Interpolation is the practice of estimating values between observed data points. Economists use it to fill gaps in datasets (for example missing months inside a time series), but it can also introduce bias if the interpolation method imposes patterns that are not truly in the data.
Linear interpolation (common baseline)
Suppose you observe ((x_0,y_0)) and ((x_1,y_1)) with (x_0 < x < x_1). Linear interpolation estimates (y(x)) by drawing a straight line between the two points:
[ \hat y(x) = y_0 + (y_1 - y_0),\frac{x-x_0}{x_1-x_0}. ]
This is simple and transparent, but it assumes the variable changes smoothly at a constant rate between observations.
Interpolation vs extrapolation
- Interpolation: estimates inside the observed range.
- Extrapolation: extends beyond the observed range (typically riskier).
Why interpolation can be risky in economics
Interpolation can:
- smooth away volatility (important for business-cycle analysis),
- distort dynamics (autocorrelation and persistence),
- create false precision if treated as real observed data in regressions.
A good practice is to flag interpolated values, test sensitivity to alternative methods, and avoid interpolating variables where the underlying process is known to be jumpy (policy changes, discrete shocks).
Practical example
If a quarterly variable is converted to a monthly series by interpolation, month-to-month variation may be mechanically imposed rather than measured. This can affect estimated relationships in monthly regressions or forecasting models.
Related Terms
- Extrapolation
- Regression
- Linear Regression
- Multiple Regression
- Non-Parametric Regression
- Time Series Data