UI AgEc 302 Spring 2008

1. UI AgEc 302 Spring 2008 Lecture #5 Introduction to Econometric Analysis Instructor: Yuliya Bolotova yuliyab@uidaho.edu

2. 2 Lecture Outline Econometric Analysis Introduction Procedure to perform econometric analysis Example: retail demand for poultry (HW#6) Regression Analysis Simple and Multiple Regression Models Ordinary Least Squares (OLS) Estimator Hypotheses Testing Forecasting Techniques

3. 3 Econometrics Econometrics develops and applies statistical techniques to analyze various economic relationships using data Econometric analysis is used to test hypotheses developed by economic theories to estimate and explain economic relationships to evaluate business activities and government policies to predict and forecast economic relationships

4. 4 Economic Relationships: Examples Demand Function Quantity = f(Price, Psubst, Pcompl, Income) Supply Function Quantity = f(Price, Pinputs, Tech, Weather) Yield-Response Function Yield = f(N, P, K) Revenue Function Revenue = f(Quantity, ADV, MarketShare)

5. 5 Econometric Analysis: Procedure Identify and formulate a question of interest you are the one who identifies the problem you are asked to perform a project

6. 6 Econometric Analysis: Procedure (cont.) 2. Construct an economic model by writing down a mathematical expression (equation) use formal economic theories, when possible use your intuition & economic reasoning specify the dependent variable (RHS; Y) and a set of independent (explanatory) variables (LHS; X)

7. 7 Econometric Analysis: Procedure (cont.) 3. Construct an econometric model based on the economic model and data available specify the functional form of the model take into account data available are the parameters (coefficients) to be estimated the error term (a distinct feature of any econometric model)

8. 8 Econometric Analysis: Procedure (cont.) 4. Formulate a set of hypotheses you will test using the econometric model usually address the sign (direction) effect between the dependent variable and an explanatory variable use the underlining theory or economic reasoning to formulate the hypotheses a reasonable magnitude of the estimated coefficients is expected

9. 9 Econometric Analysis: Procedure (cont.) 5. Collect data on the relevant variables Data choice depends on the question of interest Data sources: internet (USDA, Economic Census, etc.), experiments, surveys of people, surveys or literature, etc. Types of data Time-series data (example: monthly prices at the same location) Cross-sectional data (prices at different locations during the same period of time) Pooled (panel) data: a combination of the two types

10. 10 Econometric Analysis: Procedure (cont.) 6. Estimate the econometric (empirical) model there are several software programs that estimate empirical models and conduct statistical tests (Excel, STATA, SAS, Shazam, SPSS, etc.) There are different estimation procedures (OLS, Logit, Tobit, etc.) 7. Conduct statistical tests

11. 11 Econometric Analysis: Procedure (cont.) 7. Interpret the estimation results interpret the results in a way that other people can understand what you are talking about Pay attention to the following aspects the explanatory power of the model magnitude of the estimated coefficients (reasonable or unreasonable) signs of the estimated coefficients (support or contradict the stated earlier hypotheses) statistical significance of the estimated coefficients Discuss implications of the results for a business decision-making or a policy decision-making process (depending on your research question)

12. 12 Example: Step 1. A Question of Interest Retail Demand for Poultry You represent a consulting firm. An agribusiness company involved in poultry production and distribution has asked you to analyze the retail demand for poultry In particular, the firm is interested in factors influencing the quantity of poultry demanded (consumed) impact of changes in poultry price on the retail demand for poultry impact of changes in prices of products-substitutes on the retail demand for poultry impact of changes in consumer income on the retail demand for poultry

13. 13 Example: Step 2. Economic Model We use consumer theory to specify the appropriate economic model Qpoultry = f(Ppoultry, Psubstit., Income) beef and pork are major products-substitutes for poultry The final specification of our economic model: Qpoultry = f(Ppoultry, Pbeef, Ppork, Income) at this stage we do not know anything about the functional form of f

14. 14 Example: Step 3. Econometric Model Quantity of poultry demanded is the dependent variable Prices and income are independent (explanatory) variables Alpha (a or �0) and Betas (�) are the parameters to be estimated; the former is known as the intercept (constant) e is the error term (a distinct feature of econometric models) contains unobserved factors that are not included in the model this model assume a linear relationship between the dependent variable and each of the explanatory variables

