For statistical analysis of this study, nonfinancial firms from the period 2005–2018 are selected. The only nonfinancial sector is selected as the financial sector has a different regulatory environment and works under different rules and regulations [54]. At the first stage, only those family-owned firms are included which are registered on PSX throughout the period of study and have data of all dependent and independent variables of the study. At next, by applying the method of Roychowdhury [51], suspect companies are filtered. After that, by following Nazir and Afza [47] Z score is applied to remove outliers in the data set. At the last level, suspect firms are further divided into firms having a higher level of uncertainty, and a lower level of uncertainty detail is discussed in Sect. 3.3. All data for statistical analysis are collected from electronic resources, e.g., PSX, business recorder, and from the data portal of the Central bank of Pakistan.

In a total of 380 registered companies (only nonfinancial), 177 are owned by families. According to Anderson and Reeb [5] a firm will be a family business if it falls in any of the following categories: (i) A family owns maximum shares, (ii) family have twenty-five percent rights for voting, and (iii) family holds a supervisory position or is in BOD of a firm. All data about ownership of family-owned companies are taken from respective company web resources or are manually collected.

### Sample distribution

Sr. No | Sectors | Listed firms | Initial sample | % | Final sample | % |
---|

1 | Automobile Assembler | 22 | 17 | 92 | 17 | 77 |

2 | Cable and Electrical Goods | 8 | 4 | 50 | 4 | 50 |

3 | Cement | 22 | 15 | 68 | 14 | 64 |

4 | Chemicals and Fertilizers | 36 | 27 | 75 | 24 | 67 |

6 | Food and Personal Care Products | 21 | 14 | 64 | 14 | 64 |

7 | Glass and Ceramics | 10 | 5 | 50 | 5 | 50 |

9 | Paper and Board | 9 | 5 | 56 | 4 | 44 |

10 | Pharmaceutical | 10 | 6 | 60 | 6 | 60 |

11 | Power Generation and Distribution | 19 | 6 | 32 | 6 | 32 |

12 | Sugar and Allied Industries | 35 | 23 | 66 | 23 | 60 |

13 | Technology and Telecommunication | 10 | 6 | 60 | 6 | 60 |

14 | Textile | 152 | 49 | 31 | 46 | 31 |

| Total | 389 | 177 | 56 | 169 | 53 |

### Proxy for SPC

Earlier studies identified 3 approaches that can be used as a proxy for SPC (15; An and Zhang 2013) [12]. To calculate these proxies returns (weekly) are used as weekly data of returns to facilitate more accurate estimations. The market-based model is used for the calculation of price crashes. Below is the market model is given

$${r}_{j,t} = {\alpha }_{j}+{\beta }_{1,j}{r}_{m,(t-1)}+{\beta }_{2,j}{r}_{m,t}+{\beta }_{3,j}{r}_{m,(t+1)}+{\beta }_{5,j}{r}_{i,(t-1)}+{\beta }_{6,j}{r}_{i,t}+{\beta }_{7,j}{r}_{i,(t+1)} +{\in }_{t}$$

(1)

where \({r}_{j,t}\) for stock return j during weekly time t; \({r}_{m}\) for weekly market return; \({r}_{i}\) for weekly industry returns. The crash week is during which returns (weekly) are greater of the given standard deviation that is 3.09. When standard deviation is greater than 3.09, then this week is declared as jump week and it facilitates in the calculation of SPC proxies. COUNT is the first proxy for SPC and is measured as a difference of SD lesser than a mean value of 3.09 and greater than a mean value of 3.09.

The second proxy for SPC is NSKEW which is estimated as given below:

$$NSKEWj,i = -\, [n(\,n - 1)^{3/2} \sum^{{\mathop W\nolimits^{3} }} j,t]/[(n - 1)(n - 2)\{ \sum_{{}}^{{\mathop W\nolimits^{{}} 2}} j,t\}^{3/2} ]$$

(2)

N for total observations. Higher the value of NSKEW higher will be the chances that the value of the stock will crash. Third and last proxy for SPC is down, up volatility and it is measured as follow:

$$DUVOLj,i = \,\log\left \{ (\,n_{u} - 1)\sum_{Down}^{{\mathop W\nolimits^{{}} 2_{j} }} ,t/(n\mathop {}\nolimits_{d} - 1)\sum_{Up}^{{\mathop W\nolimits^{{}} 2_{j} }} ,t\right\}$$

(3)

where \({n}_{u}\) for up weeks;\({n}_{d}\) for down weeks. All the above-given measures are widely used in the literature to estimate SPC [14].

