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125-643: However, the existence of some kind of demographic transition is widely accepted in the social sciences because of the well-established historical correlation linking dropping fertility to social and economic development. Scholars debate whether industrialization and higher incomes lead to lower population, or whether lower populations lead to industrialization and higher incomes. Scholars also debate to what extent various proposed and sometimes inter-related factors such as higher per capita income, lower mortality , old-age security, and rise of demand for human capital are involved. Human capital gradually increased in

250-410: A + bX and Y to c + dY , where a , b , c , and d are constants ( b and d being positive). This is true of some correlation statistics as well as their population analogues. Some correlation statistics, such as the rank correlation coefficient, are also invariant to monotone transformations of the marginal distributions of X and/or Y . Most correlation measures are sensitive to

375-484: A simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus , who wrote An Essay on the Principle of Population (1798), one of the earliest and most influential books on population . Malthusian models have the following form: where The model can also be written in

500-526: A Stage Five. Some countries have sub-replacement fertility (that is, below 2.1–2.2 children per woman). Replacement fertility is generally slightly higher than 2 (the level which replaces the two parents, achieving equilibrium) both because boys are born more often than girls (about 1.05–1.1 to 1), and to compensate for deaths prior to full reproduction. Many European and East Asian countries now have higher death rates than birth rates. Population aging and population decline may eventually occur, assuming that

625-409: A causal relationship between the variables. This dictum should not be taken to mean that correlations cannot indicate the potential existence of causal relations. However, the causes underlying the correlation, if any, may be indirect and unknown, and high correlations also overlap with identity relations ( tautologies ), where no causal process exists. Consequently, a correlation between two variables

750-442: A correlation coefficient is not enough to define the dependence structure between random variables. The correlation coefficient completely defines the dependence structure only in very particular cases, for example when the distribution is a multivariate normal distribution . (See diagram above.) In the case of elliptical distributions it characterizes the (hyper-)ellipses of equal density; however, it does not completely characterize

875-414: A correlation matrix by a diagram where the "remarkable" correlations are represented by a solid line (positive correlation), or a dotted line (negative correlation). In some applications (e.g., building data models from only partially observed data) one wants to find the "nearest" correlation matrix to an "approximate" correlation matrix (e.g., a matrix which typically lacks semi-definite positiveness due to

1000-568: A demographic transition with high death rate and low fertility rate from 1959 to 1961 due to the great famine. However, as a result of the economic improvement, the birth rate increased and mortality rate declined in China before the early 1970s. In the 1970s, China's birth rate fell at an unprecedented rate, which had not been experienced by any other population in a comparable time span. The birth rate fell from 6.6 births per women before 1970 to 2.2 births per women in 1980.The rapid fertility decline in China

1125-424: A fertility decline of 25–50% include: Guatemala , Tajikistan , Egypt and Zimbabwe . Countries that have experienced a fertility decline of less than 25% include: Sudan , Niger , Afghanistan . This occurs where birth and death rates are both low, leading to a total population stability. Death rates are low for a number of reasons, primarily lower rates of diseases and higher production of food. The birth rate

1250-449: A fertility transition beginning in post-1965. As of 2013, India is in the later half of the third stage of the demographic transition, with a population of 1.23 billion. It is nearly 40 years behind in the demographic transition process compared to EU countries , Japan , etc. The present demographic transition stage of India along with its higher population base will yield a rich demographic dividend in future decades. Cha (2007) analyzes

1375-404: A framework for promotion and services in health, education, and family planning. Economic liberalization increased economic opportunities and risks for individuals, while also increasing the price and often reducing the quality of these services, all affecting demographic trends. Goli and Arokiasamy (2013) indicate that India has a sustainable demographic transition beginning in the mid-1960s and

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1500-506: A group and may not accurately describe all individual cases. The extent to which it applies to less-developed societies today remains to be seen. Many countries such as China , Brazil and Thailand have passed through the Demographic Transition Model (DTM) very quickly due to fast social and economic change. Some countries, particularly African countries, appear to be stalled in the second stage due to stagnant development and

1625-463: A growth rate of 2.4% between 2000 and 2005, above the European average. More than two-thirds of that growth can be ascribed to a natural increase resulting from high fertility and birth rates. In contrast, France is one of the developed nations whose migratory balance is rather weak, which is an original feature at the European level. Several interrelated reasons account for such singularities, in particular

1750-495: A negative demographic force. Infertility and infant mortality, which were probably more significant influences on overall population levels than the adult mortality rate, increased from 1820 due to disease, malnutrition, and stress, all of which stemmed from state forced labor policies. Available estimates indicate little if any population growth for Madagascar between 1820 and 1895. The demographic "crisis" in Africa, ascribed by critics of

1875-489: A negative migratory flow – two-thirds of rural communities have shown some since 2000. The spatial demographic expansion of large cities amplifies the process of peri-urbanization yet is also accompanied by movement of selective residential flow, social selection, and sociospatial segregation based on income. McNicoll (2006) examines the common features behind the striking changes in health and fertility in East and Southeast Asia in

2000-717: A negative or positive correlation if there is any sort of relationship between the variables of our data set. The population correlation coefficient ρ X , Y {\displaystyle \rho _{X,Y}} between two random variables X {\displaystyle X} and Y {\displaystyle Y} with expected values μ X {\displaystyle \mu _{X}} and μ Y {\displaystyle \mu _{Y}} and standard deviations σ X {\displaystyle \sigma _{X}} and σ Y {\displaystyle \sigma _{Y}}

