Applied Econometrics Econometric modeling.

Applied Econometrics Econometric modeling.

1. Statement of Theory or Hypothesis Keynes stated: The fundamental psychological law . . . is that men are disposed, to increase their consumption as their income increases, but not as much as the increase in their income. Keynes postulates that the marginal propensity to consume (MPC), the rate of change of consumption for a unit (say, a dollar) change in income, is greater than zero but less than 1.

Applied Econometrics Econometric modeling. Specification of the Mathematical Model

The following form of the Keynesian consumption function might be suggested: Y = β1 + β2X with 0 < β2 < 1 where Y = consumption expenditure X = income, β1 and β2, parameters of the model, are, respectively, the intercept and slope coefficients.

Applied Econometrics Econometric modeling. Specification of the Mathematical Model

Applied Econometrics Econometric modeling. Specification of the Mathematical Model

The following form of the Keynesian consumption function might be suggested: Y = β1 + β2X 0 < β2 < 1 where Y = consumption expenditure X = income, β1 and β2, parameters of the model, are, respectively, the intercept and slope coefficients.

Applied Econometrics Econometric modeling. Specification of the Mathematical Model This purely mathematical model of the consumption function given in is of limited interest, for it assumes an exact or deterministic relationship between consumption and income.In reality the relationships between economic variables are generally inexact. If we were to obtain data on consumption expenditure and disposable income of a sample of, say, 500 American families and plot these data on a graph paper with consumption expenditure on the vertical axis and disposable income on the horizontal axis, we would not expect all 500 observations to lie exactly on the straight line of Eq. (I.3.1) because, in addition to income, other variables affect consumption expenditure.

To allow for the inexact relationships between economic variables, the econometrician would modify the deterministic consumption function as follows:

Y = β1 + β2X + u

Applied Econometrics Econometric modeling. The data

Applied Econometrics Econometric modeling. Estimation of the Econometric Model Next task is to estimate the parameters of the consumption function. The numerical estimates of the parameters give empirical content to the consumption function. The statistical technique of regression analysis is the main tool used to obtain the estimates. Using this technique and the data given we obtain the following estimates of β1 and β2, namely, −184.08 and 0.7064. Thus, the estimated consumption function is: Yˆ = −184.08 + 0.7064Xi From this figure we see that for the period 1982–1996 the slope coefficient (i.e., the MPC) was about 0.70, suggesting that for the sample period an increase in real income of 1 dollar led, on average, to an increase of about 70 cents in real consumption expenditure

Applied Econometrics Econometric modeling. Specification of the Mathematical Model

Applied Econometrics Econometric modeling. Specification of the Mathematical Model From this figure we see that for the period 1982–1996 the slope coefficient (i.e., the MPC) was about 0.70, suggesting that for the sample period an increase in real income of 1 dollar led, on average, to an increase of about 70 cents in real consumption expenditure. We say on average because the relationship between consumption and income is inexact. According to our data, the average, or mean, consumption expenditure went up by about 70 cents for a dollar’s increase in real income.

Applied Econometrics Econometric modeling. Hypothesis Testing Assuming that the fitted model is a reasonably good approximation of reality, we have to develop suitable criteria to find out whether the obtained estimates are in accord with the expectations of the theory. Milton Friedman: « a theory or hypothesis that is not verifiable by appeal to empirical evidence may not be admissible as a part of scientific enquiry » Keynes expected the MPC to be positive but less than 1.The estimated MPC is 0.70. Before we accept this finding as confirmation of Keynesian consumption theory, we must enquire whether this estimate is sufficiently below unity to convince us that this is not a chance occurrence or peculiarity of the particular data we have used. In other words, the question is : Is 0.70 statistically less than 1? If it is, it may support Keynes’ theory. Confirmation or refutation of economic theories on the basis of sample evidence is based on a branch of statistical theory known as statistical inference (hypothesis testing). The contents of the course is how this inference process should be conducted.

