the convergence hypothesis implies

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The convergence hypothesis: History, theory, and evidence

1998, Open economies review

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The Convergence Hypothesis: Types and Paths | Economic Growth

Let us make an in-depth study of the Convergence Hypothesis. After reading this article you will learn about: 1. Types of Convergence 2. Possible Paths of Convergence.

Types of Convergence :

There are three types of convergence unconditional convergence, conditional conver­gence and no convergence.

(i) Unconditional Convergence:

By unconditional convergence we mean that LDCs will ultimately catch up with the industrially advanced countries so that, in the long run, the standards of living throughout the world become more or less the same. The Solow model predicts unconditional convergence under certain special conditions. For example, let us suppose that different countries of the world differed mainly in their capital-labour ratios.

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Normally, rich countries have high capital-labour ratio and high levels of output per worker. By contrast, low income countries have low capital-labour ratios and low levels of output per worker. We also assume that two groups of countries are the same in all other respects such as saving rates, population growth rates and the production function.

If this is true then the Solow model predicts that, in spite of any differences in initial capital-labour ratios, all these countries will ultimately attain the same steady state. Differently put, if countries have the same fundamental characteristics, capital-labour ratios and living standards will uncon­ditionally converge, even though some countries may start from way behind.

(ii) Conditional convergence:

Even if countries differ in their saving rates, population growth rates and production functions (due to unequal access to technology) they will converge to different steady state with different capital-labour ratios and different standards of living in the long run. If countries differ in the fundamental characteristics, the Solow model predicts conditional convergence.

This means that standards of living will converge only within groups of countries having similar characteristics. For example, if there is conditional convergence, a low income country with a low saving rate may catch up, one day or the other, a richer country that also has a low saving rate, but it will never catch up a rich country that has a high saving rate.

One reason for this is that poor countries have less capital per worker and thus higher marginal products of capital than do rich countries. So savers in all countries will be able to earn the highest return by investing in poor countries. Eventually, borrowing abroad will allow initially poor countries’ capital-labour ratios and output per worker to be the same as in initially rich countries.

(iii) No convergence:

The third possibility is no convergence. This means that the low income countries will never catch up over time. Therefore living standards may even diverge due to widening income gap — the rich getting richer and poor getting poorer.

Possible Paths of Convergence :

In Fig. 4.14(a) and 4.14(b) we show the possible paths of convergence and divergence of per capita output. In Fig. 4.14(a) T r represents the steady state growth path of the rich country. The slope of this line represents the rate of growth for the poor country. Three options are open to them.

Here T p represents a steady state growth path in which the rich and poor countries grow at the same rate. A favourable shock at time t 0 leads to convergence of output per capita in rich and poor countries as shown by the steady state growth path T p .

An adverse shock that slows down the growth rate of the poor country in the short run but leads to the same steady state growth as in T p is indicated by the growth path T’ p . The dotted line indicates movement outside of steady state.

Fig 4.14(b) shows divergence between the rich and poor countries. T r and T represent the steady state growth paths of the rich and poor country. We find divergence of per capita outputs across two countries over time. Here the scenario is different.

Irrespective of favourable shock (T h ) or an adverse shock (T’ p ) the steady state growth rate is the same as in T p , and long-run income per capita in the rich country will increasingly diverge from that in the poor country. The solid lines in both diagrams are steady state paths whereas the dotted lines represent transitions to equilibrium in response to a shock.

The path T h in Fig 4.14(a) shows how absolute convergence — in the sense of the same growth rates as also the same growth path — occurs. This is a strong form of convergence. A weaker form of convergence — called conditional convergence — is depicted by the paths T’ p and T p which show the same growth rates but different growth paths among countries.

The vertical distance of the growth path of a poor country from that of a rich country represents income differences due to differences in underlying parameters such as savings rates and population growth.

The developing countries can have free access to the technology developed by the pioneers. This implies that latecomers have a potential advantage over pioneers — an advantage of backwardness.

In the course of adopting and adapting new techniques, IRS appear in the guise of learning-by-doing. No doubt the firms which adopt new techniques find an improvement in efficiency following the adoption.

Hence, if firms in LDCs organise themselves so as to profit from the accumulated experienced as fully as do firms in developed countries and such improvements have a ceiling that is reached in finite time or cumulative output, as seems plausible, then catching up in that particular time of production with the technique in question will be complete.

Unfortunately from the point of view of the world’s low income countries there is hardly any empirical support for unconditional convergence. Most studies have found little tendency for low income countries to catch up with their rich counterparts.

Related Articles:

• Solow Model of Economic Growth: Prediction and Theory
• Convergence and Poor Countries: 3 Mechanisms | Economics
• Solow’s Neoclassical Growth Model | Economic Growth | Economics
• Economic Growth in Asian Countries

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Convergence Hypotheses

Convergence refers to a situation where countries with low per capita incomes grow faster than countries with high per capita incomes. Consequently, with time, the per capita income for developing countries converges with that of developed countries.