2125-464: A panel data set to explore how industrial revolution, demographic transition, and human capital accumulation interacted in Korea from 1916 to 1938. Income growth and public investment in health caused mortality to fall, which suppressed fertility and promoted education. Industrialization, skill premium, and closing gender wage gap further induced parents to opt for child quality. Expanding demand for education

2250-468: A population has reached below replacement levels of fertility , and as result does not have enough people in the working ages to support the economy, and the growing dependent population. Between 1750 and 1975 England experienced the transition from high to low levels of both mortality and fertility. A major factor was the sharp decline in the death rate due to infectious diseases, which has fallen from about 11 per 1,000 to less than 1 per 1,000. By contrast,

2375-557: A possible causal relationship, but cannot indicate what the causal relationship, if any, might be. The Pearson correlation coefficient indicates the strength of a linear relationship between two variables, but its value generally does not completely characterize their relationship. In particular, if the conditional mean of Y {\displaystyle Y} given X {\displaystyle X} , denoted E ⁡ ( Y ∣ X ) {\displaystyle \operatorname {E} (Y\mid X)} ,

2500-409: A propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources: "Through the animal and vegetable kingdoms, nature has scattered the seeds of life abroad with the most profuse and liberal hand.   ... The germs of existence contained in this spot of earth, with ample food, and ample room to expand in, would fill millions of worlds in

2625-618: A series of n {\displaystyle n} measurements of the pair ( X i , Y i ) {\displaystyle (X_{i},Y_{i})} indexed by i = 1 , … , n {\displaystyle i=1,\ldots ,n} , the sample correlation coefficient can be used to estimate the population Pearson correlation ρ X , Y {\displaystyle \rho _{X,Y}} between X {\displaystyle X} and Y {\displaystyle Y} . The sample correlation coefficient

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2750-499: A sharp chronological divide between the precolonial and colonial eras, arguing that whereas "natural" demographic influences were of greater importance in the former period, human factors predominated thereafter. Campbell argues that in 19th-century Madagascar the human factor, in the form of the Merina state , was the predominant demographic influence. However, the impact of the state was felt through natural forces, and it varied over time. In

2875-411: A straight line. Although in the extreme cases of perfect rank correlation the two coefficients are both equal (being both +1 or both −1), this is not generally the case, and so values of the two coefficients cannot meaningfully be compared. For example, for the three pairs (1, 1) (2, 3) (3, 2) Spearman's coefficient is 1/2, while Kendall's coefficient is 1/3. The information given by

3000-556: A substantial portion of which traditionally had been performed by children in farm families. A simplification of the DTM theory proposes an initial decline in mortality followed by a later drop in fertility. The changing demographics of the U.S. in the last two centuries did not parallel this model. Beginning around 1800, there was a sharp fertility decline; at this time, an average woman usually produced seven births per lifetime, but by 1900 this number had dropped to nearly four. A mortality decline

3125-506: A value of zero implies independence. This led some authors to recommend their routine usage, particularly of Distance correlation . Another alternative measure is the Randomized Dependence Coefficient. The RDC is a computationally efficient, copula -based measure of dependence between multivariate random variables and is invariant with respect to non-linear scalings of random variables. One important disadvantage of

3250-875: Is 0. However, because the correlation coefficient detects only linear dependencies between two variables, the converse is not necessarily true. A correlation coefficient of 0 does not imply that the variables are independent . X , Y  independent ⇒ ρ X , Y = 0 ( X , Y  uncorrelated ) ρ X , Y = 0 ( X , Y  uncorrelated ) ⇏ X , Y  independent {\displaystyle {\begin{aligned}X,Y{\text{ independent}}\quad &\Rightarrow \quad \rho _{X,Y}=0\quad (X,Y{\text{ uncorrelated}})\\\rho _{X,Y}=0\quad (X,Y{\text{ uncorrelated}})\quad &\nRightarrow \quad X,Y{\text{ independent}}\end{aligned}}} For example, suppose

3375-449: Is 0.7544, indicating that the points are far from lying on a straight line. In the same way if y {\displaystyle y} always decreases when x {\displaystyle x} increases , the rank correlation coefficients will be −1, while the Pearson product-moment correlation coefficient may or may not be close to −1, depending on how close the points are to

3500-440: Is a causal relationship , because extreme weather causes people to use more electricity for heating or cooling. However, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation ). Formally, random variables are dependent if they do not satisfy a mathematical property of probabilistic independence . In informal parlance, correlation

3625-492: Is a corollary of the Cauchy–Schwarz inequality that the absolute value of the Pearson correlation coefficient is not bigger than 1. Therefore, the value of a correlation coefficient ranges between −1 and +1. The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship ( anti-correlation ), and some value in

3750-418: Is any statistical relationship, whether causal or not, between two random variables or bivariate data . Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and

3875-410: Is consideration of the copula between them, while the coefficient of determination generalizes the correlation coefficient to multiple regression . The degree of dependence between variables X and Y does not depend on the scale on which the variables are expressed. That is, if we are analyzing the relationship between X and Y , most correlation measures are unaffected by transforming X to

Demographic transition - Misplaced Pages Continue

4000-448: Is defined as where x ¯ {\displaystyle {\overline {x}}} and y ¯ {\displaystyle {\overline {y}}} are the sample means of X {\displaystyle X} and Y {\displaystyle Y} , and s x {\displaystyle s_{x}} and s y {\displaystyle s_{y}} are

