The Next Hundred Years of Growth and Convergence

Richard Startz*

Revised May 2019

Abstract

World GDP per capita is forecast to grow at 2.6 percent annually over the next 100 years.

Convergence of less developed countries toward output levels of the world frontier accounts

for much of the forecast. Projecting recent growth in China and India accounts for much of the

forecast convergence. The forecast differs from the earlier literature because the facts of

convergence have changed in recent decades. A Markov-switching model is estimated for each

country, allowing each country to switch on-or-off a path of convergence to the world output

frontier. Bayesian estimates of the historical process and posterior forecasts are offered.

JEL codes: O40, O47, C11

Keywords: growth, convergence, Markov-switching, Bayesian estimation

* Department of Economics, University of California, Santa Barbara, startz@ucsb.edu. I am grateful to Jeremy Piger for code and comments and to Shelly Lundberg, the UCSB Econometrics Working Group, the co-editor, and the referees for comments.

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1. Introduction

How well-off will the world be in 100 years, as measured by per capita GDP? The question is

critically important for many issues, notably including projections of climate change (National

Academies of Sciences (2017), Raftery et. al. (2017)). The answer to the question posed

depends on growth in the world productivity frontier and on the rate at which poorer countries

move toward that frontier. The latter is key: Which countries are already on a convergent path;

What is the probability that non-convergent countries switch to the convergent path; and What

is the rate of convergence once on that path?

Three basic points are made. The first, the answer to the substantive question, is that the

world is likely to have much, much higher per capita output 100 years from now than is true

today and that in large part this will be due to the convergence of poorer countries to the

frontier. The second point is that the high future growth rate comes mostly from forecasting

that countries that have already started along a convergent path will continue to converge—

slowly. The third point is that the emphasis placed here on convergence follows from looking at

recent data. In other words, much of the literature on growth and convergence was written at a

time in which convergence was hard to detect. The world has changed in a way that the model

and estimates offered here demonstrate.

The conclusions found here appear to be at odds with what much of the literature reports.

Johnson and Papageorgiou (2017) summarize the evidence writing, “there is a broad consensus

of no evidence supporting absolute convergence in cross-country per capita incomes—that is

poor countries do not seem to be unconditionally catching up to rich ones.” The evidence

presented here is entirely consistent with their summary…with a critical exception which is

quantitatively dominant: In recent decades the convergence behavior of China and India has

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changed. Because China and India hold one-third of the world’s population, the behavior of

these two countries has an enormous effect on world output in the future even if very few

other poor countries show significant convergence. (This point is consistent with Jones (1997),

Schultz (1998), and Sala-i-Martin (2006).) The quantitative conclusion is drawn from a formal

econometric model which is designed to be flexible with regard to the behavior of different

countries at different times. As such, the historical data drive the model.

The basic idea of the formal model is simple: At a point in time a country may be on a path

that will eventually lead it to converge to the world frontier, or it may be on a path in which the

gap from the frontier is not closing, or possibly on a path in which the country is falling further

below the frontier. I model each path as a state of a Markov process, estimating the probability

that each country is currently on a given path and the probabilities that countries switch from

one path to another. Combine the probability of being on the convergent path with an estimate

of the rate of convergence on the convergent path and an estimate of frontier growth, and

projecting probabilistic future paths for world output is straightforward.

The empirical work here is motivated by a variant of the theoretical model in Lucas’ (2000)

“Some Macroeconomics for the 21st Century.” Lucas answers these questions with a “reduced-

form,” calibrated model. I maintain Lucas’ reduced-form set-up and also maintain his

assumption that eventually countries begin to converge to the frontier. Since I estimate the

probability of a being on a convergent path, the data decide whether convergence is

quantitatively important or not. My approach picks parameters in a manner that is mid-way

between Lucas’ calibration and the unrestricted estimation used in much of the literature,

through use of a Bayesian framework. The Bayesian framework allows one to impose

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assumptions that limit the range of parameters. In particular, this helps the model pick out

changes at horizons which plausibly correspond to long-run growth. The Bayesian framework

forces one to be explicit about what assumptions are made and I specify priors that are

informed by what we know about growth. At the same time, the priors are loose enough that

the data rather than the priors choose parameter estimates within a broad range.

The literature on convergence is enormous. Rather than attempting to summarize it here,

the reader is referred to the excellent review article by Johnson and Papageorgiou

(forthcoming) with some nearly 300 references. (See also Temple (1999), Barro and Sala-i-

Martin (2004, Chapter 12), Durlauf (2005), Acemoglu (2009, sections 1.3-1.5), and Jones and

Vollrath (2014, section 3.2.).)

To see why focusing on convergence matters, I offer two not-very-sophisticated back-of-

the-envelope calculations before beginning an econometric analysis. First, why might

convergence matter at all for the next 100 years of growth? Won’t world growth over such a

long period be dominated by growth of the frontier, presumably due to technology raising TFP?

Second, is the gap between world and frontier output large enough that even slow reduction of

a large gap might add substantially to growth of the frontier?

What might be a reasonable range for the frontier growth rate? Frontier output per capita

has been growing at about 1.7 percent per year since 1970, although growth has slowed

somewhat recently.1 Of course, that growth rate might change in the future. Gordon (2016, p.

1 Data are from 1950 through 2014 in 2011 dollars, as given in the Penn World Table 9.0 including updates through August 2016. See Feenstra et. al. (2015). “Frontier output” means U.S. GDP per capita throughout, while “rest of world” means all countries other than the U.S.; including other countries with output that is also at the frontier, but excluding the petro-states Brunei, Kuwait, United Arab Emirates, and Qatar, as well as Macao which has questionable GDP numbers and Curaçao and Sint Maarten (Dutch part) which are very small and for which the data only begin in 2005.

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14) offers some estimates that suggest a plausible range for growth in the frontier. He reports

that U.S. output per capita grew at a 1.8 percent annual rate from 1870 to 1920 and 2.4 percent

from 1920 through 1970. Notably, Gordon argues that future growth won’t exceed the current

1.7 percent rate. Forecasting frontier growth over the next 100 years is a difficult and open

question, as there might be further productivity slowdowns or there might be quickened

growth due to increased automation. Taking 1.7 percent as a benchmark, we can ask if

convergence is quantitatively important by asking whether growth forecasts are notably

different from 1.7.

The potential for faster world growth through convergence is enormous, because most of

the world is still very far from the frontier. Taking the United States as representative of the

world frontier, as is customary in the postwar period, frontier output per capita is now $51,600

while population-weighted output per capita in the rest of world is $12,600. If the rest of the

world were to catch up to the frontier in a single, 20-year generation (miraculously), then the

world growth rate would equal 9.2 percent. If convergence were complete in a less miraculous

time frame, say, 50 or 100 years, then the world growth rate would have to be 4.7 or 3.2

percent, respectively. All these numbers are much larger than plausible rates of frontier

growth. Thus convergence is potentially key.

