Global Journal of Management and Business Research, D: Accounting and Auditing, Volume 21 Issue 2

stationarity assumptions hold, we can estimate the ARMA models without correcting for non- stationarity. Next, we model the indirect production labor costs as an ARMA process with direct labor cost (for model 1), and direct labor costs, number of setups and number of distinct parts (for model 2), as the explanatory variables. We estimated several linear models with only autoregressive or moving average terms using the maximum likelihood method. Diagnostic tests based on the Q- statistic indicated that the resulting error terms were not consistent with the white noise assumption. Since trend and seasonal components of economic time series tend to combine multiplicatively, logarithmic transformations are usually applied to obtain an additive formulation upon which the statistical treatment is based (Harvey 1993, pp. 107). Therefore, we took logarithms of all variables, observing that seasonal patterns were more stable after the logarithmic transformation. For model 1, higher order ARMA processes without differencing resulted in errors that are not white noise. Therefore, we estimated the ARMA processes after differencing by specifying the following models: Model 3: ln ILCOST t = β 0 + β 1 ln DLCOST t + α 1 ln ILCOST t-1 - μ 1 ε t-1 + ε t . Model 4: ln ILCOST t = γ 0 + γ 1 ln DLCOST t + γ 2 ln NUMSETUPS t + γ 3 ln NUMPARTS t + δ 1 ln ILCOST t-1 - μ 1 ε t-1 + ε t . Here α 1 and δ 1 are the autoregressive coefficients and μ 1 is the moving average coefficient. The coefficients β 1, γ 1, γ 2 and γ 3 are interpreted as the short-term or impact effects of the independent variables on ILCOST (Greene, 2011). We used the Akaike Information Criterion (AIC) and the Schwarz Bayesian Criterion (SBC) to select the best model among higher order ARMA processes. The first-order ARMA model yielded the minimum AIC and SBC values indicating that the error process was best represented by a first-order ARMA process. The resulting Q-statistics were insignificant indicating that this first-order ARMA model is the best parsimonious model. Table 7: Tests of a Labor Based Cost Model with an ARMA (1,1) Model (Daily Data) (t-statistics in parentheses) ln (ILCOST t ) = β 0 + β 1 ln (DLCOST t ) + α 1 ln (ILCOST t-1 ) - μ 1 ε t-1 + ε t ILCOST = Indirect Labor Cost DLCOST = Direct Labor Cost NUMSETUPS = Number of Setups NUMPARTS = Number of Distinct Parts * indicates significant at the 5% level. ** indicates significant at the 1% level. Table 8: Parameter Estimates Relating Overhead Costs to Multiple Cost Drivers in an ARMA (1,1) Model (Daily Data) (t-statistics in parentheses) ln (ILCOST t ) = γ 0 + γ 1 ln (DLCOST t ) + γ 2 ln (NUMSETUPS t ) + γ 3 ln (NUMPARTS t ) + α 1 ln (ILCOST t-1 ) - μ 1 ε t-1 + ε t Variable Sheet Metal (n=1365) Machine Shop (n=1423) Brush & Steel Wool (n=1314) Paint Shop (n=1302) Component Assembly (n=1368) Welding (n=1327) Final Assembly (n=1391) Intercept 1.26 (14.06) ** -0.10 (-0.65) 1.40 (5.21) ** -1.43 (-6.66) ** -0.51 (-1.69) * -0.33 (-1.69) * -1.80 (-3.19) ** ε t-1 (MA parameter) 0.84 (25.99) ** 0.23 (2.19) * -- -- 0.54 (6.69) ** 0.19 (1.94) * 0.69 (14.97) ** ln (ILCOST t-1 ) (AR parameter) 0.94 (45.01) ** 0.45 (4.63) ** 0.49 (20.11) ** 0.16 (5.77) ** 0.72 (10.67) ** 0.45 (3.16) ** 0.87 (27.77) ** 11 Global Journal of Management and Business Research Volume XXI Issue II Version I Year 2021 ( ) D © 2021 Global Journals Cost Hierarchy: Evidence and Implications Variable Sheet Metal (n=1365) Machine Shop (n=1423) Brush & Steel Wool (n=1314) Paint Shop (n=1302) Component Assembly (n=1368) Welding (n=1327) Final Assembly (n=1391) Intercept -0.0002 (-2.14) ** -0.0002 (-0.61) 0.0006 (0.72) -0.0001 (-0.15) -0.0003 (-0.47) -0.0001 (-0.43) -0.0006 (-0.37) ε t-1 (MA parameter) 0.98 (215.56) ** 0.97 (148.69) ** 0.95 (106.37) ** 0.96 (125.66) 0.97 (122.37) ** 0.98 (175.36) ** 0.93 (81.23) ** ln ILCOSTt-1 (AR parameter) 0.14 (5.30) ** 0.19 (6.95) ** 0.09 (3.04) ** 0.06 (2.21) * 0.17 (5.92) ** 0.10 (3.57) ** 0.16 (5.24) ** ln DLCOST H0 : β 1 = 0 H0 : β 1 = 1 1.03 71.57) ** (1.75) * 1.32 (70.69) ** (17.04) ** 0.85 (21.63) ** (-3.85) ** 1.05 (36.04) ** (1.81) * 1.12 (30.53) ** (3.18) ** 1.02 (43.60) ** (0.82) 1.03 (13.86) ** (0.46)