4125-845: Is defined as: ρ X , Y = corr ⁡ ( X , Y ) = cov ⁡ ( X , Y ) σ X σ Y = E ⁡ [ ( X − μ X ) ( Y − μ Y ) ] σ X σ Y , if   σ X σ Y > 0. {\displaystyle \rho _{X,Y}=\operatorname {corr} (X,Y)={\operatorname {cov} (X,Y) \over \sigma _{X}\sigma _{Y}}={\operatorname {E} [(X-\mu _{X})(Y-\mu _{Y})] \over \sigma _{X}\sigma _{Y}},\quad {\text{if}}\ \sigma _{X}\sigma _{Y}>0.} where E {\displaystyle \operatorname {E} }

4250-495: Is designed to use the sensitivity to the range in order to pick out correlations between fast components of time series . By reducing the range of values in a controlled manner, the correlations on long time scale are filtered out and only the correlations on short time scales are revealed. The correlation matrix of n {\displaystyle n} random variables X 1 , … , X n {\displaystyle X_{1},\ldots ,X_{n}}

4375-409: Is exerting evolutionary pressure for higher fertility, and that eventually due to individual natural selection or cultural selection, birth rates may rise again. Part of the "cultural selection" hypothesis is that the variance in birth rate between cultures is significant; for example, some religious cultures have a higher birth rate that is not accounted for by differences in income. In his book Shall

4500-885: Is low because people have more opportunities to choose if they want children; this is made possible by improvements in contraception or women gaining more independence and work opportunities. The DTM (Demographic Transition model) is only a suggestion about the future population levels of a country, not a prediction. Countries that were at this stage ( total fertility rate between 2.0 and 2.5) in 2015 include: Antigua and Barbuda, Argentina, Bahrain, Bangladesh, Bhutan, Cabo Verde, El Salvador, Faroe Islands, Grenada, Guam, India, Indonesia, Kosovo, Libya, Malaysia, Maldives, Mexico, Myanmar, Nepal, New Caledonia, Nicaragua, Palau, Peru, Seychelles, Sri Lanka, Suriname, Tunisia, Turkey and Venezuela. The original Demographic Transition model has just four stages, but additional stages have been proposed. Both more-fertile and less-fertile futures have been claimed as

4625-426: Is not a sufficient condition to establish a causal relationship (in either direction). A correlation between age and height in children is fairly causally transparent, but a correlation between mood and health in people is less so. Does improved mood lead to improved health, or does good health lead to good mood, or both? Or does some other factor underlie both? In other words, a correlation can be taken as evidence for

4750-460: Is not linear in X {\displaystyle X} , the correlation coefficient will not fully determine the form of E ⁡ ( Y ∣ X ) {\displaystyle \operatorname {E} (Y\mid X)} . The adjacent image shows scatter plots of Anscombe's quartet , a set of four different pairs of variables created by Francis Anscombe . The four y {\displaystyle y} variables have

4875-462: Is related to x {\displaystyle x} in some manner (such as linearly, monotonically, or perhaps according to some particular functional form such as logarithmic). Essentially, correlation is the measure of how two or more variables are related to one another. There are several correlation coefficients , often denoted ρ {\displaystyle \rho } or r {\displaystyle r} , measuring

5000-418: Is synonymous with dependence . However, when used in a technical sense, correlation refers to any of several specific types of mathematical relationship between the conditional expectation of one variable given the other is not constant as the conditioning variable changes ; broadly correlation in this specific sense is used when E ( Y | X = x ) {\displaystyle E(Y|X=x)}

5125-406: Is the n × n {\displaystyle n\times n} matrix C {\displaystyle C} whose ( i , j ) {\displaystyle (i,j)} entry is Thus the diagonal entries are all identically one . If the measures of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of

Demographic transition - Misplaced Pages Continue

5250-516: Is the Pearson product-moment correlation coefficient (PPMCC), or "Pearson's correlation coefficient", commonly called simply "the correlation coefficient". It is obtained by taking the ratio of the covariance of the two variables in question of our numerical dataset, normalized to the square root of their variances. Mathematically, one simply divides the covariance of the two variables by the product of their standard deviations . Karl Pearson developed

5375-1087: Is the expected value operator, cov {\displaystyle \operatorname {cov} } means covariance , and corr {\displaystyle \operatorname {corr} } is a widely used alternative notation for the correlation coefficient. The Pearson correlation is defined only if both standard deviations are finite and positive. An alternative formula purely in terms of moments is: ρ X , Y = E ⁡ ( X Y ) − E ⁡ ( X ) E ⁡ ( Y ) E ⁡ ( X 2 ) − E ⁡ ( X ) 2 ⋅ E ⁡ ( Y 2 ) − E ⁡ ( Y ) 2 {\displaystyle \rho _{X,Y}={\operatorname {E} (XY)-\operatorname {E} (X)\operatorname {E} (Y) \over {\sqrt {\operatorname {E} (X^{2})-\operatorname {E} (X)^{2}}}\cdot {\sqrt {\operatorname {E} (Y^{2})-\operatorname {E} (Y)^{2}}}}} It

5500-400: Is unexpected, as natural selection would be expected to favor individuals who are willing and able to convert plentiful resources into plentiful fertile descendants. This may be the result of a departure from the environment of evolutionary adaptedness . Most models posit that the birth rate will stabilize at a low level indefinitely. Some dissenting scholars note that the modern environment

5625-405: Is zero; they are uncorrelated . However, in the special case when X {\displaystyle X} and Y {\displaystyle Y} are jointly normal , uncorrelatedness is equivalent to independence. Even though uncorrelated data does not necessarily imply independence, one can check if random variables are independent if their mutual information is 0. Given