Types of Convergence Hypotheses

• Absolute convergence.
• Conditional convergence.
• Club convergence.

The neoclassical growth theory forecasts unconditional and conditional convergence. The endogenous growth model, however, does not predict any occurrence of convergence.

Absolute Convergence

The Absolute convergence implies that the developing countries, despite their unique features, will grow and eventually attain the developed countries’ per capita income. Since the neoclassical model assumes that all countries have the same level of technology, the per capita income in all countries should grow at the same rate. However, neoclassical growth theory means that the per capita income level will be equal in all countries, given the prevailing characteristics (does not insinuate the absolute convergence).

Conditional Convergence

Conditional convergence is where the convergence is dependent on countries that have equal saving rates, population growth rates, and production functions. If these conditions hold, the neoclassical growth theory will imply convergence to the same per capita output and steady-state growth rate.

Club Convergence

Club convergence implies a group (club) of only rich and middle-income countries whose income converges to that of the wealthiest country in the world. Therefore, member countries of the club with low per capita income will grow faster than the non-members. Emerging countries will only join the club if they execute necessary institutional changes. If the new members fail to implement these changes, they will fall into a non-convergence gap.

Ways in Which Convergence Occurs

Capital deepening and accumulation : Developed countries are almost at the flattened point of the production function (point B). This implies that more capital injection will not impact output much. On the other hand, developing countries operate at the lowest point of the production function(point A), as seen in the graph below. Therefore, any capital injection will have a positive impact on the output.

• Adoption of technology that is already popular in advanced countries . Developing countries employ technology from developed countries to boost their incomes.

Question 1 A developing country is concerned about its illiteracy and the low standard of living. The government appoints a committee to benchmark an advanced country and develop strategies to increase the country’s output. Which of the following plans considered by the committee will most likely delay convergence with the advanced (developed) country? Creation of policies that encourage the return of highly educated citizens. Enforcing high tariffs on imports to protect the growing local industries. Use of external debt to improve transport and manufacturing infrastructure. Solution The correct answer is B . Enforcing high tariffs on imports to protect the growing local industries will discourage growth, and thus it is not supportive of convergence with developed economies. Question 2 An economic researcher asserts that “many countries with the same population growth rate, savings rate, and production function will eventually have growth rates that converge over time.” The convergence the researcher has described is most likely to be: Conditional convergence. Absolute convergence. Club convergence. Solution The correct answer is A . Conditional convergence depends on countries with the same saving rate, population growth rate, and production function. If this condition holds, then the neoclassical model implies convergence to the same per capita output and steady-state growth rate.

Reading 9: Economic Growth 

LOS 9 (j) Explain and evaluate convergence hypotheses.

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What is convergence theory in sociology?

This theory is one of social change that has been given by economic professor Clark Kerr in a book by him and his colleagues called ’Industrialism and Industrial Man’ in the 1960s. The convergence theory is the one which postulates that all the societies as they move from the early industrial development to complete industrialization tend to move towards a condition of similarity in terms of the general societal and technological norms. This is to say that as the societies move towards development they look become alike will similar structures, which means that the differences among the societies will reduce as they are ultimately on the same path of development. This would thus lead to a single global culture.

This theory given by Clark Kerr is what is known as the ‘logic of industrialization’ which he has also mentioned in his writing, this logic is the thesis of the theory and states that industrialization everywhere has similar consequences whether the society is a capitalist one or a communist one.

This convergence may reflect in the form of what can be called the ‘catch up effect’. This ‘catch up’ refers to the process of opening up the economy of a country to the foreign economy allowing the inflow of capital, this investment helps the economy to maintain pace with the more advanced societies, this process usually takes place when the society is introduced to the industrialization process. However, there might be cases when the reverse may happen i.e. the economy may diverge instead of converging. Such divergence takes place in the case of economies in which the foreign capital is not invested, this may be due to the political and social factors such as lack of education or job training, etc. often these nations are the ones that are unstable.

It is believed that the third world nations are supposed to get out of their conditions of poverty through the process of convergence as they take up the form of western industrial societies.

The convergence theory is often related to the study of modernization, it is believed that the path of development is the one that has been taken by the western industrial societies, which will be undertaken by every society in order to reach complete development and modernization. Thus there is a foxed pattern of development which will be followed. There is thus a convergence if the ideas attitudes and beliefs, thus the overall way of thinking and doing things.

However, it has often been seen that though there are similarities among the industrialized societies, it is often only found in the case of the technology that they use and their patterns of change in this technology. However, the other aspects such as the political systems, the religious systems, and the beliefs, and even the economic conditions to a very large extent remain specific to society and thus are variable.

