Appendix : Misallocation under alternative assumptions
In this Appendix we investigate how changes in assumptions about the model impact the estimates for misallocation in the manufacturing and service sectors. In order to take the model to the data it is necessary to choose a value for the elasticity of substitution parameter (σ), decide how to treat outliers, and choose the group of firms included in the analysis. Although it is already known that these assumptions will impact the estimated level of misallocation (see Hsieh and Klenow (2009) or Dias et al. (2016)), our interest is knowing whether the effect is homogeneous across industries and thus whether they significantly affect the misallocation differences between the manufacturing and service sectors.
As is common in the literature (see, for instance, Hsieh and Klenow (2009), Dias et al. (2016), Gopinath et al. (2015)), we use the wage bill paid by the firm (total labor costs) to measure labor input. Implicitly, we are assuming that wages per worker adjust for firm differences in hours worked per worker and worker skills. For the rental price of capital, we define an industry specific price equal to the industry depreciation rate plus a 5 percent real interest rate, so that Rs = δs + 0.05. For the intermediate inputs, we make a similar assumption as in the case of the labor input, and assume that the price of intermediate products, Zs, is equal to 1, so that the expenditure on intermediate inputs reflects not only the amount of inputs but also their quality.31
In line with other studies (see, for instance, Hsieh and Klenow (2009), Ziebarth (2013) and Dias et al. (2016)), we define a baseline by making the following set of assumptions: i) the elasticity of substitution, σ, equal to 3; ii) trimming the top and bottom 1.0 percent tails of scaled TFPR and TFP distributions across industries;32 iii) inclusion of all firms in the retained industries.33
Next, we change assumptions i), ii) and iii) to gauge the impact each one and altogether have on the estimated efficiency gains and, more importantly, on the difference of misallocation between the service and manufacturing sectors. Specifically, we will investigate the implications of changing σ and the level of trimming, as well as excluding smaller firms.
The efficiency gains for 2008 and 2010, obtained under the baseline assumptions, are recorded in Table A1. We can see from the first row that, if distortions in the economy were eliminated (by equalizing TFPR across firms in each industry and keeping industry level factor demand constant), the gross-output efficiency gains (or TFP gains) for the whole economy would be around 43 percent in 2008 and 49 percent in 2010 (this figure also includes firms from agriculture). Efficiency gains are also clearly higher in the service sector (around 59 percent in 2008 and 66 percent in 2010) than in the manufacturing sector (around 16 and 17 percent in 2008 and 2010, respectively). Thus, the service sector emerges as far more inefficient than the manufacturing sector, in line with the results in Dias et al. (2016). However, one question that may arise here is whether the documented difference in misallocation between the two sectors can be explained by one or more of the assumptions that underly the baseline results. We therefore now consider the implications of alternative assumptions to the baseline.
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Board of Governors of the Federal Reserve System and CEMAPRE; Banco de Portugal; and International Monetary Fund, respectively. We thank seminar participants at Banco de Portugal, 5th UECE Conference on Economic and Financial Adjustments, and 2016 African Meeting of the Econometric Society as well as Era Dabla-Norris, Romain Duval, and Veronique Salins for helpful comments and suggestions. The views expressed herein are those of the authors and should not be attributed to the Federal Reserve Board of Governors, the Federal Reserve System, Banco de Portugal, the Eurosystem, the International Monetary Fund, the IMF Executive Board, or IMF management.
Equation (4) expresses the distortions in terms of output, capital and labor relative to the intermediate inputs distortion. Thus, in the model, an intermediate input distortion will show up as a higher output distortion and as lower capital and labor market distortions. An observationally equivalent characterization would be in terms of distortions to the absolute levels of capital, labor and intermediate input prices (and no output distortion).
Using equation (10), it is straightforward to show that these weights also correspond to the firm’s gross-output market share, when all resources are efficiently allocated across firms, that is,
Note that efficiency gains are zero if scaled TFPR is equal to one for all firms, i.e., if there are no distortions in the industry, which means that dispersion of
According to information from the National Accounts, in 2008, agriculture, manufacturing and services contribute 2.4, 14.1 and 83.5 percent for aggregate GDP, respectively. Thus, if anything, our dataset appears to be slightly skewed towards manufacturing and against the service sector.
In our model, it is not possible to separately identify the average input distortions (average wedges) and the input elasticities in each industry. Thus, using factor shares from the U.S. economy is a simple way to control for distortions that could affect the input shares in the Portuguese economy, while the U.S. is taken as a benchmark of a relatively undistorted economy.
In the small number of cases for which we were not able to find a good match, we used the average for the whole economy in the U.S.. Between 1998 and 2010, gross output was composed of 46 percent consumption of intermediate inputs, 33 percent labor compensation and the remaining 21 percent were the compensation to capital owners.
In the Appendix we compute the efficiency gains under alternative assumptions and discuss the implications for the estimated level of misallocation and for the difference of allocative efficiency between the service and manufacturing sectors.
Note that these figures are for gross output and that the efficiency gains evaluated in terms of value added (the type of estimates usually available in the literature) are significantly higher. For 2008, the corresponding value-added efficiency gains, under the ”final model” assumptions, are 71.75 percent for the whole economy, 47.64 percent for manufacturing and 84.05 percent for services.
The efficiency gains in terms of gross output are computed as (1.3766/1.1415) θs, where θs is the share of the service sector in aggregate gross output. The value-added efficiency gains are computed using equation (24) in Dias et al. (2016). Notice that this exercise is similar to the one carried out in Hsieh and Klenow (2009) where the authors estimate the TFP losses in China and India stemming from the misallocation gap between these countries and the U.S..
