# Hansen 1999 threshold effects in the relationship

Advancing on Hansen (J Econom –, ) and Caner and our model allows the estimation of threshold effects with panel data. Apr 7, Threshold Effects of Human Capital: Schooling and Kremer, Bick & Nautz ( ), which is essentially an extension of the Hansen () static set up, . development thresholds in the relationship between human capital. employ the panel threshold model introduced by Hansen () which is designed to estimate the .. Threshold effects in the Relationship between. Inflation.

However, few researchers consider the dynamic and nonlinear relationships simultaneously and the purpose of this paper is to combine these two factors in one model. Many results exist in the theoretical literature concerning the estimation and inference for dynamic panel data models. Since the lagged dependent variables and the disturbance term are correlated due to the unobserved effects, standard least square methods could not obtain consistent estimators when the model is dynamic.

To overcome this problem, Anderson and Hsiao [ 6 ] suggested that we difference the model first to get rid of the unobserved effects and then use instrumental variable IV estimation for the transformed model. Nevertheless, this IV estimation method leads to consistent but not necessarily efficient estimates of the parameters because it does not use all the available moment conditions. Arellano and Bond [ 10 ] proposed a generalized method of moments GMM procedure that is more efficient than the Anderson and Hsiao [ 6 ] estimator.

This literature is generalized and extended by Arellano and Bover [ 11 ] and Blundell and Bond [ 12 ], which are called forward orthogonal deviation and system GMM, respectively. For the latest development of dynamic panel data models, see Baltagi [ 13 ] and Han and Phillips [ 14 ] for more details. Several models could be chosen to describe the nonlinear relationship such as mixture models, switching models, smooth transition threshold models, and threshold models.

In this paper threshold model is used because of wide applications in empirical researches. This model splits the sample into classes based on an observed variable—whether or not it exceeds some thresholds. In most situations, the complexity of the problem increases because the exact threshold is unknown and needed to be estimated. The estimation and inference are fairly well developed for linear models with exogenous regressors [ 15 — 17 ], in which only the nondynamic case is considered. The dynamic panel threshold models have been used in empirical literature.

Ho [ 20 ] applied a dynamic panel threshold model to examine whether the low-income countries catch up with the rich ones. So far, the theory of dynamic panel threshold model has not been available as we know except for Dang et al.

Recent studies improve on the limitation of subsequent measures of target debt by allowing for a time dependent target debt that is mean reverting 1819 However, the dynamic panel threshold regression applied in our study is able to estimate the optimal debt level that maximizes returns, which has received inadequate attention in the capital structure literature. Modigliani and Miller 22 theoretical model with taxes establish positive relationship between debt and firm value or returns.

Extending the Modigliani and Miller 1422 theoretical model, Bhandari 23 findings revealed that debt has positive effects on returns. The author argues that the debt-equity ratio is a natural proxy for financial risk and it should have positive effects on returns.

Bhandari 23 empirical results confirmed debt has positive effects on returns, after controlling for firm size variable. Empirical studies examining the effects of debt on returns report mixed results.

Likewise, Matemilola et al. Similarly, Ahmad et al. The findings indicate that, growth, liquidity and profits are significant determinants of returns and debt. Precisely, growth has positive effects on debt and returns while size has insignificant effects on both debt and stock returns. Moreover, profits have negative effect on debt but positive effect stock returns.

Conversely, Dawar 12 investigated the impact of debt on returns. His panel fixed effects regression reveal that debt has a negative effect on returns, after controlling for size and growth, among other variables. Dimitrov and Jain 25 hypothesized that changes in debt contain information about returns focusing on the relationship between debt changes and returns. Dimitrov and Jain 25 empirical findings indicated that debt has negative effects on current and future adjusted returns.

Likewise, Penman et al. They break down the book-to-price component into a debt component which reflects the financing risk and an enterprise book-to-price which reflects the operating risk.

In summary, the empirical evidence revealed that the effects of debt on returns is either positive or negative which suggest that there should be an optimal debt level that maximizes returns. One issue has received inadequate attention in the capital structure literature.

What is the optimal debt level that maximizes returns? This issue is resolved by applying Kremer et al. Conversely, this study applies their dynamic panel threshold to examine if there is a threshold level of debt in the debt-returns relationship using firm-level data. The exogenous variables are growth opportunity, corporate taxes and size.

