Econometric Analysis - Walmart Sales

STUART SCHOOL OF BUSINESS

Econometric Analysis Wal-Mart Stores Rohan S. Patil 2/16/2008

Wal-Mart Sales

Econometric Analysis

MSF 562

Wal-Mart: Net Monthly Sales Econometric Analysis MSF 562

Abstract

This report contains a description of econometric analyses of net monthly sales of WalMart Stores, Inc. The analyses are focused on:    

Macroeconomic factors indicating the state of the overall economy Various macro-economic factors affecting the production costs The overall consumer sentiment and disposable income Miscellaneous factors affecting sales ( e.g. retail gas price)

I begin with the description of the business of Wal-Mart and their various internal segments. In part II, I will explain all the macro-economic indicators and their intuitive effects on the net sales of a company in the retail segment. Part III explains the initial stages of the analyses wherein I shall de-trend the time-series data and then remove the seasonality effects. Part IV discusses the construction of the econometric model and tests of significance. The advanced analysis is presented in part V wherein the model will be tested for possible autocorrelation and heteroskedasticity. In part VI, the concluding remarks, I shall elaborate on the pattern in the monthly net sales of Wal-Mart as explained by all the significant independent variables. I have appended an appendix at the very end of the report which supports the analyses with graphs, tables and also shows all the important statistics.

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Wal-Mart Sales

I. Introduction Business Description:

Econometric Analysis

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Wal-Mart Stores NYSE Code: WMT Sector: Variety Stores

Wal-Mart is the world’s largest general merchandise retailer, operating nearly 6,800 stores worldwide. It is the world's largest public corporation by revenue, according to the 2007, Fortune Global 500. Wal-Mart has three main divisions as far as the revenues are concerned. They are WalMart stores, Sam’s club and international sales. Wal-Mart also deals with online product selling through the Internet which is aggregated into three divisions mentioned above. Among these business divisions, Wal-Mart Stores Divisio n, U.S. is Wal-Mart's largest business subsidiary, accounting for 67.2% of net sales for financial year 2006. It consists of three retail formats that have become commonplace in the United States: Discount Stores, Supercenters, and Neighborhood Markets. Wal-Mart Discount Stores are discount department stores which carry general merchandise and a selection of food. Many of these stores also have a garden center, a pharmacy, Tire & Lube Express, optical center, one-hour photo processing lab, portrait studio, and a fast food outlet. Some also sell gasoline. Wal-Mart Supercenters are hypermarkets with an average size of about 197,000 square feet. These stock everything a Wal-Mart Discount Store does, and also include a fullservice supermarket, including meat and poultry, baked goods, frozen foods, dairy products, garden produce, and fresh seafood. Many Wal-Mart Supercenters also have a garden center, pet shop, pharmacy, Tire & Lube Express, optical center, one-hour photo processing lab, portrait studio, and numerous alcove shops, such as cellular phone stores, hair and nail salons, video rental stores, local bank branches, and fast food outlets. Some also sell gasoline. Wal-Mart Neighborhood Markets are grocery stores. They offer variety of products, including full lines of groceries, pharmaceuticals, health and beauty aids, photo developing services, and a limited selection of general merchandise. Sam's Club is a chain of warehouse clubs which sell groceries and general merchandise in large quantities. Sam's has found a niche market in recent years as a supplier to small businesses. According to Wal-Mart's 2007 Annual Report, Sam's Club's annual sales were $42 billion, or 12.1% of Wal-Mart's total sales. Wal-Mart's internat ional operations currently comprise 2,980 stores in 14 countries outside the United States. According to Wal-Mart's 2006 Annual Report, the International division accounted for about 20.1% of sales. There are wholly-owned operations in Argentina, Brazil, Canada, Puerto Rico (although PR is part of the US, the company's operations there are managed through its international division), and the UK. With 1.8 million employees worldwide, the company is the largest private employer in the US and Mexico, and one of the largest in Canada.