5750-402: The uncorrected sample standard deviations of X {\displaystyle X} and Y {\displaystyle Y} . If x {\displaystyle x} and y {\displaystyle y} are results of measurements that contain measurement error, the realistic limits on the correlation coefficient are not −1 to +1 but a smaller range. For

5875-829: The Newton's method for computing the nearest correlation matrix ) results obtained in the subsequent years. Similarly for two stochastic processes { X t } t ∈ T {\displaystyle \left\{X_{t}\right\}_{t\in {\mathcal {T}}}} and { Y t } t ∈ T {\displaystyle \left\{Y_{t}\right\}_{t\in {\mathcal {T}}}} : If they are independent, then they are uncorrelated. The opposite of this statement might not be true. Even if two variables are uncorrelated, they might not be independent to each other. The conventional dictum that " correlation does not imply causation " means that correlation cannot be used by itself to infer

6000-439: The Pearson product-moment correlation coefficient , and are best seen as measures of a different type of association, rather than as an alternative measure of the population correlation coefficient. To illustrate the nature of rank correlation, and its difference from linear correlation, consider the following four pairs of numbers ( x , y ) {\displaystyle (x,y)} : As we go from each pair to

6125-448: The coefficient of multiple determination , a measure of goodness of fit in multiple regression . In statistical modelling , correlation matrices representing the relationships between variables are categorized into different correlation structures, which are distinguished by factors such as the number of parameters required to estimate them. For example, in an exchangeable correlation matrix, all pairs of variables are modeled as having

6250-412: The corrected sample standard deviations of X {\displaystyle X} and Y {\displaystyle Y} . Equivalent expressions for r x y {\displaystyle r_{xy}} are where s x ′ {\displaystyle s'_{x}} and s y ′ {\displaystyle s'_{y}} are

6375-444: The open interval ( − 1 , 1 ) {\displaystyle (-1,1)} in all other cases, indicating the degree of linear dependence between the variables. As it approaches zero there is less of a relationship (closer to uncorrelated). The closer the coefficient is to either −1 or 1, the stronger the correlation between the variables. If the variables are independent , Pearson's correlation coefficient

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6500-401: The standardized random variables X i / σ ( X i ) {\displaystyle X_{i}/\sigma (X_{i})} for i = 1 , … , n {\displaystyle i=1,\dots ,n} . This applies both to the matrix of population correlations (in which case σ {\displaystyle \sigma } is

6625-483: The 1940s and 1950s Frank W. Notestein developed a more formal theory of demographic transition. In the 2000s Oded Galor researched the "various mechanisms that have been proposed as possible triggers for the demographic transition, assessing their empirical validity, and their potential role in the transition from stagnation to growth." In 2011, the unified growth theory was completed, the demographic transition becomes an important part in unified growth theory. By 2009,

6750-423: The 1960s–1990s, focusing on seven countries: Taiwan and South Korea ("tiger" economies), Thailand, Malaysia, and Indonesia ("second wave" countries), and China and Vietnam ("market-Leninist" economies). Demographic change can be seen as a by-product of social and economic development and, in some cases, accompanied by strong government pressure. An effective, often authoritarian, local administrative system can provide

6875-405: The 20/1000 as well as falling below 12/1000. In the 1980s and 1990s, Russia underwent a unique demographic transition; observers call it a "demographic catastrophe": the number of deaths exceeded the number of births, life expectancy fell sharply (especially for males) and the number of suicides increased. From 1992 through 2011, the number of deaths exceeded the number of births; from 2011 onwards,

7000-407: The DTM clearly arrested and reversed between 1975 and 2005. DTM assumes that population changes are induced by industrial changes and increased wealth, without taking into account the role of social change in determining birth rates, e.g., the education of women. In recent decades more work has been done on developing the social mechanisms behind it. DTM assumes that the birth rate is independent of

7125-491: The French population therefore seems increasingly defined not only by interregional mobility but also by the residential preferences of individual households. These challenges, linked to configurations of population and the dynamics of distribution, inevitably raise the issue of town and country planning. The most recent census figures show that an outpouring of the urban population means that fewer rural areas are continuing to register

7250-546: The Religious Inherit the Earth? , Eric Kaufmann argues that demographic trends point to religious fundamentalists greatly increasing as a share of the population over the next century. Jane Falkingham of Southampton University has noted that "We've actually got population projections wrong consistently over the last 50 years... we've underestimated the improvements in mortality... but also we've not been very good at spotting

7375-540: The ability of women to bear children. Emigration depressed death rates in some special cases (for example, Europe and particularly the Eastern United States during the 19th century), but, overall, death rates tended to match birth rates, often exceeding 40 per 1000 per year. Children contributed to the economy of the household from an early age by carrying water, firewood, and messages, caring for younger siblings, sweeping, washing dishes, preparing food, and working in

7500-450: The alternative, more general measures is that, when used to test whether two variables are associated, they tend to have lower power compared to Pearson's correlation when the data follow a multivariate normal distribution. This is an implication of the No free lunch theorem theorem. To detect all kinds of relationships, these measures have to sacrifice power on other relationships, particularly for

7625-412: The assumption of normality. The second one (top right) is not distributed normally; while an obvious relationship between the two variables can be observed, it is not linear. In this case the Pearson correlation coefficient does not indicate that there is an exact functional relationship: only the extent to which that relationship can be approximated by a linear relationship. In the third case (bottom left),

