Power properties of the Sargan test in the presence of measurement errors in dynamic panels

Abstract

This article investigates the power properties of the Sargan test in the presence of measurement errors in dynamic panel data models. The conclusion from Monte Carlo (MC) simulations and an application on the data used by Arellano and Bond (1991), is that in the very likely case of measurement errors in either the dependent or any of the independent variables, we will, if we rely on the Sargan test, quite likely accept a misspecified model and end up with biased results.

Notes

¹ An exception to this is Bowsher (2002), where the power properties of the Sargan test is explored when the error term follows an AR(1) process.

² In Dahlberg, Johansson (now Mörk) and Tovmo (2002), we show that the moments are not fulfilled when there is measurement errors in x or y.

³ The weighting matrix we use is the one proposed by Holtz-Eakin et al. (1988)

⁴ For γ = 0.5 and measurement errors in x, the Sargan test get worse power properties compared to the γ = 0.8 case. The results for γ = 0.5 are available upon request.

⁵ When we treat x as endogenous, we use lags of x as instruments (dated one period back and more) instead of contemporaneous values of x. The results when x is treated as endogenous, presented in Table 2 in Dahlberg, Johanson (now Mörk) and Tovmo (2002), show a similar pattern as the one found when x is treated as exogenous.

⁶ The power properties are unaffected of the size of γ when there are measurement errors in y. However, the lower the autoregressive process in x is, the lower is the bias in β.

⁷ It has been suggested, see for example Bowsher (2002), that the power of the Sargan test can be improved by using fewer moment conditions. Doing this does not solve the problem in our case. Another question is whether the power of the Sargan test can be improved by relying on bootstrap critical values using the GMM bootstrap estimator proposed by Hall and Horowitz (1996). The answer is no. It turns out that in the experiments conducted, the bootstrapped Sargan test almost never rejects a false null.

⁸ In their application, they have 140 cross-sectional units (quoted UK companies) for the period 1979–1984. The equation we estimate is given by

where n_it denotes the logarithm of UK employment in company i at the end of year t, w_it is the log of the real wage, k_it is the log of gross capital, ys_it is the log of industry output, λ _t is a time effect that is common to all companies, η _i is a fixed but unobservable firm-specific effect and υ _it is the error term (for exact definitions of the variables, see Arellano and Bond (1991)). The estimation of Equation 4 yields the results in column b in Table 4 in Arellano and Bond (1991).

⁹ The SD of the wage variable is 5.6 (unlogged values). We have also estimated with less variation in the measurement errors (we have used distributions of the errors that corresponds to five and ten percent of the distribution in the wage variable). This did, however, not change the results substantially.

¹⁰ The SD of the employment variable is 15.9 (unlogged values). The measurement errors are imposed before the variables are logged. The reason for having a mean of five in the errors is to ensure that the resulting employment variable is positive.

¹¹ The logn-run wage elasticity is −0.5 in the Arellano and Bond estimations, −0.33 with additive errors and −0.63 with multiplicative errors.