Single-equation Regression Models Research Articles

Even correctly specified and well-estimated regression models can mislead

It should be possible to draw causal conclusions from happenstance data. However, there are many well-known reasons for doubting the causal interpretation of single equation regression models based on such data. Still, hope springs eternal. The hope is founded on the belief that if the function linking the response variable to the predictor variables was known and its parameters estimated from plentiful data then one could predict what change in the response variable is caused by a change in a predictor variable. But what if this foundational belief was incorrect?I use a thought experiment to show even perfect models can lead to incorrect conclusions. The problem is that to say what change in the response variable is caused by a change in a predictor variable one must assume that all the other predictor variables remain unchanged. This may not be possible or may require changes to reality that are outside of the model, changes that almost certainly will not exist. To interpret the estimated model equation correctly one must trace all real-world consequences of holding the predictor variables constant. This is not easy to do. The history of regression-based research about the road safety effect of speed supports my case.

The Millennial’s Investment Decisions: Implications of Financial Literacy, Motivation, and Digitalization

Investment as a means of developing assets is no longer a luxury activity reserved for a select few. Nowadays, as financial technology advances, everyone has equal access to investment information. This change generates new perspectives in which investing is not restricted to the wealthy, leading everyone, even on-budget millennials to be investors. The purpose of this research is to determine the variables affecting investing decisions at an early age, especially among millennials. This research adopted single-equation regression models to examine the dependent variable on several explanatory variables and estimate mean or average value. The data was generated using a questionnaire to 140 respondents. Three distinct variables utilized as independent variables are financial literacy, motivation, and the digitization of investing platforms. The findings indicate that financial literacy and motivation substantially affect millennials’ investment decisions, while digitization presents no correlation to the Millennials’ investment decisions.

Investigating the fatal pedestrian crash occurrence in urban setup in a developing country using multiple-risk source model

Pedestrian fatalities and injuries are a major public health burden in developing countries. In the safety literature, pedestrian crashes have been modelled predominately using single equation regression models, assuming a single underlying source of risk factors. In contrast, the fatal pedestrian crash counts at a site may be an outcome of multiple sources of risk factors, such as poor road infrastructure, land use type, traffic exposures, and operational parameters, site-specific socio-demographic characteristics, as well as pedestrians’ poor risk perception and dangerous crossing behavior, which may be influenced by poor road infrastructure and lack of information, etc. However, these multiple sources are generally overlooked in traditional single equation crash prediction models.In this background, this study postulates, and demonstrates empirically, that the total fatal pedestrian crash counts at the urban road network level may arise from multiple simultaneous and interdependent sources of risk factors, rather than one. Each of these sources may distinctively contribute to the total observed crash count.Intersection-level crash data obtained from the “Kolkata Police”, India, is utilized to demonstrate the present modelling methodology. The three-components mixture model and a joint econometric model are developed to predict fatal pedestrian crashes. The study outcomes indicate that the multiple-source risk models perform significantly better than the single equation regression model in terms of prediction ability and goodness-of-fit measures. Moreover, while the single equation model predicts total fatal crash counts for individual sites, the multiple risk source model predicts crash count proportions contributed by each source of risk factors and predicts crashes by a particular source.

Oil Prices, Gasoline Prices and Inflation Expectations: A New Model and New Facts

The conventional wisdom that inflation expectations respond to the level of the price of oil (or the price of gasoline) is based on testing the null hypothesis of a zero slope coefficient in a static single-equation regression model fit to aggregate data. Given that the regressor in this model is not stationary, the null distribution of the t-test statistic is nonstandard, invalidating the use of the normal approximation. Once the critical values are adjusted, these regressions provide no support for the conventional wisdom. Using a new structural vector regression model, however, we demonstrate that gasoline price shocks may indeed drive one-year household inflation expectations. The model shows that there have been several such episodes since 1990. In particular, the rise in household inflation expectations between 2009 and 2013 is almost entirely explained by a large increase in gasoline prices. However, on average, gasoline price shocks account for only 39% of the variation in household inflation expectations since 1981.

Oil Prices, Gasoline Prices and Inflation Expectations: A New Model and New Facts

The conventional wisdom that inflation expectations respond to the level of the price of oil (or the price of gasoline) is based on testing the null hypothesis of a zero slope coefficient in a static single-equation regression model fit to aggregate data. Given that the regressor in this model is not stationary, the null distribution of the t-test statistic is nonstandard, invalidating the use of the normal approximation. Once the critical values are adjusted, these regressions provide no support for the conventional wisdom. Using a new structural vector regression model, however, we demonstrate that gasoline price shocks may indeed drive one-year household inflation expectations. The model shows that there have been several such episodes since 1990. In particular, the rise in household inflation expectations between 2009 and 2013 is almost entirely explained by a large increase in gasoline prices. However, on average, gasoline price shocks account for only 39% of the variation in household inflation expectations since 1981.

