83 0.54 0.44 1992 0.95 0.93 1.02 1.08 1.05 0.94 0.92 1993 1.23 1.09 1.16 1.17 1.20 1.14 1.25 $500 million$1 b i l l i o n $1 bill ion-f- Table 9 P e r c e n t a g e R e t u r n o n Equity (Insured commercial banks by consolidated $50-$100 million assets) Year All Banks $0-$25 million $25-$50 million $100-$500 million 1989 7.90 6.10 8.12 10.11 11.93 12.78 6.17 1990 7.64 5.85 7.43 9.01 9.95 10.25 6.68 1991 8.05 6.24 7.86 9.40 10.51 7.50 7.35 1992 13.24 9.25 10.82 11.93 12.61 12.52 13.86 1993 15.78 10.38 11.82 12.40 13.77 14.06 16.98 Table 10 D e p o s i t Classes as a P e r c e n t a g e of T o t a l D o m e s t i c D e p o s i t s (Insured commercial Year Transactions Accounts banks) MMDAs Other Savings T i m e Deposits less than $ 1 0 0 , 0 0 0 T i m e Deposits m o r e than $ 1 0 0 , 0 0 0 1989 30.6 16.2 8.8 27.6 16.7 1990 29.5 16.3 8.6 29.7 15.8 1991 29.4 17.1 9.5 30.7 13.3 1992 31.6 18.7 11.3 28.3 10.2 1993 35.3 19.0 13.0 24.4 8.3 DigitizedF efor d e FRASER r a l R e s e r v e B a n k of A t l a n t a Economic Review 33 Table 11 P e r c e n t a g e R e t u r n o n Assets 2 5 t h Percentile According to Profitability (Insured commercial banks by consolidated assets) Year All Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$ 5 0 0 million $500 millionSi billion $1 b i l l i o n + 1989 0.58 0.37 0.58 0.70 0.77 0.64 0.50 1990 0.51 0.34 0.52 0.62 0.64 0.48 0.10 1991 0.56 0.45 0.56 0.67 0.64 0.52 0.21 1992 0.78 0.67 0.80 0.86 0.85 0.74 0.62 1993 0.88 0.71 0.88 0.94 0.96 0.92 0.94 Table 12 P e r c e n t a g e R e t u r n o n Assets 5 0 t h Percentile A c c o r d i n g to Profitability (Insured commercial banks by consolidated assets) Year All Banks $0-$25 million $25-$50 million $50-$100 million $100-$ 5 0 0 million $500 million$1 b i l l i o n $1 b i l l i o n + 1989 0.98 0.84 0.98 1.04 1.07 1.06 0.96 1990 0.92 0.82 0.92 0.98 1.01 0.99 0.74 1991 0.95 0.86 0.94 1.00 1.01 0.94 0.81 1992 1.13 1.02 1.14 1.18 1.19 1.10 1.02 1993 1.19 1.04 1.18 1.23 1.26 1.24 1.24 Table 13 P e r c e n t a g e R e t u r n o n Assets 7 5 t h Percentile According to Profitability (Insured commercial banks by consolidated assets) Year All Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$500 million $500 million$1 b i l l i o n $1 b i l l i o n + 1989 1.29 1.20 1.28 1.34 1.36 1.30 1.20 1990 1.23 1.15 1.23 1.26 1.28 1.30 1.12 1991 1.24 1.18 1.24 1.27 1.28 1.25 1.16 1992 1.43 1.34 1.44 1.48 1.46 1.37 1.33 1993 1.50 1.38 1.49 1.52 1.56 1.51 1.55 34 Econom ic Review J u l y / A u g u s t 1994 Table 14 A d j u s t e d N e t Interest M a r g i n as a P e r c e n t a g e o f I n t e r e s t - E a r n i n g Assets (Insured commercial banks in the Southeast by consolidated assets) Year A l l SE Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$500 million $500 million$1 b i l l i o n $1 b i l l i o n + 1989 3.91 4.16 4.34 4.29 4.32 3.59 3.71 1990 3.56 4.13 4.29 4.11 4.17 4.07 3.15 1991 3.78 4.04 4.18 4.18 4.20 3.89 3.53 1992 4.45 4.58 4.73 4.69 4.56 4.50 4.34 1993 4.53 4.80 4.81 4.75 4.64 4.53 4.45 Table 15 Loan-Loss Expense as a P e r c e n t a g e o f I n t e r e s t - E a r n i n g Assets (Insured commercial banks in the Southeast by consolidated assets) Year A l l SE Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$500 million $ 5 0 0 mil lionSi billion $1 b i l l i o n + 1989 0.79 0.85 0.63 0.53 0.60 0.95 0.88 1990 1.07 0.80 0.59 0.69 0.65 1.05 1.30 1991 0.90 0.67 0.63 0.65 0.63 0.76 1.07 1992 0.59 0.66 0.46 0.50 0.51 0.55 0.65 1993 0.32 0.34 0.34 0.28 0.30 0.41 0.31 Table 16 T a x - E q u i v a l e n t I n t e r e s t R e v e n u e as a P e r c e n t a g e o f I n t e r e s t - E a r n i n g Assets (Insured commercial banks in the Southeast by consolidated assets) Year A l l SE Banks $0-$25 million 1989 11.18 11.24 11.31 11.14 11.11 11.08 11.20 1990 10.90 11.00 11.09 10.97 10.88 11.46 10.82 1991 9.91 10.16 10.33 10.25 10.10 9.86 9.75 1992 8.57 9.20 9.08 9.00 8.70 8.46 8.42 1993 