Terje Skjerpen

Heterogeneity in Returns to Scale: A Random Coefficient Analysis with Unbalanced Panel Data ∗

This paper analyses the importance of scale economies by means of unbalanced plant-level panel data from three Norwegian manufacturing industries. Focus is on heterogeneous technologies, and unlike most previous work on micro data, the model description includes heterogeneity in both the scale properties (the slope coefficients) and the intercept term, represented by random coefficients in the production function. Three (nested) functional forms are investigated: the Translog, an extended Cobb-Douglas, and the strict Cobb-Douglas. Although constant or moderately increasing returns to scale is found for the average plant, the results reveal considerable variation across plants. Variations in both input and scale elasticities are to a larger extent due to randomness of the production function parameters than to systematic differences in the input mix.

Engel Functions, Panel Data, and Latent Variables

Systems of consumer expenditure functions are estimated from Norwegian household panel data. Total consumption expenditure is modeled as a latent variable, as indicators of it are purchase expenditures on different goods and two income measures. The usual assumption of no measurement error in total expenditure is clearly rejected while a parsimonious alternative is not. The authors test hypotheses regarding the distribution of measurement errors, the evolution of the distribution of latent total expenditure across households, the distribution of individual differences in preferences, and the possible correlation between preferences and latent total expenditure. Copyright 1993 by The Econometric Society.

Unit Roots, Polynomial Transformations and the Environmental Kuznets Curve

Properties of estimators of long-run parameters in a polynomial regression with nonstationary, strongly exogenous regressors are considered in the context of the Environmental Kuznets Curve using Monte Carlo simulations. Standard inferential procedures seem to work well in this context.

Using the Helmert-Transformation to Reduce Dimensionality in a Mixed Model: Application to a Wage Equation with Worker and Firm Heterogeneity

A model for matched data with two types of unobserved heterogeneity is considered – one related to the observation unit, the other to units to which the observation units are matched. One or both of the unobserved components are assumed to be random. This mixed model allows identification of the effect of time-invariant variables on the observation units. Applying the Helmert transformation to reduce dimensionality simplifies the computational problem substantially. The framework has many potential applications; we apply it to wage modeling. Using Norwegian manufacturing data shows that the assumption with respect to the two types of heterogeneity affects the estimate of the return to education considerably.

Random Coefficients in Unbalanced Panels: An Application on Data from Chemical Plants

A framework for analyzing substitution and scale properties from plant-level panel data is presented. Focus is on comparing the constant and random coefficient specification of the substitution and scale parameters and investigating the variation of the parameters across plants. Characteristics of the model framework are (i) an equation system consisting of a three-factor translog cost function and the corresponding cost-share equations, (ii) random plant specific heterogeneity in coefficients, and (iii) a Maximum Likelihood procedure allowing for unbalanced panel data. The empirical results, based on data from Norwegian chemical plants, indicate pronounced plant specific heterogeneity in substitution and scale properties. Substantial parts of the variances of the cost and the cost shares can be ascribed to variation in the coefficient vector. The estimated mean scale properties are considerably influenced by the choice of model specification, while conclusions regarding price effects are more robust.

Changing trend? Sex ratios of children born to Indian immigrants in Norway revisited

BackgroundIn some Western countries, a disturbingly low share of girls has been observed among new-borns from Indian immigrants. Also in Norway, a previous study based on figures from 1969–2005 showed a high percentage of boys among children of Indian origin living in Norway, when the birth was of higher order (third birth or later). This was suggested to reflect a practice of sex-selective abortions in the Indian immigrant population. In this article we have seen whether extended time series for the period 2006–2012 give further support to this claim.MethodsBased on data from the Norwegian Central Population Register we used observations for the sex of all live births in Norway for the period 1969–2012 where the mother was born in India. The percentage of boys was calculated for each birth order, during four sub periods. Utilising a binomial probability model we tested whether the observed sex differences among Indian-born women were significantly different from sex differences among all births.ResultsContrary to findings from earlier periods and other Western countries, we found that Indian-born women in Norway gave birth to more girls than boys of higher order in the period 2006–2012. This is somewhat surprising, since sex selection is usually expected to be stronger if the mother already has two or more children.ConclusionsThe extended time series do not suggest a prevalence of sex selective abortions among Indian-born women in Norway. We discuss whether the change from a majority of boys to a majority of girls in higher order could be explained by new waves of immigrant women, by new preferences among long-residing immigrant women in Norway – or by mere coincidence.

Can Random Coefficient Cobb-Douglas Production Functions Be Aggregated to Similar Macro Functions?

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.

Forecasting Immigration in Official Population Projections Using an Econometric Model

Although substantial research has been conducted to quantify the determinants of international migration, most official population projections do not include such determinants in a formal migration model. Statistics Norway forecasts gross immigration to Norway using an econometric model based on standard migration theories. The main variables include income level, unemployment, and population size in Norway and the sending countries, and the number of immigrants already living in Norway. Projections of exogenous variables are drawn from international and Norwegian sources. Three different alternatives are specified for the income variables, leading to three different forecasts for gross immigration until 2100.

Modelling and forecasting rig rates on the Norwegian Continental Shelf

Knowledge about rig markets is crucial for understanding the global oil market. In this paper we first develop a simple bargaining model for rig markets. Then we examine empirically the most important drivers for rig rate formation of floaters operating at the Norwegian Continental Shelf in the period 1991q4 to 2013q4. We use reduced form time series models with two equations and report conditional point and bootstrapped interval forecasts for rig rates and capacity utilization. We then consider two alternative simulations to examine how the oil price and remaining petroleum reserves influence rig rate formation of floaters. In the first alternative simulation we assume a relatively high crude oil price equal to 100 USD (2010) per barrel for the entire forecast period, whereas the reference case features the actual oil price with extrapolated values for the last quarters in the forecast period. According to our results, the rig rates will be about 34 percent higher in 2016q4 with the higher oil price. In the second alternative simulation we explore the effects of opening the Barents Sea and areas around Jan Mayen for petroleum activity. This contributes to dampening the fall in the rig rates and capacity utilization over the last part of the forecast period.

Macroeconomic shocks and the probability of being employed

Macroeconomic theories take polar views on the importance of choice versus chance. At the micro level, it seems realistic to assume that both dimensions play a role for individual employment outcomes, although it might be difficult to separate these two effects. Nevertheless the choice and chance dimension are seldom treated symmetrically in models that use micro data. We estimate a logistic model of the probability of being employed among married or cohabitating women that are in the labor force. Besides variables that measure individual characteristics (choice), we allow a full set of indicator variables for observation periods that represent potential effects of aggregate shocks (chance) on job probabilities. To reduce the number of redundant indicator variables as far as possible and in a systematic way, an automatic model selection is used, and we assess the economic interpretation of the statistically significant indicator variables with reference to a theoretical framework that allows for friction in the Norwegian labor market. In addition, we also estimate models that use the aggregate female and male unemployment rates as ‘sufficient’ variables for the chance element in individual employment outcomes. Data are for Norway and span the period 1988q22008q4.