Basic Econometric Exercises Resolution, Chapter 1 by Juan Jose Salcedo Cruz

Basic Econometric Exercises Resolution Chapter 1 Juan Jos´e Salcedo March 2011 Abstract This document contains my proposed resolutions to the exercises of the first chapter of the book Basic Econometrics (fourth edition) by Damodar N. Gujarati. It hasn’t been revised by any scholar, it sole purpose it my econometrics and latex skills. The first chapter of the book focuses on the visual aspect and causal relationship or regression analysis. There aren’t any regressions nor estimation procedures here.

Contents 1 Questions and answers

2 Tables and figures

List of Tables 1 2 3 4

CPI in seven Industrial countries, 1973-1997 . . . . . . . . . Inflation rates of studied contries . . . . . . . . . . . . . . . Correlation coeffecients between selected countries’ inflation Impact of advertising expenditure . . . . . . . . . . . . . . .

. . . . . . rates . . .

. . . .

4 5 5 6

. . . .

6 7 7 7

List of Figures 1 2 3 4

Inflation rates of study countries . . . . . . . . . . . Exchange rates of study countries . . . . . . . . . . . M1 money supply: United States; 1951m1-1999m9 . Advertising expenditure relationship with impression

. . . .

Questions and answers

1. Table 1 gives data on the Consumer Price Index (CPI) for seven industrialized countries with 1982−194 = 100 as the base of the index. (a) From the given data, compute the inflation rate for each country. Solution: See table 2 on page 5. (b) Plot the inflation rate for each country against time. Solution: See figure 1 on page 6. (c) What broad conclusion can you draw about the inflation experience in the seven countries? Solution: It seems like the inflation rates of the countries revolve around that of the United States (U.S.). The level of trade between any country and the U.S. is assumed to be greater than with any other country, this situation makes the inflations rates of the countries be positively correlated. When the United Stated faces inflationary processes, the other countries economies get affected in lesser quantities. The transmission mechanism of inflation between countries is their trade intensity. On table 3 we can see that the inflation correlation coefficients US is the highest or second highest for each individual country. (d) Which country´s inflation rate seems to be most variable? Can you offer any explanation? Solution: The most variable inflation rate is that of Italy. 2. (a) Plot the inflation rate of Canada, France, Germany, Italy, Japan and the United Kingdom against the United States inflation rate. Solution: Same as we did back on the first question. The plot is on figure 1. (b) Comment generally about the behavior of the inflation rate in the six countries via-`a-vis the U.S. inflation rate. Solution: As we mention earlier there the inflation rates of the countries is correlated to that of the United States. (c) If you find the the six countries’ inflation rates move in the same direction as the U.S. inflation rate, would that suggest that U.S. inflation “causes” inflation in the other countries? Why or why not? Solution: although we found evidence that the countries’ inflation rates are correlated to U.S. inflation rate it doesn’t prove a causal relationship between the two. In the previous question we affirm that the transmission mechanism of inflation is the intensity of trade. Yet to prove weather or not the relationship is significant more test should be run. 3. Table 1.31 gives the foreign exchange rates for seven industrialized counties for the year 1977-1998. Except for the United Kingdom , the exchange rate is defined as the units of foreign currency for one US dollar; for the United Kingdom, it is defined as the number of U.S. dollars for one U.K. pound. (a) Plot these exchange rates against time and comment on the general behavior of the exchange rates over the given time period. Solution: The exchange rates are plotted in figure 2. Some of the currencies experience high variations, yet on general term we can argue that the currencies follow a trend. The Japanese Yen, JPY, on the upper right corner seems to moving downwards; The U.K. pound sterling, GBP, 1 Due

to its excessive length, table 1.3 hasn’t been included in the solution manual.

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on the other hand shows quite a stable behavior; and the Canadian dollar and the euro are moving upwards. The direction of the currency movement will become increasingly important as we study economics. For the moment we will just identify the direction of the movement. (b) The dollar is said to appreciate if it can buy more units of a foreign currency. Contrarily, it is said to depreciate if it buys fewer units of a foreign currency. What can be said about the dollar during the time period? Solution: Let’s start analyzing the dynamics behind the direction of a currency relationship. Take the Japanese yen for example: In 1980 if you wanted to buy one dollar, you had to pay around 230 JPY, 15 years later in 1995, if you wanted to buy that same dollar, you had to pay around 100 JPY. So now you need less JPY to buy one USD. When this happens it is said that tha JPY has appreciated or equivalently that the USD has depreciated. 4. The data behind the M1 money supply in figure 3 are given in table 1.4.2 Can you give reason why the money supply has been increasing over the time period shown in the table? Solution: The money supply is determined many factors, we will check the Quantitative theory of money to answer this questions. According to this theory money is determined by the i) the transaction velocity of money, ii) the economy price level and iii) an the real value of transactions. M=

