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.matched employer-employee data, high-dimensional two-way unobserved components, ECM-algorithm

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 identi…cation of the e¤ect of time-invariant variables on the observation units. Applying the Helmert transformation to reduce dimensionality simpli…es 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 a¤ects the estimate of the return to education considerably.High-dimensional two-way unobserved components; Matched employer-employee data; ECM-algorithm.

Dynamics of First-Time Patenting Firms

This paper investigates firm dynamics in the period before, during, and after an event consisting of a first published patent application. The analysis is based on patent data from the Norwegian Industrial Property Office merged with data from several business registers covering a period of almost 20 years. We apply an event study design and use matching to control for confounding factors. The first patent application by a young firm is associated with significant growth in employment, output, assets and public research funding. Moreover, our results indicate that economic activity starts to increase at least three years ahead of the first patent application. However, we find no evidence of additional firm growth after patent approval for successful applicants. Our findings indicate that the existence of a properly functioning patenting system supports innovation activities, especially early in the life cycle of firms

The impact of new varieties on aggregate productivity growth*

Although there is an extensive body of literature on aggregate productivity growth, reallocation, and firm turnover, the contribution to overall productivity growth from new firms that produce new varieties is not well understood. In this paper, we propose a framework for aggregating productivity that identifies the contribution from new firms that produce new varieties. Our framework generalizes the frameworks currently used in the literature. To illustrate the decomposition, we analyse the case of firm turnover in Norway. We find that the net creation of new varieties due to firm turnover contributes about half a percentage point to annual aggregate labour productivity growth in the manufacturing sector.The impact of new varieties on aggregate productivity growth*publishedVersio

Dynamics of first-time patenting firms

This paper investigates firm dynamics in the period before, during, and after an event consisting of a first published patent application. The analysis is based on patent data from the Norwegian Industrial Property Office merged with data from several business registers covering a period of almost 20 years. We apply an event study design and use matching to control for confounding factors. The first patent application by a young firm is associated with significant growth in employment, output, assets and public research funding. Moreover, our results indicate that economic activity starts to increase at least three years ahead of the first patent application. However, we find no evidence of additional firm growth after patent approval for successful applicants. Our findings indicate that the existence of a properly functioning patenting system supports innovation activities, especially early in the life cycle of firms

The Importance of Skill Measurement for Growth Accounting

In a growth accounting context one usually constructs a quality adjusted index of labor services by aggregating over predefined groups of workers, using the groups' relative wage bills as weights. In this article we suggest a method based on decomposing individual predicted wages into a skill-related part and a part unrelated to skill, where the former consists of both observed and unobserved components. The predicted wages, associated with individual skill attributes, are sorted and classified into deciles. The median predicted skill-related wage in each decile is used to construct an alternative skill-adjusted index of labor services. We find that Total Factor Productivity (TFP) growth decreases significantly when using the latter method. This means that when using the alternative method one explains more of the growth in labor productivity than what a more traditional labor quality adjustment procedure does.wage equation, skill measures, TFP growth

Multivariate stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck processes : a quasi-likelihood approach

This paper extends the ordinary quasi-likelihood estimator for stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck (OU) processes to vector processes. Despite the fact that multivariate modeling of asset returns is essential for portfolio optimization and risk management -- major areas of financial analysis -- the literature on multivariate modeling of asset prices in continuous time is sparse, both with regard to theoretical and applied results. This paper uses non-Gaussian OU-processes as building blocks for multivariate models for high frequency financial data. The OU framework allows exact discrete time transition equations that can be represented on a linear state space form. We show that a computationally feasible quasi-likelihood function can be constructed by means of the Kalman filter also in the case of high-dimensional vector processes. The framework is applied to Euro/NOK and US Dollar/NOK exchange rate data for the period 2.1.1989-4.2.2010.Financial support from the Norwegian Research Council ("Finansmarkedsfondet") is gratefully acknowledged

A bankruptcy probability model for assessing credit risk on corporate loans with automated variable selection

We propose an econometric model for predicting the share of bank debt held by bankrupt firms by combining a novel set of firm-level financial variables and macroeconomic indicators. Our firm-level data include payment remarks in the form of debt collections from private agencies and attachments from private and public agencies and cover all Norwegian limited liability companies for the period 2010–2021. We use logistic Lasso regressions to select bankruptcy predictors from a large set of potential predictors, comparing a highly sparse variable selection criterion (“the one standard error rule”) with the minimum cross validation error (CVE) criterion. Moreover, we examine the implications of using debt shares as weights in the estimation and find that weighting has a large impact on variable selection and predictions and, generally, leads to lower out-of-sample prediction errors than alternative approaches. Debt weighting combined with sparse variable selection gives the best predictions of the risk of bankruptcy in firms holding high shares of the bank debt.publishedVersio

Identifying the elasticity of substitution between capital and labour: a pooled GMM panel estimator

Simultaneity represents a fundamental problem when estimating the elasticity of substitution between capital and labour. To overcome this problem, a wide variety of external instruments has been applied in the literature. However, the use of instruments may lead to wrong inference if they are either weak, or endogenous to the system being estimated. In this paper, we extend the widely used Feenstra (1994) estimator, which does not depend on external instruments, to make it applicable to the problem of estimating the elasticity of substitution between capital and labour. We propose a pooled GMM (PGMM) estimator, examine its properties in a Monte Carlo study and apply it to a Norwegian sample of manufacturing firms. We identify the conditions under which P-GMM yields unbiased estimates and compare it to a fixed effects estimator which is unbiased when factor prices are exogenous – a typical assumption in the literature. We find that the fixed effects estimator is heavily downward biased in the presence of simultaneity. In contrast, the P-GMM estimator is nearly unbiased provided the number of time periods (T) is not too small (say, more than 10). In our application, with an unbalanced sample and T = 12, we estimate the elasticity of substitution to be 1.8 using P-GMM and 1.0 using a fixed effects estimator. Hence, neglecting simultaneity may lead to the conclusion that capital and labour are complements when, in fact, they are substitutes

A new approach to estimating private returns to R&D

This paper revisits the estimation of private returns to R&D. In an extension of the standard approach, we allow for endogeneity of production decisions, heterogeneity of R&D elasticities, and asymmetric treatment of intramural and extramural R&D. Our empirical analyses are based on an extended Cobb-Douglas production function that allows for firms with zero R&D capital, which is especially useful for studying firms’ transition from being R&D-non—active to becoming R&D-active. Using a large panel of Norwegian firms observed in the period 2001-2018, we estimate the average private net return to be in the range 0-5 percent across a variety of model specifications if we treat intra- and extramural R&D symmetrically. If in compliance with the Frascati manual, we treat intramural R&D as investment and extramural R&D as intermediate input, the estimated net return increases to 5-10 percent