Econometrics

1. Econometrics Degree of Business Administration and Management

2. What is econometrics? Econometric models Types of econometric models Assumptions of the econometric model

3. 1. Econometrics Etymology of the word • Econometrics = oiko-nomos + metrics rule for the domestic administration + to measure • Therefore, econometrics means the measurement of the economy • Greene’s definition

4. Definitions Econometrics is the application of mathematics, statistical methods, and computer science, to economic data and is described as the branch of economics that aims to give empirical content to economic relation M. Hashem Pesaran (1987). "Econometrics, “ The New Palgrave: A Dictionary of Economics, v. 2, p. 8 [pp. 8-22].

5. Definitions Econometrics is the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference. P. A. Samuelson, T. C. Koopmans, and J. R. N. Stone (1954). "Report of the Evaluative Committee for Econometrica," Econometrica 22(2), p. 142. [p p. 141-146],

6. Definitions Econometrics is the branch of economics concerned with the use of mathematics to describe, model, prove, and predict economic theory and systems. wikibook

7. Econometrics This a very powerful tool which can help us to: • Finding causal relationship between variables (sales vs. Prices, rent…) • Knowing the effect of a particular variable on the evolution of our objective variables (marketing effort over sales. ) • Quantifying any aspect of very important business variables. (Cost function, Production function…) • Forecasting the evolution of an economic variable (sales).

8. 2. Econometric Models We need an economic problem Then, we need some data: • Dependent variable: the variable we want to study (y) • Some explanatory variables (x1, x2, …, xk) • A set of parameters that can measure the response of the dependent variable when the explanatory variables changes (b1, b2, …, bk)

9. 2. Econometric Models Let us assume that we dispose of a sample of size T, t=1, …, T, for all the abovementioned variables. Thus, we need the following data set: y1, y2, …, yT x11, x12, …, x1T x21, x22, …, x2T …………………. xk1, xk2, …, xkT

10. 2. Econometric model We can link the dependent variable and the explanatory variables as follows: y1 = b1 x11 + b2 x21 + … + bk xk1 y2 = b1 x12 + b2 x22 + … + bk xk2 ………………………………… yT = b1 x1T + b2 x2T + … + bk xkT

11. 2. Econometric Models We can express it in a compact way: Y= X b

12. 2. Econometric models Alternatively, we can also use the following expression yt = xt’b where xt’ = (x1t, x2t,…, xkt)

13. 2. Econometric Models However, these are not econometric models, given that: • The relationship Y= X b is an identity. Then, this is a mathematical model. • Economics invite us to think in stochastic terms, rather than in deterministic ones. Why? • Then, we need a random component • We should include a random vector (u) in the precedent equations

14. 2. Econometric models • The vector u is perturbation that has a stochastic nature. • It incorporates the effect of all the variables that may explain a little proportion of the evolution of the dependent and, therefore, are not include in the econometric model for the purposes of simplicity.

15. 2. Modelos econométricos Thus, an econometric model can be stated as follows: y1 = b1 x11 + b2 x21 + … + bk xk1 + u1 y2 = b1 x12 + b2 x22 + … + bk xk2 + u2 ………………………………… yT = b1 x1T + b2 x2T + … + bk xkT + uT

16. 2. Econometric models But, we will always use this one. Which is the difference ? y1 = b1 + b2 x21 + … + bk xk1 + u1 y2 = b1 + b2 x22 + … + bk xk2 + u2 ………………………………… yT = b1 + b2 x2T + … + bk xkT + uT

17. 2. Econometric models Thus, the econometric model can be stated as follows: • y= X b + u • yt = xt’ b + ut X b is the systematic part u is the random part

18. 3. Types of econometric models Accordingly to the types of data, econometric models can be: • Time Series models • Cross-Section models • Pool of data or data panel models

19. 3. Types of models Time Series • These model studies the relationship of the variables across the time (t). • We have information for all the variables for a sample size of dimension T (t=1, 2…, T). yt = xt’b + ut t = 1,2,…, T • We can find problems of autocorrelation • Macroeconometric models (aggregated analysis).

20. 3. Types of models Cross-Section • We analyze the relationship between variables for a given and unique period of time. • We dispose of information for all the variables of N individuals (i= 1, 2, …, N) yi = xi’ b + ui i = 1,2,…, N • We can find problems of heteroskedasticity • Microeconometric models (individual analysis)

21. 3. Types of models Pool of data/Data panel • These models combine both time series and cross-section data • We dispose of information of k variables for N individuals and T periods of time. yit = xit’ b + uit t=1,2,…T. i = 1,2,…, N • If N>T, microeconometric models • If N<T, macroeconometric models

22. 4. Classical Assumptions Y = X b + u • E(ut) = 0,  t =1, 2, …, T • E(ut us) = 0,  t  s • Var(ut) = s2 ,  t • b is fixed • E(X) = X

23. 4. Classical Assumptions E(ut) = 0  t =1, 2, …, T • This implies that the mean of distribution of the perturbation is 0. • Its influence is 0 on average • Consequently, there are not specification errors.

24. 4. Classical assumptions E(ut us) = 0  t  s • The errors are not correlated. • Under the presence of normality, this implies independence. • If this assumption does not hold, then we have autocorrelation (big problem in time series).

25. 4. Classical assumptions Var(ui) = s2 ,  i= 1, 2, …, N • The distribution of the perturbation has a constant variance. • This assumption is commonly known as homoskedasticity. • It this does not hold, we have heteroskedasticity, a common problem in cross-section models.

26. 4. Classical assumptions The perturbation follows a Normal distribution. (This assumption is not strictly necessary, as we will see later). • Then, ut follows a N(0, s2) • The vector u follows a N(0, s2 I) • If this does not hold, we have problems of non normality. • There are less relevant than autocorrelation/heteroskedasticity.

27. 4. Classical assumptions • is a fixed vector of dimension kx1 b=(b1, b2, ..., bk)’ • The response of the dependent variable is constant when X changes across the time/individuals • We have structural permanence. • If this does not hold, we have structural change.

28. 4. Classical assumptions E(X) =X • The expectancy of the matrix of explanatory variables is the matrix X. • Then, the explanatory variables are not stochastic, but deterministic. • Then, this implies that these variables are exogenous. • If this does not hold, then we can have problems of endogeneity.