15. 15 Example: Step 4: Hypotheses In this particular example, the hypotheses are formulated using the theory of consumer demand The estimated coefficient for Ppoutlry is expected to be negative (own-price effect) The estimated coefficients for Pbeef and Ppork are expected to be positive (cross-price effects of product substitutes) The estimated coefficient for Income is expected to be positive

16. 16 Example: Step 5. Data US Department of Agriculture (USDA) Economic Research Service (ERS) is the major source of data for this and similar projects http://www.usda.gov/wps/portal/usdahome http://www.ers.usda.gov/AboutERS/ This project data http://www.ers.usda.gov/Data/FoodConsumption/ http://www.ers.usda.gov/Data/FoodConsumption/spreadsheets/mtpoulsu.xls#Poultry!A1

17. 17 Example: Step 6. Estimation of Empirical Model Step 7. Statistical Tests The ordinary least squares (OLS) estimation procedure is one of the most widely used empirical techniques Excel can be used to estimate regression models using OLS It also conducts major statistical tests You have to learn how to interpret the regression output HW#6 Modified estimation results (next slide)

18. 18 Example: Step 6 and 7 Estimation and Tests

19. 19 Example: Step 8. Interpretation  of the Estimation Results Evaluate the explanatory power of the empirical model Do the signs of the estimated coefficients support the stated hypotheses? (HW#6) If no, what are the possible reasons? Data problem, misspecification of the model or changes in consumer preferences? Interpret the magnitude and signs of the estimated coefficients (HW#6) Interpret the statistical significance of the estimated coefficients (to be learned) (HW#6)

20. 20 Example: Step 8. Interpretation  of the Estimation Results (cont.)

21. 21 Example: Step 8. Interpretation  of the Estimation Results (cont.) The coefficient for Ppoultry is: -0.820 Correct interpretation: If retail price of poultry increases by 10 cents per pound, the quantity of poultry demanded decreases by 8.2 pounds per person per year Incorrect interpretation: If P increases by 10, Q decreases by 8.2

22. 22 Example: Step 8. Interpretation  of the Estimation Results (cont.) Problems with this interpretation: The model includes prices of poultry, beef and pork; which one do you mean? The model includes three types of meat; quantity of which type do you discuss? Units??? a few pounds of poultry demanded per person per year is different from several tons demanded by a market segment consisting of thousands of consumers Is price measured in $ or cents? Is it $ per pound or $ per ton?

23. 23 Regression AnalysisTypes of Regression Models Simple Regression Model: studies the relationship between one dependent variable and one independent variable Linear Reg Model: The coefficient (beta) is marginal effect (dY/dX) Log-Linear Reg Model: The coefficient (beta) is elasticity

24. 24 Types of Regression Models Multiple Regression Model: studies the relationship between one dependent variable and two or more independent variables Linear : The betas are marginal effects (dY/dX1,dY/dX2,�) Log-Linear: The betas are elasticities (Ey,x1; Ey,x2; �)

25. 25 Simple Linear Regression Model: Example the model assumes a linear relationship between the yield and the amount of phosphorus applied the model states that the amount of P applied explains the level of yield all other determinants of the yield that are not in the model are captured by the error term amount of nitrogen and/or potassium applied soil productivity, crop rotation weather, etc

26. 26 Multiple Linear Regression Model: Example the model assumes a linear relationship between the yield and the amount of phosphorus and potassium applied the model states that the amount of P and K applied explain the level of yield all other determinants of the yield that are not in the model are captured by the error term amount of nitrogen applied soil productivity, crop rotation, weather, etc

27. 27

28. 28 Regression Analysis Explanations of the equation terms Y - a column of observations for the dependent variable (Y1, Y2, �Yn) X1 � a column of observations for independent variable X1 (X11, X12,�X1n) X2 � a column of observations for independent variable X2 (X21, X22,�X2n) e � a column of errors (e1, e2, �, en) N - the number of observations

29. 29 Regression Analysis (cont.) Collect data on the dependent variable (Y) and a set of independent variables (Xs) The error term is calculated after a model has been estimated To estimate an econometric model: The number of the estimated coefficients has to be less than the number of observations. To get reliable results, you should have at least 30 observations

