The standard formalization of the econometric analysis of treatment response assumes that each member of a population of interest receives one of a set of mutually exclusive and exhaustive treatments, and that the outcome under the realized treatment is observable. Outcomes under the nonrealized treatments are necessarily unobservable; hence these outcomes are censored. This paper investigates what may be learned about treatment response when it is assumed that response functions are monotone, semi-monotone, or concave-monotone. The analysis assumes nothing about the process of treatment selection and imposes no cross-individual restrictions on response. The basic idea is to determine, for every member of the population, the set of response functions that pass through that person's realized (treatment, outcome) pair and that are consistent with the functional-form assumption imposed. These person-specific findings are then explicitly aggregated across the population to determine what can be learned about the distribution of response. The findings have application to the econometric analysis of market demand and of production.
This paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak, here modeled as local to zero. Asymptotic representations are provided for various instrumental variable statistics, including the two-stage least squares (TSLS) and limited information maximum- likelihood (LIML) estimators and their t-statistics. The asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument. Even in large samples, TSLS can be badly biased, but LIML is, in many cases, approximately median unbiased. The theory suggests concrete quantitative guidelines for applied work. These guidelines help to interpret Angrist and Krueger's (1991) estimates of the returns to education: whereas TSLS estimates with many instruments approach the OLS estimate of 6%, the more reliable LIML and TSLS estimates with fewer instruments fall between 8% and 10%, with a typical confidence interval of (6%, 14%).
IF THE SENDER'S PREFERENCES are monotonic in the Receiver's action, then it is known that the Sender reveals its type in every sequential equilibrium of a Sender-Receiver game with verifiable messages (see, e.g., Milgrom (1981)). Monotonicity is a natural condition in social situations such as buyer-seller relationships; but there are obviously other situations in which the ideal action for a Sender varies with its type. Accordingly, we generalize Milgrom's result by replacing monotonicity with more general conditions on the Sender's preferences, which are sufficient for existence and uniqueness of a fully revealing equilibrium in verifiable message games. These conditions include all games in which preferences satisfy the conditions which Crawford-Sobel (1982) imposed on cheap talk games.
THE PROTECTION OF POOR HOUSEHOLDS in high-risk agrarian economies from shocks to their incomes has often been seen as a compelling motive for various forms of policy intervention including transfers of cash or food, credit subsidies, and public employment schemes (for a survey see Lipton and Ravallion (1995)). The desirability of such safety net policies clearly depends on how well pre-existing risk-sharing arrangements work. While it is commonly thought that, without effective policy intervention, rural households are vulnerable to village-wide shocks such as adverse prices or poor rains, it is less clear to what extent risk-sharing institutions within the village mitigate the effects of idiosyncratic income risk stemming, for instance, from ill-health or localized crop damage.2 Several recent papers have used household-level data to implement tests of risk-sharing that might inform such concerns.3 These tests are based on the proposition that with perfect risk-sharing, consumption at the household level should be insured against idiosyncratic risks and thus depend solely on the realization of the aggregate risk (Wilson (1968); Diamond (1967)). Townsend (1994) tests this implication of perfect intra-village risk-sharing using longitudinal household data on consumptions and incomes for three villages in India. He reports that the full-insurance hypothesis provides a surprisingly good benchmark in that household consumptions co-move and do not appear to be much influenced by contemporaneous own income. Our aim here is to examine the robustness of this potentially important finding. We have two main concerns. The first is that the specification Townsend adopts potentially biases his test towards the null hypothesis of full insurance because it yields inconsistent estimates of the key test parameter under a plausible alternative. We therefore estimate a different specification that generates consistent estimates under both the null and the alternative. Our second concern is that a particular form of measurement error in the consumption data Townsend uses may have further biased his results toward the null hypothesis of full-insurance. To address this concern, we use an instrumental variables procedure when we implement the test of consumption insurance with Townsend's consumption data. We also re-estimate the test equations with a measure of consumption derived from the same underlying primary data by an alternate method. Finally, Townsend reports 1Discussions with Robert Townsend stimulated our interest in this investigation. The staff of the
The authors consider a repeated game between two long-run players, one of whom is relatively patient. Each player has a small amount of uncertainty about the other's strategy. Given a weak assumption about the support of this uncertainty, the more patient player obtains (in any Nash equilibrium) approximately the highest payoff consistent with the individual rationality of the other player, if the latter is patient enough. If the less patient player is relatively impatient, any Nash equilibrium gives the more patient player at least the Stackelberg payoff: this generalizes K. M. Schmidt's (1993) result, which applies only to games of conflicting interests.
This paper extends the Kiyotaki-Wright search model of fiat money to allow for divisible money and goods. The extension allows me to examine the standard issues in monetary economics, such as the neutrality and superneutrality of money, by severing the artificial link in the Kiyotaki-Wright model between the money supply and the number of money holders. It is shown that money is neutral, but not superneutral. Money growth generates a trading opportunity effect: it changes the fraction of different agents in the economy and hence changes the probability with which agents have a successful match. In addition, money growth has a negative effect on the real money balance that is familiar in Walrasian monetary models. The balance of the two effects can imply a positive optimal money growth rate.
In this paper we derive the asymptotic distribution of the test statistic of a generalized version of the integrated conditional moment (ICM) test of Bierens (1982, 1984), under a class of Vn-local alternatives, where n is the sample size. The generalized version involved includes neural network tests as a special case, and allows for testing misspecification of dynamic models. It appears that the ICM test has nontrivial local power. Moreover, we show that under the assumption of normal errors the ICM test is asymptotically admissible, in the sense that there does not exist a test that is uniformly more powerful. The asymptotic size of the test is case-dependent: the critical values of the test depend on the data-generating process. In this paper we derive case-independent upperbounds of the critical values
For conditional heteroskedasticity models, the authors study the identification condition that is required for consistency of a non-Gaussian quasi-maximum-likelihood estimator. They show that, if the conditional mean is zero or if a symmetry condition is satisfied, then the identification condition is satisfied. Without symmetry, an additional parameter, for the location of the innovation density, must be added for identification. For the conditional variance parameters of a GARCH process, there is no efficiency loss from adding the parameter under symmetry, when the parameter is not needed.