The backup regressions are given below
a. OLS regression of consumption on a constant and Income using EViews Dependent Variable: Consumption Method: Least Squares Sample: 1959 2007 Included observations: 49 b. The Breusch-Godfrey Serial Correlation LM …
Moment Generating Function (MGF)
a. For the Binomial Distribution, Mx(t) = E(eXt) = XX) eX‘0X (1 - 0) X=0 -X = [(1 - 0) + 0e‘] where the last equality uses the binomial expansion …
For parts (b) and (c), SAS will automatically compute confidence intervals for the mean (CLM option) and for a specific observation (CLI option), see the
SAS program in 3.17. 95% CONFIDENCE PREDICTION INTERVAL Dep Var Predict Std Err Lower95% Upper95% Lower95% Upper95% COUNTRY LNEN1 Value Predict Mean Mean Predict Predict AUSTRIA 14.4242 14.4426 0.075 14.2851 …
What is Econometrics?
This chapter emphasizes that an econometrician has to be a competent mathematician and statistician who is an economist by training. It is the unification of statistics, economic theory and mathematics …
Using EViews, Qt+i is simply Q(1) and one can set the sample range from 1954-1976
a. The OLS regression over the period 1954-1976 yields RSt = -6.14 + 6.33 Qt+1 - 1.67 Pt (8.53) (1.44) (1.37) with R2 = 0.62 and D. W. = 1.07. …
Moment Generating Function Method
a. If Xi,.., Xn are independent Poisson distributed with parameters (Xi) respectively, then from problem 2.14c, we have MXi (t) = eAi(e-1) for i = 1,2,... ,n n n Y …
Multiple Regression Analysis
4.1 The regressions for parts (a), (b), (c), (d) and (e) are given below. a. Regression of LNC on LNP and LNY Dependent Variable: LNC Analysis of Variance Sum of …
A Review of Some Basic Statistical Concepts
2.1 Variance and Covariance of Linear Combinations of Random Variables. a. Let Y = a + bX, then E(Y) = E(a + bX) = a + bE(X). Hence, var(Y) = …
The back up regressions are given below. These are performed using SAS
a. Dependent Variable: EMP Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 1 2770902.9483 2770902.9483 4686.549 0.0001 Error 73 43160.95304 591.24593 C Total 74 …
Best Linear Prediction. This is based on Amemiya (1994)
a. The mean squared error predictor is given by MSE = E(Y — a — "X)2 = E(Y2) + a2 + "2E(X2) — 2aE(Y) — 2"E(XY) + 2a"E(X) minimizing this …
Prediction
How is prediction affected by nonspherical disturbances? Suppose we want to predict one period ahead. What has changed with a general Q? For one thing, we now know that the …
Sample Selectivity
In labor economics, one observes the market wages of individuals only if the worker participates in the labor force. This happens when the worker’s market wage exceeds his or her …
Pooling Time-Series of Cross-Section Data
12.1 Introduction In this chapter, we will consider pooling time-series of cross-sections. This may be a panel of households or firms or simply countries or states followed over time. Two …
Grouped Data
In the biometrics literature, grouped data is very likely from laboratory experiments, see Cox (1970). In the insecticide example, every dosage level xi is administered to a group of insects …
The W, LR and LM Statistics Revisited
In this section we present a simplified and more general proof of W > LR > LM due to Breusch (1979). For the general linear model given in (9.1) with …
Sample Selection and Non-response
Non-response is a big problem plaguing survey data. Some individuals refuse to respond and some do not answer all the questions, especially on relevant economic variables like income. Suppose we …
The Error Components Model
The regression model is still the same, but it now has double subscripts yit = a + Xite + uit (12.1) B. H. Baltagi, Econometrics, Springer Texts in Business and …
Individual Data: Probit and Logit
When the number of observations ni in each group is small, one cannot obtain reliable estimates of the n^s with the p^s. In this case, one should not group the …
Seemingly Unrelated Regressions
When asked “How did you get the idea for SUR?” Zellner responded: “On a rainy night in Seattle in about 1956 or 1957, I somehow got the idea of algebraically …
Time-Series Analysis
14.1 Introduction There has been an enormous amount of research in time-series econometrics, and many economics departments have required a time-series econometrics course in their graduate sequence. Obviously, one chapter …
The Fixed Effects Model
If the Hi’s are thought of as fixed parameters to be estimated, then equation (12.1) becomes yit = a + Х'ив + S i=1 HiDi + v it (12.5) where …
The Binary Response Model Regressio
Davidson and MacKinnon (1984) suggest a modified version of the Gauss-Newton regression (GNR) considered in Chapter 8 which is useful in the context of a binary response model described in …
Seemingly Unrelated Regressions with Unequal Observations
Srivastava and Dwivedi (1979) surveyed the developments in the SUR model and described the extensions of this model to the serially correlated case, the nonlinear case, the misspecified case, and …
The Box and Jenkins Method
This method fits Autoregressive Integrated Moving Average (ARIMA) type models. We have already considered simple AR and MA type models in Chapters 5 and 6. The Box-Jenkins methodology differences the …
Maximum Likelihood Estimation
Under normality of the disturbances, one can write the log-likelihood function as NT N 1 L(a, в, ф2, cr2v) = constant----- logaV +--- log^2------- 2 UE-1u 2 2 2^v where …
Asymptotic Variances for Predictions and Marginal Effects
Two results of interest after estimating the model are: the predictions F(x'в) and the marginal effects dF/dx = f (Xв) в• For example, given the characteristics of an individual x, …
Simultaneous Equations Model
11.1 Introduction Economists formulate models for consumption, production, investment, money demand and money supply, labor demand and labor supply to attempt to explain the workings of the economy. These behavioral …
Vector Autoregression
Sims (1980) criticized the simultaneous equation literature for the ad hoc restrictions needed for identification and for the ad hoc classification of exogenous and endogenous variables in the system, see …
Empirical Example
Baltagi and Griffin (1983) considered the following gasoline demand equation: log Car = a + в ilog 7Ф + e2log ppMO + в 3log Cf + U (12.40) where Gas/Car …
Goodness of Fit Measures
There are problems with the use of conventional A2-type measures when the explained variable y takes on two values, see Maddala (1983, pp. 37-41). The predicted values р are probabilities …
Simultaneous Bias
Example 1: Consider a simple Keynesian model with no government Ct = a + f3Yt + Ut t = 1,2,...,T (11.1) Yt = Ct + It (11.2) where Ct denotes …
Trend Stationary Versus Difference Stationary
Many macroeconomic time-series that are trending upwards have been characterized as either Trend Stationary: xt = a + /3f + ut (14.10) or Difference Stationary: xt = 7 + xt_1 …
Testing in a Pooled Model
(1) The Chow-Test Before pooling the data one may be concerned whether the data is poolable. This hypothesis is also known as the stability of the regression equation across firms …
Empirical Examples
Example 1: Union Participation To illustrate the logit and probit models, we consider the PSID data for 1982 used in Chapter 4. In this example, we are interested in modelling …
The Identification Problem
In general, we can think of any structural equation, say the first, as having one left hand side endogenous variable y,g right hand side endogenous variables, and k right hand …
