You may have a look in the following paper;

- http://unfccc.int/resource/docs/2016/tp/03.pdf

You may also go through the following IMF paper;

- https://www.imf.org/external/np/seminars/eng/2010/afrfin/pdf/Gelb2.pdf

There's also an explanation bt Hawaii Economic Issues;

- http://files.hawaii.gov/dbedt/economic/data_reports/reports-studies/2011-12-diversification.pdf

Centralization in sectors may be a helpful indicator; also check the Balassa index

Florian Kaulich's paper: Diversification vs. specialization as alternative strategies for economic development (cited in two posts above) taught me much about trade and development. The first part of this paper may well serve as a good introductory textbook for students who work on trade and development.

Douglas A. Irwin in his book Against the Tide: An Intellectual History of Free Trade (1996) argued many aspects of trade policies but did not focus on the diversity. The term "diversity" appears only twice in the same citations from Hume. However, if we want to fully understand the trade policy, it is inevitable to think about balance between specialization and diversity. Although in the history of trade policies, protection policies in particular, diversity was not argued much, as Irwin’s book testifies, to get and keep diversity of industrial activities is one of crucial views for the economic development for developing and even more for least developed countries.

As Ha-joon Chang and other people (like those who gathered in The Other Canon) argue, all developed countries have adopted protective policies in its early period of their economic development. Friedrich List and John Stuart Mill argued for the protection of infant industries. Frank D. Graham pointed the difference between decreasing and increasing returns. But, if we really consider the problem in a really dynamic viewpoint of the economic development, diversity must be the most important key word for many of developing countries.

Florian Kaulich thoroughly surveys the past discussion on this theme, both theoretical and empirical and abode to define how to measure diversity and then gives his own extensive research results. Although I have no ability to assess these empirical parts of the study, I was much stimulated by his paper. A new perspective may be opened vis- à-vis protection and trade liberalization.

I will come back again on this theme in the near future.

I have posted an idea of a new policy scheme for the least developed countries as a comment to Florian Kaulich's above cited paper:

Diversification vs. specialization as alternative strategies for economic development

https://www.researchgate.net/publication/281450398_Diversification_vs_specialization_as_alternative_strategies_for_economic_development?ev=prf_high

 Please read my comment.

Research Diversification vs. specialization as alternative strategies...

While I was studying  Florian Kaulich's above cited paper, I came to find a new scheme of development policy. I reproduce the comment that I have posted tp Kaulich's paper.

A new scheme of development policy for least developed countries

I agree with by Florian Kaulich's conclusion. As far as I see figures after Figure 5, the (re)specialization is not so steep and distinctive. It would not be too big error to assume that the diversification curve is L-shaped. This finding may tells us an development strategy for the least developed countries.

Let us call for the moment the least developed countries the nations whose GDP per capita is less than 2000 US dollars (this may not be identical to the common usage of the term). Kaulich's figures show that at least half of least developed countries are too highly specialized that we cannot see the similar cases in more developed countries. It is not good for those countries to stay in that state, because of various reasons: too vulnerable to international economic situations, small possibility to escape from monoculture-type economy, no big hope to raise GDP per capita, big chance to stay in the least developed state for a long time, etc.

I came to get an idea on the policy to be adopted by those countries. It is the uniform rate of import tariff, for example 50 % at the first period.

N.B. 50% is the tariffs of the Great Britten on manufactured goods at the time of its industrial revolution, around 1820. At the same period, the USA had imposed 45% tariffs for imports.

The General Framework:

(1) When a least developed country is specialized above the minimal diversification level, it can adopt a uniform tariff for example 50% on all imports. The minimal diversification level is defined in (2).

(2) Measuring by an appropriate diversification/specialization index, the minimal diversification level is defined as the level of diversification/specialization index that is just above the levels of two third countries (or three quarters) with GDP per capita more than 10,000. The average diversification level is defined as the level of diversification/specialization index that is just above the half of countries with GDP per capita more than 10,000.

(3) When the diversification level approaches to the average diversification level, the uniform import tariff is reduced proportionally up to tariff 0.

(4) No export tariffs or bounties are imposed.

(5) If a least developed country satisfies the condition (1), the richer country with 10,000 US dollars per capita must not impose tariffs on products of origin of the least developed country above the most favored country one.

Some merits of the scheme: 

(1) There is no price distortion for imported goods.

(2) No arbitrary government intervention is possible.

(3) No necessity to find and select infantry industry to enhance.

Why does this scheme help to diversify its industrial structure?

This policy scheme does not automatically assure that the concerned country can diversify its economy. However, it relaxes abusive external pressure against establishing a new industry (i.e. new firms). This contention is supported by the new theory of international values (see the paper below. The paper is already published but I cite the draft version).

The new theory of international values tells that countries specialize strongly when there are no transaction and transport costs and no tariffs. When there are M-countries and N-commodities, the total number of products producible by country (the same products in different countries are counted once at each country) is M+N-1. When the uniform tariff rate of the world increases sufficiently, all countries can produce any products. Then the total number of products by country is M・N. For example, when M = 100, and N = 10,000 (this is in fact a very small estimation), then

                M+N-1 = 10,099 M・N = 1,000,000. M・N/(M+N-1) = 99.

By imposing uniform tariffs, we can increase the total number of products by country that are at lest domestically producible. As we see easily by this simple thought experiment, the uniform rate of tariffs cam relax too strong international competition and gives the chance to enhance some industries which are appropriate for each country. The new policy has the least administrative costs and does not require high ability from the part of the government. If once domestic production starts, the firms have a chance to bring the productivity higher by learning by doing.

The history shows that the now developed countries had adopted protection tariffs at the early stage of their industrialization. The unique exception might be be Meiji Japan. It inherited tariff agreement imposed by western powers before the Meiji revolution. The agreement was uniform 5% for all imports at the starting point. Japan could get tariff autonomy at first in 1907 with Russia after the Nippo-Russian war and in 1911 with other countries including the USA. However, it is important to know that Japan profited by its relatively isolated location separated from American and European countries. Although the USA was neighbor to Japan across the Pacific Ocean, the American west coast was not industrially well developed at that time. In this sense, Japan was rather well protected from Western industrial nations.

The New Theory of International Values: An Overview

https://www.researchgate.net/publication/304717720_New_Theory_of_International_Values_A_General_Introduction

Working Paper The New Theory of International Values: An Overview