### Proxy for REM

Roychowdhury [51] suggested the following three methods for estimations of REM practices: Overproduction (RProd), sales-related manipulation (ROPCF), and manipulation related to discretionary cost (RDISX). All three methods are used for the purpose of estimating REM. The first method is the summation of general and sales-related costs and R&D costs. By following the study of [29] R&D cost is equal to zero if data are not obtainable about this variable. The discussion about each proxy is as below:

$${RDISX}_{it}/{A}_{it-1}={\beta }_{0}+{\beta }_{1}(1/{A}_{it-1})+{\beta }_{2}({S}_{it-1}/{A}_{t-1})+{\varepsilon }_{it}$$

(4)

where \({RDISC}_{it}\)= \({R\&DE}_{it}\)+\({S\&AE}_{it}\)+\({ADVE}_{it}\), \({R\&DE}_{it}\)= Research & Development cost for any company during time t, \({S\&AE}_{it}\)= Sales related cost for any company \(i\) during period \(t\), \({ADVE}_{it}\)= Advertisement related cost for any company \(i\) during period \(t\), \({S}_{it-1}\)= Sales revenue for any company \(i\) at the time \((t-1)\), and \({A}_{t-1}\)= total resources(assets) for any company \(i\) during the period \((t-1)\)

To attain uniformity for residuals, they are multiplied by − 1 and negative output indicates the use of RDISX practices by firm.

Overproduction (OvProd) is the second proxy for REM. Per unit fixed expense used to decrease as a result of a higher level of production and lower per-unit expense will result in higher income from operations for the current time period. When REM uses OvProd practices, then it results in a higher level of storage cost in order to carry overproduced items and it results in more cash flow from operations as compared to revenue from sales. The normal level of production is estimated as given below

$$\frac{\mathrm{RPr}o{d}_{i,t}}{{A}_{i,t-1}} = {\beta }_{0}+{\beta }_{1}\left(\frac{1}{{A}_{i,t-1}}\right)+{\beta }_{2}\left(\frac{sale{s}_{i,t}}{{A}_{i,t-1}}\right)+{\beta }_{3}\left(\frac{\Delta sale{s}_{i,t}}{{A}_{i,t-1}}\right)+{\beta }_{4}\left(\frac{\Delta {S}_{i,t-1}}{{A}_{i,t-1}}\right)+{\varepsilon }_{i,t}$$

(5)

_{where} \({RProd}_{i,t}\)=\({COGS}_{i,t}\)+∆\({Inventories}_{i,t}{, COGS}_{i,t}\)=goods sold cost for any company \(i\) during period \(t\), \({\Delta Inventories}_{i,t}\)= change in the stock of inventory (\({Inventories}_{i,t}\)-\({Inventories}_{i,t-1}\)) for any company \(i\) during period \(t\), \({S}_{i,t}\)= revenue from Sales for a firm \(i\) during time \(t\), \({S}_{i,t-1}\)= Sales for firm \(i\) during time \(t-1\), \({\Delta S}_{i,t}\)= variation in sales (\({S}_{i,t}\)-\({S}_{i, t-1}\)) for any firm \(i\) at period \(t\), \({\Delta sales}_{i,t-1}\)= change in sales (\({S}_{i,t-1}\)-\({S}_{i,t-2}\)) for firm \(i\) at time \(t-1\), \({A}_{i,t-1}\)= firm’s Assets during time \(t-1\) for any firm \(i\).

Third and last proxy to observe REM practices is the OCF method. By applying this method, managers can show an increase in their revenues artificially. It can be done either by offering frequent discounts or offering lenient terms for credit sales. Dechow et al. [18] proposed the following method to estimate normal OCF. Later, several academic researchers are applying this method [51, 15, 10]

$$\frac{ROPC{F}_{it}}{{A}_{it-1}} = {\beta }_{0}+{\beta }_{1}\left(\frac{1}{{A}_{it-1}}\right)+{\beta }_{2}\left(\frac{sale{s}_{it}}{{A}_{it-1}}\right)+{\beta }_{3}\left(\frac{\Delta sale{s}_{it}}{{A}_{it-1}}\right)+{\varepsilon }_{it}$$

(6)

where \({ROPCF}_{it}\)= cash flow due to operations of any firm \(i\) during period \(t\).

