Firm-Level Investment Dynamics in Hungary

The study builds upon the work of Katay and Wolf (2004), using their dataset of Hungarian corporate tax returns from 1992 to 2002, focusing on the manufacturing sector to minimize investment cost heterogeneity. The initial dataset consisted of 110,808 year-observations, reduced to 92,293 after removing missing values and outliers. The analysis utilizes a firm-level investment model incorporating adjustment costs. Unlike Katay and Wolf (2004), which emphasized the user cost of capital, this model uses a profitability shock as the main determinant of investment, incorporating various influencing factors. The model incorporates 'new investment models' characteristics like lumpiness and irreversibility, drawing upon prior research (Doms and Dunne, 1998; Ramey and Shapiro, 2001; Abel and Eberly, 1994; Bertola and Caballero, 1994), focusing on fixed, convex, and irreversibility costs. The key variables employed are investment rate (following Katay and Wolf's construction), capital stock (calculated using the Perpetual Inventory Method), and operating profit.

To estimate the structural parameters of the investment cost function (fixed costs F, convex costs γ, and irreversibility costs p), the paper employs a modified indirect inference method (Gourieroux and Monfort, 1993). This involves selecting empirically observable statistics (regression coefficients, inaction rate, and skewness of investment rates) influenced by the model's structural parameters. The method matches theoretical counterparts of these selected statistics to their observed values. The data moments (φ0) are calculated, and the model is simulated with various cost parameters (F, γ, p) to find the values that minimize the weighted distance between theoretical and data moments. The inclusion of these three cost components allows for a comprehensive analysis of their individual and combined influence on investment behavior. The model's calibration ensures the same proportion of inactive firms under both convex and non-convex cost structures, facilitating a clear comparison of the effects on investment size among active firms.

The identification of profitability shocks is crucial for the model. The study adapts a method from Cooper and Haltiwanger (2005), assuming identical, constant returns-to-scale Cobb-Douglas production functions for firms. The model incorporates a productivity shock (Bt) and a profitability shock (Ait). A key parameter, θ, representing the curvature of the profit function, is estimated. The estimation process addresses challenges posed by observations with negative profits. The resulting θ value (0.3372) is compared against similar estimates from the US and Germany, revealing that Hungarian profits are less responsive to capital changes than those in the US. The reliability of the θ estimate is further assessed by examining parameter estimates across different manufacturing sub-sectors and over time, showing relative stability and consistency with sector-specific capital intensity.

The estimation results are presented in Table 5, showing the estimated structural cost parameters and their standard errors for different cost scenarios. When only convex costs are considered, the estimated convex cost parameter (γ) is high, but the model fit is poor. Adding fixed costs significantly improves the model fit, reducing the distance between simulated and observed statistics. Further inclusion of irreversibility costs enhances the model fit, further decreasing this distance. The results highlight the importance of including all three cost components (fixed, convex, and irreversibility costs) to accurately capture the investment dynamics. The estimated irreversibility parameter is significantly different from 1, indicating a relatively small degree of irreversibility, a finding consistent with other similar studies (Cooper and Haltiwanger 2005; Bayrakhtar et al. 2005).

The data used in this study originates from the dataset compiled by Katay and Wolf (2004), which comprises corporate tax returns of double-entry bookkeeping firms in Hungary between 1992 and 2002. This study utilizes a subsample focusing solely on manufacturing firms to mitigate the influence of investment cost heterogeneity across different industries. The initial data cleaning process by Katay and Wolf reduced the original 1,269,527 year-observations to 308,850. Further refinement, restricting the analysis to manufacturing firms, resulted in a sample size of 110,808 year-observations. Additional data cleaning steps were implemented in this study, removing missing observations and outliers for key variables (investment rate, sales revenue, capital stock, profits), resulting in a final sample size of 92,293 year-observations. The exclusion of 18,308 observations due to missing investment rates, predominantly from 1992, is explicitly noted.

Three key variables are central to this research: investment rate, capital stock, and profit. The gross investment rate is adopted directly from Katay and Wolf (2004), utilizing their calculations derived from accounting capital data. Capital stock is measured using a real capital variable constructed by Katay and Wolf using the Perpetual Inventory Method (PIM), factoring in calculated gross investment levels and observed depreciations. Operating profit serves as a measure of firm profitability. The choice to use Katay and Wolf's previously constructed investment rate variable underscores a methodological consistency and reliance on their established methods. The utilization of the PIM for capital stock highlights a robust approach to constructing this crucial variable. The selection of operating profit as the measure of profitability represents a conventional approach to capturing firm performance.

The paper employs a methodology adapted from Cooper and Haltiwanger (2005) to identify profitability shocks. This approach assumes firms have identical, constant returns-to-scale Cobb-Douglas production functions (Yit = BitLαitLK1−αL), where labor (Lit) is considered adjustable in the short-run, while capital (Kit) is not. A constant elasticity demand curve (D(p) = pξ) is also assumed, leading to an inverse demand curve p(y) = y1/ξ. The firm's problem is to maximize profits given this framework. A key parameter, θ, representing the curvature of the profit function (Π∗it = AitKθit), is estimated. This estimation is made more complex by the presence of observations with negative profits, requiring alternative estimation methods beyond simple log-linear models. The estimated θ is compared to comparable studies in the US and Germany to assess the sensitivity of profits to capital changes in the Hungarian context. This comparison highlights relative differences in the responsiveness of profits to capital changes across different countries. A type-2 profitability shock is calculated after obtaining an estimate of θ.