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Wal-Mart Sales

Econometric Analysis

II. Macroeconomic and other Indicators

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(Independent variables)

1. Consumer Price Index (CPI): As a proxy for inflation CPI is used to analyze the effects of inflation in the overall economy on the net sales. As Wal-Mart sells a variety of products ranging from food to fuel, it is interesting to analyze how the sales of essential and non-essential items are affected by inflation. Since the prices of essential items such as food and energy are much more volatile compared to the other items I used several indicators such as CPI – for all items, all but food, only food, food and energy, all but food and energy. 2. Unemployment Rate: Keynesian economics emphasizes unemployment resulting from insufficient effective demand for goods and service in the economy (cyclical unemployment). Thus, this variable has been used as a proxy for the state of the overall economy. 3. Consumer Sentiment Index: (This is similar to the Consumer Confidence Index)

CSI is a closely watched barometer of where the economy might be headed next. It is defined as the degree of optimism on the state of the economy that consumers are expressing through their activities of savings and spending. The main Index of Consumer Sentiment is based on the results of two subset indices: the Index of Current Economic Conditions, which explores consumers’ thinking about their current finances and buying plans, and the Index of Consumer Expectations, which is designed to gauge consumers’ outlook over the coming one-and fiveyear periods. 4. Gasoline Prices: I have used the monthly prices of gasoline available to retail customers. Most of the customers of Wal-Mart travel to the stores by a car. Thus, I think it is interesting to analyze the relationship between gasoline prices and sales. 5. Consumer Credit Outstanding Consumer debt is consumer credit which is outstanding. In macroeconomic terms, it is debt which is used to fund consumption rather than investment. The permanent income hypothesis suggests that consumers take debt to smooth consumption throughout their lives, borrowing to finance expenditures earlier in their lives and paying down debt during higher-earning periods. Thus the amount of debt in the economy may affect retail sales.

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Econometric Analysis

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Dummy explanatory variables: 1. Dummy for December Sales: After observing the data we find that the December sales are substantially higher than the rest of the months. A plausible reason for this seasonal effect could be the holiday season. In order to offset this effect, a dummy variable has been used which captures the increased sales due to holiday spending. 2. Dummy for November Sales: The data on the November sales for the years 1996-2006 were considerably higher than other months even though it was reported only for four weeks. Thus we add a dummy variable for the sales in November. 3. Dummy for number of weeks (as reported): This dummy variable is introduced in order to remove the effect of the number of weeks over which the sales have been reported by the company. The company publishes the data for monthly sales in the following pattern: 4,4,5 4,4,5 - 4,4,5 -4,4,5. These are the number of weeks included in the monthly sales. This dummy variable has no economic significance and thus we will not discuss this further. Following is the list of all the variables with their names and short-forms: Independent Variables.* ShortForm

Name

1

x1

Consumer Sentiment Index

2

x2

CPI- All

3

x3

CPI – All but food

4

x4

CPI- All but food energy

5

x5

CPI- All but energy

6

x6

CPI for food only

7

x7

Consumer(individual) loans-non-revolvingOutstanding

8

x8

Consumer credit( revolving) Outstanding

9

x9

Unemployment

10

x10

PPI- Finished Consumer Goods

11

x11

PPI- Fuels and Power

12

x12

PPI- Finished Consumer Foods

13

x13

Motor Gasoline Retail Prices, U.S. City Average

14

x14

Disposable Income

15

dummy1

Number of weeks ( 1 = 5 weeks, 0 = 4 weeks)

16

dummy2

December sales

17

dummy3

November sales

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Wal-Mart Sales

Econometric Analysis

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III. De-trending, Seasonality and Co-linearity: In this section, we will start of with de-trending of the dependent and independent variables. After this I adjusted the log (sales) for seasonality using the dummy variables for the month of November and December. Additionally I added a dummy for number of weeks. All my independent variables (macro-economic indicators) are adjusted for seasonality. Following is the regression that I carried out to de-trend y. y   0  1timeline  u

… Reg.1

*Refer appendix for details of this regression.

I obtained following equation after this regression: y  2.126634  0.009988timeline  u (0.0308) (0.000368) n = 142, R 2 = 83.84% We find out the residuals from the above regression (i.e. log( sales ) using the following equation: y  y  yˆ 1 These residuals will be used for the purpose of our analysis in place of log (sales). Similarly, all the independent variables were de-trended and henceforth the residuals of these regressions will be used for the furtherance of the analysis. Now let us turn to the adjustments for the seasonality in the net sales of Wal-Mart. From the residual plot of regression 1 *, we note that the net sales are substantially higher in November and December of each year. In order to partial out this effect I used two dummies (one for each month). Following is the equation for removing seasonality:

y   0  1dummy1   2 dummy2   3 dummy3  u

… Reg.2

I obtained the following equation after this regression:

y  -0.11455  0.228121 dummy1  0.326261 dummy2  0.126337dummy3  u (0.0084) (0.0153) (0.025511) (0.023636) n = 142, R 2 = 82.27% We use the residuals of this regression for further analysis: y  y  yˆ

1.

yˆ is the predicted value of y by the equation. y is log (sales) after de-trending and y is after de-seasonality. * Refer the appendix for the plot.

