This paper suggests that the weak empirical effect of human capital on growth in existing cross-country studies is partly the result of an inappropriate specification that does not account for the different channels through which human capital aspects growth. A systematic replication of earlier results from the literature shows that both, initial levels and changes in human capital, have positive growth effects, while in isolation, each channel often appears insignificant. Studies that do not account for both channels might underestimate the effect of human capital due to convergence in human capital, in particular when measuring human capital in log average years of schooling. This study therefore complements alternative explanations for the weak growth effects of human capital based on outlier observations and measurement issues.
Despite the conventional view that human capital is one of the main determinants of growth, the evidence for the effect of human capital on growth is weak and controversial. While studies since Mankiw, Romer, and Weil (1992) and Benhabib and Spiegel (1994) found significant positive effects of human capital (e.g., in terms of years of schooling) on income levels, the findings regarding the growth effect have been rather contradictory. For instance, Mankiw et al. (1992) reported a positive effect of human capital on growth in a human capital augmented Solow (1956) framework, whereas Benhabib and Spiegel (1994) found no effect in a growth accounting exercise and suggested instead a different specification with human capital affecting growth through productivity. These contradictory findings have given rise to a lengthy debate about the growth effects of human capital in the literature. Several explanations have been suggested, including the role of outlier observations (Temple, 1999), the way human capital is measured in terms of quantity or quality (Barro, 2001, Hanushek and Woessmann, 2008), data quality of human capital measures (de la Fuente and Domenech, 2006, Cohen and Soto, 2007, Portela, et al., 2010), or the correct specification of human capital in the growth regression (in terms of a log specification in the context of a production function or in terms of levels as in a Mincerian specification, see, e.g., Krueger and Lindahl, 2001). To the best of our knowledge, however, no consensus has been reached regarding the effect of human capital on growth.
Consider the canonical empirical growth model, that combines the different channels of human capital on output growth. For illustrative purposes, this canonical model can be written as
gi,t = ln yi,t − ln yi,t−1 = α + β ln hi,t−1 + γ∆ ln hi,t + ΓXiJ,t−1 + Λ∆Zi,t + εit , (1)
where gi,t is the growth rate of annual real per capita GDP, y, in country i between periods (years) t − 1 and t, and the vectors X and ∆Z include other controls that have been considered in the empirical growth literature, either in levels as of t − 1, such as lagged income to account for convergence effects, or in changes between t − 1 and t, for instance in log physical capital, respectively. The corresponding coefficient vectors are captured by Γ and Λ. The main interest lies on the effect(s) of human capital, reflected by β and γ, where ln hi,t−1 is the initial level of the human capital measure, which is typically measured by the log of average school years (e.g., taken from the data assembled by Barro and Lee, 2001), and ∆ ln hi,t is the change in log average school years.1 The effect of human capital in terms of an increase in effective factors as in an augmented Solow framework or along the lines of a Lucas model is reflected by the coefficient γ, while β accounts for growth effects of human capital due to the higher adaptiveness to a changing environment in the spirit of Nelson and Phelps.
