Much of the search literature that seeks to account for equilibrium unemployment uses `matching functions' that resembles the production function that relate `inputs' of unemployment and vacancies and the corresponding `output' of job matches. Identifying this relationship requires continuous-time data, which is rarely available for the latter, so most of the empirical literature aggregates total flows of output over each month. A high matching rate reduces the stocks of unemployment and vacancies, however, which are therefore negatively correlated with the matching rate. Many have sought to avoid this `simultaneity problem' by regressing the aggregate flow of matches on the stock variables measured at the beginning of that month.

In Discussion Paper No. 967, Kenneth Burdett, Melvyn Coles and Jan Van Ours argue that this procedure of using the aggregate flow of matches over the subsequent period rather than the flow of matches at that point in time mismeasures the dependent variable. This biases the resulting estimates downward if the conditioning variables are mean reverting but there is no such bias if they follow a trendless Brownian motion. If the conditioning variables are mean reverting and their values are above the mean at the start of the period, the flow of matches will initially be quite high, but the stocks of vacancies and unemployment fall over the period. The flow of matches also falls but time aggregation implies that the measured flow will be too low (and if the conditioning variables are initially low, the measured flow will be too high), which systematically biases the estimates downwards. Burdett, Coles and Van Ours illustrate how to correct for this bias if it is small. It will then be proportional to the length of the data period, so aggregating from monthly to quarterly data triples the bias, which enables the original bias to be determined from the parameter estimates.

Temporal Aggregation Bias in Stock-Flow Models
Kenneth Burdett, Melvyn Coles and Jan Van Ours

Discussion Paper No. 967, May 1994 (HR)