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We establish a `map' for describing a wide class of Limited Dependent Variables models much used in the econometric literature. The classification system, or language, is an extension of Amemiya's typology for tobit models and is intended to facilitate communication among researchers. The class is defined in relation to distributions of latent variables of an arbitrarily high dimension; the region of support can be divided into an arbitrary number of subsets, and the observation rules in each subset can be any combination of the observed, censored, and missing status. Consistent labeling is suggested at different levels of detail.

The aim of this paper is two-fold: (a) to establish a 'map' for describing the wide class of Limited Dependent Variables (LDV) univariate and multivariate models in the econometric literature and (b) to localize typical models in this tradition within the structure, extending typologies of Heckman (1976) and Amemiya (1984). The classification system, or language, proposed, is given at different level of detail. Its scope is (1) that the latent variables can have any parametric distribution, (2) that a set of observation rules which include the observed, censored, missing status, is imposed, (3) that it should be possible to write a model combining (1) and (2) by means of a computer algorithm, also potentially applicable for generating samples and (4) that the models belonging to the system should have names to facilitate communication among researchers. The likelihood functions corresponding to the models' observed endogenous variables are discussed, but the paper is not concerned with describing the application of these functions for inference.

The seminal paper by Pissarides and Weber (1989) is one of several previous studies trying to measure the size of the black economy. Pissarides and Weber compared the relationship between food expenditure and income in two groups of workers, self-employed and employees in employment, assuming that employees reported income correctly. For a given level of reported income, the self-employed had a higher food expenditure than employees. Pissarides and Weber concluded that self-employed's actual income was 1.55 times reported income, and that this part of the black economy was about 5.5 percent of GDP in the UK in 1982. Presumably due to a too informal argumentation, Pissarides and Weber's estimators are not entirely correct and alternative estimators have been overlooked. In all, I suggest three different interval estimators for mean under-reporting. The first is obtained by formally solving optimization problems which Pissarides and Weber tried to solve informally. The other two follows from recognizing, and incorporating, parameter restrictions which were not fully appreciated.

Parametric aggregation of heterogeneous micro production technologies is discussed. A four-factor Cobb-Douglas function with normally distributed firm specific coefficients and with log-normal inputs (which agrees well with the available data) is speciffied. Since, if the number of micro units is large enough, aggregates expressed as arithmetic means can be associated with expectations, we consider conditions ensuring an approximate relation of Cobb-Douglas form to exist between expected output and expected inputs. Similar relations in higher-order moments are also derived. It is shown how the aggregate input elasticities depend on the coefficient heterogeneity and the co-variance matrix of the log-input vector and hence vary over time. An implementation based on firm panel data for two manufacturing industries gives estimates of industry level input elasticities and decomposition for expected output. Finally, aggregation errors which emerge when the correct aggregate elasticities are replaced by the expected micro elasticities, are explored.

The econometric implementation of rational addiction theory has been highly influenced by Becker, Grossman and Murphy (BGM). They specify an Euler equation where current consumption is determined by current price and past and future consumption. This model is claimed to be able to discriminate between rational addictive, myopic addictive, and non-addictive behavior. However, as demonstrated in this paper, the coefficients of the Euler equation are not structural parameters. Provided that two implausible assumptions do not hold, the Euler equation coefficients for the rational addict are shown to be non-constant. But even when these assumptions are assumed to be valid, the coefficients of the Euler equation will vary under the alternative hypothesis of myopic addiction. Moreover, and in contrast to the common interpretation, BGM's non-addicted consumer is influenced by past consumption, implying that a rational and a myopic non-addict behave differently. These problems makes it unclear how analyses based on the BGM approach can support, or reject, rational addiction theory.

The paper presents a panel data analysis of tobacco demand. The purpose is threefold: (i) to measure income, own-price, and cross-price responses for two tobacco commodities: cigarettes and handrolling tobacco, (ii) to investigate sociodemographic effects, and (iii) to utilize the potential offered by panel data to investigate unobserved heterogeneity. The latter is crucial for commodities where consumers have different tastes and where users tend to become addicted. Several linear and non-linear specifications of a two-equation system are estimated, using an unbalanced panel data set of Norwegian households over the period 1975 - 1994 and a modified Maximum Likelihood procedure. Differences between the results based on the sub-sample of smokers and on the pooled sample of smokers and non-smokers are interpreted. For both commodities we find a high degree of unobserved heterogeneity and several robust and "heory consistent" patterns with respect to price responses and demographic effects.

This paper analyzes tobacco demand within a discrete choice framework. Using binomial and multinomial logit models with random effects, and an unbalanced panel data set of Norwegian households over a twenty year period, we first consider the decisions a) whether to smoke or not, and b) given the choice is to smoke, whether to smoke hand rolled or manufactured cigarettes. Next, we consider a multinomial logit framework, in which the households choose between no tobacco, only manufactured cigarettes, only hand rolled cigarettes, and a combination of manufactured and hand rolled cigarettes. In this process, we utilize the potential offered by panel data to investigate unobserved heterogeneity, which is crucial for commodities where consumers have different tastes and where users tend to become addicted. Using Maximum Likelihood in combination with bootstrap estimation of standard errors, we find that income and prices influence the 'type of tobacco choice probabilities' at least as strongly as the 'smoking/non-smoking probabilities'. Cet.par., an increase in the price of manufactured cigarettes could lead consumers to switch to hand rolled cigarettes, rather than quit smoking. Socio-demographic variables seem to be at least as important in explaining the discrete aspects of tobacco consumption as income and prices. Finally, we find significant unobserved household specific effects in the smoking pattern.