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7750-402: The case of a linear model with a single independent variable, the coefficient of determination (R squared) is the square of r x y {\displaystyle r_{xy}} , Pearson's product-moment coefficient. Consider the joint probability distribution of X and Y given in the table below. For this joint distribution, the marginal distributions are: This yields

7875-469: The city was characterized as the "death capital of the United States" – at the level of 50 per 1000 population or higher – well into the second half of the 19th century. Today, the U.S. is recognized as having both low fertility and mortality rates. Specifically, birth rates stand at 14 per 1000 per year and death rates at 8 per 1000 per year. Because the DTM is only a model, it cannot necessarily predict

8000-467: The coefficient from a similar but slightly different idea by Francis Galton . A Pearson product-moment correlation coefficient attempts to establish a line of best fit through a dataset of two variables by essentially laying out the expected values and the resulting Pearson's correlation coefficient indicates how far away the actual dataset is from the expected values. Depending on the sign of our Pearson's correlation coefficient, we can end up with either

8125-424: The correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve . Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there

8250-495: The correlation-like range ⁠ [ − 1 , 1 ] {\displaystyle [-1,1]} ⁠ . The odds ratio is generalized by the logistic model to model cases where the dependent variables are discrete and there may be one or more independent variables. The correlation ratio , entropy -based mutual information , total correlation , dual total correlation and polychoric correlation are all also capable of detecting more general dependencies, as

8375-473: The course of a few thousand years. Necessity, that imperious all pervading law of nature, restrains them within the prescribed bounds. The race of plants, and the race of animals shrink under this great restrictive law. And the race of man cannot, by any efforts of reason, escape from it. Among plants and animals its effects are waste of seed, sickness, and premature death. Among mankind, misery and vice. " A model of population growth bounded by resource limitations

8500-404: The death rate falls or improves, this may include lower infant mortality rate and increased child survival. Over time, as individuals with increased survival rates age, there may also be an increase in the number of older children, teenagers, and young adults. This implies that there is an increase in the fertile population proportion which, with constant fertility rates , may lead to an increase in

8625-765: The death rate from other causes was 12 per 1,000 in 1850 and has not declined markedly. Scientific discoveries and medical breakthroughs did not, in general, contribute importantly to the early major decline in infectious disease mortality. In the 1980s and early 1990s, the Irish demographic status converged to the European norm. Mortality rose above the European Community average, and in 1991 Irish fertility fell to replacement level. The peculiarities of Ireland's past demography and its recent rapid changes challenge established theory. The recent changes have mirrored inward changes in Irish society, with respect to family planning, women in

8750-471: The death rate. Nevertheless, demographers maintain that there is no historical evidence for society-wide fertility rates rising significantly after high mortality events. Notably, some historic populations have taken many years to replace lives after events such as the Black Death . Some have claimed that DTM does not explain the early fertility declines in much of Asia in the second half of the 20th century or

8875-537: The decline in mortality in Stage Two is an increasingly rapid growth in population growth (a.k.a. " population explosion ") as the gap between deaths and births grows wider and wider. Note that this growth is not due to an increase in fertility (or birth rates) but to a decline in deaths. This change in population occurred in north-western Europe during the nineteenth century due to the Industrial Revolution . During

9000-647: The degree of correlation. The most common of these is the Pearson correlation coefficient , which is sensitive only to a linear relationship between two variables (which may be present even when one variable is a nonlinear function of the other). Other correlation coefficients – such as Spearman's rank correlation – have been developed to be more robust than Pearson's, that is, more sensitive to nonlinear relationships. Mutual information can also be applied to measure dependence between two variables. The most familiar measure of dependence between two quantities

9125-533: The delays in fertility decline in parts of the Middle East. Nevertheless, the demographer John C Caldwell has suggested that the reason for the rapid decline in fertility in some developing countries compared to Western Europe, the United States, Canada, Australia and New Zealand is mainly due to government programs and a massive investment in education both by governments and parents. Correlation and dependence In statistics , correlation or dependence

9250-548: The demographic transition theory to the colonial era, stemmed in Madagascar from the policies of the imperial Merina regime, which in this sense formed a link to the French regime of the colonial era. Campbell thus questions the underlying assumptions governing the debate about historical demography in Africa and suggests that the demographic impact of political forces be reevaluated in terms of their changing interaction with "natural" demographic influences. Russia entered stage two of

9375-424: The dependence structure (for example, a multivariate t-distribution 's degrees of freedom determine the level of tail dependence). For continuous variables, multiple alternative measures of dependence were introduced to address the deficiency of Pearson's correlation that it can be zero for dependent random variables (see and reference references therein for an overview). They all share the important property that

9500-414: The early 2000s. However, fertility rates declined significantly in many very high development countries between 2010 and 2018, including in countries with high levels of gender parity . The global data no longer support the suggestion that fertility rates tend to broadly rise at very high levels of national development. From the point of view of evolutionary biology , wealthier people having fewer children

9625-445: The effects of under-invested and under-researched tropical diseases such as malaria and AIDS to a limited extent. In pre-industrial society, death rates and birth rates were both high, and fluctuated rapidly according to natural events, such as drought and disease, to produce a relatively constant and young population. Family planning and contraception were virtually nonexistent; therefore, birth rates were essentially only limited by

9750-558: The existence of a negative correlation between fertility and industrial development had become one of the most widely accepted findings in social science. The Jews of Bohemia and Moravia were among the first populations to experience a demographic transition, in the 18th century, prior to changes in mortality or fertility in other European Jews or in Christians living in the Czech lands . John Caldwell (demographer) explained fertility rates in