The second back-of-the-envelope calculation looks at how in recent years convergence

appears to have become more important than it was in the earlier postwar period. Figure 1

shows output in the rest of the world relative to the frontier on the left axis. At some point in

the last decade of the twentieth century, relative world output began to grow notably more

quickly than in the earlier postwar period. Importantly, between 1990 and 2014 relative output

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in China increased by almost a factor of four. Relative output in India doubled. Since China and

India account for a third of the world’s population, growth in these two countries alone can

make a huge difference to long-run world output. The right-hand scale for Figure 1 shows my

econometric estimates of the probability that the average, population-weighted, country has

started to converge to the frontier, with separate estimates allowed pre- and post-1990. The

methodology is discussed below. For now, Figure 1 illustrates that the changes in the estimated

probability that countries are converging are largely consistent with the pattern one sees in the

raw data for world output, and suggests that by the end of the sample about two-thirds of

(population-weighted) countries had started on a convergent path. While the population-

weighted number is high, the results are also consistent with the literature in that many smaller

countries do not appear to be converging. Among the non-high-output countries (using the

Johnson and Papageorgiou Table A.1 classification), I estimate the median probability of being

on a convergent path to be just under a half. In contrast, the probabilities for China and India

are 0.98 and 0.96 respectively.2

<Figure 1 goes about here>

Continuing with simple calculations, suppose we think that convergence in recent decades

might continue. Say there are two chances in three it will continue and one chance in three that

the distance to the frontier will close no further, in other words that convergence will come to a

complete halt. Suppose further that if a country is converging, it takes 50 years to close half the

gap to the frontier. Together these assumptions imply that in 100 years there are two chances

2 The probabilities of being nonconvergent or divergent at the end of the sample are 0.014 and 0.001 for China and 0.038 and 0.000 for India respectively.

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in three that the gap will be reduced to one quarter of its current level. That adds one

percentage point above the frontier to the world growth rate.

Neither theory nor back-of-the-envelope calculations dictate that the next century should

see complete convergence. Indeed, the estimate here is that output per capita in the rest of the

world will rise from 24 percent of the frontier to 57 percent of the frontier level over the next

hundred years. This suggests an overall growth rate of 2.6 percent, which is almost a

percentage point higher than frontier growth. Predictions are shown in Figure 2.3 Without

convergence, i.e. assuming that each country maintains the gap from the frontier observed in

the last year of the data, I estimate a hundred years of growth will put world output per capita

about twenty percent higher than today’s U.S. output per capita. With estimated convergence,

world output will be three-and-a-half times today’s U.S. output per capita. (U.S. output per

capita will be nearly six times today’s output per capita.) These are median point estimates;

fiducial intervals are presented below.

<Figure 2 goes about here>

2. Models and related literature

Many models of economic growth explicitly suggest that at some point a country is likely to

switch growth paths. As Jerzmanowski (2006) writes, “growth experiences differ over time

within a country almost as much as they differ among countries.” Hausmann et. al. (2005)

3 Here and in later Figures, a circle is drawn at the last observed datum to supply a reference point.

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report over 80 instances of growth accelerations between 1950 and 2000. Jones and Olken

(2008) document that growth can stop as well as take off.4

Projections of long-run world growth are often done using “scenarios” or calibration, unlike

the purely econometric methods used here. The work closest in spirit to this paper is Lucas

(2000). Lucas (his Figure 3) forecasts a growth rate starting around 3 percent and declining to

about 2.2 percent over the period in which I forecast. (Lucas assumes slightly higher frontier

growth.) Other forecasts often project out factor inputs and then run these inputs through a

production function. Examples include Johansson et. al. (2012) and Dellink et. al. (2017). The

econometric forecast closest to the one here is Raftery et. al. (2017), which estimates

convergence rates for each country in the world based on historical convergence rates. Using

Bayesian techniques somewhat similar to those used here, but assuming that countries never

change convergence paths, Raftery et. al. (2017) estimate that for over half the countries the

rate of convergence is zero. As a result Raftery et. al. projects world output to grow at little

more than the rate of frontier growth. Jerzmanowski (2006) offers a Markov-switching model of

growth, focusing on the role played by government anti-diversion policies. Jerzmanowski allows

four states of growth (for individual countries rather than relative to the frontier) and the data

set ends in 1996. The Bayesian technique used here helps separate long-run from business

cycle dynamics in a way that cannot be done using the maximum-likelihood estimation in

Jerzmanowski. These differences notwithstanding, Jerzmanowski’s results suggest that the

Markov-switching approach is a fruitful way to identify growth regimes.

4 Kraay and McKenzie (2014, p. 128) argue that no-growth states are rare in the modern era, writing “stagnant incomes…over long periods is rare in practice, with the typical poor country growing at least as fast as the global average over the last 60 years.”

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The empirical model proposed here can be thought of as a variant of the calibrated model

in Lucas (2000). Lucas (2000), focusing on the period since 1800, has countries either in no

growth status or in convergent status. A given country has no growth until it begins

convergence, which happens probabilistically. The estimates here, based on the modern era,

look at growth relative to the frontier rate without or with convergence. The mechanics are the

same when there is convergence, but the alternative is no growth in Lucas (2000) or conditional

convergence here.

To allow for full generality, each country is assumed to be in one of three discrete states at

each point in time: non-convergent (𝑛), convergent (𝑐), and divergent (𝑑). The first two states

are as in Lucas (2000); the divergent state allows for the fact that countries sometimes undergo

growth disasters in which they diverge from the frontier for extended periods (see Pritchett

(1997)). The model to be estimated becomes

𝑦𝑖,𝑡 − 𝑦𝑡∗ = 𝐼𝑆𝑖,𝑡=𝑛 × [𝑦𝑖,𝑡−1 − 𝑦𝑡−1

∗ ] + 𝐼𝑆𝑖,𝑡=𝑐 × 𝜃𝑐 × [𝑦𝑖,𝑡−1 − 𝑦𝑡−1∗ ]

+𝐼𝑆𝑖,𝑡=𝑑 × 𝜃𝑑 × [𝑦𝑖,𝑡−1 − 𝑦𝑡−1∗ ] + 𝜀𝑖,𝑡

(1)

where 𝑦𝑖,𝑡 is the log of per capita GDP in real, U.S. dollars for a given country and 𝑦𝑡∗ is the log of

frontier per capita GDP. Countries are indexed by 𝑖 = 1, … , 𝑛. 𝑆𝑖,𝑡 ∈ {𝑛, 𝑐, 𝑑}. During the

convergence period, the log ratio between a country’s output and the frontier closes at an

expected rate of 1 − 𝜃𝑐 percent, 𝜃𝑐 < 1.5 Outside the convergence period, if 𝑆𝑖,𝑡 = 𝑛, the gap is

unchanged except for random fluctuations and if 𝑆𝑖,𝑡 = 𝑑 output falls relative to the frontier. In

5 Assuming a common value for 𝜃 surely oversimplifies the world. Note, however, that some version of such an assumption is necessary as many countries have few observations with 𝑆𝑖𝑡 = 𝑐. Essentially, 𝜃 must be inferred from countries that are on the convergent path but not yet converged. In principle, some heterogeneity could be added by making 𝜃 a function of observables. Doing so might be interesting for its own sake, but doing so would then add the difficulty of forecasting out those conditioning observables for 100 years in order to know future 𝜃.

