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# Logarithmic specifications - PowerPoint PPT Presentation

Logarithmic specifications. Jane E. Miller, PhD. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Overview. Types of logarithmic specifications Prose interpretation of coefficients from logarithmic specifications

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### Logarithmic specifications

Jane E. Miller, PhD

The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.

• Types of logarithmic specifications

• Prose interpretation of coefficients from logarithmic specifications

• Considerations for contrast size for logarithmic specifications

• Descriptive statistics for multivariate models with logarithmic specifications

The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.

• Another approach to comparing βs across variables with different ranges and scales is to take logarithms of the

• dependent variable (Y),

• independent variable(s) (Xis),

• or both.

• The βs on the transformed variable(s) lend themselves to straightforward interpretations such as percentage change.

• Lin-lin

• Lin-log

• Log-lin

• Log-log

• Also known as “double log”

• Review: For OLS models in which neither the IV nor the DV is logged, βmeasures the change in Y for a 1-unit increase in X1,

• the changes are measured in the respective units of the IV and DV.

• In the lingo of logarithmic specifications, these models are termed “lin-lin” models because they are linear in both the IV and DV

Y = β0 + β1X1

• Lin-log models are of the form Y = β0 + β1 lnX1.

Where lnX1 is the natural log (base e) of X1

• For such models, β1 ÷ 100 gives the change in the original units of the DV for a 1 percent increase in the IV.

• E.g., in a model of earnings, βlog(hours worked) = 5,905.3:

• “Each 1 percent increase in monthly hours worked is associated with a NT\$ 59 increase in monthly earnings.”

• Log-lin models are of the form lnY = β0 + β1X1.

• For such models, 100  (eβ – 1) gives the percentage change in Y for a 1-unit increase in X1,

• Where the increase in X1 is in its original units.

• E.g., “For each additional child a woman has, her monthly earnings are reduced by 3.6 percent.”

• Log-log models are of the form lnY = β0 + β1lnX1

• For such models, β1 estimates the percentage change in the Y for a one percent increase in X1.

• This measure is known in economics as the elasticity (Gujarati 2002).

• E.g., “A 1 percent increase in monthly hours worked is associated with a 0.6% increase in monthly earnings.”

• Caveat: The scale of the logged variable must be taken into account when choosing an appropriate-sized contrast.

• E.g., a 1-unit increase in ln(monthly hours worked) from 5.3 to 6.3 is equivalent to an increase from 200 to 544 hours per month.

• That contrast is nearly a 2.5 fold increase in hours.

• Implies working three-quarters of all day and night-time hours, 7 days a week.

Review: Assess whether a 1-unit increase in the variable is the right sized contrast

• Always consider whether a 1-unit increase in the variable as specified in the model makes sense in its real world context!

• Topic

• Distribution in the data

• If not, use theoretical and empirical criteria for choosing a fitting sized contrast.

• See podcast on measurement and variables approaches to resolving the Goldilocks problem

• In a table of descriptive statistics, report the mean and range both

• In the original, untransformed units, such as income in dollars, which are

• more intuitively understandable

• easier than the logged version to compare with values from other samples.

• In the logged units, so readers know the range and scale of values to apply to the estimated coefficients.

• Taking logs of the IV(s) and/or DV affects interpretation of the estimated coefficients.

• If your models include any logged variables, report the pertinent units as you write about the βs, especially if

• your specifications include a mixture of logged and non-logged variables;

• you are testing the sensitivity of your findings to different logarithmic specifications.

Summary specification

• Consider whether a logarithmic specification fits your:

• Topic,

• Data,

• Field.

• Report descriptive statistics for each variable in original and transformed units.

• Convey the pertinent units for each coefficient as you interpret it.

The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.

Suggested resources specification

• Chapter 10 of Miller, J. E., 2013. The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.

• Gujarati, Damodar N. 2002. Basic Econometrics. 4th ed. New York: McGraw-Hill/Irwin.

• Miller, J. E. and Y. V. Rodgers, 2008. “Economic Importance and Statistical Significance: Guidelines for Communicating Empirical Research.” Feminist Economics 14 (2): 117–49.

Supplemental online resources specification

• Podcasts on

• Defining the Goldilocks problem

• Resolving the Goldilocks problem – model specification

• Online appendix on interpreting coefficients from logarithmic specifications.

Suggested practice exercises specification

• Study guide to The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition.

• Questions #9 and 10 in the problem set for chapter 10

• Suggested course extensions for chapter 10

• “Reviewing” exercise #4.

• “Applying statistics and writing” questions #5 and 6.

• “Revising” questions #7 and 9.

Contact information specification

Jane E. Miller, PhD

Online materials available at

http://press.uchicago.edu/books/miller/multivariate/index.html