9875-428: The far future). The decline in death rate and birth rate that occurs during the demographic transition may transform the age structure. When the death rate declines during the second stage of the transition, the result is primarily an increase in the younger population. The reason being that when the death rate is high (stage one), the infant mortality rate is very high, often above 200 deaths per 1000 children born. When

10000-484: The fertility rate does not change and sustained mass immigration does not occur. Using data through 2005, researchers have suggested that the negative relationship between development, as measured by the Human Development Index (HDI), and birth rates had reversed at very high levels of development. In many countries with very high levels of development, fertility rates were approaching two children per woman in

10125-500: The fertility which causes fertility constantly to increase until 2018.However fertility started to decline after 2018 and meanwhile there was no significant change in mortality in recent 30 years. Campbell has studied the demography of 19th-century Madagascar in the light of demographic transition theory. Both supporters and critics of the theory hold to an intrinsic opposition between human and "natural" factors, such as climate, famine, and disease, influencing demography. They also suppose

10250-402: The fields. Raising a child cost little more than feeding him or her; there were no education or entertainment expenses. Thus, the total cost of raising children barely exceeded their contribution to the household. In addition, as they became adults they became a major input to the family business, mainly farming, and were the primary form of insurance for adults in old age. In India, an adult son

10375-416: The following expectations and variances: Therefore: Rank correlation coefficients, such as Spearman's rank correlation coefficient and Kendall's rank correlation coefficient (τ) measure the extent to which, as one variable increases, the other variable tends to increase, without requiring that increase to be represented by a linear relationship. If, as the one variable increases, the other decreases ,

10500-664: The form of a differential equation: with initial condition: P(0)= P 0 This model is often referred to as the exponential law . It is widely regarded in the field of population ecology as the first principle of population dynamics , with Malthus as the founder. The exponential law is therefore also sometimes referred to as the Malthusian Law . By now, it is a widely accepted view to analogize Malthusian growth in Ecology to Newton's First Law of uniform motion in physics. Malthus wrote that all life forms, including humans, have

10625-568: The future, but it does suggest an underdeveloped country's future birth and death rates, together with the total population size. Most particularly, of course, the DTM makes no comment on change in population due to migration. It is not necessarily applicable at very high levels of development. DTM does not account for recent phenomena such as AIDS ; in these areas HIV has become the leading source of mortality. Some trends in waterborne bacterial infant mortality are also disturbing in countries like Malawi , Sudan and Nigeria ; for example, progress in

10750-632: The high fertility rates of their parents. The bottom of the " age pyramid " widens first where children, teenagers and infants are here, accelerating population growth rate. The age structure of such a population is illustrated by using an example from the Third World today. In Stage 3 of the Demographic Transition Model (DTM), death rates are low and birth rates diminish, as a rule accordingly of enhanced economic conditions, an expansion in women's status and education, and access to contraception. The decrease in birth rate fluctuates from nation to nation, as does

10875-406: The impact of pro-family policies accompanied by greater unmarried households and out-of-wedlock births. These general demographic trends parallel equally important changes in regional demographics. Since 1982 the same significant tendencies have occurred throughout mainland France: demographic stagnation in the least-populated rural regions and industrial regions in the northeast, with strong growth in

11000-626: The important special case of a linear relationship with Gaussian marginals, for which Pearson's correlation is optimal. Another problem concerns interpretation. While Person's correlation can be interpreted for all values, the alternative measures can generally only be interpreted meaningfully at the extremes. For two binary variables , the odds ratio measures their dependence, and takes range non-negative numbers, possibly infinity: ⁠ [ 0 , + ∞ ] {\displaystyle [0,+\infty ]} ⁠ . Related statistics such as Yule's Y and Yule's Q normalize this to

11125-412: The late 18th and early 19th centuries Merina state policies stimulated agricultural production, which helped to create a larger and healthier population and laid the foundation for Merina military and economic expansion within Madagascar. From 1820, the cost of such expansionism led the state to increase its exploitation of forced labor at the expense of agricultural production and thus transformed it into

11250-450: The latter case. Several techniques have been developed that attempt to correct for range restriction in one or both variables, and are commonly used in meta-analysis; the most common are Thorndike's case II and case III equations. Various correlation measures in use may be undefined for certain joint distributions of X and Y . For example, the Pearson correlation coefficient is defined in terms of moments , and hence will be undefined if

11375-714: The limited amount of available agricultural land) which led to high mortality in the Old World. With low mortality but stage 1 birth rates, the United States necessarily experienced exponential population growth (from less than 4 million people in 1790, to 23 million in 1850, to 76 million in 1900). The only area where this pattern did not hold was the American South. High prevalence of deadly endemic diseases such as malaria kept mortality as high as 45–50 per 1000 residents per year in 18th century North Carolina. In New Orleans , mortality remained so high (mainly due to yellow fever ) that

11500-430: The linear relationship is perfect, except for one outlier which exerts enough influence to lower the correlation coefficient from 1 to 0.816. Finally, the fourth example (bottom right) shows another example when one outlier is enough to produce a high correlation coefficient, even though the relationship between the two variables is not linear. Malthusian growth model A Malthusian growth model , sometimes called

11625-404: The manner in which X and Y are sampled. Dependencies tend to be stronger if viewed over a wider range of values. Thus, if we consider the correlation coefficient between the heights of fathers and their sons over all adult males, and compare it to the same correlation coefficient calculated when the fathers are selected to be between 165 cm and 170 cm in height, the correlation will be weaker in