Oil Prices, Gasoline Prices and Inflation Expectations: A New Model and New Facts

The conventional wisdom that inflation expectations respond to the level of the price of oil (or the price of gasoline) is based on testing the null hypothesis of a zero slope coefficient in a static single-equation regression model fit to aggregate data. Given that the regressor in this model is not stationary, the null distribution of the t-test statistic is nonstandard, invalidating the use of the normal approximation. Once the critical values are adjusted, these regressions provide no support for the conventional wisdom. Using a new structural vector regression model, however, we demonstrate that gasoline price shocks may indeed drive one-year household inflation expectations. The model shows that there have been several such episodes since 1990. In particular, the rise in household inflation expectations between 2009 and 2013 is almost entirely explained by a large increase in gasoline prices. However, on average, gasoline price shocks account for only 39% of the variation in household inflation expectations since 1981.

A comprehensive joint econometric model of motor vehicle crashes arising from multiple sources of risk

In the safety literature, motor vehicle crashes are modelled predominately using single equation regression models, albeit with a variety of distributional assumptions and econometric enhancements. These models rely on a single linear additive predictive equation—which becomes multiplicative with a log transform—to specify the expected mean crash count conditioned on predictors. The models also specify the distribution of observations around the conditional mean, with common examples including the Poisson, Negative Binomial, and Conway-Maxwell distribution among others. This mainstream probabilistic conceptualization (i.e. model) of motor vehicle crash causation assumes that crashes are well-approximated by a single source of risk, wherein several contributing factors exert their collective, non-independent influences on the occurrence of crashes via a linear predictor.This study first postulates, and then demonstrates empirically, that crash occurrence may be more complex than can be adequately captured by a single equation regression model. The total crash count recorded at a transport network location (e.g. road segment) may arise from multiple simultaneous and inter-dependent sources of risk, rather than one. Each of these sources may uniquely contribute to the total observed crash count. For instance, a site’s crash occurrence may be dominated by contributions from driver behaviour issues (e.g. speeding, impaired driving), while another site’s crashes might arise predominately from design and operational deficiencies such as deteriorating pavements and worn lane markings. Stated succinctly, this research hypothesises that the unobserved heterogeneity in the accumulation of motor vehicle crashes at transport network locations arises because multiple sources of risk, not one, better captures complexity in the crash occurrence process.A stochastic multiple risk source methodological approach is developed to correspond with and empirically test this hypothesis. A joint econometric model with random parameters and instrumental variables demonstrates the applicability of the proposed theory and the corresponding methodological approach. The proposed model assumes that complexity of crash occurrence is well approximated using three sources of risk comprised of engineering, unobserved spatial, and driver behavioural factors. It is empirically tested using crash data from state controlled roads in Queensland, Australia. Finally, the multiple risk source model is compared to the traditional single risk source model to assess the viability of the proposed approach based on the sample data.The multiple risk source model significantly outperformed the single risk source model in terms of prediction ability and goodness of fit measures. In addition, while the single risk source model predicts total crash counts for individual sites, the multiple risk source model predicts crash count proportions contributed by each source of risk, and predicts crashes by risk source. The improvement in fit combined with the theoretical appeal of a multiple risk source model to explain unobserved heterogeneity in crashes suggests—at least for the sample used in the study—that the complexity in crash occurrence is better explained using multiple equation linear predictors. Further research should examine other datasets for repeatability and should further explore and test risk sources.

Impact of restaurant owners'/managers' handling of customers' unexpected incidents on customers' revisit intention

The main purpose of this research is to explore whether or not restaurant owners/managers handle customers' unexpected incidents can affect customers' intention to revisit the same restaurant. We used the case of coupon incident as an example. We then designed an experiment and conducted a survey, and also developed single-equation regression models (both two-stage least squares and ordinary least squares procedures) to test the hypothesis. Results demonstrate that customers who were unhappy when restaurant owners/managers denied them the use of effective coupons were less likely to revisit the same restaurant, as well as no matter the reasons for disallowing coupon use, customers' intention to revisit the same restaurant was frustrated by the experience. Consequently, the main contribution of this study is in offering a different analytical perspective on customer post-purchase behavioural intention by verifying whether the way restaurant owners/managers handle customers' unexpected incidents may influence customers' revisit intention.

