Com relação a desigualdade de Tchebycheff e ao Teorema Central do Limite, pode-se afirmar que :

Item 0 - Se uma variável aleatória !$ X !$ tem média !$ μ !$, !$ E(X) = μ !$, e variância igual a zero, !$ Var(X) = 0 !$, então !$ P\{|X - μ| ≤ ε\} = 1 !$ para todo !$ ε > 0 !$, ou seja, toda a probabilidade estará concentrada na média !$ E(X) = μ !$.

Com relação aos modelos Auto - Regressivo, Média - Móvel e Misto, pode - se afirmar que :

Item 0 - No modelo !$ Z_t = ∅ \ Z_{t-1} + a _t + θa_{t-1} + θ_0 !$, onde !$ θ_0 !$ é uma constante e !$ a_t !$ um ruído branco, a média do processo será igual a zero se !$ θ_0 = 0 !$.

Com relação a desigualdade de Tchebycheff e ao Teorema Central do Limite, pode-se afirmar que :

Item 3 - Se !$ X !$ tem distribuição desconhecida com média 500 e variância 2.500, para uma amostra aleatória de tamanho 100 podemos afirmar que a média da amostra tem distribuição aproximadamente normal com média 500 e variância 25.

Based on your interpretation of the text you are about to read, determine whether each statement is right or wrong.

Part III

“The Swedish Investment Funds System” in Macroeconomics, by N.G. Mankiw, P.449. Worth Publisher, 1992

Tax incentives for investment are one-tool policymakers can use to control aggregate demand. For example, an increase in the investment tax credit reduces the cost of capital, shifts the investment function outward, and raises aggregate demand. Similarly, a reduction in the tax credit reduces aggregate demand by making investment more costly.

From the mid-1950s to the mid-1970s, the government of Sweden attempted to control aggregate demand by encouraging or discouraging investment. A system called the investment fund subsidized investment, much like an investment tax credit, during periods of recession. When government officials decided that economic growth had slowed, they authorized a temporary investment subsidy. When the officials concluded that the economy had recovered sufficiently, they revoked the subsidy. Eventually, however, Sweden abandoned the use of temporary investment subsidies to control the business cycle, and the subsidy became a permanent feature of Swedish tax policy.

Should investment subsidies be used to combat economic fluctuations? Some economists believe that, for the two decades it was in effect, the Swedish policy reduced the magnitude of the business cycle. Others believe that this policy can have unintended and perverse effects: for example, if the economy begins to slow down, firms may anticipate a future subsidy and delay investment, making the slowdown worse. Thus, the implications of this policy are complex, which makes its effect on economic performance hard to evaluate.

Item 0 - The author argues that the Swedish tax credit system had a serious implication for the business cycles to the extent that business responded very well to its incentives.

Com relação aos modelos Auto - Regressivo, Média - Móvel e Misto, pode - se afirmar que :

Item 2 - O processo ARMA(p,q) (Auto-Regressivo Média-Móvel) será estacionário e invertível, se todas as raízes dos operadores Auto - Regressivo e de Média Móvel caírem dentro do círculo unitário.

Based on your interpretation of the text you are about to read, determine whether each statement is right or wrong.

Part-I

“Trade, Jobs, and Wages” in Pop Internationalism, by Paul Krugman, Chapter 3, pp.-35-37.

The MIT Press, 1996.

The real wage of the average American worker more than doubled between the end of World War II and 1973. Since then, however, those wages have risen only 6 percent. Furthermore, only highly educated workers have seen their compensation rise; the real earnings of blue-collar workers have fallen in most years since 1973.

Why have wages stagnated? A consensus among business and political leaders attributes the problem in large part to the failure of the U.S. to compete effectively in an increasingly integrated world economy. This conventional wisdom holds that foreign competition has eroded the U.S. manufacturing base, washing out the high-paying jobs that a strong manufacturing sector provides. More broadly, the argument goes, the nation's real income has lagged as a result of the inability of many U.S. firms to sell in world markets. And because imports increasingly come from Third World countries with their huge reserves of unskilled labor, the heaviest burden of this foreign competition has ostensibly fallen on less educated American workers.

Many people find such a story extremely persuasive. It links America's undeniable economic difficulties to the obvious fact of global competition. In effect, the U.S. is (in the words of President Bill Clinton) "like a big corporation in the world economy" -- and, like many big corporations, it has stumbled in the face of new competitive challenges.

Persuasive though it may be, however, that story is untrue. A growing body of evidence contradicts the popular view that international competition is central to U.S. economic problems. In fact, international factors have played a surprisingly small role in the country's economic difficulties. The manufacturing sector has become a smaller part of the economy, but international trade is not the main cause of that shrinkage. The growth of real income has slowed almost entirely for domestic reasons. And -- contrary to what even most economists have believed -- recent analyses indicate that growing international trade does not bear significant responsibility even for the declining real wages of less educated U.S. workers.

The fraction of U.S. workers employed in manufacturing has been declining steadily since 1950. So has the share of U.S. output accounted for by value added in manufacturing. (Measurements of "value added" deduct from total sales the cost of raw materials and other inputs that a company buys from other firms.) In 1950 value added in the manufacturing sector accounted for 29.6 percent of gross domestic product (GDP) and 34.2 percent of employment; in 1970 the shares were 25.0 and 27.3 percent, respectively; by 1990 manufacturing had fallen to 18.4 percent of GDP and 17.4 percent of employment.

Before 1970 those who worried about this trend generally blamed it on automation -- that is, on rapid growth of productivity in manufacturing. Since then, it has become more common to blame deindustrialization on rising imports; indeed, from 1970 to 1990, imports rose from 11.4 to 38.2 percent of the manufacturing contribution to GDP.

Yet the fact that imports grew while industry shrank does not in itself demonstrate that international competition was responsible. During the same 20 years, manufacturing exports also rose dramatically, from 12.6 to 31.0 percent of value added. Many manufacturing firms may have laid of workers in the face of competition from abroad, but others have added workers to produce for expanding export markets.

To assess the overall impact of growing international trade on the size of the manufacturing sector, we need to estimate the net effect of this simultaneous growth of exports and imports. A dollar of exports adds a dollar to the sales of domestic manufacturers; a dollar of imports, to a first approximation, displaces a dollar of domestic sales. The net impact of trade on domestic manufacturing sales can therefore be measured simply by the manufacturing trade balance -- the difference between the total amount of manufactured goods that the U.S. exports and the amount that it imports. (in practice, a dollar of imports may displace slightly less than a dollar of domestic sales because the extra spending may come at the expense of services or other nonmanufacturing sales. The trade balance sets an upper bound on the net effect of trade on manufacturing.)

Item 3 - This article shows how facts often contradict popular notions.