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a divergent state 𝑦𝑖,𝑡−1 < 𝑦𝑡−1∗ and 𝜃𝑑 > 1. In this specification a country that has caught up to

the frontier is expected to stay there in both states 𝑛 and 𝑐, except for random fluctuations. For

such countries the state is not identified, but this is of no consequence because the predictions

are the same. The model accommodates a country which has an idiosyncratic steady-state that

leaves it permanently below the frontier by allowing the country to begin in the convergent

state but eventually switch to the non-convergent state as it approaches its permanent

deviation from the frontier.6 Note that landing in the 𝑛-state is consistent with the finding of

convergence in growth rates but not levels in Pesaran (2007).

To complete the empirical specification, I take 𝑆𝑖,𝑡 to follow a discrete first-order Markov

process.7 For each pair of the nine possible pairs of [𝑡 − 1, 𝑡] states, I estimate the probability of

transition between states from one period to the next. So there is a probability that a country

that was non-convergent (𝑛) last period becomes convergent (𝑐), etc., this period. Given initial

estimated states, the forecast works by drawing a subsequent state based on the transition

probabilities, then a new shock 𝜀𝑖,𝑡 is drawn and added to the right-hand-side to give the new

level of output, and then repeat for later periods.

Note that equation (1) considers convergence to the world frontier, but does not provide

for the possibility of club convergence. Canova (2004) provides evidence of club convergence

both across European regions and within the OECD. For 100-year forecasting, whether a

country’s growth depends on a club and the club’s growth responds to the frontier or whether

6 For a very different approach based on linear models estimated in a state-space framework rather than the model here with discrete switching, see Carvalho and Harvey (2005). 7 Quah (1993) introduces a Markov specification in which countries evolve across quintiles of the world income distribution. In a related paper, Jones (1997) emphasizes the importance of convergence in determining the world income distribution. Durlauf and Johnson (1995) divide countries into different growth regimes, although not using a Markov-switching model.

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the country’s growth depends directly on the frontier is likely a second-order issue. However,

note that the model here does not speak to the question of whether there are or are not

economic reasons leading to club convergence.

I close the model by assuming that log frontier output per capita, 𝑦∗, follows a random walk

with drift, so the expected growth rate is 𝜇 > 0. (For a contrast, see Müller and Watson (2016,

pp. 1731-32) which forecasts higher growth rates, although the growth rate estimated here is

well within the coverage sets that Müller and Watson present.)

𝑦𝑡∗ = 𝜇 + 𝑦𝑡−1

∗ + 𝜀𝑡∗

(2)

Finally, note that equations (1) and (2) are very close to equations (2) and (1) in Lucas

(2000).

3. Data

The data used here are from the Penn World Table (Feenstra et. al. (2015)) version 9.0. GDP

per capita is measured in 2011, PPP converted, U.S. dollars and is calculated according to the

PWT variables 𝑌 = 𝑅𝐺𝐷𝑃𝑁𝐴/𝑃𝑂𝑃.8 The data measure output per capita for 174 countries

annually with various starting dates beginning in 1950 and all ending in 2014, for a total of

9,129 observations. Descriptive statistics of the underlying data, showing both population-

weighted and unweighted descriptive statistics are given in Table 1.9 Observations start in

various years; the weighted mean first observation comes in 1955. The shortest observation

8 I use output per capita as being the target of interest for thinking about welfare, but many models of growth theory would use output per worker instead. 9 Weighting for historical data is done throughout using 2014 population weights. Weighting for future simulations is done using population forecasts from Raftery et. al. (2012) and United Nations (2017). I interpolate between the demi-decade figures given there and extrapolate for years post-2100.

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period is 25 years; the longest is 65. The ratio of average output to frontier output declined in

the data set from individual country starting dates through 1953, but this largely reflects later

entry into the data set of poorer, smaller countries. Note that the population-weighted ratio of

country output to the frontier closed moderately between the first-observation for a country

and 2014 (from 13 percent to 24 percent). PWT provides an unbalanced panel. There is likely

some selection bias in terms of when coverage begins for a particular country. However, 89

percent of the world’s population, by 2014 population weights, is covered by 1960.

Mean (weighted by

2014 population)

Mean

(unweighted)

Min Max

Starting year 1955 1963 1950 1990

Average growth rate, rest of

world

2.71% 1.97% -1.71% 7.14%

Average growth rate, U.S. 1.99%

2014 output, rest of world $12,571 $16,594 $570 $82,297

2014 output, USA $51,621

Ratio of income to US output,

first observed year

0.13 0.40 0.01 3.68

Ratio of output to US output,

2014

0.24 0.32 0.01 1.59

Source: Penn World Table 9.0. Data in 2011, PPP-adjusted U.S. dollars

Summary statistics of sample data

Table 1

One generally expects that most countries will have positive growth at or above the rate of

frontier growth, except perhaps for random fluctuations. Postwar data are not entirely

consistent with that expectation, but the deviations represent a very small part of world

population. Mean growth was negative for 17 countries, although significantly negative with a

one-tailed, five percent test for only one. Quite a few countries, 89, had mean growth lower

than the frontier, but only 21 had growth significantly below the frontier on a one-tailed, five

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percent test of the difference between country and U.S. mean growth rates. Total 2014 GDP of

the countries with growth significantly below the mean was 1.4 percent of world GDP, with

almost half of that accounted for by South Africa.

4. Estimation

Estimation follows fairly standard Bayesian algorithms, which are described first. I then

describe the important identifying restrictions. The model consists of 174 equations for the

output gap plus a random walk equation for frontier output, as specified in equations (1) and

(2).

The frontier equation is estimated assuming normal errors and independent normal-gamma

priors. The priors are diffuse, so that the posteriors mimic the standard frequentist distribution

for a sample mean. 𝜇 and ℎ∗ ≡ 1/𝜎𝜀∗2 are estimated by Gibbs sampling with 100,000 samples

retained after discarding 10,000 samples. The significant issue is that the U.S. underwent a

growth slowdown somewhere around 1970; Gordon (2016) uses the date 1970 while Perron

(1989) prefers 1973. Since projections for the future should reflect current growth, I estimate 𝜇

beginning in 1970. Priors and posteriors for 𝜇 and ℎ∗ are given in Table 2, with the posterior

distribution summarized by its median, mean, standard deviation, and 95 percent region of

highest posterior density (HPD). As a practical matter, the posterior mean and median for 𝜇

match sample mean growth to two digits.

