Get Ready for the Postgraduate Entrance English Exam. Working with Texts. Часть 1. Учебное пособие

Analysis

The analysis will isolate the underlying factors that explain the data. Factor analysis is an interdependence technique. The complete sets of interdependent relationships are examined. There is no specification of either dependent variables, independent variables, or causality. Factor analysis assumes that all the rating data on different attributes can be reduced down to a few important dimensions. This reduction is possible because the attributes are related. The rating given to any one attribute is partially the result of the influence of other attributes. The statistical algorithm deconstructs the rating (called a raw score) into its various components, and reconstructs the partial scores into underlying factor scores. The degree of correlation between the initial raw score and the final factor score is called a factor loading. There are two approaches to factor analysis: “principal component analysis” (the total variance in the data is considered); and “common factor analysis” (the common variance is considered).

Note that there are very important conceptual differences between the two approaches, an important one being that the common factor model involves a testable model whereas principal components model does not. This is due to the fact that in the common factor model, unique variables are required to be uncorrelated, whereas residuals in principal components are correlated. Finally, components are not latent variables; they are linear combinations of the input variables, and thus determinate. Factors, on the other hand, are latent variables, which are indeterminate. If your goal is to fit the variances of input variables for the purpose of data reduction, you should carry out principal components analysis. If you want to build a testable model to explain the intercorrelations among input variables, you should carry out a factor analysis.

The use of principle components in a semantic space can vary somewhat because the components may only “predict” but not “map” to the vector space. This produces a statistical principle component use where the most salient words or themes represent the preferred basis.

Advantages of Factor Analysis

•both objective and subjective attributes can be used

•it is fairly easy to do, inexpensive, and accurate

•it is based on direct inputs from customers

•there is flexibility in naming and using dimensions.

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Disadvantages of Factor Analysis

•usefulness depends on the researchers ability to develop a complete and accurate set of product attributes – If important attributes are missed the procedure is valueless.

•naming of the factors can be difficult – multiple attributes can be highly correlated with no apparent reason.

•factor analysis will always produce a pattern between variables, no matter how random.

II. Vocabulary Items

amount n – количество approach n – подход aptitude v – способность

attribute n – качество, свойство

causality n – причинная связь или обусловленность device n – схема, план

dimension n – измерение

infer v – заключать, делать вывод input v – вводить данные

linear a – линейный loading n – загрузка

misnomer n – неправильное употребление имени, названия или термина

psychometrics n – психометрия random a – случайный

rating n – оценка

residual n – остаток, разность respondent n – ответчик score n – множество

stage n – фаза, период, стадия survey n – обзор

technique n – способ, метод variable n – переменная via prep – через

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III. Exercises

1.Read the text.

2.Learn the vocabulary items by heart.

3.Translate the text in written form.

4.Retell the text using the following expressions and terms: factor analysis, to originate in, to be modeled as, to be chosen randomly, factor loading, to be inferred from the data, to run the factor analysis procedure, to be coded and input into a statistical program, to build a testable model.

IV. Test V (4)

1. Read the text again and decide which statements are true.

1.The observable random variables are modeled as linear combinations of the factors, plus “error” terms.

2.Survey questions ask the respondent to rate a product sample or descriptions of product concepts on a range of attributes. Anywhere about fifty attributes are chosen.

3.Factor analysis assumes that all the rating data on different attributes can be reduced down to a few important dimensions.

4.There are very important conceptual differences between the two approaches, an important one being that the common factor model involves a testable model whereas principal components model does not.

2. Match the words given in the left column with the words in the right column.

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Final Test V

1. Match the Russian terms on the left with the English ones on the right.

2. Match the English terms on the left with the Russian ones on the right.

4. Fill in the gaps with words from the list below.

1. The most well known type of statistical procedure performed by government is the … in which various statistics are collected about the national population.

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2.Statistics is a partial foundation of the relatively new field of … , which uses a combination of statistics, pattern recognition, artificial intelligence, and other algorithms to find meaningful information in large sets of data.