7.61 8.20 8.16 8.05 7.80 7.40 7.46 Digitized F e d efor r a lFRASER Reserve B a n k of Atlanta $25-$50 million $50-$100 million $ 1 0 0 - $ 5 00 million $500 millionSi billion Economic $1 b i l l i o n + Review 35 Table 17 I n t e r e s t Expense as a P e r c e n t a g e of I n t e r e s t - E a r n i n g Assets (Insured commercial banks in the Southeast by consolidated assets) Year A l l SE Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$ 500 million $500 millionSi billion $1 b i l l i o n + 1989 6.48 6.23 6.34 6.32 6.19 6.53 6.62 1990 6.28 6.07 6.21 6.17 6.07 6.34 6.36 1991 5.23 5.45 5.52 5.42 5.27 5.22 5.16 1992 3.53 3.96 3.89 3.81 3.62 3.41 3.43 1993 2.76 3.05 3.01 3.01 2.87 2.48 2.70 Table 18 Securities G a i n s (Losses) b e f o r e T a x e s as a P e r c e n t a g e o f T o t a l Assets* (Insured commercial banks in the Southeast by consolidated assets) Year A l l SE Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$500 million $500 millionSi billion $1 bill ion-h 1989 0.02 0.00 0.01 0.01 0.00 0.00 0.04 1990 0.02 0.00 0.00 (0.01) (0.01) 0.01 0.04 1991 0.11 0.09 0.07 0.05 0.06 0.04 0.14 1992 0.09 0.09 0.10 0.08 0.08 0.03 0.09 1993 0.04 0.07 0.08 0.07 0.05 0.09 0.02 * 0.00 indicates securities gains (losses) that are less than 0.01 percent of total assets. Table 19 N o n i n t e r e s t I n c o m e as a P e r c e n t a g e of T o t a l Assets (Insured commercial banks in the Southeast by consolidated assets) Year A l l SE Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$500 million $500 million$1 b i l l i o n $1 b i l l i o n + 1989 1.17 1.54 0.85 1.05 1.06 1.35 1.23 1990 1.26 1.23 0.91 1.06 1.08 1.12 1.39 1991 1.35 1.67 0.90 1.15 1.17 1.19 1.48 1992 1.42 1.83 0.95 1.00 1.15 1.21 1.62 1993 1.45 2.44 1.42 0.91 1.26 1.21 1.60 Econom 36 ic Review J u l y / A u g u s t 1994 Table 20 T o t a l N o n i n t e r e s t Expense as a P e r c e n t a g e of T o t a l Assets (Insured commercial banks in the Southeast by consolidated assets) Year A l l SE Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$500 million $500 millionSi billion $1 b i l l i o n + 1989 3.48 4.72 3.64 3.46 3.51 3.62 3.41 1990 3.54 4.54 3.69 3.60 3.45 3.71 3.49 1991 3.72 4.97 3.75 3.72 3.58 3.60 3.74 1992 3.82 4.82 3.82 3.63 3.57 3.71 3.92 1993 3.68 5.25 4.21 3.52 3.64 3.57 3.68 Table 21 P e r c e n t a g e R e t u r n o n Assets (Insured commercial banks in the Southeast by consolidated assets) Year A l l SE Banks $0-$25 million $25-$50 million $50-$100 million $100-$500 million $500 millionSi billion $1 b i l l i o n + 1989 0.68 0.20 0.64 0.89 0.87 0.55 0.62 1990 0.52 0.03 0.60 0.64 0.82 0.65 0.41 1991 0.66 0.14 0.58 0.75 0.88 0.67 0.60 1992 1.05 0.73 0.98 1.06 1.13 0.97 1.05 1993 1.26 1.06 1.17 1.23 1.30 1.23 1.27 Table 22 P e r c e n t a g e R e t u r n o n Equity (Insured commercial banks in the Southeast by consolidated assets) Year A l l SE Banks $0-$25 million $25-$50 million $50-$ 100 million $100-$ 500 million $500 millionSi billion $1 b i l l i o n + 1989 9.50 1.69 6.63 9.97 11.05 8.29 9.71 1990 7.14 0.13 6.33 7.22 10.34 7.65 6.28 1991 8.96 1.26 6.08 8.39 11.10 9.70 8.79 1992 13.72 6.52 10.00 11.79 13.76 13.10 14.73 1993 15.56 9.23 11.49 13.17 15.00 15.43 16.62 F e d e r a l R e s e r v e B a n k of A t l a n t a Economic Review 37 Table 23 Adjusted N e t Interest M a r g i n as a Percentage of Interest-Earning Assets (Insured commercial banks in the Southeast by state) Year All SE Banks Alabama Florida Georgia Louisiana Mississippi Tennessee 1989 3.91 4.14 3.83 4.71 2.87 3.95 3.64 1990 3.56 4.11 3.18 4.30 3.08 3.84 3.33 1991 3.78 4.20 3.51 4.18 3.08 4.21 3.91 1992 4.45 4.59 4.42 4.47 4.51 4.55 4.26 1993 4.53 4.50 4.52 4.31 5.14 4.61 4.44 Table 2 4 Loan-Loss Expense as a Percentage of Interest-Earning Assets (Insured commercial banks in the Southeast by state) Year All SE Banks Alabama Florida Georgia Louisiana Mississippi Tennessee 1989 0.79 0.42 0.78 0.58 1.48 0.51 