1 AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Chapters 6.3 Variables & Model Specifications

2 Lagged Variables In many cases the value of Y in time period t is more likely be explained by the value taken by X in the previous time period: Investment (Y t ) is dependent on last year’s price X (t-1)

3 Lagged Variables In multiple regression models (i.e. models with more than one explanatory variable), it can be assumed that Y is affected by different lags of X: 

4 Lagged Variables ?

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6 Suppose we want to estimate cotton acres planted in the US (Y) as a function of the last 3 years price of cotton lint (X t ), cents/lb. What's the interpretation of: = 1.2 ? If the price of cotton lint three years ago (t-3), changed (went up) by 1 cent per pound; the cotton acreage planted today would increase by 1.2 mil. acres, while holding all the other X’s constant

7 First Differences of a Variable (6.3) The first difference of a variable is its change in value from one time period to the next A common specification in time series models involves letting the dependent or the independent variable, or both, be specified in first differences

8 First Differences of a Variable First difference on Y: First difference on X: The only reason you do this is if you believe that it is not the previous year that affects Y t ; but the difference between the previous year and current year that affects Y t.

9 First Differences of a Variable Suppose you wanted to estimate the function where investment is a function of the change in GNP (i.e. first difference).

10 First Differences of a Variable