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Parameter Conditional prior Posterior

median

95 Percent HPD Posterior

mean

Posterior

standard

deviation

𝜇 𝑁(0, .0016) ×

Γ((4.1 × 10−4)−1, 1)

0.017 < 0.011, 0.023 > 0.017 0.0031

ℎ∗ 2388 < 1462, 3436 > 2,424 510

Priors and posteriors for independent normal-gamma mean growth for frontier

Table 2

The individual country equations in equation (1) are estimated by a Gibbs sampler, again

with 100,000 samples retained after discarding 10,000 samples. The sampler proceeds in four

blocks, the draw for each block being conditional on the previous draws for the other four

blocks and on the data.

1. Estimates of the state vector for each country for the entire sample period are

drawn, using a modified version of the algorithm in Carter and Kohn (1994).

2. Estimates of the precision parameter, ℎ𝑖 ≡ 1/𝜎𝜀𝑖

2 , are drawn for each country, based

on what can be thought of as the residuals from equation (1).

3. Next, estimates of 𝜃𝑐 and 𝜃𝑑 are drawn, where the parameters can be thought of as

regression parameters in equation (1), stacking the data for all the countries.

4. Estimates of the transition probabilities between states are drawn, based on the

observed transitions drawn in step (1). (Separate transition probabilities are

estimated in the early and late subperiods.)

The states 𝑆𝑖𝑡 are treated as latent variables (and so do not have separate priors).

Conditional state draws are made using a multi-move algorithm based on Carter and Kohn

(1994). (See also Chib (1996), and Kim and Nelson (1999).) The standard algorithm is modified

to restrict a draw of the divergent state to cases where the country’s output is below the

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frontier in a given year. This is consistent with the model and avoids drawing a small number of

explosive paths (primarily for Norway). In other words, when 𝑦𝑖𝑡 > 𝑦𝑡∗ a random draw of 𝑑 is

recoded to 𝑛. Posterior means for each state are shown in Figure 3 below.

The countries with notable posterior estimates of being in a divergent state at the end of

the sample include the Central African Republic (48%), Greece (43%), Cayman Islands (41%),

Italy (38%), and Syria (30%). No other countries have posterior mean estimates as high as 20

percent of being in a divergent state at the end of the sample.

Note that the values for 𝜃𝑐 and 𝜃𝑑 and the values of the probabilities of switching between

states are common for all countries. Holding these parameters in common across countries

permits identification for countries in which a particular state is rarely observed, meaning there

would be no data to permit idiosyncratic identification. The switching probabilities are

estimated separately for the two subperiods; other estimates are common across the entire

sample. The break at 1990 is chosen as a year in which there is arguably a change in the raw

data, as seen in Figure 1, with some attention to leaving an adequate sample length in the later

sub-sample. In other words, the results should not be interpreted to say something special

changed precisely in 1990.

The advantage of the Bayesian technique is that it allows imposing restrictions that assist in

identification and for being explicit about what is being imposed. (Gibbs sampling also allows

for considerable computational simplicity.) We want state estimates that are consistent with

the economic idea that at a point in time economies either are or are not on a convergent path,

and that once on the path generally stay there. I impose priors consistent with a plausible—but

broad—range of speeds of convergence. I do this with an informative uniform distribution that

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bounds 𝜃𝑐 away from 1.0. At the lower bound of the prior, a country would close half the

output gap from the frontier (starting at the average gap) in an implausibly fast 21 years. At the

upper bound, the half-life of the average gap is 54 years. The priors for 𝜃𝑑 are then set to be

above 1.0, symmetrically with the priors for 𝜃𝑐. The half-life to close the average gap at the

posterior mean is 45 years.

The values of 𝜃𝑐, 𝜃𝑑 , and ℎ𝑖 are estimated using standard Bayesian regressions assuming

uniform priors for 𝜃𝑐 and 𝜃𝑑 and an independent gamma prior for ℎ𝑖. The prior for the precision

for individual countries is Γ (var(𝑦𝑖𝑡 − 𝑦∗) ,1

8), which is quite diffuse. The uniform priors on

𝜃𝑐 and 𝜃𝑑 lead to truncated normal posteriors for 𝜃𝑐 and 𝜃𝑑. Somewhat surprisingly, the draws

from the truncated normal sometimes run into numerical difficulties, which are solved by using

the algorithm given in Botev (2016) as well as code Botev makes publicly available. The priors

for the precision are diffuse, with the prior mean for each country set to the unconditional

variance of 𝑦𝑖,𝑡 − 𝑦𝑡∗ and the prior standard deviations set to four times the prior means.

Each country’s data is weighted according to its 2014 population share, although weighting

the regression makes very little difference. The posterior for 𝜃𝑐 shows considerable pile up

close to the upper bound—approximately 34 percent of the simulation draws—indicating the

prior restriction does play an important role in identification. The posterior for 𝜃𝑑 has a small

pile-up—not quite 10 percent—near the upper bound. Priors and posteriors are given in Table

3, with the posteriors converted to standard deviation units for ease of interpretation.

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Parameter Conditional prior

Posterior median

95 Percent HPD Posterior mean

Posterior standard deviation

𝜃𝑐 𝑈(0.95,0.98) 0.979 < 0.963, 0.980 > 0.978 0.005

𝜃𝑑 𝑈(1.02,1.05) 1.036 < 1.022, 1.05 > 1.037 0.0087

ℎ̅ Γ(51.2,0.125) 536 < 29.6,1,613 > 409 118

Priors and posteriors for convergence and divergence rates and shock precision

Table 3

The prior for the nine parameter (less three adding up constraints) transition probability

matrix is chosen to place a strong weight on a country remaining in a given state, particularly

that once a country begins to converge it is likely to continue to do so as suggested by the Lucas

(2000) model. The priors for states 𝑛 and 𝑑 are symmetric. The prior for state 𝑐 is slightly more

persistent, and makes it slightly less likely to transit into state 𝑑 than into state 𝑛. The Dirichlet

distribution provides conjugate priors.10 In order to ease interpretation, prior means are shown

first and prior standard deviations are shown in parentheses in Table 4. The parameters for the

Dirichlet priors are given in square brackets.

10 Dirichlet priors are an extension of beta priors which constrain parameters to be between zero and one and force parameters to add to one. Thus, Dirichlet priors are standard for modeling probabilities.