The parameter θ, representing the curvature of the profit function, is central to the identification of profitability shocks. The estimation of θ is discussed, noting the challenges presented by observations with negative profits, requiring the use of alternative methods like NLLS and IV estimation on a shifted log-log model. The robustness of the estimated θ (0.3372) is evaluated by comparing it with existing estimates from the US (Cooper and Haltiwanger (2005), Reiff (2006)) and Germany (Bayrakhtar et al. (2005)). This comparison reveals that the Hungarian estimate is lower than those found in the US but is in line with the German findings, suggesting a difference in profit responsiveness to capital across countries. Further analysis explores the stability of θ across different manufacturing sub-sectors and over time (1993-1997 vs. 1998-2002), showing a degree of consistency and suggesting the overall parameter estimate is sensible. These comparative analyses demonstrate the importance of considering international and temporal contexts when interpreting the estimate.

The core estimation strategy relies on a modified version of the indirect inference method, as detailed by Gourieroux and Monfort (1993). This approach begins by selecting empirically observable statistics significantly influenced by the model's structural parameters. These statistics can include regression equations or other descriptive statistics derived from the data. The estimation process then aims to match the theoretical counterparts of these selected statistics—generated by simulating the model with various parameter values—to their empirical counterparts from the data. The goal is to find the parameter values that best reproduce the observed data moments. This indirect approach offers a flexible way to estimate parameters, particularly useful when direct maximum likelihood estimation is challenging. The method's flexibility in accommodating diverse statistical moments makes it well-suited for examining the complex interactions between different types of adjustment costs.

The indirect inference method is used to estimate the structural cost parameters (F, γ, p) representing fixed, convex, and irreversibility costs, respectively. The process involves choosing arbitrary cost parameters, solving the theoretical model using value function iteration, and comparing the simulated moments (inaction rate, skewness of investment rates, and regression coefficients) to their data counterparts. The parameters are adjusted to minimize the weighted distance between theoretical and empirical moments. Table 5 presents the estimated parameters and standard errors under different specifications. The model's fit is assessed by this distance; including fixed and irreversibility costs substantially improves the model's ability to replicate the observed data. The finding that the estimated convex cost parameter (γ) decreases when fixed costs are included indicates that fixed costs effectively substitute for convex costs in the model's ability to explain investment behavior. Similarly, adding irreversibility costs further improves the fit, highlighting the importance of this cost component in the overall investment decisions.

The estimated parameters offer insights into the relative importance of different adjustment costs in shaping investment decisions. The results show a significantly positive fixed cost parameter (F), indicating that a fixed cost threshold must be overcome before firms undertake investments. The significantly positive convex cost parameter (γ) suggests increasing marginal costs associated with larger investment sizes. The irreversibility parameter (p), while significantly different from 1 (implying some degree of irreversibility), is relatively close to 1, pointing towards a small degree of irreversibility. This finding aligns with those from similar studies (Cooper and Haltiwanger, 2005; Bayrakhtar et al., 2005), suggesting a relatively small impact of irreversibility on investment decisions. The significant and positive estimates of all parameters (in the 'all three types' model) support the inclusion of these costs, implying a nuanced investment decision-making process with the joint influence of these various cost components.

This section explores the aggregate implications of firm-level findings, focusing on two key comparisons. First, it analyzes the difference between firm-level and aggregate investment behavior, drawing parallels with Caballero (1992), who observed that micro-level asymmetric adjustment might vanish at the macro-level due to aggregation effects if firm-specific shocks are not perfectly correlated. Second, it contrasts adjustment patterns under different cost structures: a scenario with only convex adjustment costs (smooth adjustment) versus a scenario incorporating all types of adjustment costs (convex, fixed, and irreversibility costs). This comparison aims to determine the aggregate-level significance of non-convex cost components. The study finds a contrasting effect at the firm and aggregate levels: while firm-level investment is lumpier under non-convex costs, aggregate investment becomes more flexible.

The analysis investigates the aggregate investment response to profitability shocks under varying cost structures. The study finds that the aggregate response is larger when non-convex (fixed and irreversibility) costs are present. This contrasts with the higher convex cost parameter needed when only convex costs are considered, which penalizes large investment episodes. The presence of all three types of costs leads to a quicker and larger immediate response to a positive profitability shock; the impulse response function returns to zero more quickly. The effect of the magnitude of the shocks is also examined: a surprise, one-standard-deviation, positive permanent shock triggered a relatively small, 1.3-2.1%, immediate increase in the aggregate gross investment rate, while a credible permanent shock produced a much larger, 7.2-11.5%, immediate increase. The cumulative effects of credible shocks are significantly greater over time (24.1-24.3% over 10 years). This contrast highlights the importance of shock credibility in influencing aggregate investment.

The study's findings regarding the significant aggregate implications of non-convex investment costs contradict the conclusions of Veracierto (2002) and Khan and Thomas (2003), who found no such aggregate effects of investment irreversibility at the plant level. Two reasons for this discrepancy are suggested: the absence of general equilibrium effects (through changes in equilibrium prices) in this study, and differences in the magnitudes of identified profitability shocks. The study notes that its profitability shocks have much larger standard deviations than those in Veracierto (2002), making the irreversibility constraint binding in many of the simulations. This study concludes that the aggregate implications of non-convex costs are significant and contrasts with models having smaller shock standard deviations. Studies such as Coleman (1997), Faig (1997), and Ramey and Shapiro (1997), which feature comparable shock standard deviations, also found important aggregate effects of irreversible investment.