Schema degli appunti presi in aula di Econometria

Forecasting and error measures

The expression of RMSFE is given by:

√2[ ]^( )−RMSFE= E Y Y+1T T+ 1∨T

Steps for re-estimation and forecast

• Choose a date P for the start of the poos sample
• Re-estimate the model every period s = P-1, … , T-1
• Compute the poos forecast for S+1= P,…,T
• Compute the poos forecast errors = Y_s+1 - u_s+1 | Y_s+1|s

Compute the average of the squared forecast errors and then take its squared root.

Model estimation and exogeneity

X is exogenous if E(u | X_t, X_t–1, X_t–2, ...) = 0.

Strict Exogeneity: X is strictly exogenous if E(u | ..., X_t+1, X_t, X_t–1, ...) = 0.

Elasticity of production

β₁ e β₂ rappresentano l’elasticità della produzione rispettivamente al capitale ed al lavoro. Ciò significa che ad una variazione percentuale in K o L rispettivamente β₁ β₂ comporta una variazione in Y pari a % o %.

Sample autocorrelations

The jth sample autocorrelation is an estimate of the jth population autocorrelation. Write an auto regressive model of second order:

= β₀ + β₁ y_t−1 + β₂ y_t−2 + u

ADL(2,2) model

= β₀ + β₁ y_t−1 + β₂ y_t−2 + β₃ x_t−1 + β₄ x_t−2 + u

Binary variable impact

β₀ represents the expected value for a student when D=0.

β₁ represents the difference between the expected value E(Yi|Di=1) – E(Yi|Di=0).

Granger causality

In the 06 self evaluation (ex 4 point c), the Granger causality test is commonly known as such. This name can be misleading because it is not a causality test. It is a forecasting ability test.

Dynamic and cumulative multipliers

Write the dynamic and cumulative multipliers and draw the graph:

• Lag number: Dynamic multipliers CI
• 0: 1.2 ± 1.96 * 0.3
• 1: 0.3 ± 1.96 * 0.2
• 2: 0.1 ± 1.96 * 0.2
• 3: -0.1 ± 1.96 * 0.2

Lag numbers Cumulative DM CI

• 0: 1.2 ± 1.96 * SE(δ₁)
• 1: 1.5 ± 1.96 * SE(δ₂)
• 2: 1.6 ± 1.96 * SE(δ₃)
• 3: 1.5 ± 1.96 * SE(δ₄)

The cumulative dynamic multipliers can be estimated directly using a modification of the original regression. The SE needed to compute the required SE are therefore:

^SE(δ₁) …

Omitted variable

₂ > 0 > 0

Over Under

Cov(₂, ₁) > 0

Under Over

Cov(₂, ₁) < 0

Exercise chapter 9

This assumption implies that measurement error does not comove with the true unobserved variable. This might not be the case if the difference between the true and the reported value depends on the true value.

Chapter 15