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To From

𝑛 𝑐 𝑑

𝑛 0.965 (0.028) [39.3]

0.0175 (0.020) [0.714]

0.0175 (0.020) [0.714]

𝑐 0.018 (0.022) [0.714]

0.973 (0.025) [39.3]

0.0088 (0.015) [0.357]

𝑑 0.0175 (0.070) [0.020]

0.0175 (0.070) [0.020]

0.965 (0.005) [0.028]

Note: Prior mean shown first; prior standard deviation in parentheses; Dirichlet parameter in square brackets.

Transition Matrix Priors Table 4

The conjugate posterior is Dirichlet with parameters equal to the prior parameters plus the

number of switches. Because there are just under 9,000 switches observed—on average 1,000

per element of the transition matrix—the data should dominate the prior in computing the

posterior. In calculating the number of switches, I weight according to 2014 population.

Specifically, if country 𝑖 has 𝑆𝑖𝑗𝑘

switches from state 𝑗 to state 𝑘 and if country 𝑖 has a fraction

𝑤𝑖 of the 2014 world population, and the prior Dirichlet parameter is 𝑝𝑗𝑘, then the posterior

Dirichlet parameter is 𝑝𝑗𝑘 + ∑ (𝑆𝑖𝑗𝑘

⋅ 𝑤𝑖)𝑖

∑ (∑ 𝑆𝑖𝑗𝑘

⋅𝑤𝑖𝑖 )𝑗𝑘

∑ (∑ 𝑆𝑖𝑗𝑘

𝑖 )𝑗𝑘

⁄ .

Posterior means, medians (in braces), and 95 percent highest posterior density regions for

the transition matrices are given in Table 5 and Table 6. The posteriors for states 𝑛 and 𝑐 are

relatively close to the priors; the posterior for state 𝑑 in the early subperiod is less so.

18

To From

𝑛 𝑐 𝑑

𝑛 0.958 {0.961} <0.926, 0.986>

0.002 {0.001} <0, 0.009>

0.039 {0.037} <0.012, 0.072>

𝑐 0.012 {0.005} <0, 0.046>

0.966 {0.973} <0.913, 1.0>

0.023 {0.014} <0, 0.074>

𝑑 0.458 {0.460} <0.289, 0.630>

0.017 {0.007} <0, 0.063>

0.525 {0.525} <0.364, 0.682>

Note: Posterior mean shown first; posterior median in braces; 95% HPD in angle brackets.

Transition matrix posteriors—early subperiod Table 5

To From

𝑛 𝑐 𝑑

𝑛 0.957 {0.957} <0.931, 0.978>

0.042 {0.042} <0.019, 0.066>

0.001 {0.0} <0, 0.002>

𝑐 0.007 {0.003} <0, 0.025>

0.990 {0.992} <0.973, 1.0>

0.0040 {0.003} <0., 0.009>

𝑑 0.004 {0.004} <0.002, 0.082>

0.006 {0.003} <0, 0.023>

0.954 {0.953} <0.912, 0.996>

Note: Posterior mean shown first; posterior median in braces; 95% HPD in angle brackets.

Transition matrix posteriors—later subperiod Table 6

Posteriors may be easier to interpret by looking at the implied steady-state state

probabilities given in Table 7. The median estimate of the steady-state probability of the

convergent state rises from 0.09 in the early subperiod to 0.76 in the later subperiod. In other

words, the posterior estimates suggest that the world has changed from a situation in which

countries were largely not converging to a situation in which countries largely are converging.

Early subperiod Late subperiod

Median 𝑝𝑛

0.834 0.175

19

𝑝𝑐 0.094 0.764

𝑝𝑑 0.073 0.062

95 percent HPD steady-state 𝑝𝑐 (0.003, 0.269) (0.547, 0.973)

Steady-state estimates of state probabilities

Table 7

The Gibbs sampler generates a posterior distribution for the convergence state, 𝑆, for each

country in each year. Draws for each country are done separately, and draws depend on the

entire history of the respective country’s ratio relative to the frontier, as well as the Markov

probabilities for the relevant subperiod. The mean of the posterior 𝑆𝑖𝑡 = 𝑗 gives the probability

that country 𝑖 is in state 𝑗 in year 𝑡. The right-hand scale of Figure 1 shows the increase over the

sample period in the estimated population-weighted probability of being in the convergent

state. The estimates suggest that convergence was unlikely in the early subperiod but quite

likely in the later subperiod, particularly after the turn of the century.

Figure 3 shows the probabilities for all three states and also shows state estimates when the

model is estimated over the entire sample (dashed line).11 The average probability of being on a

convergent path rose from 11 percent in 1960 to 71 percent in 2014. Based on the posterior

estimates, the probability that Korea was in a convergent state in 2014 was 94 percent. The

probability for China was 98 percent and the probability for India was 96 percent. But the

probability that Pakistan had moved into a convergent state was under four percent.

<Figure 3 goes about here>

The apparent break in the state estimates is an artifact of estimating transition probabilities

separately for the two subperiods. The whole sample estimate shows essentially the same

11 Pesaran’s (2007) findings would be consistent with countries mostly being in the 𝑛-state rather than the 𝑐-state. But note that Pesaran’s sample ends in 2000 and so mostly covers the earlier rather than the later subperiod here.

20

pattern, but with the change between subperiods smoothed over. Since splitting the sample

makes only a modest difference to convergence estimates, why split it? The answer is that

while the in-sample estimates are largely driven by the data, forecasts at long horizons are

significantly influenced by the steady-state probabilities. As shown above, these steady-state

probabilities are estimated to have changed significantly in more recent years. Forecasts made

using a whole sample estimate are qualitatively similar, but quantitatively different. The 100-

year forecast growth rate based on the whole sample estimate is 2.1 rather than 2.6 percent.

Table 8 provides the estimated probability of being in a convergent state in 1970 and at the

end of the sample for each region as defined in United Nations (2017). (1970 is chosen as the

year in which countries holding 95 percent of the 2014 world population have appeared in the

sample.) Much of the world is estimated to have become more likely to have started on a

convergent path by the end of the sample, with the probability becoming quite high for much

of Asia. Estimates for individual countries are given in the online Appendix. It is noteworthy that

within Latin America, the 2014 probability is over 90 percent for Chile, Colombia, Panama,

Trinidad and Tobago, and Uruguay. Paap et. al. (2005) find that eight African countries can be

classified as “medium growth” using data ending in 2000. Of these, I find relatively high

probabilities of being in a convergent state in 2014 for Cape Verde, Gabon, Mauritius,

Seychelles, and Zimbabwe, but not for Congo, Lesotho or Malawi.

