Growth and the Kaldor Facts

Abstract

We revisit the Kaldor growth facts for the United States and the United Kingdom during the postwar period. We find that while overall the original Kaldor facts continue to hold, deviations occurred along several dimensions: Instead of staying constant, the growth rates of real GDP per worker and of real capital per worker have slowed down in the United States and the United Kingdom since the 1970s, the capital-to-output ratio has increased in the United Kingdom, and the share of income paid to labor has decreased in the United States since 1990. We discuss how to calculate the Kaldor facts in multi-sector growth models and establish that a slowdown in GDP-per-worker growth naturally results from secular changes in relative prices.

Introduction

The process of building economic models benefits from the existence of stylized facts that discipline the modeling choices. In the theory of economic growth, these stylized facts were first stated by Kaldor (1961) and are called the Kaldor growth facts (or sometimes for short the Kaldor facts or the growth facts). These facts are that the growth rates of real GDP per worker and real capital per worker exhibit no trend and that the gross return on capital, the capital-to-output ratio, and the GDP share of the payments to capital exhibit no trend growth. Although the field of economic growth has rapidly developed since Kaldor's article, it is fair to say that being consistent with the original Kaldor facts is still viewed as the minimum requirement for a credible model of economic growth.

In this article, we have two primary goals. The first one is to empirically revisit the Kaldor facts more than half a century after Kaldor wrote his article. The second goal is to discuss how to address the Kaldor facts in multi-sector versions of the growth model.

Given the long-standing and seemingly well-established position of the Kaldor facts in the literature, revisiting them may seem a frivolous task to undertake. There are three good reasons for nonetheless doing this. First, and somewhat ironically, the Kaldor (1961) paper that is cited for laying out the Kaldor facts does not actually contain any presentation of facts. Rather, Kaldor reported what he saw as the key patterns to be distilled after looking at various and disparate pieces of information that had been documented by other authors. Second, Kaldor described the experiences of the pre-1950 world. In contrast, many current macroeconomic studies focus on the post-1950 world, making it relevant to assess the state of the Kaldor facts for this period. Third, revisiting the Kaldor facts highlights a number of measurement issues that one needs to take a stand on. Although they are not usually discussed in detail, they can be subtle and are particularly relevant in multi-sector growth models.

We find that overall the Kaldor facts continue to hold, in that constant trends provide a reasonable first-order description to most of the data. But there are sizeable short- and medium-term fluctuations around the trend. In particular, we find evidence of deviations from the Kaldor facts along several dimensions: Instead of staying constant, the growth rates of real GDP per worker and of real capital per worker have slowed down in the United States and the United Kingdom since the 1970s, the capital-to-output ratio has increased in the United Kingdom, and the share of income paid to labor has decreased in the United States since 1990.

Establishing the existence of a balanced growth path in the one-sector growth model and connecting its properties to the Kaldor facts is a standard exercise for first-year Ph.D. students. In recent years, the profession has gone beyond that and studied multi-sector versions of the growth models that capture the effects of secular changes in relative prices and the sectoral composition of the economy ("structural change"). It is therefore natural to ask (i) under what conditions a standard multi-sector model has a balanced growth path along which the updated Kaldor facts hold and (ii) what this multi-sector model has to say about the deviations from the original Kaldor facts. This is the second goal of our article.

One of our key points is that, with the one-sector growth model, it is immediate to go from model-based measures to empirical measures; this is not the case for multi-sector growth models. The reason for this is that the one-sector model has no changes in relative prices, implying that many statistics are effectively unit free. This is not the case for multi-sector growth models, which were constructed precisely to capture the effects of secular changes in relative prices. As a result, the issue of which units should be used to measure the statistics behind the Kaldor facts takes center stage in multi-sector models.

A basic principle of connecting models with data requires measuring objects in the data and the model in the same way. It turns out that this principle has important implications for connecting multi-sector models to the Kaldor facts, in particular with regard to quantities such as gross domestic product (GDP). We report and discuss a recent result by Duernecker, Herrendorf, and Valentinyi (2017a), who showed that if GDP per worker is measured in the model as it is in the data by chaining the Fisher quantity index, then the multi-sector model can naturally generate the first deviation from the original Kaldor facts: GDP-per-worker growth slows down over time, instead of remaining constant.