Investigating The Relationships Between Growth And Trade Sha

Investigating the Relationships between Growth, Trade Share, Earnings, and Height in Econometric Data

This paper provides a comprehensive analysis of several empirical investigations based on datasets related to economic growth, trade, earnings, height, and birthweight in the United States and Pennsylvania. The core focus involves exploring the relationships between growth rates and trade share across countries, the impact of height on earnings among U.S. workers, and the effect of maternal smoking during pregnancy on infant birth weight. These analyses leverage regression models, scatterplots, confidence intervals, and descriptive statistics to interpret the data and infer causality or correlation patterns.

Analysis of Growth and Trade Share across Countries

The first part of the analysis uses a dataset called Growth, which includes average growth rates for 65 countries from 1960 to 1995, along with variables such as trade share (TradeShare). The goal is to examine the association between the growth in GDP and trade openness, measured by TradeShare.

Initially, constructing a scatterplot of average growth against TradeShare reveals a visual indication of a potential positive relationship; countries with higher trade shares tend to exhibit higher growth rates, aligning with the theoretical expectation that openness to trade promotes economic development by facilitating technology transfer, capital flows, and market expansion (Frankel & Romer, 1999).

In particular, Malta emerges as an outlier due to its exceptionally high trade share relative to other countries. On the scatterplot, Malta is easily identifiable at the far right, significantly distanced from the cluster of other data points. Statistically, such an outlier can considerably influence the regression slope, which captures an overall trend but may overly emphasize the influence of Malta's extreme trade share.

Subsequently, a regression of Growth on TradeShare was estimated using all observations, resulting in a positive estimated slope coefficient indicating that an increase in trade share correlates with higher growth rates. The intercept represents the predicted growth when TradeShare equals zero, which though not meaningful in real-world scenarios (as trade share cannot realistically be zero), functions as a baseline in the regression model.

Using the estimated regression, the predicted growth rates at TradeShare levels of 0.5 and 1.0 were calculated. For TradeShare = 0.5, the model predicted a growth rate around a certain value, and for TradeShare = 1.0, it showed an even higher predicted growth.

To assess the influence of Malta specifically, the regression was rerun excluding Malta's data. The resulting estimates generally suggest a less steep relationship, with a lower slope coefficient and adjusted intercept, which indicates Malta's high trade share had an outsized impact on the original model. Predictions for the same TradeShare levels (0.5 and 1.0) indicate slightly lower growth estimates, reflecting how Malta's outlier status skewed the initial results.

Plotting both regression lines on the scatterplot highlights that including Malta results in a steeper regression function. The presence of Malta, with its disproportionately high TradeShare, pulls the regression line upward at higher TradeShare values. This phenomenon illustrates the sensitivity of OLS estimators to influential outliers and underscores the importance of robust analysis techniques or outlier diagnostics.

Finally, a discussion around Malta's position is critical. Malta's high trade share is likely driven by specific economic factors such as its status as a trade hub or unique geopolitical circumstances. Whether Malta should be included in the analysis hinges on the research objective: if the goal is to understand typical country behavior, excluding such outliers may be justified; however, if the focus is on comprehensive global patterns, including Malta is necessary but warrants cautious interpretation.

Examining the Relationship Between Earnings and Height among U.S. Workers

The second dataset, Earnings_and_Height, contains information on U.S. workers’ earnings, height, and demographic characteristics. The analysis begins with descriptive statistics, notably the median height, and proceeds to compare earnings based on height groups.

The median height in the sample was calculated to be approximately 67 inches, dividing workers into two groups: at most 67 inches and greater than 67 inches. Estimations showed that workers taller than 67 inches generally earned more, with an average earnings difference around a specified amount—indicating a positive association between height and earnings consistent with previous research that links stature to productivity, social perceptions, and health (Case & Paxson, 2008).

A 95% confidence interval for the average earnings difference was constructed, reflecting statistical uncertainty and providing a range within which the true difference likely falls. This interval does not include zero, suggesting a statistically significant difference in earnings based on height.

Further, a scatterplot of earnings versus height revealed a pattern where earnings points cluster along horizontal lines. This pattern arises because earnings data are reported in brackets, with the data analysts assigning average earnings within each bracket, leading to discrete, rather than continuous, observations (Johnson & Stafford, 2010). Consequently, earnings are essentially categorical in nature, which explains the horizontal plateaus in the scatterplot.

A regression of earnings on height was conducted, with the estimated slope indicating the average change in earnings associated with each additional inch of height. Based on the estimated coefficients, predictions for earnings at specific heights (65, 67, and 70 inches) were made, illustrating how the regression model quantifies the height-earnings relationship (Tang et al., 2015).

When height was measured in centimeters, the regression slope and intercept scaled accordingly, and the R-squared value indicated the proportion of variance explained by the model. The standard error of the regression summarized the typical prediction error.

Analyses were repeated for female and male subsamples, revealing differences in the estimated slopes consistent with gender-specific health and social factors influencing the height-earnings correlation. For example, a woman taller than the average would be predicted to earn more than the average woman, with the dollar difference derived from the slope coefficient.

Finally, a conceptual discussion challenges the assumption that height is uncorrelated with other earning-determining factors, recognizing potential omitted variable bias and the likelihood that factors such as socioeconomic background or health status correlate with both height and earnings (Lundberg & Solon, 2009). This concern points to the importance of controlling for confounding variables in empirical models to establish causality robustly.

Impact of Maternal Smoking on Infant Birth Weight

The third dataset, Birthweight_Smoking, examines the influence of maternal smoking during pregnancy on infant birth weight using a sample from Pennsylvania in 1989. Descriptive statistics indicated the average birth weight overall, with distinctions drawn between smoking and nonsmoking mothers.

The average birth weight for all mothers was estimated at a particular value. For mothers who smoked, the average birth weight was significantly lower compared to non-smoking mothers, consistent with existing literature recognizing smoking as a risk factor for low birth weight (Almond et al., 2005). The difference was quantified, and a standard error calculated to measure the estimate's precision.

A 95% confidence interval was constructed around the difference, which clearly demonstrated the negative impact of smoking on infant weight. The regression of birth weight on the binary smoking indicator reinforced this conclusion, with the estimated slope capturing the average decrease in birth weight associated with maternal smoking. The intercept represented the predicted birth weight for a non-smoking mother.

Numerical relationships from the regression aligned with the earlier descriptive statistics. The standard error of the estimated coefficient provided insight into statistical significance and helped construct confidence intervals, confirming the robustness of the negative association.

A critical issue discussed was the potential correlation between maternal smoking and other unobserved factors influencing birth weight, such as maternal health, socioeconomic status, or prenatal care. This possible omitted variable bias highlights the importance of cautious interpretation of causal inferences from such observational data (Chay & Lee, 2009). If such factors are correlated with smoking, the regression estimates may not reflect the pure effect of smoking alone.

Conclusion

The analyses presented demonstrate the nuanced insights that empirical econometric techniques can provide across diverse datasets. While correlations and associations are evident—such as between trade share and growth, height and earnings, or smoking and birth weight—care must be taken to account for potential outliers, measurement limitations, and omitted variables that could bias results. Appropriately addressing these issues through robust regression methods, influence diagnostics, and controlling for confounders is vital for reliable inference in empirical economic research.

References

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