Pt T Vt

(1)

So as the economy experiences heated periods, where everyone is selling and buying (Vt is up) the need for money diminishes because the people are passing on the moeny they’ve got fast enough. The other two components (Pt T ) is basically the gross domestic product which is intuitively directly related to money supply, as a growing economy needs money to back up the growth. 5. Suppose you were to develop an economic model of criminal activities, say, the hours spent in criminal activities. What variables would you considerar in developing such model? Solution: I’d believe that the hours spent in criminal activities depend on : 1. years of schooling 2. the gross domestic product of the country 3. the level of unemployment The economy Nobel prize Gary Becker established a model to explain criminal activities. In it Becker argues that criminal misbehave cause the benefits are much greater than the punishment and the probability of being apprehended. 6. The data presented in table 4 was published in March 1, 1984 issue of the Wall Street Journal. It relates to the advertising budget (in millions of dollars) of 21 firms for 1983 and millions of impression retained per week by the viewers of the producto of these firms. Tha data are based on a survey of 4,000 adults in wich users of the products were asked to cite a comercial they had seen for the product category in the last week. (a) Plot impression on the vertical axis and advertising expenditure on the horizontal axis. 2 Due

to its excessive length, table 1.4 hasn’t been included in the solution manual.

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Solution: We can appreciate it on figure 4. (b) What can you say about the nature of the relationship between the two variables. Solution: We can say that they are positively correlated. The higher the advertising expenditure the higher de impressions (on the average). Yet, the existence of a causal relationship ih hard to prove. In this case the solution is quietly intuitively: the more I advertise the more people will remember my advertising. (c) Looking at the graph, do you think it pays to advertise? Solution: Looking rapidly at figure 4 we can see that advertising is a good thing, yet the figure also hides very important details, as the nature of the product (hardly, advertising backpacks can be compare to advertising a Ferrari); or the length of the advertisment, we could be comparing apples and oranges; the personal motivations regarding any specific product; etc.

Tables and figures Table 1: CPI in seven Industrial countries, 1973-1997

Year

Canada

France

Germany

Italy

Japan

1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

40.80 45.20 50.10 53.90 58.10 63.30 69.20 76.10 85.60 94.90 100.40 104.70 109.00 113.50 118.40 123.20 129.30 135.50 143.10 145.30 147.90 148.20 151.40 153.80 156.30

34.60 39.30 43.90 48.10 52.70 57.50 63.60 72.30 81.90 91.70 100.40 108.10 114.40 117.30 121.10 124.40 128.70 133.00 137.20 140.50 143.50 145.80 148.40 151.40 153.20

62.80 67.10 71.10 74.20 76.90 79.00 82.20 86.70 92.20 97.10 100.30 102.70 104.80 104.70 104.90 106.30 109.20 112.20 116.30 122.10 127.60 131.10 133.50 135.50 137.80

20.60 24.60 28.80 33.60 40.10 45.10 52.10 63.20 75.40 87.70 100.80 111.50 121.10 128.50 134.40 141.10 150.40 159.60 169.80 178.80 186.40 193.70 204.10 212.00 215.70

47.90 59.00 65.90 72.20 78.10 81.40 84.40 90.90 95.30 98.10 99.80 102.10 104.10 104.80 104.80 105.60 108.10 111.40 115.00 116.90 118.40 119.30 119.10 119.30 121.30

27.90 32.30 40.20 46.80 54.20 58.70 66.60 78.50 87.90 95.40 99.80 104.80 111.10 114.90 119.70 125.60 135.30 148.20 156.90 162.70 165.30 169.40 175.10 179.40 185.00

44.40 49.30 53.80 56.90 60.60 65.20 72.60 82.40 90.90 96.50 99.60 103.90 107.60 109.60 113.60 118.30 124.00 130.70 136.20 140.30 144.50 148.20 152.40 156.90 160.50

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Table 2: Inflation rates of studied contries

Year

Canada

France

Germany

Italy

Japan

1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

10.78% 10.84% 7.58% 7.79% 8.95% 9.32% 9.97% 12.48% 10.86% 5.80% 4.28% 4.11% 4.13% 4.32% 4.05% 4.95% 4.80% 5.61% 1.54% 1.79% 0.20% 2.16% 1.59% 1.63%