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Econometric Analysis

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Proceeding with the analysis of the data, we check all probable independent variables for a possible co-linearity. In case two variables are found to be highly collinear then one of them is rejected. After calculating the correlation between the independent variables I found the following: 1. Variables x2 and x3 are almost the same. 2. Variable x2 is highly correlated with variables x10, x11 and x13. 3. Variable x4 is highly correlated with variable x5. 4. Variable x12 is highly correlated with variable x6. 5. Variables x10 and x13 are also correlated. *Refer appendix for the entire correlation matrix.

Thus we reject variables x3, x4, x5, x10, x11 and x13.

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Wal-Mart Sales

Econometric Analysis

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IV. Econometric Model: Following is the chart of y plotted against time:

log(sales) After removing the seasonality 0.25 0.2 0.15 0.1 0.05 0 -0.05

0

20

40

60

80

100

120

140

160

-0.1 -0.15 -0.2 -0.25

There is a definite change in the slope of this graph after about 70 samples. The most interesting thing here is sample 69 represents the month of September 2001. Thus, I selected this point as my crossover point and performed a piece-wise linear regression by including a binary variable as well as its interaction terms with all the independent variables.

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Wal-Mart Sales

Econometric Analysis

MSF 562

Initial econometric model is setup as follows:

y   0   0 dummy  1 x1   2 x2   6 x6   7 x7   8 x8   9 x9  12 x12  13 x13  14 x14  1dummy * (1 x1   2 x2   6 x6   7 x7   8 x8   9 x9  12 x12  13 x13  14 x14 )  u … Reg.3 I found following variables to be significant (and on the verge of significance): Variable

β

t-Stat

1

x6

-0.01252

-1.65666

2

x7

-0.00145

-3.45889

0.00109

2.988242

-0.02523 -0.00024756 2.27462E-06

-1.43381 -1.77712 2.2746675

3 4 5 6

x8 x9 dummy*x7 dummy*x12

* Refer appendix for further details.

Then, I ran the regression with only significant factors included in the model.

y   0   6 x6   7 x7   8 x8   9 x9  1  7 dummy * x7  1 12dummy  u

… Reg.4

Following are the significant betas and their t-stats.

1 2

Variable x7 x8

β -0.0011185 0.001177037

t-Stat -3.95484 4.170627

3

x9

-0.04566579

-3.17542

4

dummy*x7

-0.00018785

-2.26428

5

dummy* x12

9.86155E-07

1.895653

We get an adjusted R2 of 22. 18 %.

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Wal-Mart Sales

Econometric Analysis

MSF 562

V. Heteroskedasticity and Autocorrelation: I conducted the Breusch-Pagan test on the residuals from the regression 4 to check for the existence of heteroskedasticity in the residuals. Breusch-Pagan test: Model: uˆ 2   0   6 x6   7 x7   8 x8   9 x9  1  7 dummy * x7  1 12dummy  v … Reg.5 * Refer appendix for details.

Null hypothesis: H0 : βi = 0 … for all i Alternate Hypothesis: H1 : βi ≠ 0 … for all i The joint significant of all the β’s is 1.145223. Thus, we fail to reject the null hypothesis. Breusch- Pagan test does not indicate presence of heteroskedasticity. Thus, in order to further analyze the relationship of u with x’s I performed the White Test. White Test: Model:

u 2   0  1 y   2 y2  v

…Reg.6 * Refer appendix for details.

Null hypothesis: Alternate Hypothesis:

H0 : βi = 0 … i  [1, ] H1 : βi ≠ 0 … i  [1, ]

The joint significant of all the β’s is 1.213656. Thus, we fail to reject the null hypothesis.Thus, after both these tests fail to identify I assumed that the heteroskedasticity is absent.

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Econometric Analysis

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Now we shall test for the auto correlation in these residuals by running the following regression: …Reg.7 ut   0  1ut 1  v Null hypothesis: Alternate Hypothesis:

H0 : β1 = 0 … i  [1, ] H1 : βi ≠ 0 … i  [1, ]

We the following equation:

ut  -0.00056  0.038965ut 1  v (0.0039) (0.0836) n = 140, R 2 = -0.558 % The t- stat of β1 is 0.466. Thus, it is not statistically significant from zero. Thus, the residual are serially uncorrelated.