30. 30 The number of observations:Example of Time-Series Data Analysis of milk prices in Idaho over time (40 years) Yearly prices: an observation is a price corresponding to a particular year The number of observations = 40 Monthly prices: an observation is a price corresponding to a particular month The number of observations = 40*12months = 480 Daily prices: an observation is a price corresponding to a particular day The number of observations is 40*12*30 = 14,400

31. 31 The number of observations: Example of Cross-Sectional Data  The average milk prices in 2007 in 50 States The number of observations is 50 The average milk prices in 2007 at the county level The number of observations = the number of counties in the US

32. 32 The number of observations: Example of Panel (Pooled) Data Monthly milk prices in 2007 in 50 States The number of observations = 50States*12months=600 Daily milk prices in 2007 in 50 States The number of observations = 50States*12months*30days=18,000

33. 33 The Ordinary Least Squares (OLS) Estimation Procedure

34. 34 The OLS Estimation Procedure An estimator is a formula used to calculate the coefficients for the variables included in a regression model The OLS estimator minimizes the sum of squared errors (residuals) The OLS determines the values of the coefficients such that the sum of squared errors is minimized an unconstrained optimization (minimization) problem

35. 35 The OLS Estimation Procedure (cont.) Handout #1 A simple regression model of the retail demand for poultry

36. 36 Handout #1

37. 37 Handout #1 (cont.)

38. 38 Handout #1 (cont.)

39. 39 Handout #1 (cont.) The predictive (forecasting) power of regression models: Sample Mean Forecast Error (U) The smaller the error, the better is the accuracy of the model Yi -hat is the predicted value for the Yi Our example:

40. 40 Regression Output Handout #2 Regression Output: Interpretation Retail Demand for Poultry

41. 41 Regression Output: R Square Coefficient of Determination Characterizes explanatory power of regression models Range [0; 1] or [0%; 100%]

42. 42 Regression Output: Estimated Coefficients A simple regression model

43. 43 Regression Output: Estimated Coefficients Interpretation of the coefficients: Take any value (positive, 0, negative) Linear models: The coefficients are Marginal Effects Log-linear models: The coefficients are Elasticities Positive Coefficient (Linear Model) If X increases by 1 unit, Y increases by units If X decreases by 1 unit, Y decreases by units Negative Coefficient (Linear Model) If X increases by 1 unit, Y decreases by units If X decreases by 1 unit, Y increases by units

44. 44 Regression Output: Standard Errors Each estimated coefficient has associated standard error Standard error (S.E.) is the square root of the variance associated with a particular coefficient is always positive usually is not interpreted is used to calculate T-Static

45. 45 Regression Output: T-Statistic Each estimated coefficient has a corresponding T-Statistic (T-value) T-Statistic (T-test) is used to judge the statistical significance of the estimated coefficients take any value (positive & negative) has the same sign as the corresponding estimated coefficient

46. 46 Regression Output: T-Test Procedure Step 1: Formulate the null (Ho) and the alternative (Ha) hypotheses: Ho: and Ha: We are interested in rejecting Ho in favor of Ha In this case, the estimated coefficient is statically significant from zero Step 2: Choose a significance level (alpha): the probability of rejecting Ho when it is true commonly used levels are 10%, 5%, or 1% is needed to choose the cut-off value of T-Stat.

47. 47 Regression Output: T-Test Procedure (cont.) Step 3: Choose the cut-off T-value (2-tail test): |1.65| if 10%; |1.96| if 5%; |2.58| if 1% Step 4: Compare the regression output T-value with the chosen cut-off T-value If |T| > |1.65|, then Ho is rejected in favor of Ha an estimated coefficient is statistically significant If |T| < |1.65|, then Ho is failed to be rejected in favor of Ha an estimated coefficient is NOT statistically significant

48. 48 Regression Output: Summary Conclude on the overall performance of the analyzed model. Put all pieces of information together Explanatory power of the model (R2) Magnitude of the estimated coefficients Signs of the estimated coefficients Statistical significance of the estimated coefficients

49. 49 Interpretation of Reg. Output: Example Ordinary demand for poultry: Q(P) A simple linear regression model The estimated equation is

50. 50 Interpretation of Reg. Output: Example Coefficient of determination R2 = 0.93 The variation in the price of poultry explains 93% of the variation in the quantity of poultry demanded The estimated coefficient for Ppoultry is -0.76 If price of poultry increases by 1 cent per pound, the quantity of poultry demanded decreases by 0.76 pounds per person per year.

