We now apply the two new TFP growth measures to study the source of GDP growth in the federal states of Germany after reunification. To this purpose, GDP and ”national” income account data are available beginning with 1992 for 16 states: 11 ”old” states (Bavaria, Baden-W¨urttemberg, Bremen, Hamburg, Hesse, Lower Saxony, North Rhine-Westphalia, Rhineland-Palatinate, Saarland, Schleswig-Holstein), 6 ”new” states (Berlin, Brandenburg, Mecklenburg-West Pommerania, Saxony-Anhalt, Saxony, and Thuringia).13 We employ the income and product accounts and capital stock estimates at the level of the federal states published by the Working Group for State Income and Product Accounts (Volkswirtschaftliche Gesamtrechnung der L¨ander in Stuttgart).14 This dataset allows us to revisit the findings of Burda and Hunt (2001), who assessed the widely divergent evolution of labor productivity and total factor productivity between East and West and within the two groups of states using the conventional Solow residual measure. Because the capital stock data for the new states are poor, especially for structures, the alternative DS and GD methods offer an opportunity to investigate TFP growth measurements with a ”treatment” group (East Germany) as well as a ”control” group (West Germany), where the ”treatment” is an unusually bad measurement of initial capital stocks. Reunification - both market competition and the revaluation of the east German mark - rendered about 80% of East German production noncompetitive (Akerlof, Rose, Yellen, and Hessenius (1991)), implying a large loss of value of existing equipment and structures. At the same time, many structures long carried at minimal book value were suddenly activated and employed by businesses, implying higher value of the capital stock.
In Table 5, we compare TFP growth using the Solow method and our stock-free TFP mea-surements for both the new and the old German states over two sub-periods: 1992-1997 and 1998-2003. The Solow residual estimates utilize an estimate of capital stocks provided by the state statistical agencies and the working group involved in collecting and standardizing the state income and product accounts. A constant capital share (0.33) was assumed. For the DS method, the annual rental price of capital (κ) was set to be constant over the entire period at a value of 0.0752. For the GD approach, a simple two-sided moving average of 2 years was used to estimate the trend. For both approaches, a constant rate of capital depreciation δ equal to 0.0754 was employed.
13Berlin is counted as a ”new state” consisting of the union of East and West Berlin, because the western half of Berlin, while under the protection and economic aegis of Western Germany until 1989, never enjoyed full status as aBundesland.
14The data can be downloaded at the websitehttp://www.vgrdl.de/ArbeitskreisVGR/ergebnisse.asp
Table5:TFPMeasurementinGermanFederalStates:AComparison StateSolowResidualDSGD 1992-19971998-20031992-19971998-20031992-199719 Easternstates Berlin2.60.71.7-0.40.6 Brandeburg7.32.05.70.33.4 Macklenburg-WesternPomerania6.61.24.7-0.43.4 Saxony7.82.16.20.53.3 Saxony-Anhalt7.22.05.40.53.4 Thuringia9.32.17.30.63.4 WesternStates BadenWuerttenberg2.22.11.01.50.5 Bavaria2.53.01.12.20.7 Bremen2.52.41.61.90.6 Hamburg3.01.52.01.00.8 Hessen2.61.91.51.30.6 LowerSaxony1.81.10.60.30.3 NorthRhine-Westphalia2.11.31.10.70.3 Rhineland-Palatinate1.51.20.30.40.3 Saarland1.41.60.30.80.2 Schleswig-Holstein2.41.51.30.70.6 AllGermany2.91.91.61.10.8
22
Table6:GrowthAccountingUsingtheThreeMethodsfortheperiod1992-1997:ACompa State∆Y Y(1−α)∆N N∆ASolow ASolow∆KSolow KSolow∆ADS ADSα∆KDS KDS∆AGD AGD Easternstates Berlin0.9-1.12.6-0.51.70.40.6 Brandeburg7.3-1.87.31.85.73.43.4 Macklenburg-WesternPomerania7.2-1.86.62.44.74.33.4 Saxony7.2-2.27.81.66.23.23.3 Saxony-Anhalt6.9-2.67.22.25.44.03.4 Thuringia8.3-2.99.31.97.33.93.4 WesternStates BadenWuerttenberg0.9-0.12.2-1.21.00.00.5 Bavaria1.4-0.12.5-1.01.10.40.7 Bremen0.3-0.82.5-1.41.6-0.40.6 Hamburg1.2-0.33.0-1.52.0-0.50.8 Hessen1.1-0.12.6-1.41.5-0.20.6 LowerSaxony0.80.21.8-1.20.6-0.10.3 NorthRhine-Westphalia0.5-0.22.1-1.41.1-0.40.3 Rhineland-Palatinate0.40.01.5-1.10.30.10.3 Saarland0.2-0.11.4-1.10.30.00.2 Schleswig-Holstein1.20.02.4-1.21.30.00.6 AllGermany1.5-0.52.9-0.91.60.40.8
23
Table7:GrowthAccountingUsingtheThreeMethodsfortheperiod1992-1997:AComparison State∆Y Y(1−α)∆N N∆ASolow ASolow∆KSolow KSolow∆ADS ADSα∆KDS KDS∆AGD AGD Easternstates Berlin-0.5-0.40.7-0.8-0.40.3-0.1 Brandeburg1.7-1.02.00.70.32.31.2 Macklenburg-WesternPomerania0.7-0.91.20.4-0.42.00.6 Saxony1.8-0.62.10.20.51.81.1 Saxony-Anhalt1.1-1.42.00.50.52.01.0 Thuringia1.9-0.32.10.20.61.61.1 WesternStates0.00.0 BadenWuerttenberg2.01.02.1-1.11.5-0.50.6 Bavaria3.00.93.0-0.92.2-0.11.2 Bremen1.40.12.4-1.11.9-0.60.7 Hamburg1.10.71.5-1.01.0-0.60.3 Hessen1.40.71.9-1.11.3-0.50.5 LowerSaxony1.00.91.1-1.00.3-0.20.2 NorthRhine-Westphalia1.00.91.3-1.20.7-0.60.2 Rhineland-Palatinate1.21.01.2-0.90.4-0.10.3 Saarland1.60.91.6-0.90.8-0.10.5 Schleswig-Holstein1.00.31.5-0.90.70.00.4 AllGermany1.50.61.9-0.91.1-0.10.6