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Econometric Analysis

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VI. Concluding Remarks: After the econometric analysis I got the following model:

y   0   6 x6   7 x7   8 x8   9 x9  1  7 dummy * x7  1 12dummy  u log (sales) -d-s* = 0.22183 - 0.001118 x7  0.00118 x8 - 0.0457 x9 - 0.000188 dummy * x7  9.861E - 07dummy * x12  u X7

Consumer loans Outstanding (individual-non-revolving)

X8

Consumer credit( revolving) Outstanding

X9

Unemployment

X12

PPI- Finished Consumer Foods

n= 142, R 2 = 22.134%

Before September, 2001: log (sales) –d-s = 0.22183 - 0.0011185 x7  0.001177 x8 - 0.04566 x9  u After September, 2001: log (sales) –d-s = 0.22183 - 0.00130635x7  0.001177 x8 - 0.04566 x9  9.86155E - 07 * x12  u Interpretation of betas: The beta corresponding to Consumer loans outstanding (individual non-revolving) is 0.0011185. This goes to show that as the consumer debt (non-revolving) in the economy increases, ceteris paribus, the net effect on Wal-Mart sales is negative. It concurs with the fact that as people take on more and more debt their spending capacity goes down resulting in lower sales.

It is interesting to note that the effect of revolving credit is exactly opposite. When the revolving credit goes up, ceteris paribus, the sales also go up. Most of the people do pay by credit card and thus defer the payment by some time. If the revolving credit is going down, that means people are struggling to pay their last months credit. Thus, the sales for that particular month would be low.

* log (sales)-d-s is the log(sales) after de-trending and removing the seasonality.

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Econometric Analysis

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Unemployment rate has a negative impact on the net sales. This makes sense because the unemployment rate is low when the economy as a whole is doing good and it increases during recessions. Thus intuitively the sign of this beta should be negative. One more interesting thing to note is, post- September, 2001 the Producer’s Price Index for finished consumer food is significant. After analyzing the net sales of Wal-Mart I found the following factors to be significant: 1. Consumer Loans (revolving and non-revolving credit) 2. Unemployment 3. Producer’s Price Index With the help of these parameters, my econometric model could explain 22% of the variations in the net-sales of Wal-Mart.

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Econometric Analysis

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VII. Further Studies: After regressing log (sales) with respect to time and time2, I found a definite cycle of sales as shown in the following graph. log(sales) regressed against t and t2 0.2 0.15 0.1 0.05 0 0

20

40

60

80

100

120

140

160

-0.05 -0.1 -0.15 -0.2

This pattern needs further attention. In my opinion it would not be appropriate to use piecewise linear regression four times on this graph. Also, I have not considered the impact of the foreign exchange rate on the net sales. In order to do that, one needs to analyze their operations in foreign markets in detail. The data regarding this was not available to me. Also, the store has a strategy of reducing there Wal-Mart stores and increasing the number of Supercenters over last 10 years. The reasons behind this trend are unknown. It is clear that this has a significant impact on the sales.

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Econometric Analysis

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VIII. Appendix: Part II. Following table shows the sources of data used in the econometric model: Name Consumer Sentiment Index CPI- All CPI – All but food CPI- All but food energy CPI- All but energy CPI for food only Consumer(individual) loans-non-revolving Outstanding Consumer credit( revolving) Outstanding Unemployment PPI- Finished Consumer Goods PPI- Fuels and Power PPI- Finished Consumer Foods Motor Gasoline Retail Prices

Source Survey Research Center: University of Michigan* U.S. Department of Labor: Bureau of Labor Statistics* U.S. Department of Labor: Bureau of Labor Statistics* U.S. Department of Labor: Bureau of Labor Statistics* U.S. Department of Labor: Bureau of Labor Statistics* U.S. Department of Labor: Bureau of Labor Statistics* Board of Governors of the Federal Reserve System1 Board of Governors of the Federal Reserve System1 U.S. Department of Labor: Bureau of Labor Statistics* U.S. Department of Labor: Bureau of Labor Statistics* U.S. Department of Labor: Bureau of Labor Statistics* U.S. Department of Labor: Bureau of Labor Statistics* Energy Info. Administration**

