洪永淼计量经济学讲义_ch10

CHAPTER10CONCLUSION

Key word:Microeconometrics,Financial econometrics,Nonparametric econometrics,Panel data econometrics,Time series econometrics.

Abstract:In this chapter,we…rst review what we have covered in the previous chapters,and then discuss other econometric courses needed for various…elds of economics and…nance. 10.1Summary of Course Materials

Question:What have we learnt from this course?

In this chapter,we will…rst summarize what we have learnt in this book.

The modern econometric theory developed in this book is built upon the following funda-mental axioms:

Any economy can be viewed as a stochastic process governed by some probability law. Any economic phenomena can be viewed as a realization of the stochastic economic process. The probability law of the data generating process can be called the“law of economic motions.”The objective of econometrics is to infer the probability law of economic motions using observed data,and then use the obtained knowledge to explain what has happened,to predict what will happen,and to test economic theories and economic hypotheses.

Suppose the conditional pdf f(y t j t 1);where t 1=(X t;Z t 1);is available.Then we can obtain various attributes of the conditional distribution of Y t given t 1,such as

conditional mean;

conditional variance;

conditional skewness;

conditional kurtosis;

conditional quantile.

An important question in economic analysis is:what aspect of the conditional pdf will be im-portant in economics and…nance?Generally speaking,the answer is dictated by the nature of the economic problem one has at hand.For example,the e¢cient market hypothesis states that the conditional expected asset return given the past information is equal to the long-run market

average return;rational expectations theory suggests that conditional expectational errors given the past information should be zero.In unemployment duration analysis,one should model the entire conditional distribution of the unemployment duration given the economic characteristics of the unemployed workers.

It should be emphasized that the conditional pdf or its various aspects only indicate a predic-tive relationship between economic variables,that is,when one can use some economic variables to predict other variables.The predictive relationship may or may not be the causal relationship between or among economic variables,which is often of central interest to economists.Economic theory often hypothesizes a causal relationship and such economic theory is used to interpret the predictive relationship as a causal relationship.

Economic theory or model is not a general framework that embeds an econometric model.In contrast,economic theory is often formulated as a restriction on the conditional pdf or its certain aspect.Such a restriction can be used to validate economic theory,and to improve forecasts if the restriction is valid or approximately valid.

Question:Where is the role that economic theory plays in economic modeling?

Indication of the nature(e.g.,conditional mean,conditional variance,etc)of the relation-ship between Y t and X t:Which moments are important and of interest?

Choice of economic variables X t:

Restriction on the functional form or parameters of the relationship.

Help judge causal relationship.

In summary,any economic theory can be formulated as a restriction on the conditional prob-ability distribution of the economic stochastic process.Economic theory plays an important rule in simplifying statistical relationships so that a parsimoneus econometric model can eventually capture essential economic relationships.

Motivated by the fact that economic theory often has implication on and only on the con-ditional mean of economic variables of interest,we…rst develop a comprehensive econometric theory for linear regression models where by linearity we mean the conditional mean is linear in parameters and not necessarily linear in explanatory variables.We start in Chapter3with the classical linear regression model,for which we develop a…nite sample statistical theory when the regression disturbance is i.i.d.normally distributed,and is independent of the regressor. The normality assumption is crucial for the…nite sample statistical theory.The essence of the