11750-462: The mid-1920s, they were depressed by the 1931–33 famine, crashed due to the Second World War in 1941, and only rebounded to a sustained level of 3 children/woman after the war. By 1970 Russia was firmly in stage four, with crude birth rates and crude death rates on the order of 15/1000 and 9/1000 respectively. Bizarrely, however, the birth rate entered a state of constant flux, repeatedly surpassing

11875-466: The moments are undefined. Measures of dependence based on quantiles are always defined. Sample-based statistics intended to estimate population measures of dependence may or may not have desirable statistical properties such as being unbiased , or asymptotically consistent , based on the spatial structure of the population from which the data were sampled. Sensitivity to the data distribution can be used to an advantage. For example, scaled correlation

12000-492: The natality decreased at the same time, thus there was no demographic boom in the 19th century. France's demographic profile is similar to its European neighbors and to developed countries in general, yet it seems to be staving off the population decline of Western countries. With 62.9 million inhabitants in 2006, it was the second most populous country in the European Union, and it displayed a certain demographic dynamism, with

12125-516: The next pair x {\displaystyle x} increases, and so does y {\displaystyle y} . This relationship is perfect, in the sense that an increase in x {\displaystyle x} is always accompanied by an increase in y {\displaystyle y} . This means that we have a perfect rank correlation, and both Spearman's and Kendall's correlation coefficients are 1, whereas in this example Pearson product-moment correlation coefficient

12250-427: The number of children born. This will further increase the growth of the child population. The second stage of the demographic transition, therefore, implies a rise in child dependency and creates a youth bulge in the population structure. As a population continues to move through the demographic transition into the third stage, fertility declines and the youth bulge prior to the decline ages out of child dependency into

12375-566: The opposite has been the case. Greenwood and Seshadri (2002) show that from 1800 to 1940 there was a demographic shift from a mostly rural US population with high fertility, with an average of seven children born per white woman, to a minority (43%) rural population with low fertility, with an average of two births per white woman. This shift resulted from technological progress. A sixfold increase in real wages made children more expensive in terms of forgone opportunities to work and increases in agricultural productivity reduced rural demand for labor,

12500-430: The period between the decline in youth dependency and rise in old age dependency there is a demographic window of opportunity that can potentially produce economic growth through an increase in the ratio of working age to dependent population; the demographic dividend . However, unless factors such as those listed above are allowed to work, a society's birth rates may not drop to a low level in due time, which means that

12625-405: The population standard deviation), and to the matrix of sample correlations (in which case σ {\displaystyle \sigma } denotes the sample standard deviation). Consequently, each is necessarily a positive-semidefinite matrix . Moreover, the correlation matrix is strictly positive definite if no variable can have all its values exactly generated as a linear function of

12750-441: The population. In Stage One, the majority of deaths are concentrated in the first 5–10 years of life. Therefore, more than anything else, the decline in death rates in Stage Two entails the increasing survival of children and a growing population. Hence, the age structure of the population becomes increasingly youthful and start to have big families and more of these children enter the reproductive cycle of their lives while maintaining

12875-463: The random variable X {\displaystyle X} is symmetrically distributed about zero, and Y = X 2 {\displaystyle Y=X^{2}} . Then Y {\displaystyle Y} is completely determined by X {\displaystyle X} , so that X {\displaystyle X} and Y {\displaystyle Y} are perfectly dependent, but their correlation

13000-406: The rank correlation coefficients will be negative. It is common to regard these rank correlation coefficients as alternatives to Pearson's coefficient, used either to reduce the amount of calculation or to make the coefficient less sensitive to non-normality in distributions. However, this view has little mathematical basis, as rank correlation coefficients measure a different type of relationship than

13125-440: The same correlation, so all non-diagonal elements of the matrix are equal to each other. On the other hand, an autoregressive matrix is often used when variables represent a time series, since correlations are likely to be greater when measurements are closer in time. Other examples include independent, unstructured, M-dependent, and Toeplitz . In exploratory data analysis , the iconography of correlations consists in replacing

13250-404: The same mean (7.5), variance (4.12), correlation (0.816) and regression line ( y = 3 + 0.5 x {\textstyle y=3+0.5x} ). However, as can be seen on the plots, the distribution of the variables is very different. The first one (top left) seems to be distributed normally, and corresponds to what one would expect when considering two variables correlated and following

13375-407: The second half of the twentieth century less-developed countries entered Stage Two, creating the worldwide rapid growth of number of living people that has demographers concerned today. In this stage of DT, countries are vulnerable to become failed states in the absence of progressive governments. Another characteristic of Stage Two of the demographic transition is a change in the age structure of

13500-601: The second stage of the industrial revolution, which coincided with the demographic transition. The increasing role of human capital in the production process led to the investment of human capital in children by families, which may be the beginning of the demographic transition. The theory is based on an interpretation of demographic history developed in 1930 by the American demographer Warren Thompson (1887–1973). Adolphe Landry of France made similar observations on demographic patterns and population growth potential around 1934. In

13625-548: The society cannot proceed to stage three and is locked in what is called a demographic trap . Countries that have witnessed a fertility decline of over 50% from their pre-transition levels include: Costa Rica , El Salvador , Panama , Jamaica , Mexico , Colombia , Ecuador , Guyana , Philippines , Indonesia , Malaysia , Sri Lanka , Turkey , Azerbaijan , Turkmenistan , Uzbekistan , Tunisia , Algeria , Morocco , Lebanon , South Africa , India , Saudi Arabia , and many Pacific islands . Countries that have experienced

