Knowledge that Transforms

Carl Bonham and Richard Cohen (1995) are quite correct in noting the errors in our paper (Keane and Runkle, 1990), which were caused by our ignorance of cointegration. We stand chagrined. However, Bonham and Cohen are overstating their case when they claim that Keane and Runkle's results do not support the empirical validity of the rational-expectations hypothesis (p. 289). Bonham and Cohen focus on our tests of price-forecast rationality conditioned on past oil prices and Ml, which they claim are the core of our paper and provide our most stringent tests of rationality. Those particular tests account for only two paragraphs of our 20-page paper-obviously, these tests do not provide the core results of our paper. Rather, the main result of our paper is that individual price forecasts are unbiased and rational, conditioned on the forecaster's own past errors. No previous researchers had ever found even this limited support for the rational-expectations hypothesis. These core results are unaffected by the cointegration issues noted by Bonham and Cohen. Given that caveat, however, note how few of our results are actually overturned by Bonham and Cohen. Although our test statistics for determining whether forecasters properly condition on Ml growth are incorrect, Bonham and Cohen reach the same conclusion that we do: price forecasts conditioned on Ml growth are rational. Bonham and Cohen do reach different conclusions about forecast rationality than we do when they condition on oil price changes. But they themselves show that forecasters were only irrational in conditioning on oil prices after 1973 (their table 2, rows 5 and 6). To call such forecasting failure irrationality may or may not be correct. We think that Bonham and Cohen's results merely confirm the widespread view that forecasters did not completely understand the effects that oil price shocks would have on the economy because such large oil price shocks had never been seen before. Although Bonham and Cohen overturn only one of our original tests, they do provide additional evidence against forecast rationality with their tests that condition on interest-rate spreads and the unemployment rate. We have no doubt that a search over a large number of conditioning variables will uncover some instances in which forecast rationality is rejected. But conducting such a search will also incorrectly bias tests toward rejecting rationality. Since our original paper, we have also examined the rationality of earnings forecasts made by individual stock analysts-a group that has even more incentive than economic forecasters to make accurate predictions. Although all previous studies in that literature had found individual earnings forecasts to be irrational, we found (Keane and Runkle, 1994) that analysts' forecasts are rational. This additional research provides further support for the paper criticized by Bonham and Cohen.

This note characterizes the nature of Ricardian-equivalence failure when either the old generation's or the young generation's income is uncertain and the nonnegativity constraint on bequests is binding in some states of nature. Assuming a positive third derivative of the utility function, the same condition needed for precautionary savings,' it is shown that the degree of failure of Ricardian equivalence is greater when the corner has to do with parental poverty than when the corner has to do with children's wealth. The reason is that in corners associated with parental poverty (and therefore lower parental consumption) marginal utility is more sensitive to extra consumption, leading to a higher marginal propensity to consume in the first period. Consequently, government transfers cause a substantial reduction of precautionary savings in poor corners, in contrast to rich corners, where precautionary savings are only slightly affected.

This paper explores some aspects of the exchange process that should be of interest to economists who use search theory, and especially to those who use search as a foundation for monetary economics. We are mainly concerned with a question that seems basic but has not been analyzed previously: is there some way to determine endogenously which agents are willing to invest resources in the process of active search for trading partners, and which agents prefer to wait passively for trading partners to come to them? In particular, given a group of buyers with money and a group of sellers with goods, is there any reason to expect that buyers will search for sellers, rather than the other way around? One obvious factor is the relative cost of transporting goods and money; but we are interested in examining whether there is anything about the process of monetary exchange per se, and not merely exogenous search costs, that makes buyers more willing than sellers to bear the costs of seeking out trading partners. We investigate this within a generalized version of the search-theoretic model of fiat money in Kiyotaki and Wright (1991, 1993). We find that there may exist equilibria in which buyers search while sellers do not, even if the search cost is greater for the former. However, there can also exist other equilibria with different properties. Perhaps the key finding is that the situation is not symmetric: factors that determine whether to search are fundamentally different for buyers and sellers. One property of an equilibrium in which only buyers search is that money appears on one side of every transaction, because if sellers do not search they do not meet and cannot barter. This is consistent Robert W. Clower's (1967) observation that money buys goods and goods buy money, but goods do not buy goods, although here it is derived endogenously rather than assumed. Some search-based monetary models simply rule out barter, including Peter A. Diamond (1984), Douglas M. Gale (1986), Diamond and Joel Yellin (1990), Alessandra Casella and Johnathon S. Feinstein (1990), Kiminori Matsuyama et al. (1993), Victor E. Li (1995), and Alberto Trejos and Wright (1995). It is difficult to motivate this absence of barter in these papers. In a model that is similar to the one used here, except search is costless, S. Rao Aiyagari and Neil Wallace (1992) prove that all equilibria involve some barter. A contribution of this paper is to show that barter may disappear once the decision to search is endogenized.