Lastly, suspect companies are shortlisted based on the method suggested by Roychowdhury [51]. Suspect firms are those who are engaged in REM and it is shortlisted who have revenue before extraordinary items higher than 0 and lower than 0.005.

### Uncertainty proxy

To capture the level of uncertainty for any firm [38] method is applied. According to which SDR is used as a yardstick to estimate uncertainty for a specific firm. If the value of the firm median is more than the median of sample, then that specific firm has a higher level of uncertainty, and if the value of the firm median is lower than the median of sample, then that specific firm has lower uncertainty.

### Econometric analysis

Firstly, below given regression model is employed to estimate a comprehensive association between REM and SPC.

$$COUN{T}_{i,t}=\beta o+{\beta }_{1}RE{M}_{i,t}+{\beta }_{2}\sum Contro{l}_{i,t}+Industry\_FE+Year\_FE+{\varepsilon }_{i,t}$$

(7)

$$NSKE{W}_{i,t}=\beta o+{\beta }_{1}RE{M}_{i,t}+{\beta }_{2}\sum Contro{l}_{i,t}+Industry\_FE+Year\_FE+{\varepsilon }_{i,t}$$

(8)

$$DUVO{L}_{i,t}=\beta o+{\beta }_{1}RE{M}_{i,t}+{\beta }_{2}\sum Contro{l}_{i,t}+Industry\_FE+Year\_FE+{\varepsilon }_{i,t}$$

(9)

where \(N{T}_{i,t}\), \(NSKE{W}_{i,t}\), \(DUVO{L}_{i,t}\) are the SPC for any company \(i\) at duration \(t\), \(RE{M}_{i,t}\) for real earnings management and \(Contro{l}_{i,t}\) is a set of control variables as highlighted by earlier studies. We expect the \({\beta }_{1}\) to be positive and significant as our first hypothesis states a positive effect of REM on SPC. Next, given below equations are used to evaluate the spillover outcome of SPC due to REM of other firms belongs to the same family.

$${COUNT}_{i,t} = {\beta }_{0}+{\beta }_{1}({COUNT}_{i,t}-i)+{\beta }_{2}{Control}_{i,t}+Industry\_FE+Year\_FE+{\in }_{i,t}$$

(10)

$${NSKEW}_{i,t} = {\beta }_{0}+{\beta }_{1}({NSKEW}_{i,t}-i)+{\beta }_{2}{Control}_{i,t}+Industry\_FE+Year\_FE+{\in }_{i,t}$$

(11)

$${DUVOL}_{it} = {\beta }_{0}+{\beta }_{1}({DUVOL}_{i,t}-i)+{\beta }_{2}{Control}_{it}+Industry\_FE+Year\_FE+{\in }_{it}$$

(12)

where \(COUN{T}_{i,t}-iNSKE{W}_{i,t}-i\), \(DUVO{L}_{i,t}-i\) mean of crash price risk of family firms except for the firm\(i\). \(COUN{T}_{i,t}\),\(NSKE{W}_{i,t}\), \(DUVO{L}_{i,t}\) is a stock price crash for a specific firm \(i\) at time\(t\). Lastly, to analyze the third hypothesis, model (10) to model (12) are estimated again after dividing the samples into categories of higher and lower uncertainty.

### Control variables

Earlier academic researches highlighted various instruments that may have an impact on SPC (Wang and Zhang 2016; 42). A few of the control instruments also incorporated in this work which have a possible effect on the regression model. These instruments are discussed below: return volatility \((SIGMA)\); previous returns \(\left(RET\right)\) as [14] proposed that previous returns may also be an indicator for future SPC. Other variables include \(Size\); financial leverage \(\left(LEV\right)\); Return on Assets \((ROA)\); (MktTB\()\) for the market to book ratio. Opacity is controlled by using \(\left(AbDAcc\right)\) discretionary accruals, and it is measured by applying modified Jones (1995) model [32]. Spread for an annual average of daily spread scaled as the midpoint of the bid and ask price.