Randomization does not help much, comparability does

Following Fisher, it is widely believed that randomization "relieves the experimenter from the anxiety of considering innumerable causes by which the data may be disturbed." In particular, it is said to control for known and unknown nuisance factors that may considerably challenge the validity of a result. Looking for quantitative advice, we study a number of straightforward, mathematically simple models. However, they all demonstrate that the optimism with respect to randomization is wishful thinking rather than based on fact. In small to medium-sized samples, random allocation of units to treatments typically yields a considerable imbalance between the groups, i.e., confounding due to randomization is the rule rather than the exception. In the second part of this contribution, we extend the reasoning to a number of traditional arguments for and against randomization. This discussion is rather non-technical, and at times even "foundational" (Frequentist vs. Bayesian). However, its result turns out to be quite similar. While randomization's contribution remains questionable, comparability contributes much to a compelling conclusion. Summing up, classical experimentation based on sound background theory and the systematic construction of exchangeable groups seems to be advisable

Comparing Different Information Levels

Given a sequence of random variables ${\bf X}=X_1,X_2,\ldots$ suppose the aim is to maximize one's return by picking a `favorable' $X_i$. Obviously, the expected payoff crucially depends on the information at hand. An optimally informed person knows all the values $X_i=x_i$ and thus receives $E (\sup X_i)$. We will compare this return to the expected payoffs of a number of observers having less information, in particular $\sup_i (EX_i)$, the value of the sequence to a person who only knows the first moments of the random variables. In general, there is a stochastic environment (i.e. a class of random variables $\cal C$), and several levels of information. Given some ${\bf X} \in {\cal C}$, an observer possessing information $j$ obtains $r_j({\bf X})$. We are going to study `information sets' of the form $$R_{\cal C}^{j,k} = \{ (x,y) | x = r_j({\bf X}), y=r_k({\bf X}), {\bf X} \in {\cal C} \},$$ characterizing the advantage of $k$ relative to $j$. Since such a set measures the additional payoff by virtue of increased information, its analysis yields a number of interesting results, in particular `prophet-type' inequalities.Comment: 14 pages, 3 figure

Welfare effects of intellectual property in a north-south model of endogenous growth with comparative advantage

This paper develops a model for analyzing the costs and benefits of intellectual property enforcement in LDCs. The North is more productive than the South and is the only source of innovator. There are two types of goods, and each bloc has a comparative advantage in producing a specific type of good. If comparative advantage is strong enough, even under piracy there are goods that the South will not produce. Piracy will then lead to a reallocation of innovative activity in favor of these goods. That may harm consumers (including consumers in the South) to the extent that these goods have smaller dynamic learning externalities than the other goods, and that their share in consumption is small. Thus, whether or not piracy is in the interest of the South depends on how important are the goods for which it has a comparative advantage to its consumers, and what the growth potential of these goods is. While, all else equal, the North tends to lose more (or gain less) from piracy than the South, because monopoly profits eventually accrue to the North, the South may lose more than the North if there is a strong enough home bias in favor of the goods for which it has a comparative advantage

Economic growth and the design of search engines

The Internet plays a growing role in the economy. This paper extrapolates this trend and analyses a world where most transactions take place in "cyberspace". We ask the following question: how does the design of the search engine affect the incentives to innovate and the economy’s long run growth rate? This is done in the context of a "qualitative" model where growth occurs because the number of varieties grows and consumers select a shrinking fraction of the available goods, of growing quality. They must use a search engine to locate goods. The search engine affects the market size of a good over its life cycle, and thus the incentives to innovate. Its structure has two conflicting effects. A visibility effect by which a greater hit score increases market size. A selection effect by which consumers are more picky and select higher quality goods, thus reducing the life span of any given good. While these two effects on growth cancel out for simple specifications, that is no longer the case if a firm’s score is variable along its life cycle or if he search process uses resources. It is shown that the discount effect of gradual recognition of popularity tends to reduce growth. Hence, growth is enhanced if the search engine is less sensitive to popularity. Also, growth is lower when the search engine rewards "web page quality" better because of the resources diverted away from R and D into advertising. But these mechanisms generate opposite level effects on the average quality selected by consumers. As a result the net effect on welfare is ambiguous