The dynamics of production and income growth across countries, or across regions within the same country, are often thought to give evidence on whether returns to accumulation are increasing, constant, or decreasing at the local level. When poor countries or regions are found to grow no faster than richer ones, such lack of is viewed as unfavorable evidence for models in which technology offers high returns to accumulation in relatively capital-poor locations (see e.g., Paul Romer, 1987). When population growth, saving (or investment) rates, and other determinants of long-run income levels in the neoclassical model are controlled for, residual income differences across countries and across regions within the same country appear to vanish slowly, but significantly, over time. This suggests that local returns to accumulation are decreasing if the reference theoretical model takes technology to be uniform across locations, features unexplained and permanent differences in saving behavior, and eliminates or limits capital mobility across locations.' These assumptions clearly oversimplify reality in various respects, and a particular one is considered here.2 The theory that motivates empirical work on income convergence either takes saving propensities as exogenously given or else models them in terms of individual optimization under certainty. Random variability is essential to every empirical regression equation, of course, and real data are better represented by a stochastic steady state with ongoing uncertainty than by steady convergence toward steady-state uniformity (see e.g., Danny Quah, 1993). To explore the possible role of exogenous and uninsurable income sources in the joint determination of savings behavior and income dynamics, here I allow consumption and savings to draw on possibly stochastic location-specific income sources which are independent of past accumulation at the local level and which remain relevant as the aggregate economy grows. Returns to accumulation are assumed to be constant both over time and cross-sectionally, thus ruling out decreasing returns to accumulation as the driving force of income convergence and ensuring that potential capital mobility need not induce actual capital flows. Under the common assumption of constant saving propensities, this framework predicts that incomes should converge over time if the relative importance of nonaccumulated income is crosssectionally heterogeneous. When individuals optimize their savings in light of the size and composition of their accumulated and nonaccumulated income sources, consumption-smoothing behavior leads to persistent, but stationary dynamics for relative incomes and consumption levels. The concluding section briefly discusses the extent to which these saving-based insights may be applicable to international or interregional income dynamics.

Historically, Michigan has relied more heavily than most other states on local taxes and property taxes as sources of education finance. In the 1990-1991 school year, Michigan was third among states in the share of school spending financed locally (65.2 percent).1 Over the past two decades there have been more than ten propertytax-cut initiatives placed on statewide ballots. In the summer of 1993 the legislature passed a bill that abolished, with no source of revenue replacement specified, all use of local property taxes (at the time, over $6 billion) for school operating expenditures. In late December, both houses passed, and the governor signed, a financing bill that contained two options for voters to choose from, either of which would have replaced approximately all of the lost revenue. Here are the main provisions of the new system, as passed by the voters in March, 1994: (i) a combination of an increased state sales tax, a statewide property tax on all property, a (nearly) required local property tax on nonhomestead property,2 a sharp increase in the tobacco tax, and a real-estate transfer tax; (ii) a system of state foundation grants to school districts that would, when fully implemented, put a floor under spending of $5,000 per pupil in 1994-1995, while preserving nominal differences in spending per pupil among districts that currently spend $5,000 per pupil or more; (iii) strengthened requirements for an academic core curriculum, pupil performance standards, and minimum numbers of school days; (iv) provisions for authorizing charter schools, schools of choice that would be subject to the statewide curriculum and testing requirements but would not have to use certified teachers. (A Michigan court ruled these schools unconstitutional, but the legislature has since rewritten the law to meet the court's objections.) Thus, the new law switched Michigan from a modified powerequalization system to a modified foundation system.