UN Region Probability of convergent state, 1970

Probability of convergent state, 2014

Australia/New Zealand 0.11 0.81

Melanesia 0.05 0.16

Caribbean 0.07 0.42

Central America 0.05 0.19

21

South America 0.30 0.63

Central Asia - 0.00

Eastern Asia 0.13 0.96

South-Eastern Asia 0.11 0.89

Southern Asia 0.01 0.84

Western Asia 0.04 0.60

Eastern Africa 0.00 0.41

Northern Africa 0.07 0.43

Southern Africa 0.04 0.15

Western Africa 0.08 0.48

Eastern Europe 0.26 0.23

Northern Europe 0.09 0.62

Southern Europe 0.90 0.35

Western Europe 0.73 0.69

Northern America 0.15 0.69

Probability of convergent state for UN regions

Table 8

5. Projections

Predictions over the next 100 years are made by taking 10,000 draws from the posterior

distributions and then projecting the frontier and the gap from the frontier for each country. I

begin with a draw for 𝜇 and ℎ∗. The frontier is then forecast by taking 10,000 100-long normal

draws for 𝜀∗ and running out the random walk with drift in equation (2). Next, draws are taken

for the remaining parameters and the latent 𝑆𝑖,2014. With respect to the latter, note that while

each state draw is either zero or one, the expected value of each draw is the posterior mean for

each country. The states are then forecast out according to a first-order Markov process

governed by the draw from the posterior for the 1990-2014 transition matrix. Finally, 10,000

100-long normal draws are taken for 𝜀𝑖,𝑡 and output is projected for the country using equation

(1).

As shown in Figure 2, the median forecast for the world in 100 years is $180,000. This

compares to a forecast frontier output per capita of $293,000. In contrast, absent further

22

convergence world output per capita would be predicted to rise only to $62,000. Of course,

each of these numbers would be changed if the average growth rate of the frontier over the

next 100 years turns out to be significantly higher or lower than the average growth rate over

the last 40.

A large part of the forecast of movement toward the frontier, 32 percent, arises from the

forecasts for two countries: China and India.12 This may be unsurprising, as China and India

have 37 percent of the world’s population. (Indonesia, Nigeria, and Brazil, are the only other

countries to account for as much as two percent of the result.) The estimated model does not

make use of idiosyncratic information about likely future growth prospects for individual

countries, above and beyond the information encapsulated in the historical growth record. The

fact that nearly all countries play small roles in the overall world forecast suggests mis-forecasts

for individual countries are unlikely to have much effect on the final result so long as one

believes that China and India are likely to continue to converge. However, if the growth in

recent decades in China and India were too stall, then the overall world outcome would likely

be quite different than the forecast.

As seen in Figure 2—which gives the median forecast—world output per capita is projected

to grow substantially over the next 100 years. Since the forecasts are based on how much

countries have converged to the frontier, it is useful to consider projections for the gap from

the frontier and the probability of being in a convergent state. The upper panel in Figure 4

shows the forecast ratio of world output per capita outside the United States (each country’s

12 I calculate the population-weighted distance from the frontier for each country in the final year of the forecast and add the gaps to find the gap for the world. The population-weighted gaps for China and India account for 32 percent of the total.

23

contribution being population-weighted) to frontier output. The 100-year forecast is that the

ratio will have risen a great deal, from 24 to 57 percent. The lower panel shows the probability

of being on the convergent path, again with population weights applied to each country. The

probability of being in a convergent state is forecast to rise only slightly. In other words, the

growth forecast largely reflects growth in countries that have already started the convergence

process rather than a forecast future increase in the fraction converging.

<Figure 4 goes about here>

Uncertainty about future convergence comes from two sources. The first source of

uncertainty is due to uncertainty about future switches between Markov states and to future

additive errors in equations (1) and (2). The second source of uncertainty is due to estimation of

the parameters, i.e. posterior spread. This second source can be examined by comparing

projections based on median posterior values for the parameters, while retaining posterior

uncertainty about 𝑆𝑖,2014.

Figure 5 gives median projections and 90 percent highest posterior density intervals both

with and without parameter uncertainty and with and without shocks to frontier growth. Most

uncertainty arises from real shocks over the next 100 years to equations (1) and (2) and to state

uncertainty; parameter estimation uncertainty plays only a small role.

<Figure 5 goes about here>

Lucas (2000) wrote “I think the restoration of inter-society income equality will be one of

the major economic events of the century to come.”13 While the principal topic of interest here

13 For a differing view, see Pritchett (1997).

24

is forecasting future world output levels, the model also generates forecasts of the distribution

of output across countries. Figure 6 graphs the fraction of the world’s population living at or

below a given income level in 2014 and one hundred years later, using median country

forecasts. In 100 years, most of the world’s population will be in countries with far higher

output per capita levels than today’s U.S. output.

<Figure 6 goes about here>

Inter-country output inequality will also have decreased, although there is considerable

uncertainty. The 2014 Gini coefficient is equals 0.58. 100 years later the median estimate of the

inter-country Gini coefficient is 0.41. Estimates of the Gini coefficient, together with fiducial

bands, are shown in Figure 7.

<Figure 7 goes about here>

6. Conclusion

In 100 years, most of the world’s population will live in countries with higher output per

capita than the United States today. And the majority of the world’s population will have a

much higher output than the United States today. The typical standard of living will be much,

much improved, and inter-country inequality will be lower. This forecast is based on the

assumption that the pattern of convergence and frontier growth observed in the last quarter

century will not be reversed.

These are median forecasts; as is clear in Figure 5 and 7 a good deal of uncertainty remains.

Policymakers likely have asymmetric loss functions so that median estimates of future welfare

may differ from median estimates of output. If you are worried about poverty, very low growth

25

forecasts are of more concern than high forecasts. If you are worried about CO2 production,

high output forecasts are likely more worrisome.

While Bayesian posterior densities offer measures of uncertainty such measures do not, of

course, include model uncertainty. There are three places in the model where different

outcomes could make a big difference. First, the model treats the mean growth rate of the

frontier as a constant. In fact the constant is estimated on data since 1970, a break date

suggested by Gordon (2016). If there has been a break in average growth in the post-war

period, it will not be surprising if there are more breaks over the next hundred years. The effect

of a change in the average frontier growth rate is fairly straightforward, as the entire forecast

shifts by the amount of such a change. The estimated growth rate is 1.7 percent. If it were to

drop permanently to zero at the beginning of the forecast period, the world forecast growth

rate would fall by about 1.7 percent—with analogous changes for increases in frontier growth.

The second issue that matters is the assumption that the convergence process since 1990

will continue to hold in the future. As mentioned above, allowing a break around 1990 makes a

substantial difference to long-run forecasts. The long-run growth estimate without allowing for

the break falls from 2.6 to 2.1. The first element is that the change in the estimated

convergence probability transition matrix matters over long periods. The transition matrix

might change again. (The posterior bands account for estimation uncertainty, not for changes in

the true parameters.) Kremer et. al. (2001) show that even fairly small changes in a transition

matrix can have a large effect on long-run outcomes. The second element is that the

contribution of convergence turns out to largely reflect forecasts for China and India. The

model offers statistical evidence driven largely by the observed recent growth in the economies

26

of China and India. Future idiosyncratic shocks to either of these large countries, perhaps due to

political changes, could limit the accuracy of the forecasts given here.