13.58% 11.70% 9.57% 9.56% 9.11% 10.61% 13.68% 13.28% 11.97% 9.49% 7.67% 5.83% 2.53% 3.24% 2.73% 3.46% 3.34% 3.16% 2.41% 2.14% 1.60% 1.78% 2.02% 1.19%

6.85% 5.96% 4.36% 3.64% 2.73% 4.05% 5.47% 6.34% 5.31% 3.30% 2.39% 2.04% -0.10% 0.19% 1.33% 2.73% 2.75% 3.65% 4.99% 4.50% 2.74% 1.83% 1.50% 1.70%

19.42% 17.07% 16.67% 19.35% 12.47% 15.52% 21.31% 19.30% 16.31% 14.94% 10.62% 8.61% 6.11% 4.59% 4.99% 6.59% 6.12% 6.39% 5.30% 4.25% 3.92% 5.37% 3.87% 1.75%

23.17% 11.69% 9.56% 8.17% 4.23% 3.69% 7.70% 4.84% 2.94% 1.73% 2.30% 1.96% 0.67% 0.00% 0.76% 2.37% 3.05% 3.23% 1.65% 1.28% 0.76% -0.17% 0.17% 1.68%

15.77% 24.46% 16.42% 15.81% 8.30% 13.46% 17.87% 11.97% 8.53% 4.61% 5.01% 6.01% 3.42% 4.18% 4.93% 7.72% 9.53% 5.87% 3.70% 1.60% 2.48% 3.36% 2.46% 3.12%

11.04% 9.13% 5.76% 6.50% 7.59% 11.35% 13.50% 10.32% 6.16% 3.21% 4.32% 3.56% 1.86% 3.65% 4.14% 4.82% 5.40% 4.21% 3.01% 2.99% 2.56% 2.83% 2.95% 2.29%

Table 3: Correlation coeffecients between selected countriesâ&#x20AC;&#x2122; inflation rates

Canada France Germany Italy Japan UK US

Canada

France

Germany

Italy

Japan

1.00 0.93 0.67 0.90 0.65 0.81 0.86

1.00 0.72 0.98 0.68 0.79 0.85

1.00 0.72 0.68 0.66 0.70

1.00 0.69 0.83 0.83

1.00 0.76 0.67

1.00 0.82

1.00

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Table 4: Impact of advertising expenditure

Firm

Impressions, millions

Expenditure millions of 1983 dollars

Miller Lite Pepsi Stroh’s FedEx Burger King Coca Cola Mc Donald’s MCI Diet Cola Ford Levi’s Bud Lite ATT/Bell Calvin Klein Wendy’s Polaroid Shasta Meow Mix Oscar Meyer Crest Kibbles ’n Bits

32.1 99.6 11.7 21.9 60.8 78.6 92.4 50.7 21.4 40.1 40.8 10.4 88.9 12 29.2 38 10 12.3 23.4 71.1 4.4

50.1 74.1 19.3 22.9 82.4 40.1 185.9 26.9 20.4 166.2 27 45.6 154.9 5 49.7 26.9 5.7 7.6 9.2 32.4 6.1

Percentage (%) 10 15

Figure 1: Inflation rates of study countries

1970

1980 Canada Japan

1990 France UK

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Germany US

2000 Italy

Foreign currency per one US dollar

Figure 2: Exchange rates of study countries 10 8 6 4 2 0

US dollaer per one UK pound

1975

1980

1985

1990

1995

300 250 200 150 100

2000

1975

2.5

1980

1985

1990

1995

2000

Canada

France

Germany

Sweden

Switzer

2 UK

1.5 Japan

1 1975

1980

1985

1990

1995

2000

Figure 3: M1 money supply: United States; 1951m1-1999m9

Billions of dollars (seasonally adjusted)

1,200

1,000

800

600

400

200 1960m1

1970m1

1980m1

1990m1

2000m1

Figure 4: Advertising expenditure relationship with impression 100

Pepsi Mc Donald’s ATT/Bell

Impression (millions)

Coca Cola Crest Burger King

60 MCI Levi’s Polaroid

Ford Miller Lite Wendy’s

Oscar FedEx Meyer Diet Cola

MeowKlein Mix Calvin ShastaStroh’s

Bud Lite

Kibbles ’n Bits

0 0

50 100 150 Expenditure (millions of 1983 dollars)

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200