The coefficients in a distributed lag regression of Y on X and its lags can be interpreted as the dynamic causal effects when the time path of X is determined randomly and independently of other factors that influence Y. Explain How?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
The coefficients in a distributed lag regression of Y on X and its lags can be interpreted as the dynamic causal effects when the time path of X is determined randomly and independently of other factors that influence Y. Explain How?
Time series data provide the possibility to estimate the time path of the effect on Y of a change in X, that is, the dynamic causal effect on Y of a change in X. To estimate dynamic causal effects employing a distributed lag regression, however, X must be exogenous, because it might be if it were set randomly during a perfect randomized experiment. If X is not just exogenous but is strictly exogenous, then the dynamic causal effects is estimated using an autoregressive distributed lag model or by GLS.
In some applications, like estimating the dynamic causal effect on the price of fruit crush of freezing weather in Florida, a convincing case is made that the regressor (freezing degree days) is exogenous; thus the dynamic causal effect are going to be estimated by OLS estimation of the distributed lag coefficients. Even during this application, however, theory suggests that the weather isn't strictly exogenous, that the ADL or GLS methods are inappropriate. Moreover, in many relations of interest to econometricians, there's simultaneous causality, therefore the regressor in these specifications don't seem to be exogenous, strictly or otherwise. Ascertaining whether the regressor is exogenous (or strictly exogenous) ultimately requires combining theory, institutional knowledge, and careful judgment.
Step by step
Solved in 2 steps