The model does not identify a causal economic mechanism. This leaves open the question

as to whether whatever has happened in China and India might be transmitted to other

developing economies in the future. In principle, this could make a large difference in

outcomes. There is a third element that could drive a wedge between forecasts and outcomes;

equation (1) assumes that convergence is complete. It is easy to imagine that growing

economies only converge to 90 percent (as an example) of frontier output due to differences

including natural resource endowments and labor force participation rates.14 This last element

is likely not an important source of forecast error, not because such differences are unlikely but

simply because an error of 10 percent (for example) is small relative to the statistical

uncertainty already present.

A good forecast for 100 years hence is that output per capita will be more than triple

today’s U.S. output per capita and that most of the world’s population will be living in countries

with high output by today’s standard. Such growth reflects a great increase in the number of

countries which have begun to converge to the world output frontier in recent years. Both the

raw data and the econometric estimates suggest that the world has changed in a way that

makes convergence much more important than it may have appeared to be based on research

that relied on earlier data.

14 This is accounted for in the historical data by allowing for switches from state 𝑐 to state 𝑛, but the such switches might be dependent on how close a country is to the frontier; a dependency which would not be picked up by the model.

27

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31

Figure 1

Figure 2

32

Figure 3

Figure 4

33

Figure 5

Figure 6

34

Figure 7

35

Online Appendix

Figure A 1 shows population coverage as well as the population-weighted, observed gap

from the frontier. The average country experienced a slowly closing gap except for the first four

years of data, which covered a much smaller fraction of the population than did the remainder

of the sample.

Figure A 1

As suggested in the main text, what really matters is that several large countries are

estimated to be on a convergent path. Figure A 2 provides a bubble plot where the horizontal

axis gives the output-per-capita ratio to the frontier, the vertical axis gives the estimated

probability of being in the convergent state, and the size of the bubble is proportional to a

country’s population. The diamonds give positions in 1970 and the circles give positions in

2014. The probabilities of convergence for the well-off countries toward the right of the chart

do not matter terribly much simply because these countries are already close to the frontier.

36

What matters a great deal is the large countries which appear to have moved onto a

convergent path and whose output, while greatly increased, still has room to move significantly

close to the frontier over the next 100 years. Note specifically the two large superimposed

diamonds at the lower left which by the end of the sample period had moved to the circles at

top and further to the right on the chart: China and India.

Figure A 2

Table A 1 gives the estimated probability of being in a converging state for each country in

the sample in both 1970 and 2014. (Countries holding approximately 95 percent of the 2014

population had entered the sample by 1970.) The table also shows the first year in the sample

and the United Nations region designation. With respect to the most developed economies—

37

those which have essentially converged to the frontier—note that the model does not strongly

differentiate between convergent and nonconvergent states, as both predict small future

changes in the gap with the frontier.

Country Probability of convergent state 1970

Probability of convergent state 2014

First year in sample

UN region

Aruba 0.00 0.70 1970 Caribbean

Angola 0.00 0.66 1970 Middle Africa

Anguilla 0.00 0.75 1970 Caribbean

Albania 0.00 0.90 1970 Southern Europe

Argentina 0.02 0.83 1950 South America

Armenia -- 0.00 1990 Western Asia

Antigua and Barbuda

0.00 0.46 1970 Caribbean

Australia 0.12 0.82 1950 Australia/New Zealand

Austria 0.85 0.79 1950 Western Europe

Azerbaijan 0.00 1990 Western Asia

Burundi 0.01 0.84 1960 Eastern Africa

Belgium 0.49 0.65 1950 Western Europe

Benin 0.00 0.05 1959 Western Africa

Burkina Faso 0.00 0.04 1959 Western Africa

Bangladesh 0.02 0.87 1959 Southern Asia

Bulgaria 0.00 0.89 1970 Eastern Europe

Bahrain 0.00 0.75 1970 Western Asia

Bahamas 0.00 0.45 1970 Caribbean

Bosnia and Herzegovina

-- 0.00 1990 Southern Europe

Belarus

0.00 1990 Eastern Europe

Belize 0.00 0.03 1970 Central America

Bermuda 0.00 0.83 1970 Northern America

Bolivia (Plurinational State of)

0.00 0.50 1950 South America

Brazil 0.57 0.48 1950 South America

Barbados 0.41 0.05 1960 Caribbean

Bhutan 0.00 0.95 1970 Southern Asia

Botswana 0.98 0.81 1960 Southern Africa

Central African Republic

0.00 0.01 1960 Middle Africa

38

Canada 0.15 0.69 1950 Northern America

Switzerland 0.07 0.85 1950 Western Europe

Chile 0.01 0.93 1951 South America

China 0.00 0.98 1952 Eastern Asia

Côte d'Ivoire 0.01 0.28 1960 Western Africa

Cameroon 0.00 0.07 1960 Middle Africa

D.R. of the Congo 0.00 0.14 1950 Middle Africa

Congo 0.06 0.30 1960 Middle Africa

Colombia 0.00 0.92 1950 South America

Comoros 0.00 0.01 1960 Eastern Africa

Cabo Verde 0.13 0.49 1960 Western Africa

Costa Rica 0.01 0.80 1950 Central America

Cayman Islands 0.00 0.08 1970 Caribbean

Cyprus 0.59 0.58 1950 Western Asia

Czech Republic -- 0.00 1990 Eastern Europe

Germany 0.79 0.80 1950 Western Europe

Djibouti 0.00 0.38 1970 Eastern Africa

Dominica 0.00 0.23 1970 Caribbean

Denmark 0.22 0.70 1950 Northern Europe

Dominican Republic 0.11 0.87 1951 Caribbean

Algeria 0.05 0.65 1960 Northern Africa

Ecuador 0.14 0.54 1950 South America

Egypt 0.11 0.47 1950 Northern Africa

Spain 0.88 0.63 1950 Southern Europe

Estonia -- 0.00 1990 Northern Europe

Ethiopia 0.00 0.92 1950 Eastern Africa

Finland 0.63 0.69 1950 Northern Europe

Fiji 0.05 0.16 1960 Melanesia

France 0.84 0.51 1950 Western Europe

Gabon 0.24 0.64 1960 Middle Africa

United Kingdom 0.02 0.63 1950 Northern Europe

Georgia -- 0.00 1990 Western Asia

Ghana 0.01 0.75 1955 Western Africa

Guinea 0.00 0.00 1959 Western Africa

Gambia 0.00 0.01 1960 Western Africa

Guinea-Bissau 0.00 0.05 1960 Western Africa

Equatorial Guinea 0.02 0.92 1960 Middle Africa

Greece 0.90 0.17 1951 Southern Europe

Grenada 0.00 0.23 1970 Caribbean

Guatemala 0.00 0.02 1950 Central America

China, Hong Kong SAR

0.95 0.89 1960 Eastern Asia

39

Honduras 0.00 0.05 1950 Central America

Croatia -- 0.00 1990 Southern Europe

Haiti 0.00 0.04 1960 Caribbean

Hungary 0.00 0.57 1970 Eastern Europe

Indonesia 0.01 0.90 1960 South-Eastern Asia

India 0.00 0.96 1950 Southern Asia

Ireland 0.09 0.89 1950 Northern Europe

Iran (Islamic Republic of)