Our analysis replicates earlier studies on the growth effects of human capital, using the data sets and sources as well as specifications that have been applied most frequently. We consider different data sources in order to document the consistency of our results with earlier findings and to demonstrate the relevance of the correct specification by accounting for the different growth channels of human capital. The estimations are based on the typical cross-country empirical growth model that has been estimated in the literature by using data for GDP, GDP per capita and investment from the Penn World Table (version 6.3), and population data from the UN.3 As a benchmark, we use the original data set constructed by Cohen and Soto (2007), which contains data for 81 countries over the period 1970-1990 and measures human capital in terms of the average years of schooling of the population aged 25+ in each country. An alternative data source for measures of human capital in terms of average years of schooling of the population aged 25+ is the most recent release of the data constructed by Barro and Lee (2010) for 97 countries. As a third data set for human capital, we use the data constructed by Lutz et al. (2007) (IIASA-VID data set), which we have for 88 countries over the period 1970-2000.4 Additional robustness checks investigate the relevance of the empirical specification also for qualitative measures of human capital.5
In order to gauge the potential relevance of the bias that arises from only accounting for one of the two human capital channels, we begin by presenting the (unconditional) correlation between initial levels of human capital and the subsequent changes. Figure 1 plots the relationship between initial human capital (in terms of the log average years of schooling) in 1970, against the subsequent change in human capital (in terms of log average years of schooling) between 1970 and 1990, for the three different data sets. Figure 1(a) reveals a strong negative (unconditional) correlation between the log average years of schooling and the subsequent change in log years of schooling in the Cohen-Soto data, indicating that the (percentage) change in human capital is smaller the higher the initial log years of schooling. The negative correlation (ρ = −0.84, p-value
< 0.01) suggests that any estimate of the effect of human capital on growth that is based on a
specification with only log changes or only log initial levels of human capital as regressor should be biased downward if both channels are indeed active as becomes clear from the expressions in (2) and (3).
This subsection shows that the conclusion from the previous findings that human capital is likely to affect growth through both channels, initial levels and changes, is unchanged when considering different specifications of human capital. In particular, several authors, including Topel (1999) and Krueger and Lindahl (2001) have criticized the specification of human capital in terms of logged variables as a potential source of bias and misspecification.13 These authors suggest that the growth equation should be specified by explicitly accounting for the log-linear relationship between earnings and education that emerges from a Mincerian human capital production function. In other words, rather than specifying the growth equation as in (1), these studies recommend a specification in levels of human capital,
The conclusion that human capital affects growth through both channels, through the change and the initial level, is supported also in alternative estimation frameworks. In this section, we present results for alternative sample periods, for alternative specifications of the growth equation, for samples that correct for outlier observations, as well as for measures of human capital quality.
Alternative Sample Periods. The data sets by Barro and Lee (2010) and IIASA-VID (2007) cover the years 1970-2000, which allows us to test the robustness of the previous findings for estimates over an extended time window. Figure 3 presents the respective scatter plots for the (unconditional) correlation between (log) years of schooling in 1970 and the change in (log) years of schooling over the period 1970-2000. As before, we find strong indications of convergence (in terms of a negative relation) for log average years of schooling, and a weaker convergence pattern for years of schooling in absolute terms. In both data sets, there is a negative correlation between changes in human capital and initial levels, measured either in years of schooling or logs.15
The existing evidence on the growth effects of human capital in the literature is weak and in- conclusive, which has raised an intense debate that has not been fully reconciled. The findings of this paper suggest that misspecification of human capital in the empirical growth model can provide an alternative explanation for the inconclusive evidence in the literature. The misspeci- fication arises if human capital affects growth through the two distinct channels identified in the previous literature, changes in human capital and initial levels in human capital. When human capital is measured in log average years of schooling, both measures, changes and initial levels, are highly correlated in the data, which implies that estimates obtained with models that only include one channel are likely to be seriously biased. This bias is much smaller when human capital measures are included in levels, as in the Macro-Mincer approach that has been applied frequently in the recent literature, due to the weaker correlation in these measures of human capital. Indeed, there is a crucial difference between specifying human capital in levels or logs in light of the different implications for the emerging bias, because of the different convergence patterns in the human capital variables, as has been shown in Figures 1 and 2. Nevertheless, our results indicate that even in Macro-Mincer specifications human capital consistently affects growth through both channels. This implies that estimates obtained with specifications that only include one channel do not deliver an estimate of the overall relevance of human capital for growth because they omit a relevant channel.
CS 340 Milestone One Guidelines and Rubric Overview: For this assignment, you will implement the fundamental operations of create, read, update,
Retail Transaction Programming Project Project Requirements: Develop a program to emulate a purchase transaction at a retail store. This
7COM1028 Secure Systems Programming Referral Coursework: Secure
Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip
CS 340 Final Project Guidelines and Rubric Overview The final project will encompass developing a web service using a software stack and impleme
