1. Introduction

Traditional management accounting frameworks have long assumed a linear and symmetric association between operating revenues and expenditure adjustments. Under this mechanical view, costs are expected to adjust uniformly and proportionally in response to shifts in firm sales volume. However, seminal empirical contributions challenge this premise by establishing that managerial cost commitments are subject to psychological biases, resource adjustment frictions, and asymmetric agency costs. When sales decline, corporate decision-makers frequently postpone resource reduction due to optimistic future demand projections or the prohibitively high disposal and re-acquisition expenses associated with operational inputs. Conversely, when product demand accelerates, managers expand resources more promptly, creating the widespread empirical phenomenon known as cost stickiness.

While extensive research has investigated aggregate selling, general, and administrative (SG&A) expenses, discrete expenditure subcomponents—specifically marketing and promotional investments—exhibit unique strategic properties. Marketing costs represent strategic outlays aimed at establishing market presence, preserving customer loyalty, and defending market share in volatile emerging economies. In the context of the Tehran Stock Exchange (TSE), macroeconomic shocks, systemic inflationary pressures, and severe supply-chain constraints exert profound influences on marketing expenditure flexibility. Consequently, applying rigid linear models or binary switching formulations risks respecifying the underlying economic dynamics. This study addresses this limitation by deploying a continuous non-linear regime-switching econometric approach.

Research Question(s)

Do marketing expenditures of firms listed on the Tehran Stock Exchange exhibit non-linear and asymmetric adjustment patterns across different sales variation regimes?

Does the Panel Smooth Transition Regression (PSTR) framework identify an endogenous threshold and dynamic transition path for marketing cost elasticities in Iran’s capital market?



2. Literature Review

The theoretical exploration of cost stickiness originated from resource adjustment theory and organizational decision-making models. Anderson, Banker, and Janakiraman (2003) demonstrated that operational expenditures increase more with activity expansion than they decrease with equivalent activity contractions, conceptualizing cost asymmetry as the direct product of deliberate managerial choices rather than purely mechanical relationships. In the Iranian empirical accounting literature, foundational inquiries into cost behavior verified the presence of cost stickiness across manufacturing sectors. Ghaemi and Nematollahi (2006) investigated the behavior of distribution and sales expenditures among firms listed on the Tehran Stock Exchange, documenting that sales-related expenditures expand vigorously during sales upturns but experience significant stickiness when sales decline. In a subsequent study on non-operating and operating overhead adjustments, Asadi and Beigpanahi (2017) highlighted that managerial decisions regarding cost reallocation remain contingent upon market uncertainty, financial leverage, and prevailing macroeconomic expectations.

2.1. The Non-Linear Transition Mechanism

Despite the empirical validity of piece-wise linear specifications, standard binary models assume an instantaneous and knife-edge transition between cost regimes. In actual business operations, managerial adjustments are gradual and heterogeneous across industrial sectors. González, Teräsvirta, and van Dijk (2005) introduced the Panel Smooth Transition Regression (PSTR) model to resolve these structural limitations by allowing parameter elasticities to shift smoothly and continuously as a bounded function of an observable transition metric.

3. Methodology

To capture structural nonlinearities and parameter heterogeneity without imposing arbitrary regime categorizations, we formulate a two-regime PSTR specification:

Δ ln⁡〖〖"MC" 〗_it 〗=μ_i+β_0 Δ ln⁡〖〖"Sales" 〗_it 〗+β_1 Δ ln⁡〖〖"Sales" 〗_it 〗⋅g(q_itⓜ;γⓜ;c)+θ^' X_it+ε_it

where Δ ln⁡〖〖"MC" 〗_it 〗 denotes the log-difference of marketing expenditures for a firm i in year t; Δ ln⁡〖〖"Sales" 〗_it 〗 captures the contemporaneous log-difference in gross revenues; μ_i represents individual firm fixed effects; X_it is a vector of control variables, including financial leverage (LEV) and asset intensity (ASINT); and ε_it is the idiosyncratic error term.