3.A common goal for a statistical research project is to investigate causality, and in particular to draw a conclusion on the effect of changes in the values of predictors or … on a response or dependent variable.

4.Because the field of statistics attempts to make inferences from a … concerning a population, statistics must necessarily be concerned with error.

5.When carrying out sample surveys, a listing of all the elements or units in the population is often called a … .

6.The degree of correlation between the initial raw score and the final factor score is called a … .

1.independent variables

2.data mining

3.factor loading

4.census

5.sample

6.frame

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Глава VI

Математическиеиинструментальные методы экономики*

Unit 1

I. Information for study

Mathematical Growth Models

Some of the more important ideas about economic growth are based on mathematical models. This lesson looks at some of these.

The Malthusian Model

Before 1800, technological progress was relatively slow. The result was that output per worker hardly increased at all, but population grew. In 1798, Thomas Malthus wrote an essay on population that presented a pessimistic picture of economic growth. He said that when food is ample, population grows exponentially. Because there are diminishing returns to labor in food production, exponential population growth leads to starvation, and population falls again.

Here is a numerical example of a two-equation Malthusian model. [food production] Yt = 1000 + Lt

[population growth] Lt = 600 + 100*(Yt-1/Lt-1)2

* Для специальности «Математические и инструментальные методы экономики» также рекомендуется изучение материалов Главы V «Статистика».

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This generation’s food production, Yt, increases linearly with this generation’s labor supply (population). However, the next generation’s labor supply increases with the square of this generation’s ratio of food to population.

You can solve these two equations for values of Y and L that will be stable. These are called the equilibrium values. In this case, they are 2000 for Y and 1000 for L. If L is 1000, then according to the food production equation, Y will be 2000. If Y is 2000, then population will grow to be 1000.

What happens if we start out with 2000 units of food, but disease causes the population to fall to 900? You can use the calculator below to see what happens if population starts out too low or too high. If you click on “calculate” the economy will move forward in time one generation. Keep clicking on “calculate” and you will see Y and L oscillate back and forth until they converge to their equilibrium values. You can try starting out with different values of Y and L and see the convergence process from different starting points.

2000 900

Next, suppose that we get better technology in food production, so that the food production equation becomes

Yt = 1200 + Lt

What happens to the equilibrium values of Y, L, and Y/L? Use the calculator below to find out. Keep clicking on calculate until the values stop changing.

2000 1000

What is the equilibrium level of food? What is the equilibrium level for the population? What is the equilibrium ratio of food to population?

At first, with the population at 1000, the technological improvement brings food production to 2200, and the ratio of food to population rises to 2.200. However, in the final equilibrium, because of population increases, the ratio of food to population is only 2.136. This is the Malthusian effect by which population growth dissipates technological advances. In fact, prior to 1800, the Malthusian effect was so strong that there was very little progress in average output per capita; instead, nearly all of the inventions and technological advances until 1800 served primarily to increase population.

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Capital Accumulation

When the Industrial Revolution broke out of the Malthusian trap, economies began to accumulate capital goods. In order to accumulate capital, you have to save. This means that you cannot consume all of your output.

Start with a constant level of output, Y, and no growth. Suppose that capital depreciates at a rate of 5 percent per year. In order to keep the level of capital constant we have to replace 5 percent of the capital stock each year. This means that saving, S, must equal 5 percent of the capital stock.

[1] S = .05K

We think of the saving rate, s, as the ratio of savings to income, S/Y. Writing equation [1] in terms of s, we have

[2] s = S/Y = .05(K/Y)

where all we did was divide the previous equation by Y on both sides. What this equation says is that in order to maintain constant output, we need a savings rate that equals the rate of depreciation times the capital/output ratio. If we want to have high labor productivity, we need a high ratio of capital to output, and therefore we need a high saving rate. Thus, we expect to find a relationship between countries with high saving rates and countries with high productivity, and this is indeed what Brad DeLong found when he indicated that countries with high productivity tend to have saving rates over 20 per cent.