Thus we see that while the convergence theory has made many countries into market economies such as the ones found in the western societies, as it has in Russia and Vietnam which were communist countries earlier and are now market economies.

https://www.thoughtco.com/convergence-theory-3026158

https://www.encyclopedia.com/social-sciences/encyclopedias-almanacs-transcripts-and-maps/convergence-theories

http://www.encyclopedia69.com/eng/d/convergence-theory/convergence-theory.htm

https://www.britannica.com/topic/logic-of-industrialization

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Researchers have also observed that as models become larger and more competent across tasks, their representations become more aligned (Figure 2). This alignment extends beyond individual models, with language models trained solely on text exhibiting visual knowledge and aligning with vision models up to a linear transformation.

The researchers attribute several factors to the observed convergence in representations:

1. Task Generality : As models are trained on more tasks and data, the volume of representations that satisfy these constraints becomes smaller, leading to convergence.

2. Model Capacity : Larger models with increased capacity are better equipped to approximate the globally optimal representation, driving convergence across different architectures.

3. Simplicity Bias : Deep neural networks exhibit an inherent bias towards finding simple solutions that fit the data, favoring convergence towards a shared, simple representation as model capacity increases.

The central hypothesis posits that the representations are converging toward a statistical model of the underlying reality that generates our observations. This representation will be useful for a wide range of tasks grounded in reality and relatively simple, aligning with the notion that the fundamental laws of nature are indeed simple functions.

The researchers formalize this concept by considering an idealized world consisting of a sequence of discrete events sampled from an unknown distribution. They demonstrate that certain contrastive learners can recover a representation whose kernel corresponds to the pointwise mutual information function over these underlying events, suggesting convergence toward a statistical model of reality.

The Platonic Representation Hypothesis has several intriguing implications. Scaling models in terms of parameters and data could lead to more accurate representations of reality, potentially reducing hallucination and bias. Additionally, it implies that training data from different modalities could be shared to improve representations across domains.

However, the hypothesis also faces limitations. Different modalities may contain unique information that cannot be fully captured by a shared representation. Furthermore, the convergence observed so far is primarily limited to vision and language, with other domains like robotics exhibiting less standardization in representing world states.

In conclusion, the Platonic Representation Hypothesis presents a compelling narrative about the trajectory of AI systems. As models continue to scale and incorporate more diverse data, their representations may converge toward a unified statistical model of the underlying reality that generates our observations. While this hypothesis faces challenges and limitations, it offers valuable insights into the pursuit of artificial general intelligence and the quest to develop AI systems that can effectively reason about and interact with the world around us.

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New paper: The Platonic Representation Hypothesis In which we posit that _different_ foundation models are converging to the _same_ representation of reality. paper: https://t.co/z0rh2gPeCc website: https://t.co/Qo3BLTo25I code: https://t.co/T0YUxG77mg 1/8 — Phillip Isola (@phillip_isola) May 14, 2024

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Convergence: Theory, Econometrics, and Empirics

• First Online: 25 November 2013

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This chapter presents the theoretical background, the econometrics, and some empirical evidence with regard to convergence. Section 4.1 presents the basic Solow–Swan model, the starting point for analyses of convergence as well as the convergence properties in Schumpeterian models of endogenous growth. Section 4.2 discusses the econometric methods for examining convergence applied in this analysis. Those include growth regressions, (dynamic) panel approaches in terms of fixed effects models as well as panel unit root tests (Im, Pesaran, and Shin as well as Maddala and Wu/Choi). This chapter concludes with a review of empirics of convergence of different economic variables like for instance per capita income, labor productivity, energy productivity, or CO 2 emissions.

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Faculty of Business, Economics and Social Sciences, University of Hohenheim, Stuttgart, Germany

Larissa Talmon-Gros

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Talmon-Gros, L. (2014). Convergence: Theory, Econometrics, and Empirics. In: Development Patterns of Material Productivity. Contributions to Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-02538-4_4

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DOI : https://doi.org/10.1007/978-3-319-02538-4_4

Published : 25 November 2013

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Mathematics > Optimization and Control

Title: subgradient convergence implies subdifferential convergence on weakly convex functions: with uniform rates guarantees.

Abstract: In nonsmooth, nonconvex stochastic optimization, understanding the uniform convergence of subdifferential mappings is crucial for analyzing stationary points of sample average approximations of risk as they approach the population risk. Yet, characterizing this convergence remains a fundamental challenge. This work introduces a novel perspective by connecting the uniform convergence of subdifferential mappings to that of subgradient mappings as empirical risk converges to the population risk. We prove that, for stochastic weakly-convex objectives, and within any open set, a uniform bound on the convergence of subgradients -- chosen arbitrarily from the corresponding subdifferential sets -- translates to a uniform bound on the convergence of the subdifferential sets itself, measured by the Hausdorff metric. Using this technique, we derive uniform convergence rates for subdifferential sets of stochastic convex-composite objectives. Our results do not rely on key distributional assumptions in the literature, which require the population and finite sample subdifferentials to be continuous in the Hausdorff metric, yet still provide tight convergence rates. These guarantees lead to new insights into the nonsmooth landscapes of such objectives within finite samples.

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