51. 51 Interpretation of Reg. Output: Example Statistical Significance of the estimated coefficient for Ppoultry Associated T-value is -12.85 Use a 10% significance level ? |1.65| cut-off T-value Compare the Reg Output T-value with the cut-off: |12.85| > |1.65| Conclusion: Reject Ho in favor of Ha the estimated coefficient for Ppoultry is statistically significant at a 10% alpha level

52. 52 Interpretation of Reg. Output: Example Summary the estimated model has a high level of explanatory power the estimated coefficient for the price of poultry is statistically significant the magnitude of the coefficient is reasonable the sign of the estimated coefficient is negative, as expected ? the estimation results are relatively reliable

53. 53 Interpretation of Reg. Output: Example Use the estimation results to predict the quantity of poultry demanded at a price of poultry equal to $0.95 and $1.20 per pound

54. 54 Interpretation of Reg. Output: Example If the price increases from $0.90 per pound to $1.20 per pound, the quantity of poultry demanded decreases from 57.8 pounds to 38.8 pounds per person per year Agribusiness firms can use the results in the strategic management decision-making process the results are helpful because they can be used to quantify possible changes and to predict the quantity demanded under different scenarios. consequently, it is possible to project sales and profit.

55. 55 Forecasting Techniques

56. 56 Forecasting Techniques Analysis of economic variables evolving over time Qualitative Analysis Expert opinions Surveys; interviews Regression (Econometric) analysis Trend Analysis (linear trend analysis) Time-Series Regression Analysis

57. 57 Econometric Analysis Advantages of using econometric analysis You can include in a regression model a set of independent variables (Xs) that you believe explain the behavior of a variable you analyze the forecast results based on this model are more accurate than the qualitative analysis results You can conduct a series of statistical tests to examine the predictive (forecasting) power of the alternative econometric models to test statistical significance of the estimated coefficients (effects)

58. 58 Trend analysis Trend analysis examines historical behavior of economic variables uses the results to project the future behavior based on the historical experience

59. 59 Trend Analysis (cont.) Yt is the analyzed variable T � trend (= 0,1,2,3�) T = 0 for Y1, T=1 for Y2, T = 3 for Y3, etc Trend represents time periods (years, months, days, hours �) --- historical experience Linear trend analysis:

60. 60 Trend Analysis (cont.) Time-Series data Yearly, quarterly, monthly, daily data for the same location/business entity/region a group of countries, a single country, a region, a group of companies, an individual firm (farm) Variables: Sales, Profit, Revenue, Output & Input Prices, etc You will not use trend analysis to examine the data that are not time-series Crop yield, animal weight, sales across different regions during the same period of time

61. 61 Trend Analysis (cont.) Trend equations are estimated to be used for prediction or forecasting purposes Potential forecasting problems with TREND The forecast relies on historical information It assumes that what happened in the past will happen in the future This is not always true in Agriculture/AgBusiness Economic and legal environment is changing International trade, changes in farm policy, structural changes in the food supply chain, changing consumer preferences Future will be different from what has happened in the past

62. 62 Econometric Methods Any regression model you estimate can be used to explain the economic variable (relationship) you are analyzing can be used to predict the values of the variable of interest under different scenarios Example: Retail Demand for Poultry Time-series models are also used to forecast the behavior of economic variables for future periods Example: Feed Barley Price Analysis

63. 63 Econometric Methods (cont.) To calculate a predicted value of Y or to forecast a future value of Y substitute the level of X�s you are interested in into the estimated equation to calculate the value of Y at these levels of X�s

64. 64 Econometric Methods: Predicting and Forecasting Examples: Handout #3 Forecasting Idaho Feed Barley prices Homework #9 Forecasting Idaho Milk Prices Homework #6 Predicting US retail demand for poultry