Suppose that we want the capital stock to grow at a rate of 2 percent per year. In that case, we need

[3] S = .05K + .02K

Or, in terms of s and K/Y, we need [4] s = .05(K/Y) + .02(K/Y)

If we use the symbol δ to represent depreciation, the symbol κ to stand for the capital-output ratio, and the symbol x to stand for the growth rate of capital, then we can write

[5] s = δκ + xκ

To see how the saving rate affects the growth rate of capital, we can solve [5] for x, the growth rate of capital.

[6] x = s/κ – δ

If the labor force is growing at a rate n, then the capital/labor ratio will grow at the rate of x-n. For example, suppose that the saving rate s is

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.25 (i.e., 25 percent), the capital/output ratio κ is 2.5, the depreciation rate δ is .05, and the growth rate of the labor force n is .01. Then we have

[7] x – n = s/κ – δ – n = .25/2.5 – .05 -.01 = .04

which says that the capital/labor ratio grows at 4 percent per year.

Labor Productivity

We are interested in the growth rate of labor productivity, Y/L. To look at productivity, we return to the production function that we used in

the growth accounting lesson. [8] (Y/L) = (K/L)0.25E0.75

where E is the efficiency of labor. When we took logs of both sides, we obtained an equation for the growth rate of productivity. If y is the growth rate of output and n is the growth rate of the labor force, then the growth rate of productivity is y-n. Letting g be the symbol for the growth rate of E, the efficiency of labor, we have

[9] y – n = 0.25(x – n) + .75g

When we made numerical assumptions in equation [7], we found that x-n = .04. Plugging this into equation [9] and assuming that the growth rate of the efficiency of labor, g, is .02, we have

[10] y – n = 0.25(.04) + .75(.02) = .025

Thus, the assumptions about saving rate, depreciation, and so forth imply growth in labor productivity of 2.5 percent per year.

Balanced Growth

Economists define a balanced growth path as a path along which capital and output grow at the same rate. The alternatives to a balanced growth path are not sustainable. If capital grows more slowly than output, then the capital stock will eventually drop to zero. If capital grows more quickly than output, then the share of output that you set aside for capital goods will increase until you reach the point where the amount available for consumption is zero.

Looking at equation [9], the only way that x and y can be equal is if [11] g = x – n

That is, for balanced growth, the growth rate of the efficiency of labor must be matched by the growth rate of capital minus the growth rate of the labor force.

The requirement for balanced growth implies that there is only one sustainable ratio of capital to output. That is, there is only one ratio of

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capital to output, κ that is consistent with a balanced growth path. Using equations [11] and [7] we have

[12] g = x – n = s/κ – δ – n

We can solve this equation for a balanced-growth value for κ, given the other parameters. Using s = .25, g = .02, n = .01 and δ = .05, we have

[13] κ = s/(g + n + δ) = .25/(.02+.01+.05) = 3.125

Therefore, the balanced-growth capital-output ratio is 3.125. If the capital-output ratio happens to be above this level, the savings rate is not high enough to maintain it, and the ratio will tend to fall back to 3.125. Conversely, if the capital-output ratio happens to start out below the ba- lanced-growth level, the savings rate is high enough to generate capital accumulation until the ratio rises back to 3.125. Back at equation [10] when we computed labor productivity growth, we had assumed earlier an arbitrary capital-output ratio of 2.5. Now, we know that this is not a ba- lanced-growth ratio given the saving rate, depreciation rate, and other assumed parameters. Using the balanced-growth ratio of 3.125 in equation [7] gives

[7’] x – n = .25/3.125 – .05 – .01 = .02 Putting this into [10], we have

[10’] y – n = .25(.02) + .75(.02) = .02

What we have found is that on a balanced growth path, output per worker and capital per worker grow at the same rate as the efficiency of labor. In our example, this is 2 percent per year.

II. Vocabulary Items

accumulation n – накопление, аккумуляция arbitrary a – произвольный, случайный assumption n – предположение, допущение average a – средний

capital goods – средства производства, основной капитал capital stock – основной капитал, основные производственные фонды

constant a – постоянный consume v – потреблять converge v – стремиться

convergence n – конвергенция, сходимость

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