Imperfect information has also been suggested as a foundation for adjustment costs, giving rise to a sluggish response of inputs to fundamentals and thus to misallocation (see David et al. (2014)). In our model it is not possible, however, to distinguish between alternative sources of adjustment costs (technological versus informational frictions).
Information costs and/or menu costs incurred by the firm to determine the optimal price and/or to change the price are usually suggested in the literature as the main sources of price rigidity. For empirical evidence on price rigidity at the firm level see, for instance, Fabiani et al. (2006) for the euro area and Dias et al. (2015) for Portugal.
Our framework does not allow for distinguishing productivity shocks from other type of shocks. In what follows we use the term productivity shocks to designate a range of time-varying shocks to production that include TFP shocks, demand shocks, natural disasters, changes to informal barriers, etc.
Bartelsman et al. (2013) show that misallocation stemming from policy induced distortions may affect the correlation between the distribution of productivity and the size of the firm. Recall also that, according to the discussion in Section 2, industry-level misallocation will be higher the stronger the (positive) firm-level correlation is between TFP and scaled TFPR.
IMF (2016) notes that product market regulations are a key distortion. However, if all firms in an industry are affected equally by these regulations, our framework will not capture the effect of the regulations on the level of misallocation.
In the model suggested by Peters (2013), TFPRsi is proportional to the firm-specific markup, which replaces the right-hand side of equation (8).
A well-established finding in the literature is that nominal price rigidities are more prevalent in less competitive industries or sectors. See, for example, Martin (1993) or Gopinath and Itskhoki (2010). It has also been documented that the service sector faces more price rigidity than other sectors (see Dias et al. (2015) for evidence in Portugal).
In the analysis that follows we drop the agriculture sector, as we are only interested in explaining the differences between misallocation in the manufacturing and service sectors.
We note that the Gelbach decomposition for our particular model is similar to the so-called Oaxaca-Blinder decomposition that has been extensively used in the literature to decompose mean wage differentials (see, for instance, Blinder (1973), Oaxaca (1973) and Jann (2008)). One important difference, however, is that the methodology developed in Gelbach (2016) allows for statistical inference regarding the decomposition, while the Oaxaca-Blinder method did not.
Note that the difference in efficiency gains between the two sectors in Table 3 is a non-weighted average, which explains the difference vis-à-vis the figures reported in the last row of Table 2.
To identify the productivity shocks, we assume that TFP follows an AR(1) process: asi,t = μs + ρsasi,t-1 + 4ϕvsi,t, where asi, t stands for the log of TFP of firm asi,t, in industry 5, in period t, and si,t~N(0, 1) is an independent and identically distributed (i.i.d.) standard normal random variable. The ϕs term measures productivity shocks in industry 5. To estimate ϕs we use two years of consecutive data, but restrict the sample to firms that appear in both years. When estimated freely, ps is close to unity for the great majority of industries. Thus, ultimately, we compute the productivity shocks as the industry-level standard deviation of (asi, t−asi,t-1).
Of course, this does not necessarily mean that capital adjustment costs are not present in the economy, as the adjustment costs are not the only source of dispersion of the marginal product of capital.
Of course, besides competition, there might be other factors that contribute to higher price rigidity in the service sector, such as higher information or search costs due to higher geographical dispersion.
Skewness of the productivity distribution is computed using the usual Fisher-Pearson formula:
Note that, according to equation (13), the lower the correlation between productivity and the output wedge the higher the correlation between productivity and TFPR.
We proxy the importance of young firms at the industry level by the ratio of the number of firms 3 years of age or less to the total number of firms.
Note the qualitative differences vis-à-vis the evidence in Figure 3, where small firms appear as benefitting from capital subsidies, on average.
Note that the values of Ws, Rs and Zs affect the corresponding average wedges, but not the relative comparison between firms in a given industry. In other words, the choices of Ws, Rs and Zs affect the estimates of the wedges (capital, labor, and output wedges), but not the efficiency gains calculated in this paper. Note also that to compute efficiency gains we only need to compute TFPRsi, TFPQsi (or Asi) and
That is, the distributions of
In order to avoid computing misallocation with a very small number of firms, we drop industries that are left with less than 10 firms after the trimming. This condition is imposed in all variants considered in Table A1 below, to ensure comparability. After excluding industries with less than 10 firms, we are left with 162 different industries for 2008 (7 for agriculture, 80 for manufacturing and 75 for services) and 163 industries for 2010 (8 for agriculture, 79 for manufacturing and 76 for services).
Note that, in the model, both TFP and TFPR are computed using the production function, i.e.,
Another one could be to compute winsorized efficiency gains at a given percent level.
It has been claimed (see, for instance, Vollrath (2015)) that, for historical reasons, data collection and classification is skewed towards manufacturing in the sense that it provides a much more detailed industry classification in manufacturing than in the service sector. In order to understand how the estimates of the difference of efficiency gains between the two sectors depend on the level of industry classification, we computed the efficiency gains using a 5-digit industry definition. Compared to the 3-digit results in Table A1, we conclude that global efficiency gains decrease, but not by much, which means that misallocation is not a spurious outcome of aggregation. Efficiency gains stay virtually unchanged in the manufacturing sector, but decrease somewhat in the service sector, reflecting the impact of a higher increase in disaggregation in this sector. Nevertheless, the difference of efficiency gains between the two sectors remains very high. For instance, in the ”final model” case of Table A1, the difference in the 5-digit case is 17.64 p.p., in 2008 (compared to 23.51 p.p. in the 3-digit case), and 21.67 p.p. in 2010 (compared to 26.39 p.p. in the 3-digit case). Thus, in the paper we focus on the 3-digit case, not only because it does not make a significant difference in quantitative terms, but also because in the 5-digit case, industries have, on average, a smaller number of firms, implying more volatile estimates of industry-level efficiency gains and of the regressors used in the analysis.