Applied Econometrics Econometric modeling. Forecasting or Prediction If the chosen model does not refute the hypothesis or theory under consideration, we may use it to predict the future value(s) of the dependent, or forecast, variable Y on the basis of known or expected future value(s) of the explanatory, or predictor, variable X. To illustrate, suppose we want to predict the mean consumption expenditure for 1997. The GDP value for 1997 was 7269.8 billion dollars. Putting this GDP figure on the right-hand side of the estimated equation, we obtain: Yˆ1997 = −184.0779 + 0.7064 (7269.8) = 4951.3167 Thus given the value of the GDP, the mean,or average, forecast consumption expenditure is about 4951 billion dollars. The actual value of the consumption expenditure reported in 1997 was 4913.5 billion dollars. The estimated model overpredicted the actual consumption expenditure by about 37.82 billion dollars. We could say the forecast error is about 37.82 billion dollars, which is about 0.76 percent of the actual GDP value for 1997.

Applied Econometrics Econometric modeling. Use of the Model for Control or Policy Purposes Suppose that, as a result of the proposed policy change, investment expenditure increases. What will be the effect on the economy? As macroeconomic theory shows, the change in income following, say, a dollar’s worth of change in investment expenditure is given by the income multiplier M, which is defined as

If we use the MPC of 0.70 obtained from the regression, this multiplier becomes about M = 3.33. That is, an increase (decrease) of a dollar in investment will eventually lead to more than a threefold increase (decrease) in income;

Applied Econometrics Econometric modeling. Use of the Model for Policy simulation Suppose we have the estimated consumption function. Suppose further the government believes that consumer expenditure of about 4900 (billions of 1992 dollars) will keep the unemployment rate at its current level of about 4.2 percent (early 2000). What level of income will guarantee the target amount of consumption expenditure? If the regression results seem reasonable, simple arithmetic will show that 4900 = −184.0779 + 0.7064X which gives X = 7197, approximately. That is, an income level of about 7197 (billion) dollars, given an MPC of about 0.70, will produce an expenditure of about 4900 billion dollars.

Applied Econometrics Econometric modeling. Use of the Model for Policy simulation and evaluation

The simulation of the possible outcomes of using complex econometric models Simulation ex ante (microsimulation models) Monitoring and ex post evaluation of policy impact

Types of data and data basis Cross-section data Time series data Panel Data. Cross section – time series data Cross section – time series grouped data (pseudo panels)

Types of data and data basis Cross-section data Cross section: every observation is a new unity (economic agents: individuals, enterprises, countries…) with information associated with one time unit

The data are supposed random otherwise correction for selection

Types of data and data basis Cross-section data

Types of data and data basis Time series data Time series data main characteristic: one observation=one time period year, month, week, day, second… Time series are not random data – some particular problems have to be discussed. The specicficity ot thease data is the analysis of trends, seasonal variations, volatility, persistence and dynamics of observed phenomena.

Types of data and data basis Time series data

Types of data and data basis Time series-cross section data

The cross-section data for several periodes can be “pooled” (Surveys repeated in several years can be stacked when the common variables are identified. The new data base from pooled surveys forms a special case of a cross- section with control of time dimension (this kind of data sometimes is called “panel” (international economy)

Types of data and data basis Time series-cross section data

Types of data and data basis panels The same individual (observation unit) is observed during a period of time (several yars, months, days…). The most often it concerns survey type data (random sample). Problem: attrition (balanced and not balanced panels)

Types of data and data basis panels

Types of data and data basis pseudo-panels

Pseudo-panels: structure is identical as panel data but individual are grouped (clustered).

Types of data and data basis pseudo-panels

Data analysis and processing

Missing values (prediction and matching methods) Measurment errors (instrumental varibles approach) Outliers (correcting for unusual observations) Selection biais (correcting for non random subsamples) Combining (matching) datasets

Outliers Atypical dependent variable (Y) observations (large residuals)

Outliers

Atypical independent (X) variable observations (leverage points)