Disposable Income

Bureau of Economic Analysis

Net Sales of Wal-Mart

www.walmartfacts.com

Part III: Regression 1 Summary Output for regression 1: Regression Statistics Multiple R 0.9163 R Square 0.8396 Adjusted R Square 0.8384 Standard Error 0.1824 Observations 143.0000 ANOVA Regression Residual Total

Intercept X Variable 1

df 1.0000 141.0000 142.0000

SS 24.5447 4.6907 29.2354

MS 24.5447 0.0333

Coefficients 2.1266 0.0100

Standard Error 0.0308 0.0004

t Stat 68.9772 27.1625

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Following chart shows the residuals of the above equation plotted against time: De-trending of log(sales) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1

0

20

40

60

80

100

120

140

160

-0.2 -0.3 -0.4

We can clearly see the seasonality in the sales. Regression 2 Following is the summary output for regression 2: Regression Statistics Multiple R 0.9091 R Square 0.8264 Adjusted R Square 0.8227 Standard Error 0.0765 Observations 143.0000 ANOVA Regression Residual Total

df 3.0000 139.0000 142.0000

Coefficients Intercept X Variable 1 X Variable 2 X Variable 3

-0.1146 0.2281 0.3263 0.1263

SS 3.8765 0.8142 4.6907 Standard Error 0.0084 0.0153 0.0255 0.0236

MS 1.2922 0.0059

F 220.6083

t Stat

P-value

13.6362 14.9359 12.7890 5.3450

0.0000 0.0000 0.0000 0.0000

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Following chart shows the residuals of the above equation plotted against time: log(sales) After removing the seasonality 0.25 0.2 0.15 0.1 0.05 0 -0.05

0

20

40

60

80

100

120

140

160

-0.1 -0.15 -0.2 -0.25

Correlation Matrix of independent variables

x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14

x1 100% -32% -34% -40% -37% -12% -25% -63% -54% -21% -22% -10% -17% 6%

x2 -32% 100% 100% 45% 65% 78% 70% -15% -28% 94% 88% 68% 88% 79%

x3 -34% 100% 100% 45% 63% 72% 66% -14% -28% 93% 88% 63% 88% 76%

x4 -40% 45% 45% 100% 93% 35% 3% 18% -1% 20% 5% 9% 17% 35%

x5 -37% 65% 63% 93% 100% 66% 30% 7% -9% 45% 26% 40% 39% 57%

x6 -12% 78% 72% 35% 66% 100% 74% -20% -20% 79% 59% 88% 69% 77%

x7 -25% 70% 66% 3% 30% 74% 100% 7% 13% 77% 68% 81% 72% 58%

x8 -63% -15% -14% 18% 7% -20% 7% 100% 79% -21% -15% -13% -23% -39%

x9 -54% -28% -28% -1% -9% -20% 13% 79% 100% -31% -30% -8% -30% -44%

x10 -21% 94% 93% 20% 45% 79% 77% -21% -31% 100% 94% 79% 92% 78%

x11 -22% 88% 88% 5% 26% 59% 68% -15% -30% 94% 100% 61% 89% 64%

x12 -10% 68% 63% 9% 40% 88% 81% -13% -8% 79% 61% 100% 64% 69%

x13 -17% 88% 88% 17% 39% 69% 72% -23% -30% 92% 89% 64% 100% 70%

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x14 6% 79% 76% 35% 57% 77% 58% -39% -44% 78% 64% 69% 70% 100%

Wal-Mart Sales

Econometric Analysis

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Part IV: Regression 3 Following is the summary output of the regression 3. Regression Statistics Multiple R 0.55637629 R Square 0.30955458 Adjusted R Square 0.22187897 Standard Error 0.04871806 Observations 143 ANOVA df

MS 0.00838 0.002373

F 3.530681

Standard Error 0.086435 0.001213 0.007505

t Stat 1.471144 0.14376 1.400746

P-value 0.143745 0.88592 0.163748

0.007555

-1.65666

0.100076

0.000419 0.000364 0.017593 0.003178 8.25E-05 0.00184

-3.45889 2.988242 -1.43381 0.541975 0.993048 1.190241

0.000741 0.003374 0.154105 0.588793 0.32259 0.23619

0.001372

-0.99728

0.320541

0.001343

-0.98508

0.326474

0.000139

-1.77712

0.077961

7.89E-05

1.172521

0.2432

X Variable 14

9.2486E-05 -1.7361E05

1.49E-05

-1.1655

0.246019

X Variable 15

2.2746E-06

1E-06

2.274668

0.024616

X Variable 16

1.7078E-08

1.23E-08

1.385531

0.168338

Regression Residual Total

Intercept X Variable 1 X Variable 2 X Variable 3 X Variable 4 X Variable 5 X Variable 6 X Variable 7 X Variable 8 X Variable 9 X Variable 10 X Variable 11 X Variable 12 X Variable 13