Impact of restaurant owners'/managers' handling of customers' unexpected incidents on customers' revisit intention

The main purpose of this research is to explore whether or not restaurant owners/managers handle customers' unexpected incidents can affect customers' intention to revisit the same restaurant. We used the case of coupon incident as an example. We then designed an experiment and conducted a survey, and also developed single-equation regression models (both two-stage least squares and ordinary least squares procedures) to test the hypothesis. Results demonstrate that customers who were unhappy when restaurant owners/managers denied them the use of effective coupons were less likely to revisit the same restaurant, as well as no matter the reasons for disallowing coupon use, customers' intention to revisit the same restaurant was frustrated by the experience. Consequently, the main contribution of this study is in offering a different analytical perspective on customer post-purchase behavioural intention by verifying whether the way restaurant owners/managers handle customers' unexpected incidents may influence customers' revisit intention.

Capital Market Integration of ASEAN6 Industries

The integration and/or segmentation of the ASEAN6 capital markets can provide guidance for investment diversification. Thus, this paper attempts to investigate the integration of the ASEAN6 industries with their international benchmarks using various regression models. Ten industries classified by ICB are considered from 3/1/2000 to 31/1/2014. Using a VAR model, it investigates the direct and indirect impacts from international industries to the corresponding ASEAN6 local industries and the impulse responses of the local industries to international shocks. The disadvantage of multivariate single-equation regression and VAR model is that they cannot separate the influence of returns, conditional return volatility and return shocks on cross return and cross conditional return volatility. To overcome this shortcoming, this paper employs a bivariate VARMA-MGARCH-asymmetric BEKK model to examine the integration of ASEAN6 industries. This paper finds that most industries of Vietnam are segmented, implying the benefit of intra-industry investment for investors having assets in the US or Asian region. The other five ASEAN countries, however, are characterised by varying industry integration/segmentation. Some industries are integrated or segmented with international benchmark industries in the US and Asia but some are segmented from those of the US and integrated with those of the Asia, or vice versa.

Housework: Cause and consequence of gender ideology?

Nearly all quantitative studies examining the association between the division of housework and gender ideology have found that gender egalitarianism results in less housework for wives, more for husbands, and more equal sharing of housework by couples. However, a few studies suggest housework has a nontrivial influence on gender ideology. An overreliance on single-direction, single-equation regression models and cross-sectional data has limited past research from making strong claims about the causal relationship between gender ideology and housework. We use data on married couples from Waves 1 and 2 of the National Survey of Families and Households and nonrecursive simultaneous equation models to assess the causal relationship between housework and gender ideology. Results show a mutual and reciprocal relationship between the division of housework and gender ideology for both husbands’ and wives’. Reciprocity is strongest for husbands while for wives the relationship is partially indirect and mediated through their husbands’ gender ideologies.

Job congruence, academic achievement, and earnings

This study combines a widely held view of how earnings are related to education and job tenure (The Mincer model 1 1 Following Heckman et al. (2003, 2006), by the term Mincer model we mean the the single equation regression model ln[ w( s, x)] = α 0 + ρ sS + β 0 x + β 1 x 2 + ε. ) with the notion that earnings are associated with the quality of an employer–employee job match. The quality of an individual's occupational choice is measured using job congruence, a commonly-used construct in the psychometric literature. Better-matched individuals should be more productive and, as a result, have higher earnings. Previous studies were unable to address the importance of job preferences to earnings because available data do not include both job congruence and individual earnings. The Alumni Outcomes Survey, recently produced by ACT Inc., is among the first data sets to include both variables. We use these data to estimate the importance of job congruence on earnings after controlling both for job tenure and for academic achievement, measured by an individual's ACT score. Results indicate that job congruence is positively correlated with earnings, and has effects on earnings that are of almost equal magnitude with years of education.

BEHAVIORAL ECONOMICS AND DRINKING BEHAVIOR: PRELIMINARY RESULTS FROM AN IRISH COLLEGE STUDY

This paper examines the results of single-equation regression models of the determinants of alcohol consumption patterns among college students modelling a rich variety of covariates including gender, family and peer drinking, tenure, personality, risk perception, time preferences and age of drinking onset. The results demonstrate very weak income effects and very strong effects of personality, peer drinking (in particular closest friend), time preferences and other substance use. The task of future research is to verify these results and assess causality using more detailed methods.

The Impact of Physical and Sexual Abuse in Childhood on Adult Economic Outcomes: Evidence from the Ontario Child Health Study

In this paper we use data from the Ontario Child Health Study, a community panel study which collected socio-demographic and health information from individuals aged 4-16 in 1983 and which was conducted in three waves (1983, 1987, 2001). A rare property of this survey is that questions were included in 2001 to obtain retrospective reports of physical and sexual abuse in childhood on an ordinal scale. We use this information to examine the neglected topic of the adulthood economic consequences of physical and sexual abuse in childhood. We present descriptive analyses which examine simple and partial correlations between our measures of adult economic outcomes and ordinal measures of abuse. We then estimate single equation regression models for each of our economic outcome variables as a function of the abuse variables and other socioeconomic characteristics. In a third stage we include education variables to examine whether these variables mediate the effects of abuse in childhood to adulthood economic outcomes.

