Methodology and Data

The previous studies on efficiency or scale economies operated with a Cobb-Douglas produc-tion funcproduc-tion or other regression-based tests (see Schäfer and Schmitz 1982 and the literature cited there). Normally, output of firms is regressed on capital, labor, and sometimes land. This approach has the disadvantage that the researcher has to specify the functional form of the production function. In this article we will employ the Data Envelopment Analysis, which is a non-parametric technique, to estimate efficiency. With this method, we are able to circumvent the question whether the chosen production function is appropriate for the industry under study. There is also no need for estimating different production functions for different regions, or to make other potentially arbitrary choices.

The Data Envelopment Analysis is able to differentiate between efficient and ineffi-cient firms. The DEA constructs a production frontier from the data and evaluates each firm against this frontier, measuring by how much the input quantities of a given firm have to be reduced so that this firm would lie on the frontier. This proportional decrease in inputs is the measure of the firms’ inefficiency. All estimated efficiency scores have values between 0 and 1.

There are several models available which differ in their assumptions, especially con-cerning the returns to scale. It is possible to use these different models to decompose the effi-ciency score into three different categories: pure technical effieffi-ciency (pte), scale effieffi-ciency and mix efficiency. Pure technical efficiency describes the technical side of production, which means how much the firm produces with the available inputs. Imagine 2 firms which have the same inputs available, but achieve different levels of output, for example because they pro-duce different amounts of waste or have different machines so that one firm can propro-duce more in the same time with the same amount of workers. The firm which has a lower output will be

shown as not technically efficient, as with the available technology it is possible to produce more from a given quantity of inputs. If firms operate under non-constant returns to scale they are called scale inefficient. Consider for example a firm that produces under increasing turns to scale. If this firm would double its inputs, the output would, due to the increasing re-turns, increase to more than double. The ratio of output to input would therefore increase and the firm be called more efficient. Firms are called mix inefficient if they are using some inputs in an excessive way, which means they could decrease the usage of one input without thereby altering their production. For example imagine two establishments that use the same amount of capital, but one uses 10 workers while the other uses 12 workers, to produce the same out-put. The second establishment could obviously decrease their labor-force by 2 compared with the first one and still produce the same output, so this second firm is mix-inefficient.

To evaluate the hypotheses a regression approach is used. After estimating the effi-ciency scores of all firms in the data set with the DEA, truncated regressions are used to es-timate the determinants of the efficiency scores. Though a regression approach after a DEA estimation needs to be handled cautiously, as it is consistent but the rate of convergence is slow, this is no point in this estimation as the DEA models use only few variables and the number of observations is about 6000 (see Simar and Wilson 2007, who propose the use of truncated regressions. In that article the rate of convergence is given in formula (11). Here we have enough observations to achieve convergence). The independent variables include dum-mies for different regions, which show whether some regions were really more efficient than others. Outliers were excluded in this setting. An outlier is defined as an observation that has an efficiency score of over 200% in a superefficiency model. In this model, the establishment which is evaluated is excluded from the estimation of the frontier, so that its efficiency-score

can exceed 100 %, which makes identification of outliers possible. Values of over 200 %, which mean that the firm could double the used input quantities to produce the same outputs and still be considered efficient, are seen as implausible in a competitive market and therefore likely come from data errors.²

The data come from various American Manufacturing Censuses, namely the ones from 1850 and 1860.³ During every Census firms were asked to give detailed information about their used inputs, the produced outputs, labor force and many more.

To estimate efficiency, we use the stated amount of capital, the effective workforce, which is estimated as LT ⁼ Lmale ^{+ 0,5}Lfemale ^{+ 0,33}Lchildren ^{+ 1} (Golding and Sokoloff 1982), and the dollar value of all inputs the firms used. The stated dollar value of outputs is used as the output here. With this information, efficiency values for every firm are estimated.⁴ To ad-just for price changes, the data for capital, inputs and outputs were deflated with price series.

The price series and sources are given in the appendix (table A1).