13750-453: The southwest and along the Atlantic coast, plus dynamism in metropolitan areas. Shifts in population between regions account for most of the differences in growth. The varying demographic evolution regions can be analyzed though the filter of several parameters, including residential facilities, economic growth, and urban dynamism, which yield several distinct regional profiles. The distribution of

13875-443: The third world are not dependent on the spread of industrialization or even on economic development and also illustrates fertility decline is more likely to precede industrialization and to help bring it about than to follow it. The transition involves four stages, or possibly five. As with all models, this is an idealized picture of population change in these countries. The model is a generalization that applies to these countries as

14000-545: The time span in which it is experienced. Stage Three moves the population towards stability through a decline in the birth rate. Several fertility factors contribute to this eventual decline, and are generally similar to those associated with sub-replacement fertility , although some are speculative: The resulting changes in the age structure of the population include a decline in the youth dependency ratio and eventually population aging . The population structure becomes less triangular and more like an elongated balloon. During

14125-562: The transition in the 18th century, simultaneously with the rest of Europe, though the effect of transition remained limited to a modest decline in death rates and steady population growth. The population of Russia nearly quadrupled during the 19th century, from 30 million to 133 million, and continued to grow until the First World War and the turmoil that followed. Russia then quickly transitioned through stage three. Though fertility rates rebounded initially and almost reached 7 children/woman in

14250-442: The trends in fertility." In 2004 a United Nations office published its guesses for global population in the year 2300; estimates ranged from a "low estimate" of 2.3 billion (tending to −0.32% per year) to a "high estimate" of 36.4 billion (tending to +0.54% per year), which were contrasted with a deliberately "unrealistic" illustrative "constant fertility" scenario of 134 trillion (obtained if 1995–2000 fertility rates stay constant into

14375-440: The twentieth century, the falls in death rates in developing countries tended to be substantially faster. Countries in this stage include Yemen , Afghanistan , and Iraq and much of Sub-Saharan Africa (but this does not include South Africa , Botswana , Eswatini , Lesotho , Namibia , Gabon and Ghana , which have begun to move into stage 3). The decline in the death rate is due initially to two factors: A consequence of

14500-459: The values of the others. The correlation matrix is symmetric because the correlation between X i {\displaystyle X_{i}} and X j {\displaystyle X_{j}} is the same as the correlation between X j {\displaystyle X_{j}} and X i {\displaystyle X_{i}} . A correlation matrix appears, for example, in one formula for

14625-543: The way it has been computed). In 2002, Higham formalized the notion of nearness using the Frobenius norm and provided a method for computing the nearest correlation matrix using the Dykstra's projection algorithm , of which an implementation is available as an online Web API. This sparked interest in the subject, with new theoretical (e.g., computing the nearest correlation matrix with factor structure ) and numerical (e.g. usage

14750-547: The wild. This is the earlier stage of demographic transition in the world and also characterized by primary activities such as small fishing activities, farming practices, pastoralism and petty businesses. This stage leads to a fall in death rates and an increase in population. The changes leading to this stage in Europe were initiated in the Agricultural Revolution of the eighteenth century and were initially quite slow. In

14875-461: The work force, the sharply declining power of the Catholic Church, and the emigration factor. France displays real divergences from the standard model of Western demographic evolution. The uniqueness of the French case arises from its specific demographic history, its historic cultural values, and its internal regional dynamics. France's demographic transition was unusual in that the mortality and

15000-406: The working ages. This stage of the transition is often referred to as the golden age, and is typically when populations see the greatest advancements in living standards and economic development. However, further declines in both mortality and fertility will eventually result in an aging population, and a rise in the aged dependency ratio . An increase of the aged dependency ratio often indicates that

15125-465: Was accommodated by an active public school building program. The interwar agricultural depression aggravated traditional income inequality, raising fertility and impeding the spread of mass schooling. Landlordism collapsed in the wake of de-colonization, and the consequent reduction in inequality accelerated human and physical capital accumulation, hence leading to growth in South Korea. China experienced

15250-686: Was all that prevented a widow from falling into destitution. While death rates remained high there was no question as to the need for children, even if the means to prevent them had existed. During this stage, the society evolves in accordance with Malthusian paradigm, with population essentially determined by the food supply. Any fluctuations in food supply (either positive, for example, due to technology improvements, or negative, due to droughts and pest invasions) tend to translate directly into population fluctuations. Famines resulting in significant mortality are frequent. Overall, population dynamics during stage one are comparable to those of animals living in

15375-419: Was caused by government policy: in particular the "later, longer, fewer" policy of the early 1970s and in the late 1970s the one-child policy was also enacted which highly influence China demographic transition. As the demographic dividend gradually disappeared, the government abandoned the one-child policy in 2011 and fully lifted the two-child policy from 2015.The two-child policy has had some positive effects on

15500-400: Was not observed in the U.S. until almost 1900—a hundred years after the drop in fertility. However, this late decline occurred from a very low initial level. During the 17th and 18th centuries, crude death rates in much of colonial North America ranged from 15 to 25 deaths per 1000 residents per year (levels of up to 40 per 1000 being typical during stages one and two). Life expectancy at birth

15625-504: Was on the order of 40 and, in some places, reached 50, and a resident of 18th century Philadelphia who reached age 20 could have expected, on average, additional 40 years of life. This phenomenon is explained by the pattern of colonization of the United States. Sparsely populated interior of the country allowed ample room to accommodate all the "excess" people, counteracting mechanisms (spread of communicable diseases due to overcrowding, low real wages and insufficient calories per capita due to

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