宏观经济学家的核心目标之一是了解世界各地人均收入的巨大差异。

索洛模型的一个关键结论是，如果物质资本在收入中的份额是对资本重要性的合理衡量，那么来自资本的差异在跨国收入差异中占的比例很小。Ramsey-Cass-Koopmans和Diamond模型也有同样的含义。内生增长模型的一个关键含义是，由于技术是无价的，技术的差异不太可能对国家间的收入差异产生重要影响。

本章试图超越这些结论。关于跨国收入差异学术界有众多讨论，而且比前几章讨论的工作更注重实证主义。

有两个主要分支：

1. 收入的决定因素。也就是说，它考虑的是对收入有明显和直接影响的因素，如物质和人力资本的数量。它一般采用growth accounting technique，我们在第1.7节讨论过。因素的边际产品是用它们在市场上的价格来衡量的；然后将这些边际产品的估计值与因素数量差异的估计值结合起来，得到因素对收入差异的估计值。

这项工作的优点是人们通常可以对其结论有相当的信心，但缺点是它只考虑收入的直接决定因素。

2. 研究人员考虑的潜在的收入决定因素（包括政治体制、人文和宗教）。Accounting的方法很少能用来衡量这些力量对收入的影响。相反，研究人员使用各种统计学技巧来试图估计其影响。因此，深入研究是以降低结果的确定性为代价的。

下面有我们具体如何将人力资本加入索洛模型来进行逻辑推演：

以下是我花了几个月整理的高级宏观经济学所需的自学笔记 (英文版), 分章分节呈现给大家。开头我会附带一段中文版的小节，后面提供给想看详细数学推导和用英语学习经济学的朋友们。

作为一个跨界自学的推动人，每一章结尾，我会附上一节习题课，并在最后给出答案，方便大家复习。

大卫· 罗默是美国经济学家、加州大学伯克利分校的赫尔曼·罗耶政治经济学教授, H-index 37, 著有高级宏观经济学教材，主攻新凯恩斯主义。他夫人是经济顾问委员会前主席克里斯蒂娜·罗默。

更多高级宏观经济学戳专栏:

跨界自学 · 教材: 高级宏观经济学

本自学笔记将会和高级宏观经济学、应用计量经济学等专栏，同步一周7更。

跨界自学 · 教材: 应用时间序列分析

跨界自学 · 教材: 应用计量经济学​​​

高级宏观经济学 · 习题与应用

应用时间序列分析 · 习题与应用

跨界自学 · 科研: 经济指标使用手册

One of our central goals over the past three chapters has been to understand the vast variation in average income per person around the world. So far, however, our progress has been very limited.

A key conclusion of the Solow model is that if physical capital’s share in income is a reasonable measure of capital’s importance in production, differences in capital account for little of cross-country income differences. The Ramsey–Cass–Koopmans and Diamond models have the same implication. And a key implication of models of endogenous growth is that since technology is nonrival, differences in technology are unlikely to be important to differences in income among countries.

This chapter attempts to move beyond these negative conclusions. Work on cross-country income differences is extremely active, and has a much greater empirical focus than the work discussed in the previous chapters.

It has two main branches:

This work has the strength that one can often have a fair amount of confidence in its conclusions, but the weakness that it considers only immediate determinants of income.

2. Among the potential underlying determinants of income that researchers have considered are political institutions, geography, and religion. Unfortunately, accounting-style approaches can rarely be used to measure these forces’ effects on incomes. Researchers instead use various statistical techniques to attempt to estimate their effects. As a result, the effort to go deeper comes at the cost of reduced certainty about the results.

Cobb-Doglas P Function

Exogenous: Saving Rate, s, Technological Progress rate, g, resources to human-capital accumulation

The model is set in continuous time. Output at time t is Y, K, and A are the same as in the Solow model: Y is output, K is capital, and A is the effectiveness of labor. H is the total amount of productive services supplied by workers, the total contribution of workers of different skill levels to production. It includes the contributions of both raw labor (skills that individuals are endowed with) and human capital (that is, acquired skills). The effectiveness of labor grows at an exogenous rate g:

The accumulation of human capital depends both on the amount of human capital created by a given amount of resources devoted to human-capital accumulation (that is, on the production function for human capital), and on the quantity of resources devoted to human-capital accumulation.

our assumption is that the quantity of human capital, H, is given by where L is the number of workers and G(•) is a function giving human capital per worker as a function of years of education per worker.

The number of workers grows at an exogenous rate n: It is reasonable to assume that the more education a worker has, the more human capital he or she has. That is, we assume G'(•) > 0. But there is no reason to impose G''(•) < 0. As individuals acquire human capital, their ability to acquire additional human capital may improve.

The microeconomic evidence suggests that each additional year of education increases an individual’s wage by approximately the same percentage amount. If wages reflect the labor services that individuals supply, this implies that G'(•) is indeed increasing