A “grid” bootstrap method is proposed for confidence-interval construction, which has improved performance over conventional bootstrap methods when the sampling distribution depends upon the parameter of interest. The basic idea is to calculate the bootstrap distribution over a grid of values of the parameter of interest and form the confidence interval by the no-rejection principle. Our primary motivation is given by autoregressive models, where it is known that conventional bootstrap methods fail to provide correct first-order asymptotic coverage when an autoregressive root is close to unity. In contrast, the grid bootstrap is first-order correct globally in the parameter space. Simulation results verify these insights, suggesting that the grid bootstrap provides an important improvement over conventional methods. Gauss code that calculates the grid bootstrap intervals-and replicates the empirical work reported in this paper'is available from the author's Web page at www.ssc.wisc.edu˜bhansen

DISCUSSIONS of municipal financial difficulties nearly always involve fundamental problems of local public investment requirements. It is curious, therefore, that studies of the determinants of such outlays have been so scant. One probable reason in the United States is that the relative financial responsibility for local investment of municipal, county, state, and federal governments may vary considerably from region to region and even among communities within any given region. This complexity of government structure, combined with a diversity of local accounting procedures, has probably hampered collection of adequate data. In general, studies of municipal expenditures have tended to combine current and capital outlays into a single variable.' As Brazer has pointed out, this procedure obscures much that should be revealed, since the forces which influence investment outlays are different from those affecting current expenditures.2 The present study develops a substantial number of hypotheses, covering four principal groups of causal factors affecting community investment. These center on demographic, housing, commercial, and industrial characteristics, the influences of which are then examined in the light of empirical evidence from East Flanders, a Belgian province which serves as an excellent laboratory for these purposes. Belgium is one of the world's most densely populated and highly industrialized nations. Although its total area is relatively small, the number of municipalities per unit area is very high. East Flanders, for example, covers 1150 square miles and contains 297 municipalities. This phenomenon results in part from the fact that Belgium has no equivalent to the American county; any given location is always within some municipality. All municipalities in Belgium participate in a common system of investment finance, making it possible to obtain highly standardized data for local investment. Consequently, variation in such outlays in Belgium is a more accurate reflection of differences in actual requirements than would be the case in the United States, where differential ability to pay muddies the analytic waters.3 A further element of homogeneity in the present case is the dominance of the clothing and textile sectors in all industrial municipalities. This has permitted fairly straightforward identification of industrial importance on the basis of employment data, without the complications that could arise from qualitative differences in industrial structure. The empirical evidence considered below consists of data obtained in a special municipal investment survey prepared by the author and completed by competent local authorities over a six-month period. The data include all investments in responding municipalities during the five-year period 1956-1960. The 269 respondents account for over 95 per cent of the population of the province.

tinue to neglect them for the present purpose. The specialists who now buy bills from the Treasury and then resell them to the ultimate investors are presumably being compensated for their activities. They have many alternatives. It is hard to see that they receive any economic rent that the Treasury in any way taps by its present method of auction. On the contrary, the Treasury enables those specialized abilities required to guess accurately the outcome of weekly auctions to earn a higher rent than they otherwise could. Private distribution costs are therefore higher under the present method of auction than they would be under the alternative method. Who pays these additional costs? Since we have assumed that the demand by ultimate investors is not affected, since the amount of bills is presumably not affected, since the Treasury does not succeed in imposing discriminatory prices on ultimate investors, the price paid by ultimate investors must be roughly the same whatever the method of distribution. It follows that the Treasury must pay the additional distribution costs by receiving less on the average from its bills than if it used the alternative method of auction. Two final comments. First, if this analysis is correct, it means that Brimmer's conclusion that noncompetitive bidding should be eliminated from present auctions is wrong. The introduction of such bidding reduces the unnecessary cost imposed by the Treasury on itself by the present method of bidding. Second, the defects of the present method of auction are quantitatively minor, and may be negligible, for bills because of their short maturity, large volume, and broad market. The defects are far more important for bonds and are more important, the longer the maturity. The main obstacle to using auctions to distribute longer-term securities has been the implicit assumption that the present method of auctioning bills must be used for them as well, as it has been in earlier experiments. The adoption of the alternative method would enable the Treasury to auction all securities issued, whatever their maturity, at a gain both to itself and to the economy.5

to study policies affecting money and credit separately from fiscal policy, because the underlying cause-effect relations are so very different. In terms of a summary characterization of the new budget, what I have tried to convey is this: Let us not say that it is designed to show the impact of economic policies; let us rather say more modestly that it shows the impact of fiscal policies; and let us make clear that a detailed and comprehensive analysis of monetary and credit policies cannot be conducted within the framework of the NIP accounts.

W HETHER or not shortages of highly educated and trained personnel, such as engineers and scientists, existed or were serious in recent years has been the subject of widespread discussion and indeed controversy.1 Typically, this discussion focuses on the question of whether there ought to be more engineers and scientists, in terms of our competition with the Russians, for example. It is not surprising then that controversy flourishes, since the answer to this question depends ultimately on one's value judgments, with respect to market and nonmarket variables. But more fundamentally, much of the disagreement over the issue stems from the variety of meanings attached to the term and the lack of empirical tests. To clarify the matter, Blank and Stigler in their recent book2 define and provide an empirical test for the existence of shortage. This paper re-examines some of the empirical evidence they submit and supplements it with additional evidence, part of which extends the analysis to more recent date. Briefly, here is summary of the BlankStigler approach and findings.3 They begin with this definition of shortage: a shortage exists when the number of workers available (the supply) increases less rapidly than the number demanded at the salaries paid in the recent past. Then salaries will rise, and activities which once were performed by (say) engineers must now be performed by class of workers who are less well trained and less expensive.4 (Italics in original.) Since I929, and more particularly since I939, they find that the earnings position of engineers has deteriorated substantially relative to all earners and to other professional earners. Although they note slight upturn in the relative earnings position of engineers since the beginning of the Korean WVar, this reversal is characterized as a minor cross-current in tide. Thus, the evidence leads them to conclude that there has been no but rather an increasingly ample supply of engineers. Furthermore, they predict that the downward trend in relative earnings position will continue.5