The Effect of Supplemental Instruction on Retention: A Bivariate Probit Model

Single equation regression models have been used to test the effect of Supplemental Instruction (SI) on student retention. These models, however, fail to account for the two salient features of SI attendance and retention: (1) both SI attendance and retention are categorical variables, and (2) are jointly determined endogenous variables. Adopting primarily from the economics education literature, this article applies the bivariate probit model, a model appropriate for the case of simultaneous binary choice, to analyze the effect of SI attendance on retention. It is demonstrated that single equation methods are likely to overestimate this effect.

An Analysis of the Effectiveness of Supplemental Instruction: The Problem of Selection Bias and Limited Dependent Variables

Single equation regression models have been used rather extensively to test the effectiveness of Supplemental Instruction (SI). This approach, however, fails to account for the possibility that SI attendance and the outcome of SI attendance are jointly determined endogenous variables. Moreover, the standard approach fails to account for the fact that these two endogenous variables are categorical. This article presents and applies a simultaneous equation, limited dependent variable model of SI effectiveness. Our analysis suggests that results from applying this type of model may differ markedly from the traditional statistical models applied in SI research. Specifically, our results suggest that students with below average academic ability are more likely to attend SI and that common measures of student ability included in single equation models fail to adequately control for this characteristic. Therefore, single equation OLS models may underestimate SI effectiveness.

The impact of the acreage allotment program on rice farming

This paper designs an acreage response model under the acreage allotment farm program incorporation a policy-inducing variable. The single-equation regression model for each rice-producing state is estimated by the ordinary least squares mulitiple regression procedure. The estimated parameter shows a significant direct relationship between the rice acreage planted and plicy-inducing price in all the rice-growing states. The estimated short-run elasticities for Arkansas, California, Louisiana, Mississippi, and Texas were 0.72, 0.59, 0.67, 0.66, and 0.81 respectively. The heterogeneity in the magnitude of the elasticities during the acreate allotment period suggests considering a rice program formulation in response to each state's variability in physical restraints, availability of irrigation water, average yields, and return over cost, thereby providing risk management incentives to rice growers to respond positively to the farm program.

Budgetary Trade-Offs Between Defense, Education and Health Expenditures: The Case of Turkey

The main objective of this paper is to evaluate empirically the existence of a budgetary trade-off between military, education and health expenditures in Turkey for the time period 1925-1998. Development economists, peace and defense economists and political economists have extensively investigated the existence of a trade-off between military, education and health spending since the 1970s. However, the literature review reveals that it is hard to establish a general theory of budgetary trade-off between military, education and health spending and make this applicable for all cases. This is mostly due to economic, social, political, and historical differences among the countries Moreover, it is likely that different research techniques, different time periods analyzed may produce different results. As a result of this, researchers have found a variety of outcomes regarding the trade-off between defense-education and health expenditures. This study presents a brief literature review within the framework of trade-offs between defense-education and health expenditures and also concentrates on theoretical model development. The discussion will center on developing a multi-variable single equation regression model and presenting estimable forms of equations.

Supply response of farm program in rice-growing states

This study aims to develop an acreage response model for rice-growing states using a policy-inducing variable. The single equation regression model for each rice-producing state is estimated by using the ordinary least square multiple regression procedure after log transformation. Data for the period 1959 to 1988 for acreage plantation, market price, target price, loan rate, and acreage reduction rate are used in designing the policy-inducing price. The estimated parameter shows a significant inverse relationship between the rice acreage planted and policy-inducing prices in all of the rice-growing states, with the exception of Louisiana. The estimated short-run elasticities for Arkansas, California, Louisiana, Mississippi, and Texas are -0.36, -0.68, 0.30, -0.37, and -0.59, respectively. The heterogeneity in the magnitude of the elasticities suggests the need for redesigning the rice programs to generate desirable acreage responses from all of the rice-growing states.

A transform-both-sides modulus power model: an application in health care

The Box-Cox transformation is suitable for stabilizing variance of the response variable and for inducing functional form flexibility in single-equation regression models. However, it becomes incapacitated if the data contain zero or negative values. This paper, using profitability data for US psychiatric hospitals, illustrates the capability of modulus power transformations to symmetrize the response variable distribution. Compared with the untransformed data model, the ML estimates of the modulus power model are found to be superior.