24
Solow-residual type estimates. This observation holds both for the old and new German states. This implies that the cyclical fluctuations characteristic of TFP estimates - total factor productivity as measured by the Solow residual is the most important evidence invoked by the RBC school as the primary source of macroeocnomic fluctuations - are exaggerated due to fluctuations in the rate of capacity utilization. Both DS and GD methods show TFP growth to be much more stable over the two halves of the sample (1992-7 and 1998-2003). Second, the dispersion of TFP growth across the states is much less volatile in both subsets. This appears more plausible for a variety of reasons. Finally, the estimates of TFP using the DS and GD methods can be used to back out an implied contribution of capital to real growth, or, given a capital share, to growth in the true (i.e. actually utilized) capital stock. These estimates are also presented in Table 6. They show indeed a larger degree of fluctuation than that implied by official estimates of capital stock growth. They support the notion, already due to Burnside, Eichenbaum, and Rebelo (1995) and others, that the fluctuation of capital in use is an important source of measurement error and should be considered carefully when computing the solow residual. Our proposed alternatives have the advantage of shutting down this source of mismeasurement, to the extent that the utilization of the most recent investment more closely tracks the ”true” utilization rate.
6 Conclusion
Over the past half-century, the Solow residual has achieved widespread use in economics and management as a measurement of total factor productivity. Its acceptability is attributable to its simplicity and independence from statistical methods. Despite this acceptance, there has been no effort to evaluate systematically the quality of this measurement tool. This complacency is remarkable in light of potentially severe measurement problems associated with capital stock data. We have documented that the error, as measured by the root mean squared error - associated with the capital stock mismeasurement can be significant in a synthetic data set. These measurements can be characterized most generously as educated guesses of quantities for which reliable measurement or complete markets simply do not exist.
While the measurement error of the Solow residual decreases with sample size, it remains especially acute for short data sets or economies in transition. Thus, the Solow residual is least accurate in applications for which TFP measurements are most valuable. Such applications the transition to a market economy, the introduction of ICT capital in the production process, and the increasing employment of weightless assets such as advertising goodwill and research and development knowledge. (Corrado, Hulten, and Sichel (2006))
Both proposed alternatives to the Solow-Th¨ornqvist meaures can be thought of as a ”marginal-ization” of the error carried forward by the capital stock across time. Most recent investment is most likely to be properly valued at acquisition cost and to be fully utilized. Our results suggest that these methods could be applied to a number of investment context and types, thus widening the scope and appeal of applied TFP measurement.
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Appendix 1: The Stochastic Growth Model
First Order Conditions and Decentralized Market Equilibrium
Let λt denote the Lagrange multiplier corresponding to the periodic resource constraint (14) The first-order conditions for the household are, for t ≥0 :
Ct : λt = 1 Ct
Kt+1 : λt =βEt[λt+1(1−δ+Ut+1κt+1)] (23) Nt : θ(1−N¯)−η =λtωt (24)
Ut: BUtχ−1 =κt+1 (25)
First-order conditions for the firms
Nt : (1−α)At(UtKt)αNt−α =ωt (26) Kt: αAtUtαKtα−1Nt1−α =κt (27) the production function
Yt=AtKtαNt−α (28) and the aggregate resource constraint (since ωtNt+κtUt−1Kt−1 =Yt).
Kt+1 = (1−δt)Kt+Yt−Ct (29) The equilibrium of this decentralized economy is defined as the sequences of wages{ωt}, rental prices for capital {κt}, output {Yt}, consumption,{Ct}, employment {Nt}, capital stocks {Kt+1}, and the capacity utilization rate {Ut} such that the above equations hold for t ≥ 0 plus a suitable transversality condition to guarantee that the capital stock path is indeed consistent with utility maximization. The equilibrium of the problem will be, due to the first and second welfare theorems, unique and equivalent to the one chosen by a social planner with the objective of maximizing the utility of the representative household.