0.95 1990 1.06 0.47 1.22 1.00 1.23 0.62 1.34 1991 0.90 0.55 1.03 0.96 1.11 0.49 0.78 1992 0.59 0.50 0.59 0.75 0.51 0.48 0.57 1993 0.32 0.32 0.36 0.57 -0.19 0.29 0.19 Table 2 5 Tax-Equivalent Interest Revenue as a Percentage of Interest-Earning Assets (Insured commercial 38 Year All SE Banks 1989 11.18 1990 banks in the Southeast by state) Tennessee Georgia 11.17 10.96 11.90 10.71 10.91 1 1.22 10.90 10.84 10.66 11.47 10.56 10.67 11.24 1991 9.91 10.04 9.68 10.48 9.33 9.98 9.98 1992 8.57 8.75 8.44 8.91 8.28 8.70 8.42 1993 7.61 7.84 7.45 7.81 7.42 7.82 7.55 Econom ic Review Louisiana Mississippi Florida Alabama July/August 1994 Table 26 I n t e r e s t Expense as a P e r c e n t a g e of I n t e r e s t - E a r n i n g Assets (Insured commercial banks in the Southeast by state) Year A l l SE Banks Alabama Florida Georgia Louisiana Mississippi Tennessee 1989 6.48 6.62 6.35 6.61 6.42 6.44 6.63 1990 6.28 6.25 6.27 6.16 6.24 6.21 6.57 1991 5.23 5.29 5.15 5.34 5.14 5.28 5.28 1992 3.53 3.66 3.42 3.69 3.26 3.66 3.59 1993 2.76 3.02 2.58 2.92 2.47 2.92 2.91 m' Table 2 7 P e r c e n t a g e R e t u r n o n Assets (Insured commercial banks in the Southeast by state) Year A l l SE Banks Alabama Florida Georgia 1989 0.68 1.01 0.61 1.10 1990 0.52 1.02 0.28 1991 0.66 1.02 1992 1.05 1993 1.26 Louisiana Mississippi Tennessee -0.13 0.79 0.61 0.89 0.18 0.72 0.42 0.48 0.87 0.22 0.91 0.77 1.24 0.86 1.26 1.13 1.11 1.03 1.36 1.15 1.19 1.73 1.27 1.26 Louisiana Mississippi Tennessee Table 2 8 P e r c e n t a g e R e t u r n o n Equity (Insured commercial banks in the Southeast by state) Year A l l SE Banks 1989 9.50 12.53 9.53 14.38 -1.89 9.95 8.29 1990 7.14 12.99 4.16 10.87 2.73 9.27 5.75 1991 8.96 13.29 7.12 9.99 3.35 11.77 10.63 1992 13.72 15.83 12.12 14.08 15.73 13.77 13.83 1993 15.56 16.58 15.41 13.05 20.88 14.97 15.76 Alabama Digitized F e d e rfor a l FRASER Reserve B a n k of Atlanta Florida Georgia Economic Review 39 Notes 1. A loan-loss provision is a noncash expense item charged against a bank's earnings; it is used to increase the reserves a bank has set aside for future bad loans. An increase in loan-loss provisions decreases net income and therefore decreases the amount available for banks to add to capital as retained earnings. For a discussion of banks' loan-loss accounting, see Wall (1988, 39-41). Adjusted net interest margin is calculated by subtracting interest expense from tax-adjusted interest revenue (net of loan-loss provisions) and dividing by net interest-earning assets and is roughly equivalent to a business's gross profit margin. For this calculation, interest revenue from tax-exempt securities is adjusted upward by the bank's marginal tax rate to avoid penalizing institutions that hold substantial state and local securities portfolios, which earn less interest but reduce tax burdens. It should be noted that there are restrictions on which securities qualify for tax-exempt status for particular institutions. Because a profit-maximizing institution would not invest in a tax-exempt bond if it were not eligible for the tax benefits provided by these securities' lower yield, it was assumed in adjusting tax-exempt securities income that a bank could claim the exemption on all of its tax-exempt securities holdings. In addition, loan-loss provisions are subtracted from interest revenue to place banks that make lower-risk loans at lower interest rates on a more equal footing with banks that make higher-risk loans at higher rates. 2. Both noncurrent loans and inventories of foreclosed properties at commercial banks declined in every quarter of 1993. 3. In connection with safety and soundness concerns, this increase in capital is beneficial because it provides a thicker cushion for banks against future losses. However, higher capital ratios decrease the cost competitiveness of banks with respect to nonbank financial institutions because capital requires a higher rate of return than lower-cost deposits. 