## Mathematical Problems in Engineering

The independent variables may also include lagged value of dependent variable and other endogenous variables. In addition to the structural Eq. Returnsit-1 is the endogenous variables and the study implements the Generalized Method of Moments GMM type estimators to resolve endogenous problem. In dynamic model 1, the standard within transformation applied by Hansen 9 leads to inconsistent estimates because the lagged dependent variable is correlated with the individual error-term.

Application of first differencing technique to remove the firm-specific effects implies negative serial-correlation of the error-term and it is impossible to apply the distributional theory for panel data developed by Hansen 9.

In order to solve this problem, we use the forward orthogonal deviations transformation 10 to eliminate the firm-specific effects. The advantage of the forward orthogonal deviations transformation is that it subtracts the average of all future observations of a variable and this technique avoids serial-correlation of the transformed error-term. Thus, for the error-term, the forward orthogonal deviations transformation is specified as: This forward orthogonal deviations transformation ensures that the explanatory variables are not correlated with the error-term.

### Estimation of Nonlinear Dynamic Panel Data Models with Individual Effects

Consequently, the estimation procedure allows for the application of Caner and Hansen 27 cross-sectional model to dynamic panel model Following Kremer et al. Then, the endogenous variables are substituted in the structural equation by their predicted values Z2it. The step is repeated for a strict subset of the threshold variable debt.

The underlying likelihood ratio was adjusted to account for the number of time period for each cross section. Data are obtained from Bloomberg.

Specifically, the study use top based on market capitalization listed firms on the Johannesburg Stock Exchange from Financial firms were excluded because their financial statement is different from that of non-financial listed firms. Regulated firms were also excluded because their debt ratio is usually higher than other non-financial listed firms.

Similar to Ahmad and Abdullah 5returns as return on equity the ratio of net income to average total equity was measured. Return on equity is one of the most widely used overall measures of firm performance 3 Total Debt TD is the ratio of total debt to total assets.

Total debt is a broader measure and it encompasses the total of all liabilities and ownership claims on a firm Debt is either measured in book-value debt or market-value debt 1529 This study focuses on book-value debt total debt to total assets ratio measure because it is not affected by stock price changes Turning to the direction of debt-returns relationship, debt has positive effects on returns in 1323 Conversely, debt has negative effects on returns in 12 Given that the effect of debt on returns could be either positive or negative; this study expects a non-linear effect of debt on returns.

As the usage of more debt initially increase returns due to interest tax-shield benefits of debt, but the costs of financial distress later decrease returns. Similar to Ahmad and Abdullah 5size is log of total assets. Conversely, Amihud 33 found that size has a negative effect on returns.

This study expects a positive effect of size on returns because bigger firms are more stable and less likely to go bankrupt. Growth opportunity is the ratio of book-equity to market-equity. Gomes and Schmid 34 documented the positive effects of growth opportunity on returns. Chan and Chen 35 noted that earning prospects of the firms are associated with risk factor in returns and firms with high book-equity to market-equity ratio have high returns.

In this study, we expect growth opportunity book-equity to market-equity ratio to have positive effects on returns because it is related to earning prospects that should increase return. Tax effective tax rate is the ratio of tax liability to taxable income. Our expectation is that tax should have negative effects on returns because as more taxes are paid, return should decrease.

Moreover, the traditional variables use as independent variables are proxy commonly use in the literature and they are good predictor of returns 513 Correlations between the variables affect the efficiency of the estimated coefficients.

The correlation coefficients between the independent variables are generally less than 0. The study specifies one model using returns return on equity as the dependent variable.

Descriptive statistics are expressed in percentages Table 2: Correlation results Return is the ratio of net income to average total equity. Debt is the ratio of total debt to total assets. Size is log of total assets. Growth opportunity GO is the ratio of book-equity to market-equity.

Tax is the ratio of tax liability to taxable income.

Debt threshold and returns results Return is the ratio of net income to average total equity. Industry dummy is a dummy variable equal to 1 if a firm belongs to a particular industry and zero otherwise.

The numbers in parentheses are test statistics. The numbers in brackets are standard errors. Number percentage of firms in each regime by year for the return model The panel threshold estimation results are presented in Table 3. In regime one where the debt ratio is less or equal to This result shows that returns increase by 0. In regime two where the debt ratio is greater than The slope coefficient of the panel threshold does not have a fixed value in the two regimes.

The estimated coefficient of debt ratio 0.