0.08 0.79 1955 Southern Asia

Iraq 0.00 0.81 1970 Western Asia

Iceland 0.28 0.79 1950 Northern Europe

Israel 0.58 0.82 1950 Western Asia

Italy 0.94 0.26 1950 Southern Europe

Jamaica 0.06 0.04 1953 Caribbean

Jordan 0.02 0.60 1954 Western Asia

Japan 0.99 0.66 1950 Eastern Asia

Kazakhstan -- 0.00 1990 Central Asia

Kenya 0.00 0.06 1950 Eastern Africa

Kyrgyzstan -- 0.00 1990 Central Asia

Cambodia 0.00 0.88 1970 South-Eastern Asia

Saint Kitts and Nevis 0.00 0.59 1970 Caribbean

Republic of Korea 0.94 0.94 1953 Eastern Asia

Lao People's DR 0.00 0.96 1970 South-Eastern Asia

Lebanon 0.00 0.79 1970 Western Asia

Liberia 0.02 0.72 1964 Western Africa

Saint Lucia 0.00 0.05 1970 Caribbean

Sri Lanka 0.00 0.99 1950 Southern Asia

Lesotho 0.00 0.26 1960 Southern Africa

Lithuania -- 0.00 1990 Northern Europe

Luxembourg 0.14 0.81 1950 Western Europe

Latvia -- 0.00 1990 Northern Europe

Morocco 0.00 0.52 1950 Northern Africa

Republic of Moldova -- 0.00 1990 Eastern Europe

Madagascar 0.00 0.02 1960 Eastern Africa

Maldives 0.00 0.97 1970 Southern Asia

Mexico 0.07 0.18 1950 Central America

TFYR of Macedonia -- 0.00 1990 Southern Europe

Mali 0.00 0.04 1960 Western Africa

Malta 0.95 0.87 1954 Southern Europe

Myanmar 0.21 0.92 1962 South-Eastern Asia

Montenegro -- 0.00 1990 Southern Europe

Mongolia 0.00 1.00 1970 Eastern Asia

40

Mozambique 0.00 0.18 1960 Eastern Africa

Mauritania 0.12 0.26 1960 Western Africa

Montserrat 0.00 0.62 1970 Caribbean

Mauritius 0.06 0.92 1950 Eastern Africa

Malawi 0.02 0.06 1954 Eastern Africa

Malaysia 0.52 0.94 1955 South-Eastern Asia

Namibia 0.01 0.42 1960 Southern Africa

Niger 0.00 0.05 1960 Western Africa

Nigeria 0.15 0.71 1950 Western Africa

Nicaragua 0.02 0.29 1950 Central America

Netherlands 0.38 0.77 1950 Western Europe

Norway 0.01 0.54 1950 Northern Europe

Nepal 0.00 0.14 1960 Southern Asia

New Zealand 0.06 0.75 1950 Australia/New Zealand

Oman 0.00 0.76 1970 Western Asia

Pakistan 0.02 0.04 1950 Southern Asia

Panama 0.09 0.97 1950 Central America

Peru 0.01 0.89 1950 South America

Philippines 0.00 0.86 1950 South-Eastern Asia

Poland 0.00 0.95 1970 Eastern Europe

Portugal 0.97 0.29 1950 Southern Europe

Paraguay 0.04 0.73 1951 South America

State of Palestine 0.00 0.53 1970 Western Asia

Romania 0.99 0.89 1960 Eastern Europe

Russian Federation -- 0.00 1990 Eastern Europe

Rwanda 0.00 0.57 1960 Eastern Africa

Saudi Arabia 0.00 0.79 1970 Western Asia

Sudan (Former) 0.00 0.06 1970 Northern Africa

Senegal 0.00 0.03 1960 Western Africa

Singapore 0.92 0.79 1960 South-Eastern Asia

Sierra Leone 0.00 0.83 1961 Western Africa

El Salvador 0.00 0.03 1950 Central America

Serbia -- 0.00 1990 Southern Europe

Sao Tome and Principe

0.00 0.17 1970 Middle Africa

Suriname 0.00 0.69 1970 South America

Slovakia -- 0.00 1990 Eastern Europe

Slovenia -- 0.00 1990 Southern Europe

Sweden 0.19 0.79 1950 Northern Europe

Swaziland 0.00 0.19 1970 Southern Africa

Seychelles 0.17 0.86 1960 Eastern Africa

41

Syrian Arab Republic

0.03 0.15 1960 Western Asia

Turks and Caicos Islands

0.00 0.09 1970 Caribbean

Chad 0.00 0.67 1960 Middle Africa

Togo 0.00 0.05 1960 Western Africa

Thailand 0.47 0.86 1950 South-Eastern Asia

Tajikistan -- 0.00 1990 Central Asia

Turkmenistan -- 0.00 1990 Central Asia

Trinidad and Tobago

0.27 0.91 1950 Caribbean

Tunisia 0.37 0.65 1960 Northern Africa

Turkey 0.02 0.81 1950 Western Asia

Taiwan 0.99 0.94 1951 Eastern Asia

U.R. of Tanzania: Mainland

0.00 0.10 1960 Eastern Africa

Uganda 0.00 0.04 1950 Eastern Africa

Ukraine -- 0.00 1990 Eastern Europe

Uruguay 0.01 0.93 1950 South America

Uzbekistan -- 0.00 1990 Central Asia

St. Vincent and the Grenadines

0.00 0.38 1970 Caribbean

Venezuela (Bolivarian Republic of)

0.05 0.52 1950 South America

British Virgin Islands 0.00 0.75 1970 Caribbean

Viet Nam 0.00 0.92 1970 South-Eastern Asia

Yemen -- 0.05 1989 Western Asia

South Africa 0.00 0.10 1950 Southern Africa

Zambia 0.00 0.60 1955 Eastern Africa

Zimbabwe 0.03 0.86 1954 Eastern Africa

Probability of convergent state by country

Table A 1