The transition function g(q_itⓜ;γⓜ;c) is continuous, bounded within the interval [0ⓜ,1], and defined as a standard logistic transition function:

g(q_itⓜ;γⓜ;c)=[1+exp⁡(-γ(q_it-c)) ]^(-1), γ>0

where q_it serves as the normalized transition variable (sales growth metric), c denotes the endogenous location/threshold parameter, and γ represents the slope parameter determining the smoothness and velocity of transition between regimes.

The empirical sample comprises 142 industrial firms listed on the Tehran Stock Exchange observed over a ten-year horizon (2015–2024), yielding a balanced panel of 1420 firm-year observations. Financial institutions, holding companies, and firms with non-continuous trading activity or missing disclosure metrics were excluded.



4. Results

Prior to estimating the core structural equations, linearity tests were evaluated to examine the null hypothesis of linearity against the alternative of a smooth transition mechanism. The test statistics rejected linearity at the p<0.01 level, confirming the necessity of a non-linear PSTR formulation.

Table 1 presents the parameter estimates for the PSTR marketing cost model.

Table 1. PSTR Model Estimates for Marketing Expenditures (1394–1403)

Parameter / Variable Estimated Coefficient Standard Error t-Statistic p-Value

Linear Elasticity (β_0) 0.219 0.054 4.055 0.000

Non-Linear Elasticity (β_1) 0.317 0.071 4.465 0.000

Transition Parameter (γ) 5777.9 824.1 7.011 0.000

Threshold Value (c) 1.757 0.890 1.974 0.048

Control: Leverage (LEV) -0.142 0.041 -3.463 0.001

Control: Asset Intensity (ASINT) 0.088 0.029 3.034 0.002



As detailed in Table 1, the baseline elasticity in the lower regime is β_0=0.219. Above the identified threshold parameter (c=1.757), the additional sensitivity parameter is β_1=0.317. Consequently, the total dynamic elasticity in the upper regime reaches β_0+β_1=0.536. The large magnitude of the slope parameter (γ=5777.9) demonstrates a rapid, steep transition between regimes, while remaining structurally continuous across firms.

5. Discussion

The empirical results confirm that marketing cost adjustment in emerging capital markets is characterized by dynamic threshold asymmetry. In the lower regime, firms exhibit restrained marketing adjustments (β_0=0.219), indicating that during periods of stagnant or declining sales, marketing allocations are preserved as defensive mechanisms to sustain brand visibility. Conversely, in the upper regime, marketing elasticity increases significantly to 0.536, confirming that corporate executives deploy aggressive marketing allocations during periods of robust revenue expansion.

These findings directly corroborate the empirical literature on non-linear operational behavior. Consistent with the foundational findings of Ghaemi and Nematollahi (2006), marketing and distribution costs show strong asymmetry under shifting revenue trajectories. Furthermore, our findings align with Asadi and Beigpanahi (2017), who demonstrated that managerial resource adjustments are fundamentally dictated by capacity utilization and revenue expectations. By introducing the continuous PSTR framework, our study extends their empirical conclusions by capturing exact regime distribution (35 versus 1385 observations) and verifying continuous elasticity gradients across Iranian firms.

6. Conclusion

This study provides empirical evidence on the non-linear and asymmetric behavior of marketing expenditures among Tehran Stock Exchange firms. Utilizing the PSTR framework across the 1394–1403 period, we show that traditional linear specifications obscure key dynamics of cost flexibility. Marketing cost behavior operates across distinct regimes, characterized by an endogenous threshold (c=1.757) and a dynamic elasticity range spanning from 0.219 to 0.536.

These insights offer practical implications for corporate financial analysts, auditors, and executive management. Recognizing non-linear cost adjustments enables market participants to benchmark marketing investment efficiency more accurately against revenue volatility. Future research may expand upon this investigation by evaluating industry-specific threshold differences and exploring the moderating effects of corporate governance and financing constraints.