16 126 142

Coefficients 0.12715894 0.00017445 0.01051257 0.01251542 0.00144774 0.00108883 -0.0252253 0.00172228 8.1943E-05 0.00218985 0.00136803 0.00132252 0.00024756

SS 0.134078 0.299055 0.433133

Significance F 3.12103E-05

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Regression 4 Following is the summary output of the regression 4. Regression Statistics Multiple R 0.520120024 R Square 0.270524839 Adjusted R Square 0.226974083 Standard Error 0.048558299 Observations 143 ANOVA df

SS

Regression Residual Total

8

0.117173219

134 142

0.31595972 0.433132939

Coefficients

F 6.21171397 7

P-value 0.00175319 8 0.45867939 2 0.30717358 3 0.00012348 4 5.42361E05 0.00185683 0.02516273 6 0.06015950 5 0.79508657 6

0.227716535

0.071310393

X Variable 1

0.00421282

0.005668712

t Stat 3.19331 5 0.74317 1

X Variable 2

-0.005142913

0.005017097

-1.02508

X Variable 3

-0.0011185

0.000282818

X Variable 4 X Variable 5

0.001177037 -0.045665729

0.000282221 0.014381006

-3.95484 4.17062 7 -3.17542

X Variable 6

-0.000187854

8.29642E-05

X Variable 7

9.86155E-07

5.20219E-07

X Variable 8

2.24494E-09

8.62679E-09

Intercept

Standard Error

MS 0.01464 7 0.00235 8

-2.26428 1.89565 3 0.26022 9

Significance F 8.11294E07

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Part V: Breusch-Pagan test: Regression Statistics Multiple R 0.252974374 R Square 0.063996034 Adjusted R Square 0.0081152 Standard Error 0.004096669 Observations 143 ANOVA df Regression Residual Total

Intercept X Variable 1 X Variable 2 X Variable 3 X Variable 4 X Variable 5 X Variable 6 X Variable 7 X Variable 8

8 134 142

Coefficients 0.008096904 0.000369668 0.000216165 -7.11742E07 0 0.001188953 0 0 0

SS 0.00015376 0.002248882 0.002402641 Standard Error 0.006016173 0.000478247 0.000423272 2.38602E-05 2.38098E-05 0.001213268 6.99936E-06 4.38888E-08 7.27808E-10

MS 1.92199E-05 1.67827E-05

F 1.145223322

t Stat 1.345856368 0.772965274 0.510699851 0.029829667 0 0.979959067 0 0 0

P-value 0.180621491

Significance F 0.337404081

0.440904263 0.610401571 0.976247281 1 0.328872274 1 1 1

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White Test: Regression Statistics Multiple R 0.039348536 R Square 0.001548307 Adjusted R Square -0.00558349 Standard Error 0.04699267 Observations 142 ANOVA df Regression Residual Total

1 140 141

Coefficients Intercept X Variable 1

0.000561449 0.038964542

SS 0.000479422 0.309163549 0.309642972

MS 0.000479422 0.002208311

F 0.21709916

Standard Error

t Stat

P-value

0.003943545 0.083625843

0.142371653 0.465939009

0.88699114 0.641983254

Significance F 0.641983254

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Wal-Mart Sales

Econometric Analysis

MSF 562

References: 1. Wooldridge J. M. , (2006), Introductory Econometrics –3rd Edition 2. Baumohl B., (2007), The secrets of economic indicators –– 2nd Edition 3. Morey E. (2003), Econ 6818: Econometric Methods and Applications. Retrieved: February 15, 2008, from University of Colorado. Website: http://www.colorado.edu/Economics/morey/6818/student/6818proj.html 4. Bureau of Economic Analysis. Retrieved: February 15 th, 2008. Website: http://www.bea.gov/ 5. Federal Research Economic Data. Retrieved: January 30th, 2008. Website: http://research.stlouisfed.org/fred2/

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