4. From 1992 to 1993, net loans outstanding at insured commercial banks increased by 6.07 percent. Because revenue is dependent on both price and quantity, this increase in loans, coupled with a decrease in loan earnings, implies that the average rate banks earned on their interest-bearing assets in 1993 was lower. Since the volume of both com- 40 Econom ic Review mercial and industrial loans and government securities was up, rates earned on these assets also averaged lower in 1993. 5. There is disagreement about the causes of this increase in securities holdings. For a discussion see Keeton (1994). 6. Capital gains occur when security prices rise above the price paid for the security. On debt securities, capital gains occur in a falling rate environment because, as interest rates fall, the value of fixed interest payments rise, and therefore prices are bid up. Such a falling rate environment existed for several years prior to 1994. 7. Banks had a net unrealized gain on marketable equity securities of approximately $2.9 billion as of December 31, 1993, representing 0.35 percent of their total securities portfolio. 8. As an example, banks have drastically increased the amount of mortgage loans packaged and sold in the secondary market (mortgage-backed securities). Mortgage-backed securities allow banks to earn fee income from loan originations and servicing fees while insulating themselves from interest rate fluctuations. In effect, banks are transferring the interest rate risk to market participants w h o are willing to hold such risk. 9. For the purposes of this article, the Southeast is defined as A l a b a m a , Florida, Georgia, Louisiana, Mississippi, and Tennessee. The Sixth Federal Reserve District comprises these six states less portions of Louisiana, Mississippi, and Tennessee. 10. Other fee income describes revenues from a variety of activities including safe deposit boxes, credit insurance, loan servicing, the purchase and sale of securities, and credit cards. Other noninterest income includes revenues from performing data processing for second parties and various types of asset disposal. 11. Noninterest expenses are composed of three categories: salaries and employee benefits, expenses of premises and fixed assets, and other noninterest expenses. 12. For a complete discussion see Goudreau and King (1991). 13. King (1993) also noted the vast improvement in the region's smallest institutions (those under $25 million in assets) in 1992. 14. The 1993 sample of small Florida banks includes those that have remained in this category since 1989 plus any de novo institutions established since that time. J u l y / A u g u s t 1994 References English, William B., and Brian K. Reid. "Profits and Balance Sheet Developments at U.S. Commercial Banks in 1993." Federal Reserve Bulletin 80 (June 1994): 483-510. Goudreau, Robert E., and B. Frank King. "Commercial Bank Profitability: Hampered Again by Large Banks' Loan Problems." Federal Reserve Bank of Atlanta Economic Review 76 (July/August 1991): 39-54. Keeton, William R. "Causes of the Recent Increase in Bank Security Holdings." Federal Reserve Bank of Kansas City Economic Review 79 (Second Quarter 1994): 45-57. King, B. Frank. "Commercial Bank Profits in 1992." Federal Reserve Bank of Atlanta Economic Review 78 (September/ October 1993): 39-53. W a l l , Larry D. " C o m m e r c i a l Bank P r o f i t s : Still W e a k in 1987." Federal Reserve Bank of Atlanta Economic Review 73 (July/August 1988): 28-42. •i Federal Reserve B a n k of Atlanta Economic Review 41 ; • . ' - • ,. • - " - c ï v ; - - ^ - • - ' / •' " • ' ^ ^ v . v i ; V • ' - Bulk Rate U.S. Postage PAID Atlanta, GA Permit 292 Public Affairs Department 104 Marietta Street, N.W. Atlanta, Georgia 3 0 3 0 3 - 2 7 1 3 ( 4 0 4 ) 5 2 1 - 8 0 2 0 ® printed on recycled paper
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