Statnote 30 : The one-way analysis of variance (ANOVA):fixed effects model

In Statnote 9, we described a one-way analysis of variance (ANOVA) ‘random effects’ model in which the objective was to estimate the degree of variation of a particular measurement and to compare different sources of variation in space and time. The illustrative scenario involved the role of computer keyboards in a University communal computer laboratory as a possible source of microbial contamination of the hands. The study estimated the aerobic colony count of ten selected keyboards with samples taken from two keys per keyboard determined at 9am and 5pm. This type of design is often referred to as a ‘nested’ or ‘hierarchical’ design and the ANOVA estimated the degree of variation: (1) between keyboards, (2) between keys within a keyboard, and (3) between sample times within a key. An alternative to this design is a 'fixed effects' model in which the objective is not to measure sources of variation per se but to estimate differences between specific groups or treatments, which are regarded as 'fixed' or discrete effects. This statnote describes two scenarios utilizing this type of analysis: (1) measuring the degree of bacterial contamination on 2p coins collected from three types of business property, viz., a butcher’s shop, a sandwich shop, and a newsagent and (2) the effectiveness of drugs in the treatment of a fungal eye infection.

Consistent estimation of the fixed effects ordered logit model

The paper considers panel data methods for estimating ordered logit models with individual-specific correlated unobserved heterogeneity. We show that a popular approach is inconsistent, whereas some consistent and efficient estimators are available, including minimum distance and generalized method-of-moment estimators. A Monte Carlo study reveals the good properties of an alternative estimator that has not been considered in econometric applications before, is simple to implement and almost as efficient. An illustrative application based on data from the German Socio-Economic Panel confirms the large negative effect of unemployment on life satisfaction that has been found in the previous literature.

Identification and estimation of thresholds in the fixed effects ordered logit model

This paper proposes a new estimator for the fixed effects ordered logit model. In contrast to existing methods, the new procedure allows estimating the thresholds. The empirical relevance and simplicity of implementation is illustrated in an application on the effect of unemployment on life satisfaction.

Designs and model effects definitions in the initial stage of a plant breeding program

The objective of this work was to compare the relative efficiency of initial selection and genetic parameter estimation, using augmented blocks design (ABD), augmented blocks twice replicated design (DABD) and group of randomised block design experiments with common treatments (ERBCT), by simulations, considering fixed effect model and mixed model with regular treatment effects as random. For the simulations, eight different conditions (scenarios) were considered. From the 600 simulations in each scenario, the mean percentage selection coincidence, the Pearsons´s correlation estimates between adjusted means for the fixed effects model, and the heritability estimates for the mixed model were evaluated. DABD and ERBCT were very similar in their comparisons and slightly superior to ABD. Considering the initial stages of selection in a plant breeding program, ABD is a good alternative for selecting superior genotypes, although none of the designs had been effective to estimate heritability in all the different scenarios evaluated.

Do laws influence the cost of real estate brokerage services? A state fixed effects approach

A FTC-DOJ study argues that state laws and regulations may inhibit the unbundling of real estate brokerage services in response to new technology. Our data show that 18 states have changed laws in ways that promote unbundling since 2000. We model brokerage costs as measured by number of agents in a state-level annual panel vector autoregressive framework, a novel way of analyzing wasteful competition. Our findings support a positive relationship between brokerage costs and lagged house price and transactions. We find that change in full-service brokers responds negatively (by well over two percentage points per year) to legal changes facilitating unbundling

Energy efficiency in the Chinese provinces: a fixed effects stochastic frontier spatial Durbin error panel analysis

Energy efficiency improvement has been a key objective of China’s long-term energy policy. In this paper, we derive single-factor technical energy efficiency (abbreviated as energy efficiency) in China from multi-factor efficiency estimated by means of a translog production function and a stochastic frontier model on the basis of panel data on 29 Chinese provinces over the period 2003–2011. We find that average energy efficiency has been increasing over the research period and that the provinces with the highest energy efficiency are at the east coast and the ones with the lowest in the west, with an intermediate corridor in between. In the analysis of the determinants of energy efficiency by means of a spatial Durbin error model both factors in the own province and in first-order neighboring provinces are considered. Per capita income in the own province has a positive effect. Furthermore, foreign direct investment and population density in the own province and in neighboring provinces have positive effects, whereas the share of state-owned enterprises in Gross Provincial Product in the own province and in neighboring provinces has negative effects. From the analysis it follows that inflow of foreign direct investment and reform of state-owned enterprises are important policy handles.

