Calculating Productivity in the Transportation Sector Using Kalman Filter Approach

Productivity improvement, considering resource scarcity and increased competition, is known, nowadays, as the best and most effective way of achieving growth. Since transportation is a very important and influential infrastructural component in the country's economy, the evaluation and improvement of its productivity is quite important. The purpose, in this paper, has been to calculate productivity in Iran transportation sector using Kalman Filter approach; the results for the potential production and production cycle have also been analyzed and compared using Hodric-Prescott (HP) and Boxter-King (BK) methods. To do so, first the unit root and random trend in the real GDP logarithm have been investigated and analyzed for the transportation sector during the period in question; results have shown that the real value-added logarithm variable of Iran transportation sector is first order integration I(I) and, therefore, the observed trend is one obtained from a random walk with drift. Next, based on the theoretical principles and experimental studies, the productivity model has been introduced and proposed for the transportation sector. The model equations can be rewritten, in the format of state-space models, as follows:ME:〖∆y〗_t=μ+y_(c,t)-y_(c,t-1)+ε_1t (1) TE:y_(c,t)=φ_1 y_(c,t-1)+φ_2 y_(c,t-2)+ε_(2t) (2) Model estimation results are shown in Table 1.Table 1. Estimated values of the model parametersParameter Estimation t-statisticµ 0.06 2.53φ1 0.74 10.52φ2 -0.8 -5.20σε1 0.24 9.86σε2 0.76 6.25AIC=-4.45 SBC=-4.23 Source: Research findingsAs shown in the above table, all the values estimated for the variables are meaningful at the critical level of 0.05. Also, the special roots of equation λ^2 〖-φ〗_1 〖λ-φ〗_2=0are: since C < 1, the business cycles in the real GDP logarithm of Iran transportation sector are stable; other parameters are meaningful too. Next, it is necessary to make sure of the model correctness regarding normality of the residues (model's error forecast) and lack of autocorrelation. To check the first, use has been made of Jarque-Bera statistic, and to check the second based on autocorrelation function (ACF) and partial autocorrelation function (PACF), it can be concluded, from the value found for the test statistic and its corresponding probability level, that the model lacks autocorrelation which is an indication of the model's goodness of fit. Test statistic results found from this model are 2.89 for the residues and 0.24 for its probability; therefore, the assumption of normal distribution at a certainty level of 5% cannot be rejected.Results have revealed that the fluctuation variance of the cycles produced by the Kalman-Filter method have been less than those by Hodric-Prescott and Boxter-King methods, but all have been similar in shape. The time series of the production total factor productivity for the time period of 1972-2007 in the transportation sector was estimated too. Fig.1 shows this sector's estimated productivity for the period 1971-2006. As shown, it has had fluctuations during that period; over time, the amplitude has declined in recent years which can be an indication of enhancement in the economic stability in this sector.Since improvement and increase in productivity in the transportation sector will cause more value added and hence more income will be distributed in this sector, and also considering the important role the transportation sector plays in the economic activities and in preparing the production's infrastructures, the productivity improvement in this sector will cause an increase in the GDP and, in fact, in the living standards in the country.