What hides behind the fixed-term contracts wage gap?

In Portugal, about 20% of full-time workers are employed under a fixed-term contract. Using a rich longitudinal matched employer-employee dataset for Portugal, with more than 20 million observations and covering the 2002-2012 period, we confirm the common idea that fixed-term contracts are not desirable when compared to permanent ones, by estimating a conditional wage gap of -1.7 log points. Then, we evaluate the sources of that wage penalty by combining a three way high-dimensional fixed effects model with the decomposition of Gelbach (2014), in which the three dimensions considered are the worker’s unobserved ability, the firm’s compensation wage policy and the job title effect. It is shown that the average worker with a fixed-term contract is less productive than his/her permanent counterparts, explaining -3.92 log points of the FTC wage penalty. Additionally, the sorting of workers into lower-paid job titles is also responsible for -0.59 log points of the wage gap. Surprisingly, we found that the allocation of workers among firms mitigates the existing wage penalty (in 4.23 log points), as fixed-term workers are concentrated into firms with a more generous compensation policy. Finally, following Figueiredo et al. (2014), we further control for the worker-firm match characteristics and reach the conclusion that fixed-term employment relationships have an overrepresentation of low quality worker-firm matches, explaining 0.65 log points of the FTC wage penalty.

Administrative costs of regulation and foreign direct investment: evidence from Standard Cost Model implementation in non-OECD countries

In recent years both developed and developing countries have experienced an increasing number of government initiatives dedicated to reducing the administrative costs (AC) imposed on businesses by regulation. We use a bi-linear fixed-effects model to analyze the extent to which government initiatives to reduce AC through the Standard Cost Model (SCM) attract Foreign Direct Investment (FDI) among 32 developing countries. Controlling for standard determinants of the SCM, we find that the SCM in most cases leads to higher FDI and that the benefits are more significant where the SCM has been implemented for a longer period.

Type-1 error inflation in the traditional by-participant analysis to metamemory accuracy: a generalized mixed-effects model perspective

In order to examine metacognitive accuracy (i.e., the relationship between metacognitive judgment and memory performance), researchers often rely on by-participant analysis, where metacognitive accuracy (e.g., resolution, as measured by the gamma coefficient or signal detection measures) is computed for each participant and the computed values are entered into group-level statistical tests such as the t-test. In the current work, we argue that the by-participant analysis, regardless of the accuracy measurements used, would produce a substantial inflation of Type-1 error rates, when a random item effect is present. A mixed-effects model is proposed as a way to effectively address the issue, and our simulation studies examining Type-1 error rates indeed showed superior performance of mixed-effects model analysis as compared to the conventional by-participant analysis. We also present real data applications to illustrate further strengths of mixed-effects model analysis. Our findings imply that caution is needed when using the by-participant analysis, and recommend the mixed-effects model analysis.

Modified Fixed Effects Estimation of Technical Inefficiency

We consider method of moment fixed effects (FE) estimation of technical inefficiency. When N, the number of cross sectional observations, is large it ispossible to obtain consistent central moments of the population distribution of the inefficiencies. It is well-known that the traditional FE estimator may be seriously upward biased when N is large and T, the number of time observations, is small. Based on the second central moment and a single parameter distributional assumption on the inefficiencies, we obtain unbiased technical inefficiencies in large N settings. The proposed methodology bridges traditional FE and maximum likelihood estimation – bias is reduced without the random effects assumption.

A finite sample improvement of the fixed effects estimator : applied to technical infficiency

The FE ('fixed effects') estimator of technical inefficiency performs poorly when N ('number of firms') is large and T ('number of time observations') is small. We propose estimators of both the firm effects and the inefficiencies, which have small sample gains compared to the traditional FE estimator. The estimators are based on nonparametric kernel regression of unordered variables, which includes the FE estimator as a special case. In terms of global conditional MSE ('mean square error') criterions, it is proved that there are kernel estimators which are efficient to the FE estimators of firm effects and inefficiencies, in finite samples. Monte Carlo simulations supports our theoretical findings and in an empirical example it is shown how the traditional FE estimator and the proposed kernel FE estimator lead to very different conclusions about inefficiency of Indonesian rice farmers.